Katharina Waha
email: katharina.waha@csiro.au

Francesco Accatino

Cecile Godde

Cyrille Rigolot

Jessica Bogard

Joao Pedro Domingues

Elisabetta Gotor

Mario Herrero

Guillaume Martin

Daniel Mason-D'croz

Francesco Tacconi

Mark Van Wijk

The benefits and trade-offs of agricultural diversity for food security in low-and middle-income countries: A review of existing knowledge and evidence

Keywords: food security, farming diversity, production diversity, agrobiodiversity, agricultural biodiversity, literature review, low-income countries, middle income countries

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

comprehensive search in Web of Science. We present an overview and synthesize results for different spatial scales and units of observation, from individual to global and for the four dimensions of food security: availability, access, stability and utilisation. Eighty-eight of the 924 surveyed publications meet the inclusion criteria and report the direction and magnitude of 314 individual diversity-food security relationships. In almost two thirds of all cases, agricultural diversity had a positive effect on food security. In about one third of the relationships there was no effect of agricultural diversity on food security, or the results were mixed. These numbers hold for the availability, access and utilisation dimensions of food security and at individual, household and farm scales, but the number of studies was too small to draw robust conclusions on the stability dimension and at global scale. Diversity can be an important driver of food security, but the magnitude of the contribution depends on the broader socio-economic and biophysical characteristics of the local farming system. We conclude that diversification can be a potential strategy to improve food and nutrition security. Yet, it is not a necessary characteristic of all agricultural systems at all costs especially in the presence of other strategies that can potentially achieve similar outcomes. We make several recommendations to strengthen future studies that can help identify how strongly related agricultural diversity and food security are.

Introduction

Diversification, the process of becoming more diverse, is studied in many scientific disciplines. At its core it is opposed to specialization, uniformity, and homogeneity and as such it is often seen as beneficial for the stability and productivity of any natural or human-made system [START_REF] Gaba | Multiple cropping systems as drivers for providing multiple ecosystem services: from concepts to design[END_REF][START_REF] Lin | Resilience in Agriculture through Crop Diversification: Adaptive Management for Environmental Change[END_REF][START_REF] Markowitz | Portfolio selection[END_REF][START_REF] Naeem | Biodiversity enhances ecosystem reliability[END_REF][START_REF] Yachi | Biodiversity and ecosystem productivity in a fluctuating environment: The insurance hypothesis[END_REF].

In food systems, diversification, defined often as an increase in crop, livestock, production or farming diversity (i.e. agrobiodiversity), has been considered as a key strategy for improving the productivity and stability of many socio-economic and ecological aspects of agricultural systems. It is a central element for example in three areas. Firstly, in sustainable intensification [START_REF] Foley | Solutions for a cultivated planet[END_REF][START_REF] Tilman | Global food demand and the sustainable intensification of agriculture[END_REF], ecological intensification [START_REF] Bommarco | Ecological intensification: Harnessing ecosystem services for food security[END_REF][START_REF] Cassman | Ecological intensification of cereal production systems: Yield potential, soil quality, and precision agriculture[END_REF], conservation agriculture (FAO, 2002) and more recently regenerative agriculture [START_REF] Schreefel | Regenerative agriculture -the soil is the base[END_REF]. For example, mixed farming and crop rotations can support pest, nutrient and water management [START_REF] Gaba | Multiple cropping systems as drivers for providing multiple ecosystem services: from concepts to design[END_REF], reduce external inputs and improve soil biodiversity. Secondly, in rural development and sustainable livelihoods [START_REF] Chambers | Sustainable rural livelihoods: practical concepts for the 21st century[END_REF][START_REF] Ellis | Household strategies and rural livelihood diversification[END_REF] as livelihood diversification has often been highlighted as contributing to reduced poverty. And thirdly, in nutrition-sensitive agriculture describing pathways from agriculture to nutrition security where diversification can increase the diversity of foods produced and of potential income sources [START_REF] Jager | Food and nutrient gaps in rural Northern Ghana: Does production of smallholder farming households support adoption of food-based dietary guidelines?[END_REF][START_REF] Herforth | Linking Agriculture and Nutrition: Understanding and Applying Primary Pathways and Principles[END_REF][START_REF] Ruel | Nutrition-sensitive interventions and programmes: How can they help to accelerate progress in improving maternal and child nutrition?[END_REF].

While diversification is often presented by the scientific and policy community as socially and environmentally beneficial, evidence from the literature warns about too broad generalizations. The outcomes of agricultural diversity can vary across spatial scales, from the genetic and species level to the ecosystem, landscape, national and global levels. While, for example, food security in subsistence farming can be achieved at the farm scale by producing a wide variety of foods, the same can be achieved at the landscape scale by having a number of specialised farms producing a single food type and trading the surplus with others [START_REF] Renard | Agro-biodiversity has increased over a 95 year period at sub-regional and regional scales in southern Quebec , Canada[END_REF]. However, a subsistence farming system that produces large variety of food types that are nutritionally similar for own consumption will not ensure a balanced and healthy diet for the household, so a consideration of the functions added to the system along with the species is important [START_REF] Remans | Assessing nutritional diversity of cropping systems in African villages[END_REF].

Another potential limitation of agricultural diversification as a key leverage for food security is that diversity can be difficult to manage and can increase the workload for members of the household [START_REF] Bendahan | Management and labour in an integrated crop-livestock-forestry system in Roraima, Brazilian Amazonia[END_REF]. Specialization, on the other hand, can reduce costs, increase efficiency through economies of scale and give farmers a comparative advantage for selling their produce at markets [START_REF] Govereh | Cash cropping and food crop productivity: Synergies or trade-offs?[END_REF][START_REF] Kurosaki | Specialization and Diversification in Agricultural Transformation: The Case of West Punjab, 1903-92[END_REF]. Moreover, diversification is not the only strategy to increase resilience, as farmers might favour other risk management strategies. While diversification can be an agricultural intervention for improved nutrition and health outcomes, other pathways can be as effective. For example, bio-fortification to increase nutritional quality of existing crops or increasing incomes through improvements to cash crop production if the income is spent on purchasing healthy foods. The latter, however, depends on appropriate market access and requires that the household prioritises the purchase of healthy foods over other competing food or non-food purchases (Fiorella et al., 2016).

In this review, we aim at synthesising the evidence on the relationship between agricultural diversity and all four dimensions of food security as defined in the FAO's conceptual framework -availability, stability, access, and utilisation. Food security is a major concern in low-and middle-income countries and has been enacted as one of the United Nations Sustainable Development Goals. Our review also explores the interactions at different spatial scales. While many measures of food security relate to individuals, such as meeting dietary energy needs, the challenge to secure healthy and diverse diets is also global in its extent and in that scale often analysed with respect to food availability and stability. A final section provides a synthesis and conclusions.

Search criteria and methods

The review is based on an exhaustive, comprehensive search in Web of Science (v.5.32). We searched with the objective of presenting evidence from original scientific studies, define eligibility criteria and attempt to identify all studies meeting them. We assess the validity of findings in the reviewed studies and present the results in a systematic way [START_REF] Moher | Preferred reporting items for systematic review and meta-analysis protocols ( PRISMA-P ) 2015 statement[END_REF]. We include articles and reviews that use at least one measure of both agricultural diversity and food security, were written in English and were published between 2010 and February 2020. Key words used in the search included a combination of terms associated with agricultural diversity (e.g. crop, farming or production diversity, agricultural biodiversity) and food security (e.g. child nutrition, dietary diversity, food availability, food access, stability, food production, income). The search on 25 February 2020 resulted in 924 articles. The Web of Science search syntax is:

(TS=((on-farm OR "on farm" OR crop OR farming OR production) near/1 divers*) AND TS=("food security" OR "food and nutrition security" OR "child nutrition" OR "diet* diversity" OR "food availab*" OR "food access*" or "food product*" OR "income")) OR (TS=("agricultural biodivers*" OR "agro-biological divers*") AND TS=("food security" OR "food and nutrition security" OR "child nutrition" OR "diet* diversity" OR "food availab*" OR "food access*" or "food product*" OR "income"))

In the next step the abstracts of these articles were screened on whether they: (1) used a study area in a low-to middle income country as per the World Bank 2021 country classification; (2) evaluated at least one metric of diversity at farm-, regional-, or global-level as specified within the search terms; (3) evaluated at least one measure of a food security dimension, and (4) presented original work quantifying the diversity-food security relationship which goes beyond qualitatively describing drivers and trends in agricultural diversity. Articles describing theoretical frameworks were also included to inform the broader context and to link to existing literature. We excluded studies on nonfarm diversification although we are aware that they can be critical strategies to increasing food security (e.g. [START_REF] Ampaw | Urban Farm-Nonfarm Diversification, Household Income and Food Expenditure in Ghana[END_REF][START_REF] Barrett | Nonfarm income diversification and household livelihood strategies in rural Africa : concepts , dynamics , and policy implications[END_REF] but we consider studies on agricultural activities that increase farmer's income as a component of food access. We also exclude studies that discuss benefits of specific crops without also clearly stating that agricultural diversity increases overall, for example high-value or wild crops [START_REF] Mavengahama | The role of wild vegetable species in household food security in maize based subsistence cropping systems[END_REF] or crops perceived as being underutilized or neglected [START_REF] Kahane | Agrobiodiversity for food security , health and income To cite this version : HAL Id : hal-01201396[END_REF][START_REF] Mabhaudhi | Status of underutilised crops in South Africa: Opportunities for developing research capacity[END_REF][START_REF] Mabhaudhi | Opportunities for underutilised crops in Southern Africa's post-2015 development agenda[END_REF]. Applying these criteria in the abstract screening leads to a shorter list of 272 publications to which we added 13 publications that were cross-referenced or otherwise known to the authors (Figure 1). After reading the full manuscripts, 110 publications were identified as relevant to the purpose of our study, 88 articles and 26 reviews. In terms of geographical spread, about two thirds of all publications have a study area in sub-Saharan Africa, and the remaining in Asia or South America. Some African countries are studied more than others, for example Malawi (14 publications) and Kenya (10 publications) while other countries with high levels of food insecurity were not found in the literature search, for example Chad and Madagascar. Articles were grouped by unit of observation and level of analysis into individual, household, farm, landscape, national or global scale. The landscape scale publications focused on discussing interaction of multiple farming households with each other or a local market that in turn influences individuals and landscape environmental or economic indicators. An example of a national scale analysis is one that uses a nationally representative agricultural and nutrition census or survey, even with households as the unit of observation. A large sample size alone is not necessarily indicative of representativeness at the national scale. Finally, the global scale publications include multi-countries studies and studies analysing global data sets such as those collated by the Food and Agriculture Organization, the World Bank or the World Health Organization.

The relationship between agricultural diversity and food security was categorized in a synthesis table according to two dimensions: the direction, i.e. positive, negative or neutral and the level of agreement, i.e. high, medium or low agreement. The synthesis table allows to put together relevant quantitative figures which helps to identify knowledge gaps and controversies.

Indicators of agricultural diversity and food security

Agricultural diversity

Diversity can be defined for different types of agricultural commodities, plant species for food or fodder, or domesticated animals raised for food or for labour. The categories used here follow a hierarchy from including 1) cultivated plant species (crop diversity), 2) raised livestock species (livestock diversity), 3) cultivated plant and raised livestock species (farming diversity), 4) food products derived from plant and animal species (production diversity), to 5) the full diversity of organisms living in landscapes that are under agricultural management, beyond cultivated species and foods produced (agrobiodiversity or agricultural biodiversity).

Records identified through

WoS search (n=924)

Record abstract screening (n=272)

Adding cross-referenced articles (n=285)

Full-text article assessed for eligibility (n=110)

Studies included in quantitative synthesis (n=88)

Review articles included (n=26)

Production diversity refers to the different food products, while farming diversity refers to the plant and animal species. For example, a farm raising chickens for meat and eggs and cultivating maize for corn would have a production diversity of three (chicken meat, chicken eggs, corn) and a farming diversity of two (chickens, maize) if measured as richness. Crop diversity can sometimes be measured as "crop group diversity" where crops are grouped together by similar characteristics, for example ecological functions in the agricultural system, nutrient content or importance for creating income from crop sales. Agricultural biodiversity is a broader characterisation that encompasses for example genetic resources, edible plants and crops including traditional varieties, and other genetic material, livestock and freshwater fish, soil organism vital to soil fertility, naturally occurring insects, bacteria and fungi that control insect pests and diseases, and wild resources or natural habitats which can provide ecosystem functions and services [START_REF] Thrupp | Linking Agricultural Biodiversity and Food Security : The Valuable Role of Sustainable Agriculture Lori Ann Thrupp International Affairs[END_REF]. Throughout the paper agricultural biodiversity and agrobiodiversity are used interchangeably.

Several indicators can be used to measure agricultural diversity, integrating different aspects of diversity, richness and evenness. Richness is the number of species or agricultural products in a sample. Some studies express this by comparing characteristics of cropping systems with different numbers of crops cultivated or creating a binary variable to distinguish between adopters and nonadopters of diversification [START_REF] Birthal | Assessing the impact of crop diversification on farm poverty in India[END_REF][START_REF] Boedecker | Dietary contribution of Wild Edible Plants to women's diets in the buffer zone around the Lama forest, Benin -an underutilized potential[END_REF]. Measures of evenness consider relative dominance or concentration of species or products in the sample by measuring also the abundance of each species [START_REF] Whittaker | Evolution and Measurement of Species Diversity[END_REF]. Examples of measures of evenness are the Simpson diversity index (SDI) and the Shannon diversity index (H'). They differ slightly by expressing dominance of the first few species in the sample (Simpson index) or relative evenness across the whole sample (Shannon diversity index) [START_REF] Whittaker | Evolution and Measurement of Species Diversity[END_REF]. Abundance can be measured as area used for each species, weight of produce, nutrient or energy content of each product or monetary value of products. Using area can be challenging when including livestock (Sibhatu and Qaim, 2018a), as livestock can source feed from outside the farm, graze on public land or be fed purchased feed.

Food security

The FAO's conceptual framework for food security distinguishes between four dimensions, physical availability to food, economic and physical access to food, food utilization and stability. This framework, and national level indicators to measure progress on each dimension, are used in the annual reports on the 'The State of Food Security and Nutrition in the World' published since 1999 by FAO, IFAD, UNICEF, WFP and WHO (until 2015 as 'The State of Food Insecurity in the World') (FAO, 2019). In addition to these national level indicators, this literature review identified indicators to measure food security status of an individual or a household. The full list of indicators considered in this review is shown in Table 1.

Table 1 Indicators of food security used in the reviewed literature.

Availability

Access Utilization Stability

Food production and food supply

Crop yield, livestock production, household food supply adequacy, crop production, productivity

Financial access and affordability

Income from agriculture, wealth, poverty status of a household

Individual consumption measures

Infant For food availability, yield is a frequently used indicator. A special case is nutritional yield when yield expressed in weight is multiplied with the content of a certain nutrient or converted to calories. The unit change is not to be confused with a change in the food security dimension. It is still a measure of availability and it is unclear how the product is used, for self-consumption, markets, or livestock feed and if consumed within the household who is eating what. An example of a household food supply adequacy indicator is the food availability indicator used in some studies and calculated as a ratio of energy produced and bought to the physiological requirements for energy (Douxchamps et al., 2016;[START_REF] Frelat | Drivers of household food availability in sub-Saharan Africa based on big data from small farms[END_REF][START_REF] Paul | Agricultural intensification scenarios , household food availability and greenhouse gas emissions in Rwanda: Ex-ante impacts and trade-offs[END_REF][START_REF] Rufino | Transitions in agro-pastoralist systems of East Africa: Impacts on food security and poverty[END_REF][START_REF] Waha | Agricultural diversification as an important strategy for achieving food security in Africa[END_REF].

Food access indicators are very diverse, but some standard indicators have been developed by the Food and Agriculture Organization of the United Nations (FAO), the Food and Nutrition Technical Assistance Project (FANTA) and the World Food Programme (WFP). Within the food access domain, we identify two groups of indicators. The first group are indicators reflecting the financial dimension and affordability of food access and the second group are indicators pertaining to consumption patterns measured at the household level. The household dietary diversity score (HDDS) is the most frequently used indicator to measure food access. HDDS is constructed based on consumption of 12 food groups and ranges from 0 (no food group consumed) to 12 (all 12 food groups consumed) with a recall period of 24 hours (FAO, 2013) but many studies reviewed here modified the recall period to be seven days. The food consumption score (FSC) is a similar, but composite score ranging between 0 (food insecure) and 16 (food secure) and measures the frequency of consumption of different food groups by a household during the seven days before the survey. HDDS has been validated as a good indicator of diet quantity i.e. energy consumption [START_REF] Hoddinott | Cropping system diversification for food production in Mindanao rubber plantations: A rice cultivar mixture and rice intercropped with mungbean[END_REF] but not of diet quality i.e nutrient adequacy [START_REF] Leroy | Measuring the Food Access Dimension of Food Security : A Critical Review and Mapping of Indicators[END_REF]. One reason for that is that HDDS measures also the consumption of three food groups (sweets; oils and fats; spices, condiments and beverages) that do not necessarily contribute positively micronutrient intake which weakens any potential association with micronutrient adequacy and diet quality.

Food utilization is commonly measured as individual dietary consumption or nutritional status based on anthropometry or biomarkers. It therefore describes a dimension of food security as well as the outcome linked to nutritional status [START_REF] Coates | Build it back better: Deconstructing food security for improved measurement and action[END_REF]. Around 8% of all studies reviewed use a measure of anthropometric status such as height-for-age, weight-for-height and weight-for-age. Height-for-age below two standard deviations of the mean for healthy children indicates stunting which implies insufficient nutrient intake and/or poor health over a longer time period. Weight-forheight indicates wasting which implies acute significant food shortage and/or disease. Weight-forage indicates underweight which implies both acute and chronic malnutrition [START_REF] Who | Physical status: the use and interpretation of anthropometry[END_REF]. All three are sometimes used as validation measures for indicators of food utilisation. This can however result in mixed conclusions as anthropometric status is not only evidence for nutrient or energy deficits but also for the occurrence of diseases that lead to impaired nutrient absorption or increased rate of nutrient utilization [START_REF] Who | Physical status: the use and interpretation of anthropometry[END_REF]. We group food consumption indicators within the utilisation domain when measured at the individual level, and within the food access domain when measured at the household level. This is consistent with the evidence that various individual consumption indicators such as Infant and Young Child Dietary Diversity (IYCDDS), Minimum Dietary Diversity for Women (MDD-W) and Women's Dietary Diversity Score (WDDS) are validated measures of nutrient adequacy (Jones, 2017a;[START_REF] Leroy | Measuring the Food Access Dimension of Food Security : A Critical Review and Mapping of Indicators[END_REF][START_REF] Martin-Prevel | Moving forward. On choosing a standard operational indicator of women's dietary diversity[END_REF]Working Group on Infant and Young Child Feeding Indicators, 2007). IYCDDS and WDDS include seven and nine food groups, respectively that are directly related to micronutrient intake. WDDS has been further developed to the MDD-W indicator, sometimes also referred to as the 10-food group women's dietary diversity indicator, which is used to define women as having an adequate diet diversity if consuming at least five of the ten food groups included.

Stability includes the time aspect of the other three dimensions. Stability has several meanings and is often related to the concepts of resilience, robustness, resistance, vulnerability, and variability. While a natural ecosystem might be considered stable if the system variables return to the initial equilibrium after a perturbation [START_REF] Pimm | The complexity and stability of ecosystems[END_REF], a more useful definition for agricultural systems might be related to low fluctuation or constancy in a system faced with perturbations as the definition of equilibrium state as such is more difficult. Perturbations are then shocks external to the system and ranging from short-term to long-term or chronic [START_REF] Bullock | Resilience and food security: rethinking an ecological concept[END_REF]. In the reviewed literature, stability is often measured as the spatial or temporal variability of production or income.

Experience-based indicators such as the Household Food Insecurity Access Scale (HFIAS), the Household Hunger Scale (HHS), Coping Strategies Index (CSI) and Months of Adequate Household Food Provisioning (MAHFP) are grouped separately in Table 1 because they are composite scores based on information that span the four dimensions of food security. For example, the CSI reflects all possible answers to one single question, namely "what do you do when you do not have enough food and don't have the money to buy?" [START_REF] Maxwell | The Coping Strategies Index. A tool for rapid measurement of household food security and the impact of food aid programs in humanitarian emergency[END_REF]. This is in contrast to some studies which consider HFIAS to be an indicator of food access [START_REF] Leroy | Measuring the Food Access Dimension of Food Security : A Critical Review and Mapping of Indicators[END_REF], food stability [START_REF] Coates | Build it back better: Deconstructing food security for improved measurement and action[END_REF] or food availability [START_REF] Lele | Measuring Food and Nutrition Security: An Independent Technical Assessment and User's Guide for Existing Indicators, Measuring Food and Nutrition Security: An Independent Technical Assessment and User's Guide for Existing Indicators[END_REF]. HFIAS can be seen as a good measure of both quantity and quality, in that there is no need to adopt coping strategies that lead to cheaper, less appealing and less micronutrient dense foods [START_REF] Leroy | Measuring the Food Access Dimension of Food Security : A Critical Review and Mapping of Indicators[END_REF] but not in the sense of micronutrient adequacy. We group experience-based indicators together with food access indicators in the respective results section.

Previous reviews and meta-analysis

Previous reviews and meta-analyses are listed here for completeness and as reference. They can provide a systematic overview of a specific group of literature that is outside the scope of this review, such as intercropping systems or agroforestry. Some reviews were considering both indicators of food access and utilisation, so they are described here together in one section.

Food availability

In the context of food availability, eight review articles and meta-analyses discuss the benefits of crop and agrobiodiversity for productivity [START_REF] Delaquis | On-farm diversity offsets environmental pressures in tropical agro-ecosystems: A synthetic review for cassava-based systems[END_REF][START_REF] Droppelmann | Sustainable intensification options for smallholder maize-based farming systems in sub-Saharan Africa[END_REF][START_REF] Frison | Agricultural Biodiversity Is Essential for a Sustainable Improvement in Food and Nutrition Security[END_REF][START_REF] Gaba | Multiple cropping systems as drivers for providing multiple ecosystem services: from concepts to design[END_REF][START_REF] Kremen | Ecosystem Services in Biologically Diversified versus Conventional Farming Systems : Benefits , Externalities , and Trade-Offs[END_REF][START_REF] Nagothu | Pulses-millets crop diversification by smallholders and their potential for sustainable food and nutrition security[END_REF][START_REF] Ponisio | Diversification practices reduce organic to conventional yield gap[END_REF][START_REF] Schroth | Farmer strategies for tree crop diversification in the humid tropics. A review[END_REF]. For cassava intercropping, [START_REF] Delaquis | On-farm diversity offsets environmental pressures in tropical agro-ecosystems: A synthetic review for cassava-based systems[END_REF] found a positive relationship between intercropping and system productivity in most studies reviewed which was evidenced by land equivalent ratios above 1. Other reviews for specific crops are provided in [START_REF] Nagothu | Pulses-millets crop diversification by smallholders and their potential for sustainable food and nutrition security[END_REF] for pulses-millet crop diversification and [START_REF] Schroth | Farmer strategies for tree crop diversification in the humid tropics. A review[END_REF] for tree crop diversification in the humid tropics. In another review based on 17 studies on sustainable intensification practices in maize small-scale farms in sub-Saharan Africa, [START_REF] Droppelmann | Sustainable intensification options for smallholder maize-based farming systems in sub-Saharan Africa[END_REF] show that the addition of a grain legume increased maize response to fertilizer but reduced annualized maize grain yields. Other benefits of intercropping and multiple cropping include improved soil and water regulation, reduced consumption of fertilizers and pesticide, reduced soil erosion and nitrate leaching, increased biodiversity and pest and disease suppression [START_REF] Frison | Agricultural Biodiversity Is Essential for a Sustainable Improvement in Food and Nutrition Security[END_REF][START_REF] Gaba | Multiple cropping systems as drivers for providing multiple ecosystem services: from concepts to design[END_REF]. In a meta-analysis using 115 studies, [START_REF] Ponisio | Diversification practices reduce organic to conventional yield gap[END_REF] find that multi-cropping and crop rotations can improve yields in organic systems. According to [START_REF] Gaba | Multiple cropping systems as drivers for providing multiple ecosystem services: from concepts to design[END_REF] the co-existence of multiple species can be beneficial if the species are carefully selected to provide resources for one another or to use a resource in different forms or at different times or in different places. Otherwise resource competition can result in lower system yields compared to monocultures [START_REF] Gaba | Multiple cropping systems as drivers for providing multiple ecosystem services: from concepts to design[END_REF]. [START_REF] Kremen | Ecosystem Services in Biologically Diversified versus Conventional Farming Systems : Benefits , Externalities , and Trade-Offs[END_REF] compared ecosystem services such as food production and environmental performance in biologically diversified, including organic, versus chemically based simplified farming systems, relying on monoculture, inorganic fertilizers, and synthetic pesticide input. They found that conclusions on yield gaps varied widely in previously published articles.

Food access and utilisation

We find four previous literature reviews published between 2011 and 2015 that give a systematic overview of agricultural diversity, dietary intake and consumption associations (Jones, 2017a;[START_REF] Penafiel | A Systematic Review on the Contributions of Edible Plant and Animal Biodiversity to Human Diets[END_REF][START_REF] Powell | Improving diets with wild and cultivated biodiversity from across the landscape[END_REF]Sibhatu and Qaim, 2018b). On the basis of a meta-analysis reviewing 45 studies from 26 countries, Sibhatu and Qaim, (2018b) found that farming diversity is positively associated with dietary diversity and nutritional status in some but not in all cases and that this association depended on the indicator used to measure dietary quality and nutrition outcomes and the level of production diversity. Twenty-nine studies had mixed results with positive association in some cases and insignificant or negative associations in others, eleven studies found no association and five studies found only positive associations between production and dietary diversity or nutrition. The mean marginal effect of increasing farming diversity by one crop or livestock species increases the number of food groups consumed by 0.062 (N observations = 160, standard error 0.027) and the number of foods consumed by 0.716 (N observations = 25, standard error = 0.327) (Sibhatu and Qaim, 2018b). Reasons for small effects include production diversity being already high with further diversification efforts hindering development opportunities through other pathways. In a previous literature review with 23 studies, of which 21 were also later included in Sibhatu and Qaim (2018b), Jones (2017b) found a consistent, but small, positive relationship between production diversity and dietary diversity and in addition, a very small positive relationship between production diversity and nutritional status in least developed countries. Interestingly, the conclusions are different in both reviews. While Sibhatu and Qaim (2018b) conclude that there is little evidence to support policies for increasing production diversity as a strategy for improved smallholder diets and nutrition, Jones (2017b) concludes that agricultural diversification may contribute to diversified diets and may be an important strategy for improving nutrition outcomes. Similarly to Jones 2017b, [START_REF] Powell | Improving diets with wild and cultivated biodiversity from across the landscape[END_REF] concluded that the relationship between crop diversity or agrobiodiversity and dietary diversity or nutrition outcomes is overall positive in most of the 12 reviewed studies. Altogether, [START_REF] Powell | Improving diets with wild and cultivated biodiversity from across the landscape[END_REF], Jones (2017b) and Sibhatu and Qaim (2018b) reviewed 50 studies, of which 19 are included in our review as well as the remaining did not match our selection criteria. Publications were excluded because of publication year, or because they are not peer-reviewed research articles or review articles or because of a lack of a measure of agricultural diversity as defined in this study.

Stability

A meta-analysis of 37 studies showed that cereal-grain legume intercropping significantly increased temporal and spatial yield stability (CV =22.1) compared with the respective grain legume sole crops (CV= 31.7). Temporal yield variability in cereal-grain legume intercropping was 58% lower than for grain legume sole crop but not significantly lower than for the cereal sole crop. Spatial yield variability in cereal-grain legume intercropping was 14-19% lower than grain legume and cereal sole crops [START_REF] Raseduzzaman | Does intercropping enhance yield stability in arable crop production? A meta-analysis[END_REF]. [START_REF] Hansen | Climate risk management and rural poverty reduction[END_REF] reviewed 12 articles that describe benefits of diversified farming systems including agroforestry. They concluded that interventions that encouraged diversification showed moderately positive effects on stabilizing production and consumption, as well as improving livelihoods and welfare. Crop diversification can also contribute to stabilizing income, because some crops like rubber and oil palm can provide revenue throughout the year and the mix of perennial with annual crops can secure a more regular income from harvests in different months [START_REF] Schroth | Farmer strategies for tree crop diversification in the humid tropics. A review[END_REF] Five qualitative reviews give examples of studies that present empirical evidence on differences in stability and resilience between diversified and non-diversified agricultural systems [START_REF] Altieri | Agroecology and the design of climate change-resilient farming systems[END_REF][START_REF] Di Falco | On the Value of Agricultural Biodiversity[END_REF][START_REF] Frison | Agricultural Biodiversity Is Essential for a Sustainable Improvement in Food and Nutrition Security[END_REF][START_REF] Lin | Resilience in Agriculture through Crop Diversification: Adaptive Management for Environmental Change[END_REF][START_REF] Urruty | Stability, robustness , vulnerability and resilience of agricultural systems[END_REF]. Between them they cite 31 studies but none of them provide a systematic overview of the empirical evidence which we attempt to show in Table 2. We select the 11 studies for low-and middle-income countries that were cited before and published as research articles or peer-reviewed book sections, written in English and reporting original data on a relevant measure of stability and summarise their main findings in Table 2. The most common measure of stability in the cited studies was variability of crop yield and income and resistance. For resistance there are two types of studies, one that attempts to assess the resistance of a diversified vs non-diversified system after a major perturbation, a hurricane or a drought, and one that assesses resistance to pest infestation, or heat and water stress without studying the system variables before or after an external shock.

Table 2 Summary of studies on agricultural diversity and stability cited in previous reviews.

Measure of stability

Diversity and food availability

Of the 88 studies evaluated, 19 studies reported 26 separate diversity-food security relationships using a measure of food availability. Most relationships were positive (17 cases, 65%) and only a few were negative (2 cases, 8%), neutral or ambiguous (7 cases, 27%) (Table 3). Most of the studies on food availability conducted field experiments to measure the effect of crop diversity on crop yield or crop production. The field experiments include growing crops in intercropping or rotation systems without making any other changes or embedding crop diversity as one strategy of alternative land use management systems such as agroforestry or conservation agriculture. The second experimental design makes it more difficult to assess the effect of diversification separately from other changes but also highlights the linkages between crop and soil management. In any case, the effect of crop diversity tends to be positive when an additional crop adds an additional function to the system, for example because it is a nitrogen-fixing crop, provides shade for the companion crop, can be commercialised as an additional product or adds specific nutrients to a household's diet. The direction of the relationship between diversity and food availability often depends on the crop studied, the row arrangement in intercropping and the type of crop mix.

For example, [START_REF] Isaacs | Farmer knowledge identifies a competitive bean ideotype for maize-bean intercrop systems in Rwanda[END_REF] report that when grown as sole crop, beans exhibited yields that were often more than twice that of beans intercropped with maize in Rwanda which can be related to reduced resource competition for light and nutrients in the monoculture. In another experiment in Bangladesh Islam et al. (2018) found that a four crop pattern performed better than a three crop pattern which is mostly related to the introduction of maize as a relay crop for onion. In a countrywide trial in Malawi with 991 observations, [START_REF] Snapp | Biodiversity can support a greener revolution in Africa[END_REF] found a positive effect on crop yield when diversifying maize with legumes when compared with an unfertilized maize monoculture.

All three conservation agriculture studies included here found a positive effect of crop diversity on crop yield in India and Bangladesh [START_REF] Ladha | Agronomic improvements can make future cereal systems in South Asia far more productive and result in a lower environmental footprint[END_REF][START_REF] Pradhan | Potential of conservation agriculture (CA) for climate change adaptation and food security under rainfed uplands of India: A transdisciplinary approach[END_REF][START_REF] Samal | Evaluation of long-term conservation agriculture and crop intensification in rice-wheat rotation of Indo-Gangetic Plains of South Asia: Carbon dynamics and productivity[END_REF]. In the context of agroforestry systems, we find four publications for rubber, cocoa and coffee cultivation (Hondrade et al., 2017;[START_REF] Jessy | Possibilities of diverse rubber based agroforestry systems for smallholdings in India[END_REF][START_REF] Schneider | Cocoa and total system yields of organic and conventional agroforestry vs. monoculture systems in a long-term field trial in Bolivia[END_REF][START_REF] Souza | Selection of native trees for intercropping with coffee in the Atlantic Rainforest biome[END_REF]. The results are mixed and depend on the year of the experiment, resource competition between crops, the amount of mutual benefits created by the crop mix and the method for measuring benefits. For example, the results from a 13-year experiment comparing three agroforestry systems with traditional rubber cultivation in India indicate that a range of crops can be integrated with rubber without any adverse effect on growth and yield of rubber. Crop diversification increased rubber yield but only in the first year, after which the effect was not significant [START_REF] Jessy | Possibilities of diverse rubber based agroforestry systems for smallholdings in India[END_REF]. In Brazil, a diversified agroforestry system for coffee cultivation allowed more products from a larger range of food crops to be harvested and commercialized leading to a lower cost/benefit ratio than in the coffee monoculture [START_REF] Souza | Selection of native trees for intercropping with coffee in the Atlantic Rainforest biome[END_REF].

Other data sources used are surveys and farmer interviews which also allows studying effects on farm or household scale [START_REF] Douxchamps | Linking agricultural adaptation strategies, food security and vulnerability: evidence from West Africa[END_REF][START_REF] Dzanku | Agricultural diversification , food self-sufficiency and food security in Ghana : The role of infrastructure and institutions[END_REF][START_REF] Makate | Crop diversification and livelihoods of smallholder farmers in Zimbabwe : adaptive management for environmental change[END_REF].

We cannot compare the studies to each other but each of them highlights the context in which diversity can be beneficial. For example, [START_REF] Douxchamps | Linking agricultural adaptation strategies, food security and vulnerability: evidence from West Africa[END_REF] found that crop diversity positively influenced land productivity in Burkina Faso, Senegal and Ghana, but only for a specific type of household practicing intensified farming with strong market orientation and a high proportion of income from growing pulses. Dzanku and Sarpong (2013) find a positive relationship between more diverse non-staple crop production and household food supply in one region only and the authors suggest that this is due to regional differences associated with better market conditions rather than crop diversity. They concluded that a more diverse crop portfolio did not necessarily lead to a higher probability of household level food security, with other important predictors being household composition, education, wealth, age, and other non-farm sources of income. In a multi-country study with 28,000 farming households in sub-Saharan Africa, [START_REF] Waha | Agricultural diversification as an important strategy for achieving food security in Africa[END_REF] found that median food availability increased with farming diversity. The farming households with highest farming diversity also had significantly more cropland than others, which partly explains this result. This study also find that increasing farming diversity can result in diminished returns, with food availability increasing until diversity levels reach seven species per hectare cropland, and then decreasing beyond this level. The magnitude of the relationships cannot be compared directly across studies as the methods and indicators used differ. Some indicators such as the Shannon diversity index cannot be compared across different locations as they depend on the total number of species. The type of regression model, number and types of crops and livestock species for example will all influence the result. The table shows selected results from each study as assumed relevant to the topic of this review. C = count, SC = cropping system or farming typology, CI = multiple cropping index in %, SDI = Simpson diversity index, SDI-b = Simpson diversity index converted to binary variable, d = difference in means or medians, ns = not significant (p-value > 0.05); β = regression coefficient; ATT = adoption effect

Diversity and stability of food security

We found only 3 studies focusing on this dimension of food security, reporting 7 separate diversitystability relationships. Of these, 4 relationships were positive, 2 were negative and 1 mixed (Table 4). All three studies are for Malawi, two on the farm scale and one on the landscape scale [START_REF] Chimonyo | Grain Legumes Increase Yield Stability in Maize Based Cropping Systems[END_REF][START_REF] Kassie | Production Risks and Food Security under Alternative Technology Choices in Malawi: Application of a Multinomial Endogenous Switching Regression[END_REF][START_REF] Snapp | Biodiversity can support a greener revolution in Africa[END_REF]. They measure the magnitude of fluctuation in a cropping systems as spatial crop yield variability or inter-site crop yield variability, rather than temporal variability. Crop yield stability is a function of environment and crop. For example, crop yield variability in a maize-legume system compared to a fertilized sole crop was lower when maize was grown in rotation with soybean and peanut/pigeon pea intercropped, but not when grown in rotation with peanut or intercropped with pigeon pea only [START_REF] Chimonyo | Grain Legumes Increase Yield Stability in Maize Based Cropping Systems[END_REF]. This is only partly confirmed by an extensive field experiment with more than 1,000 farm sites where crop yield variability of maize was lower compared to an unfertilized sole maize when grown in rotation with peanut but not when intercropped with pigeon pea [START_REF] Snapp | Biodiversity can support a greener revolution in Africa[END_REF].

We also found an alternative method for understanding how agricultural diversity and stability of agricultural production are related in the literature we reviewed. Farm-scale adaptation strategies often include diversification and we identified six publications researching if farmers use diversification to mitigate risks from perceived changes in weather or climate (Antwi-Agyei et al., 2014a;[START_REF] Chengappa | Climate variability and mitigation: perceptions and strategies adopted by traditional coffee growers in India[END_REF][START_REF] Eludoyin | Climate events and impact on cropping activities of small-scale farmers in a part of Southwest Nigeria[END_REF][START_REF] Fadina | Farmers' Adaptation Strategies to Climate Change and Their Implications in the Zou Department of South Benin[END_REF][START_REF] Mavhura | Adaptation to drought in arid and semi-arid environments: Case of the Zambezi Valley, Zimbabwe[END_REF][START_REF] Sanogo | Farmers' perceptions of climate change impacts on ecosystem services delivery of parklands in southern Mali[END_REF]. These 'perception studies' rarely discuss the relationship to food security directly thus are not included in the summary table below but can help to understand farmer's coping or adaptation strategies when faced with short-or long-term environmental changes. The sample size is often small. The number of farmers interviewed in the six studies reviewed ranged from 120 to 400 farmers and it is mostly unclear to what extent the chosen adaptation strategy was effective. For example, if it increased production or stability over time. Also, it is not always clear if diversification was a hypothetically preferred or a practised adaptation strategy, to what extent farmers already practiced diversification in general and in response to perturbations. Although households might claim that they have diversified their cropping patterns in response to climate variability, such patterns might have been partly influenced by non-climatic factors such as economic shocks and opportunities (Antwi-Agyei et al., 2014b). However, this method can reveal farmer's motivation to adapt and preferring a specific strategy over others. The conclusions from the six studies suggest that diversification is practiced as a risk management strategy [START_REF] Chengappa | Climate variability and mitigation: perceptions and strategies adopted by traditional coffee growers in India[END_REF][START_REF] Eludoyin | Climate events and impact on cropping activities of small-scale farmers in a part of Southwest Nigeria[END_REF][START_REF] Fadina | Farmers' Adaptation Strategies to Climate Change and Their Implications in the Zou Department of South Benin[END_REF], to cope with climate shocks [START_REF] Sanogo | Farmers' perceptions of climate change impacts on ecosystem services delivery of parklands in southern Mali[END_REF] and to take advantage of multiple growing seasons [START_REF] Eludoyin | Climate events and impact on cropping activities of small-scale farmers in a part of Southwest Nigeria[END_REF]. One perception study found that on-farm diversification was not an option for farmers in Zimbabwe faced with lower than average rainfall, and that they instead relied on food aid, income diversification and collecting wild food [START_REF] Mavhura | Adaptation to drought in arid and semi-arid environments: Case of the Zambezi Valley, Zimbabwe[END_REF]. This is perhaps an indication that major shocks cannot be compensated by diversifying as every agricultural activity is impacted severely.

To our knowledge no study has measured the relationship between diversification and stability of any food security indicator on the national scale. However, an interesting contribution is [START_REF] Sardos | Root crops diversity and agricultural resilience: a case study of traditional agrosystems in Vanuatu (Oceania)[END_REF] who discuss changes to the agricultural systems and its resilience in Vanuatu since the introduction of root and tree crops such as white and Indian yam, cocoyam, cassava and sweet potato during European settlement in the 19 th century. This seems to have neither compromised agricultural diversity nor changed the systems drastically which before consisted of local or naturalized root and tree crops such as wild yam and taro. Farmers instead used the new crops to increase the resilience of the system through increasing the farmer's ability to switch to alternative crops when facing an unforeseen change.

Diversity and food access

Fifty-two studies reported 148 separate diversity-food security relationships used a measure of food access. Of these, the authors reported positive relationships in 96 cases (65%), no or ambiguous relationships in 47 cases (32%) and negative relationships in only 5 cases (3%) (Table 5). Most of the studies reviewed used at least one indicator of food access, either to describe household dietary diversity, average household energy and nutrient intake, household food consumption or financial constraints to food security. We here include studies using measures for coping strategies at times of food shortage or self-reported food insecurity using experience-based scales.

By far the most common indicators of food access were household consumption measures, for example HDDS. Thirty-three studies used household dietary diversity as a measure for food access, sometimes modified by changing the recall period or number and types of food groups (M-HDDS).

Where the relationship between a measure of agricultural diversity and HDDS or M-HDDS is positive the regression coefficients differ between different statistical methods (e.g. [START_REF] Ayenew | Production diversification, dietary diversity and consumption seasonality: Panel data evidence from Nigeria[END_REF][START_REF] Huluka | Determinants of household dietary diversity in the Yayo biosphere reserve of Ethiopia: An empirical analysis using sustainable livelihood framework[END_REF]Jones, 2017b;[START_REF] Kissoly | Implications of smallholder farm production diversity for household food consumption diversity: Insights from diverse agro-ecological and market access contexts in rural tanzania[END_REF][START_REF] Koppmair | Farm production, market access and dietary diversity in Malawi[END_REF][START_REF] Kumar | If They Grow It, Will They Eat and Grow? Evidence from Zambia on Agricultural Diversity and Child Undernutrition[END_REF][START_REF] Makate | Crop diversification and livelihoods of smallholder farmers in Zimbabwe : adaptive management for environmental change[END_REF][START_REF] Murendo | Nutrition education, farm production diversity, and commercialization on household and individual dietary diversity in Zimbabwe[END_REF][START_REF] Romeo | Linking farm diversification to household diet diversification: evidence from a sample of Kenyan ultra-poor farmers[END_REF]Sibhatu et al., 2015a;Sibhatu and Qaim, 2018a;[START_REF] Somé | The influence of crop production and socioeconomic factors on seasonal household dietary diversity in Burkina Faso[END_REF][START_REF] Tesfaye | Crop diversity, household welfare and consumption smoothing under risk: Evidence from rural Uganda[END_REF][START_REF] Traoré | Contribution of cattle of different breeds to household food security in southern Mali[END_REF]. Sibhatu and Qaim (2018a) find that increasing agricultural diversity by one crop or livestock species slightly increases the number of food groups consumed by 0.05-0.07 in Kenya, 0.16 in Indonesia and 0.2-0.33 in Uganda. Other explaining factors such as cultivated land area and educational level of the household head also have a positive effect on M-HDDS but to a smaller extent than agricultural diversity. [START_REF] Murendo | Nutrition education, farm production diversity, and commercialization on household and individual dietary diversity in Zimbabwe[END_REF] also find a relatively small effect of increasing agricultural diversity.

Producing one additional crop or livestock species leads to a 3% increase in M-HDDS whereas market participation results in a 6% increase in M-HDDS which indicates a reliance on purchased food. Other studies found much larger effects of increased agricultural diversity on HDDS and M-HDDS [START_REF] Makate | Crop diversification and livelihoods of smallholder farmers in Zimbabwe : adaptive management for environmental change[END_REF][START_REF] Tesfaye | Crop diversity, household welfare and consumption smoothing under risk: Evidence from rural Uganda[END_REF] where crop diversity was strongly associated with HDDS and M-HDDS. A few studies also measure mean household nutrient and/or energy intake or adequacy and found positive associations with agricultural diversity for some indicators [START_REF] Brüssow | Implications of climate-smart strategy adoption by farm households for food security in Tanzania[END_REF][START_REF] Jager | Food and nutrient gaps in rural Northern Ghana: Does production of smallholder farming households support adoption of food-based dietary guidelines?[END_REF]Sibhatu and Qaim, 2018a).

Some studies examine the diversity-food access relationship differentiated by type of household. For example, while the crop diversity and HDDS relationship was positive overall, it was not significant or very weak for poorer households which depend more on income growth for increasing dietary diversity [START_REF] Ecker | Agricultural transformation and food and nutrition security in Ghana: Does farm production diversity (still) matter for household dietary diversity?[END_REF]. [START_REF] Somé | The influence of crop production and socioeconomic factors on seasonal household dietary diversity in Burkina Faso[END_REF] found that in Burkina Faso seasonal differences between post-harvest, lean and harvest period in household dietary diversity was greater among households with greater crop production and value of crop sales but not with greater crop diversity.

Nine of the twelve studies on the association between agricultural diversity and economic access found a positive association [START_REF] Bellon | To diversify or not to diversify, that is the question. Pursuing agricultural development for smallholder farmers in marginal areas of Ghana[END_REF][START_REF] Das | Farm size, livelihood diversification and farmer ' s income in India[END_REF][START_REF] Kasem | Crop diversification in Thailand: Status, determinants, and effects on income and use of inputs[END_REF][START_REF] Ladha | How extensive are yield declines in long-term rice-wheat experiments in Asia?[END_REF][START_REF] Limbu | Fish polyculture system integrated with vegetable farming improves yield and economic benefits of small-scale farmers[END_REF][START_REF] Makate | Crop diversification and livelihoods of smallholder farmers in Zimbabwe : adaptive management for environmental change[END_REF][START_REF] Mofya-Mukuka | Livelihood effects of crop diversification: a panel data analysis of rural farm households in Zambia[END_REF][START_REF] Pradhan | Potential of conservation agriculture (CA) for climate change adaptation and food security under rainfed uplands of India: A transdisciplinary approach[END_REF][START_REF] Thapa | Impact of Crop Diversification on Rural Poverty in Nepal[END_REF]. For example, in Thailand, diversifying rice monocropping systems by including asparagus and okra for international markets lead to an increase in net income [START_REF] Kasem | Crop diversification in Thailand: Status, determinants, and effects on income and use of inputs[END_REF]. Crop diversification by adding high-value crops in Nepal reduced the probability of being poor [START_REF] Thapa | Impact of Crop Diversification on Rural Poverty in Nepal[END_REF]. However, marginal households must diversify more than one third of total agricultural production value into high-value crops to move above the poverty line. Also agricultural income was significantly higher if households shifted their crop portfolio by substituting certain crops or cultivars for others instead of diversifying it by adding crops [START_REF] Brüssow | Implications of climate-smart strategy adoption by farm households for food security in Tanzania[END_REF].

Six of the ten studies using experience-based food insecurity scales or measuring the extent of coping strategies find a positive association with diversity at least for one indicator studied [START_REF] Brüssow | Implications of climate-smart strategy adoption by farm households for food security in Tanzania[END_REF][START_REF] Kc | Assessing links between crop diversity and food self-sufficiency in three agroecological regions of Nepal[END_REF][START_REF] M'kaibi | The relationship between agricultural biodiversity, dietary diversity, household food security, and stunting of children in rural Kenya[END_REF][START_REF] M'kaibi | Effects of agricultural biodiversity and seasonal rain on dietary adequacy and household food security in rural areas of Kenya[END_REF][START_REF] Nkomoki | Adoption of sustainable agricultural practices and food security threats: Effects of land tenure in Zambia[END_REF][START_REF] Vanek | Coupling of soil regeneration, food security, and nutrition outcomes in Andean subsistence agroecosystems[END_REF]. For example, HFIAS, the Household Food Insecurity Access Scale was lower at higher levels of agricultural diversity (M' Kaibi et al., 2017Kaibi et al., , 2015;;[START_REF] Vanek | Coupling of soil regeneration, food security, and nutrition outcomes in Andean subsistence agroecosystems[END_REF]. However, when HFIAS was converted into a binary variable ("food secure" and "not food secure" households), the relationship between HFIAS and agricultural diversity was not statistically significant [START_REF] Bezner Kerr | Participatory agroecological research on climate change adaptation improves smallholder farmer household food security and dietary diversity in Malawi[END_REF][START_REF] Makate | Crop diversification and livelihoods of smallholder farmers in Zimbabwe : adaptive management for environmental change[END_REF]. The results also differ between studies using the same indicator, for example HHS, the Household Hunger Scale. Whereas Ng 'Endo et al. (2015) find no association between HHS and agrobiodiversity, [START_REF] Nkomoki | Adoption of sustainable agricultural practices and food security threats: Effects of land tenure in Zambia[END_REF] report that 82% of the households reporting to experience little to no hunger practiced crop diversification.

Some studies used national agricultural, livelihoods or household surveys that present results across a representative national sample including both diversified and non-diversified farming households. For example, both [START_REF] Snapp | Filling the maize basket" supports crop diversity and quality of household diet in Malawi[END_REF] and [START_REF] Jones | Farm production diversity is associated with greater household dietary diversity in Malawi : Findings from nationally representative data[END_REF] use data from the 2010/11 Malawi Integrated Household Survey. For the same measures of diversity and food access, both studies find a positive effect. [START_REF] Jones | Farm production diversity is associated with greater household dietary diversity in Malawi : Findings from nationally representative data[END_REF] highlight that the relationship may be further influenced by gender and wealth as the effect of farming diversity on household dietary diversity was stronger in women-headed households and in wealthier households. [START_REF] Snapp | Filling the maize basket" supports crop diversity and quality of household diet in Malawi[END_REF] find a small positive effect on food security as growing one additional crop increased HDDS by only 2%. Similarly, in Nigeria the positive effect of agricultural diversity on HDDS is significant but small. A 10 per cent increase in agricultural diversity results in a 0.16-2.4 per cent increase in HDDS [START_REF] Ayenew | Production diversification, dietary diversity and consumption seasonality: Panel data evidence from Nigeria[END_REF][START_REF] Dillon | Agricultural Production, Dietary Diversity and Climate Variability[END_REF] which is still a larger effect then that from increasing agricultural revenue by 10 per cent [START_REF] Dillon | Agricultural Production, Dietary Diversity and Climate Variability[END_REF]. In some multi-country studies it was possible to compare the results across countries and geographies [START_REF] Fraval | Food Access Deficiencies in Sub-saharan Africa: Prevalence and Implications for Agricultural Interventions[END_REF][START_REF] Passarelli | Evaluating the pathways from small-scale irrigation to dietary diversity: evidence from Ethiopia and Tanzania[END_REF][START_REF] Ritzema | Household-level drivers of dietary diversity in transitioning agricultural systems: Evidence from the Greater Mekong Subregion[END_REF][START_REF] Sibhatu | Production diversity and dietary diversity in smallholder farm households[END_REF]Sibhatu and Qaim, 2018a;[START_REF] Tesfaye | Crop diversity, household welfare and consumption smoothing under risk: Evidence from rural Uganda[END_REF] and some results suggest that the association depends on geographic locations. In sub-Saharan Africa for example, the effect of production diversity is positive in semi-arid zones but negative in the humid/sub-humid zones [START_REF] Fraval | Food Access Deficiencies in Sub-saharan Africa: Prevalence and Implications for Agricultural Interventions[END_REF]. In Malawi, HDDS increased with production diversity but in Ethiopia, with almost double the average production diversity of Malawi, there is no association with household dietary diversity [START_REF] Sibhatu | Production diversity and dietary diversity in smallholder farm households[END_REF].

Five studies on food access have attempted to test whether the diversity-food access relationship is linear or rather follows an inverted U-shape and to estimate an optimal level of agricultural diversity. Sibhatu et al. (2015b) for example find that HDDS increases with production diversity initially, but then declines with further increases in production diversity. This was evident from a negative regression coefficient for squared production diversity which indicates that the effect on dietary diversity declines. Similarly [START_REF] Parvathi | Does mixed crop-livestock farming lead to less diversified diets among smallholders? Evidence from Laos[END_REF] and [START_REF] Das | Farm size, livelihood diversification and farmer ' s income in India[END_REF], find that the positive effect of production diversity on FCS and agricultural income declines as household diversify more. [START_REF] Das | Farm size, livelihood diversification and farmer ' s income in India[END_REF] find that most household already engage in the optimal number of crops, two, but not in the optimal number of animal husbandry and non-farm activities. This is confirmed by other studies (Islam et al., 2018;[START_REF] Mofya-Mukuka | Livelihood effects of crop diversification: a panel data analysis of rural farm households in Zambia[END_REF]) that find that HDDS, HDDS and FSC tended to decline with increasing diversification after a peak point which was not further quantified in the studies. * ATT = average treatment effect, ns = not significant (p-value > 0.05); β = regression coefficient; IRR = incidence rate ratios; VIP = variable importance in projection statistic; DID = difference-in-difference estimator, OR = Odds ratio, d = difference in means or median, r/r2 = Pearson correlation coefficient, rho = Spearman rank order correlation coefficient, F = ANOVA F statistic, ME = marginal effects, ns = not significant at the 95% level. The magnitude of the relationships cannot be compared directly across studies as the methods and indicators used differ. Some indicators such as the Shannon diversity index cannot be compared across different locations as they depend on the total number of species. The type of regression model, number and types of crops and livestock species for example will all influence the result. The table shows selected results from each study as assumed relevant to the topic of this review.

Diversity and food utilisation

Finally, 29 studies reported 125 separate diversity-food security relationships focused on food utilisation. Of these, the authors reported, positive relationships in 65 cases (52%), no or ambiguous relationships in 49 cases (40%) and negative relationships in 11 cases (8%) (Table 6).

There are mixed results for different measures of food utilisation and for different age groups. The indicators either measure individual food consumption or anthropometric status. We found eleven studies that assess the association between agricultural diversity and anthropometric status of children and/or their mothers. The results differ for different age groups, for example between children aged 2 years or younger and 3 years or older [START_REF] Gelli | Using a Community-Based Early Childhood Development Center as a Platform to Promote Production and Consumption Diversity Increases Children's Dietary Intake and Reduces Stunting in Malawi: A Cluster-Randomized Trial[END_REF]. Even if the same age group is studied, there are mixed results for different countries. For example, crop diversity measured as species richness and HAZ of children aged 6-24 months has a positive relationship in Malawi [START_REF] Gelli | Using a Community-Based Early Childhood Development Center as a Platform to Promote Production and Consumption Diversity Increases Children's Dietary Intake and Reduces Stunting in Malawi: A Cluster-Randomized Trial[END_REF] but a negative relationship in Zambia [START_REF] Kumar | If They Grow It, Will They Eat and Grow? Evidence from Zambia on Agricultural Diversity and Child Undernutrition[END_REF]. The negative relationship with HAZ of children in Zambia is strongest for children with HAZ scores 0 or higher. The relationship between crop diversity and HAZ and crop diversity and WAZ of children aged 6-60 months is neutral in Guatemala (Luna-González and Sorensen, 2018) but positive in Ethiopia [START_REF] Yigrem | Assessing the relative importance of dairy products to family nutrition in mixed crop-livestock production systems of Ethiopia[END_REF]. Where there is no significant association between diversity and nutritional status of children, other explanatory variables associated with nutritional status are socio-economic status such as housing conditions, assets ownership, household wealth and income, water, sanitation and hygiene, access to clean drinking water, maternal education, maternal age and child morbidity which indicates that improved nutrition can be achieved through multiple pathways in addition to diets [START_REF] Luna-González | Higher agrobiodiversity is associated with improved dietary diversity, but not child anthropometric status, of mayan achí people of Guatemala[END_REF][START_REF] M'kaibi | The relationship between agricultural biodiversity, dietary diversity, household food security, and stunting of children in rural Kenya[END_REF].

The results depend also on the anthropometric measure used. [START_REF] Malapit | Women's Empowerment Mitigates the Negative Effects of Low Production Diversity on Maternal and Child Nutrition in Nepal[END_REF], analysing data from three agro-ecological zones in Nepal, found a positive relationship between production diversity and some anthropometric scores but not all. While production diversity is positively correlated with WHZ, it is not with maternal body mass index and HAZ. While stunting and wasting indicated by low HAZ and WHZ scores share common risk factors, and both indicate impaired growth and development from poor nutrition it is possible that only one of them (stunting) is associated with production diversity. This is because stunting indicates chronic malnutrition and wasting indicates acute malnutrition and is moderated by the age of the child [START_REF] Saaka | Relationship between agricultural biodiversity and dietary diversity of children aged 6-36 months in rural areas of northern Ghana[END_REF].

Another twenty-three studies measured nutrient intake or a validated proxy for nutrient intake or adequacy, MDD-W or WDDS for women and IYCDDS, IDDS or MDD-C for children. Fifteen studies used adequacy of diet diversity of children as a measure of nutrient intake, and nine of them find a positive association with agricultural diversity (e.g. [START_REF] Gelli | Using a Community-Based Early Childhood Development Center as a Platform to Promote Production and Consumption Diversity Increases Children's Dietary Intake and Reduces Stunting in Malawi: A Cluster-Randomized Trial[END_REF][START_REF] Koppmair | Farm production, market access and dietary diversity in Malawi[END_REF][START_REF] Malapit | Women's Empowerment Mitigates the Negative Effects of Low Production Diversity on Maternal and Child Nutrition in Nepal[END_REF][START_REF] Saaka | Relationship between agricultural biodiversity and dietary diversity of children aged 6-36 months in rural areas of northern Ghana[END_REF]. The results differ by age group [START_REF] Mulmi | Household food production is positively associated with dietary diversity and intake of nutrient-dense foods for older preschool children in poorer families: Results from a nationally-representative survey in Nepal[END_REF], the measure of agricultural diversity used, and are mediated by other fators such as access to nutrition education on child feeding and care practices market participation [START_REF] Murendo | Nutrition education, farm production diversity, and commercialization on household and individual dietary diversity in Zimbabwe[END_REF] and other characteristics such as household size and wealth [START_REF] Saaka | Relationship between agricultural biodiversity and dietary diversity of children aged 6-36 months in rural areas of northern Ghana[END_REF]. Another consideration is that instead of having to increase the number of food groups a child consumes it is important to reach a certain cut off point when their diet can be considered adequately diverse, i.e. consuming four or more different food groups according to the World Health Organization (2008). The prevalence of children aged 6-23 months with MDD-C, minimum dietary diversity was found to be positively [START_REF] Kumar | If They Grow It, Will They Eat and Grow? Evidence from Zambia on Agricultural Diversity and Child Undernutrition[END_REF][START_REF] Mitchodigni | Complementary feeding practices: determinants of dietary diversity and meal frequency among children aged 6-23 months in Southern Benin[END_REF] or not [START_REF] Mulmi | Household food production is positively associated with dietary diversity and intake of nutrient-dense foods for older preschool children in poorer families: Results from a nationally-representative survey in Nepal[END_REF] associated with agricultural diversity. However, diet quality of children older than 18 months improved with diversification of farm production whereas other strategies such as improved market access to purchase complementary foods may benefit younger children [START_REF] Mulmi | Household food production is positively associated with dietary diversity and intake of nutrient-dense foods for older preschool children in poorer families: Results from a nationally-representative survey in Nepal[END_REF].

Positive associations between agricultural diversity and MDD-W or WDDS were found in seven studies [START_REF] Adubra | The Minimum Dietary Diversity for Women of Reproductive Age (MDD-W) Indicator Is Related to Household Food Insecurity and Farm Production Diversity: Evidence from Rural Mali[END_REF][START_REF] Bellon | On-Farm Diversity and Market Participation Are Positively Associated with Dietary Diversity of Rural Mothers in Southern Benin, West Africa[END_REF][START_REF] Bellows | The Relationship Between Dietary Diversity Among Women of Reproductive Age and Agricultural Diversity in Rural Tanzania[END_REF][START_REF] Boedecker | Dietary contribution of Wild Edible Plants to women's diets in the buffer zone around the Lama forest, Benin -an underutilized potential[END_REF]Jones et al., 2018;[START_REF] Murendo | Nutrition education, farm production diversity, and commercialization on household and individual dietary diversity in Zimbabwe[END_REF][START_REF] Whitney | The Role of Homegardens for Food and Nutrition Security in Uganda[END_REF]. For MDD-W the regression coefficients are 0.036-0.23 with odds ratios of 1.08-1.38. For WDDS the regression coefficients are smaller, 0.10 in a logistic regression and odds ratio of 1.03-1.05 in a multiple linear regression. In Mali, [START_REF] Adubra | The Minimum Dietary Diversity for Women of Reproductive Age (MDD-W) Indicator Is Related to Household Food Insecurity and Farm Production Diversity: Evidence from Rural Mali[END_REF] evaluate the impact of a 3 years nutrition-sensitive intervention targeting women and their children during the first 1000 days of each child's life. In a large sample with more than 5,000 women they found a positive relationship between production diversity and MDD-W and WDDS, regardless of household's overall food security and wealth status. Specifically, one more food crop or livestock group on the farm resulted in a 10% increase in WDDS-10 and a better chance of attaining the minimally needed MDD-W score. In contrast, [START_REF] Gitagia | Determinants of dietary diversity among women of reproductive age in two different agro-ecological zones of rongai sub-county, nakuru, Kenya[END_REF] find no relationship between agrobiodiversity and the quality of women's diets in central Kenya but an important relationship between education and diet quality.

Four studies used household data from nationally representative surveys for single country or multicountry studies [START_REF] Hirvonen | Agricultural production and children's diets: evidence from rural Ethiopia[END_REF]Islam et al., 2018;[START_REF] Lovo | Crop Diversification and Child Health: Empirical Evidence From Tanzania[END_REF][START_REF] Tobin | Does crop diversity at the village level influence child nutrition security? Evidence from 11 sub-Saharan African countries[END_REF] (Table 6). The association between agricultural diversity and food utilization was mostly positive irrespective of the food utilization and diversity indicator, except for some associations presented in [START_REF] Tobin | Does crop diversity at the village level influence child nutrition security? Evidence from 11 sub-Saharan African countries[END_REF]. In this study, the authors find a positive association between the Simpson diversity index and HAZ but a small negative association between crop species richness and HAZ. This indicates that crop diversity has a benefit only if proportional presence is considered in addition to total number of species [START_REF] Tobin | Does crop diversity at the village level influence child nutrition security? Evidence from 11 sub-Saharan African countries[END_REF]. HAZ increased by 0.26-0.30 with each oneunit increase in the Simpson diversity index but decreased by 0.015 with each one-unit increase in crop richness. Prevalence of stunting and wasting is defined as the percentage of children with HAZ and WHZ, respectively, of more than 2 standard deviations below median. IDDS (children) differs from IYCDDS in the number of food groups used and/or the age group which is 6-23 months for IYCDDS. MDD-C differs from IYCDDS in that it measures the prevalence of children consuming at least four of the seven food groups included. IDDS (mother) differs from WDDS in the number of food groups considered * CC = Canonical correlation coefficient, β = regression coefficient, DID = difference-in-difference estimator, VIP = variable importance in the projection. The magnitude of the relationships cannot be compared directly across studies as the methods and indicators used differ. Some indicators such as the Shannon diversity index cannot be compared across different locations as they depend on the total number of species. The type of regression model, number and types of crops and livestock species for example will all influence the result. The table shows selected results from each study as assumed relevant to the topic of this review.

Diversity and food security at the global scale

We found five studies study the relation of agricultural diversity to food security on the global scale.

Because of the low sample size, results are summarized in this separate section for all four food security dimensions together. Since 1961, global crop diversity increased which may have influenced national food supply overall. Crop diversity (H') increased by about 20% between 1961 and 2016 and crop species richness increased more strongly than evenness in two studies using different national agricultural data [START_REF] Aizen | Global agricultural productivity is threatened by increasing pollinator dependence without a parallel increase in crop diversification[END_REF][START_REF] Khoury | Increasing homogeneity in global food supplies and the implications for food security[END_REF]. In contrast to species richness, the results for evenness were mixed between different world regions with Europe being the only region with a decline in evenness but increase in richness. Dominance of the most abundant crop commodities declined and agricultural production is increasingly homogeneous [START_REF] Aizen | Global agricultural productivity is threatened by increasing pollinator dependence without a parallel increase in crop diversification[END_REF][START_REF] Khoury | Increasing homogeneity in global food supplies and the implications for food security[END_REF]. Going back even further in time, [START_REF] Nabhan | Agrobiodiversity Shifts on Three Continents Since Vavilov and Harlan : Assessing Causes , Processes , and Implications for Food Security[END_REF] analysed how agrobiodiversity has changed over time by comparing late 19 th -c. to early 20 th -c. records with their own fieldwork in 2005 in three regions of Tajikistan, Egypt, and the United States. They find that farmers adopt and abandon crop varieties for different reasons in the three locations and that local and global factors influence the conservation of agrobiodiversity. While for example diversity in the Tajikistan study area remained roughly the same over time and only certain species changed their distribution in space or time, diversity declined in the study area in the United States (northern Arizona). The reason is that water scarcity led to a loss of varieties, and livelihoods shifted away from farming.

To our knowledge, only one study relates national food supply diversity with food utilisation and finds a negative relationship between national food supply diversity (H') and the national prevalence of child stunting (β = -3.1), wasting (β = -1.15) and being underweight (β = -2.39) across 113 countries [START_REF] Remans | Measuring nutritional diversity of national food supplies[END_REF]. Functional diversity (MFAD) has a significant relation only to the prevalence of wasting (β = -1.90) and being underweight (β = -3.10). Income per capita has a strong influence on nutritional outcomes too [START_REF] Remans | Measuring nutritional diversity of national food supplies[END_REF], Table 2). For low-income countries, agrobiodiversity was a good predictor of national food diversity, because their national food supply tends to be that which they produce. Middle-to high income countries are less dependent on own production and have greater access to international markets to increase and diversify their food supply.

The diversity-stability hypothesis was tested for national crop yield between 1961 and 2010 across the 100 most populous countries [START_REF] Renard | National food production stabilized by crop diversity[END_REF]. Crop diversity at the national level (exp(H')) is statistically associated with increased temporal stability of crop yield, irrespective of aggregation to crop groups (R2 = 0.32 -0.37), and this stabilizing effect is similar in magnitude than the destabilizing effect of rainfall variability. The study did not find any crop group contributing more to yield stability than others. [START_REF] Troell | Does aquaculture add resilience to the global food system?[END_REF] shows price indices for individual food sectors and for food in the aggregate during the period 1990-2013. Cereal and oilseed prices have shown much stronger variation than have price indices for meat, aquaculture, and capture fisheries. The coefficient of variation for food in the aggregate is 0.33 over the entire period-substantially higher than that of aquaculture (0.16), fisheries, and meat (0.21) but below that of grains and oils (0.4). Lower volatility in the meat and fish sectors suggests a significant share of substitution possibilities between various animal protein products and various feed ingredients.

Synthesis and Recommendations

We performed a survey of 924 studies that yielded 88 studies meeting the inclusion requirements and giving 314 individual diversity-food security relationships across low-and middle-income countries. In almost two thirds of all cases, agricultural diversity had a positive effect on food security (Table 7). In about one third of the relationships there was no effect of agricultural diversity on food security, or the results were mixed. In very few cases food security declined when agricultural diversity increased (6%). Food access was the dimension of food security most assessed with 59% of all studies and 47% of all relationships. Thirty-three studies used household dietary diversity as a measure of food access and twenty-two studies used at least one food utilisation indicator validated as a proxy for nutrient adequacy. Studies for food utilization are more common than for food availability, 34% and 22% respectively and for both dimensions agricultural diversity had a positive effect in about 55% to 65% of all cases. For food utilization, of the 47 neutral or mixed relationships, 13 times a measure of anthropometric and nutritional status is used and 34 times a measure of individual consumption is used. The most common spatial scale of the analysis was the household and farm scale. Crop species richness was the most common indicator of agricultural diversity.

Common reasons for positive and negative relationships

There is no food security dimension that would primarily have a negative or neutral relationship with agricultural diversity. However, for each food security dimension studied there is a considerable number of relationships that are found to be neutral or ambiguous. An often-stated reason for a neutral relationship between agricultural diversity and food security is that households sourced significant proportions of their food from markets. Hence, a positive relationship between agricultural diversity at the farm scale and food security is plausible, particularly when farming households produce most of what they consume. The direction of the relationship between diversity and food availability often depends on the crop studied, the row arrangement in intercropping and the type of crop mix. The effect of crop diversity tends to be positive when a crop has an additional function for the system, for example because it is a nitrogen-fixing crop, provides shade for the companion crop or contain specific nutrients. Functional diversity can also exist in a different context, for example where a new crop or animal type increases farm income or nutrition. On the other hand, a simple coexistence of species might benefit income or nutrition but not ecosystem functioning. Other factors cited to have had a stronger influence on food security are socioeconomic status such as housing conditions, assets ownership, income and education, farm characteristics such as access to improved management strategies and farmland size, and other characteristics such as household composition and size, sanitation and hygiene, access to clean drinking water, and child morbidity [START_REF] Dzanku | Agricultural diversification , food self-sufficiency and food security in Ghana : The role of infrastructure and institutions[END_REF][START_REF] Luna-González | Higher agrobiodiversity is associated with improved dietary diversity, but not child anthropometric status, of mayan achí people of Guatemala[END_REF][START_REF] M'kaibi | The relationship between agricultural biodiversity, dietary diversity, household food security, and stunting of children in rural Kenya[END_REF][START_REF] Passarelli | Evaluating the pathways from small-scale irrigation to dietary diversity: evidence from Ethiopia and Tanzania[END_REF][START_REF] Saaka | Relationship between agricultural biodiversity and dietary diversity of children aged 6-36 months in rural areas of northern Ghana[END_REF][START_REF] Yigrem | Assessing the relative importance of dairy products to family nutrition in mixed crop-livestock production systems of Ethiopia[END_REF]. Also, the benefits of diversification are context specific and there exist potentially other solutions to improve food security. Sometimes diversity is only beneficial in conjunction with other changes in the system, for example increasing market participation or soil conservation systems. In other situations, it might be the primary coping strategy, for example, when due to limited market access households are more reliant on own food production.

The different branches of literature

The articles reviewed can be broadly grouped into three clusters, similar to Glamann's clusters of literature analysing the food security-biodiversity association [START_REF] Glamann | The intersection of food security and biodiversity conservation : a review[END_REF]. Each cluster tends to be more closely related to one of the food security dimensions. One cluster is dominated by the natural sciences focusing on the production and ecological aspects of food security (e.g. [START_REF] Samal | Evaluation of long-term conservation agriculture and crop intensification in rice-wheat rotation of Indo-Gangetic Plains of South Asia: Carbon dynamics and productivity[END_REF][START_REF] Snapp | Biodiversity can support a greener revolution in Africa[END_REF]. A second cluster is dominated by the social sciences and emphasize for example economic dimensions of food security [START_REF] Das | Farm size, livelihood diversification and farmer ' s income in India[END_REF][START_REF] Parvathi | Does mixed crop-livestock farming lead to less diversified diets among smallholders? Evidence from Laos[END_REF]. Less studies consider broader aspects of sustainability, social-ecological development and empowerment [START_REF] Jones | Farm production diversity is associated with greater household dietary diversity in Malawi : Findings from nationally representative data[END_REF][START_REF] Malapit | Women's Empowerment Mitigates the Negative Effects of Low Production Diversity on Maternal and Child Nutrition in Nepal[END_REF]. A third cluster is dominated by nutrient science emphasizing human nutrition and health aspects of food security [START_REF] Gelli | Using a Community-Based Early Childhood Development Center as a Platform to Promote Production and Consumption Diversity Increases Children's Dietary Intake and Reduces Stunting in Malawi: A Cluster-Randomized Trial[END_REF][START_REF] Tobin | Does crop diversity at the village level influence child nutrition security? Evidence from 11 sub-Saharan African countries[END_REF]. As [START_REF] Glamann | The intersection of food security and biodiversity conservation : a review[END_REF] explained, each group has specific approaches and conceptual basis for investigating the relationship, using specific measures of food security and including or excluding particular themes.

Recommendations for future research on diversity and food security

Based on our observations from the literature review, some methodological recommendations for future research can be made.  Some studies speak of "diversifying into" and it is important to clarify the nature of diversification studied in this case. A new crop can be an addition to the existing crop portfolio or a replacement for another crop. Specific crops such as cash crops can have benefits to farmers also in the absence of overall diversification of the system.

 When measuring the diversity-stability relationship, future studies should consider that the relationship might be always positive for some measures of stability, but not for others. From a statistical point of view the mean of variables is more stable as more variables and their fluctuations are averaged [START_REF] Doak | The Statistical Inevitability of Stability-Diversity Relationships in Community Ecology[END_REF].

 When choosing a measure of diversity, consider that evenness in the distribution of different food items or food groups is not necessarily desired from a nutritional perspective. A high score only indicates health benefits if calculated from a list of healthy foods. Even then it is not necessary to consume equal quantities of everything, but the amount required for a specific age and sex group.

 An element of scale-dependency should be introduced into diversity frameworks. Conclusions on the benefits of agricultural diversity on the national or global scale might not be scalable to the field scale and vice versa. The effect might be explained by a certain combination of production / agroecological zones on a larger scale that cannot be reproduced on the field scale and vice versa.

 Several alternative strategies for increasing food security should be studied along with diversification to compare the relative importance of each strategy for similar outcomes.

Several research questions are understudied in the reviewed literature and constitute interesting challenges for future research.

 An interesting question is related to thresholds in achieving benefits from diversification. There are three considerations here. Firstly, such a threshold is a probably a relative, rather than absolute threshold, depending on the ecological and economic context of the farm and potential benefits from diversification. High diversity in one context might be average in another.

Secondly, there might be a minimum requirement to achieve gains from diversification. Achieving minimum dietary diversity of children through increasing agricultural diversity is a good example. Thirdly, from a certain point, the benefits of diversity might diminish, which suggests a challenge of "optimal" level of diversity.

 The relationship between diversity, a characteristic of a farming system, and diversification, the process of increasing diversity in a farming system, should be explored further. Existing diversity can limit or enable further diversification. Already diversified systems might have characteristics such as high level of flexibility in allocating resources, that enable even more diversification. On the other hand, at already high levels of diversity there might be no further benefit from diversification, or only at high costs, that may be diminishing returns. In some reviewed articles 80% of the farmers already practiced diversification so further diversification might not be their priority.

 The question of complementarity and redundancy between several species of crops for example is understudied. This means that the benefits of diversification are not necessarily proportional to the increase in diversity and relevant functions can on the other hand be maintained at lower levels of diversity. Drought resilience for example can be achieved through the right species composition irrespective of diversity [START_REF] Dardonville | Influence of diversity and intensification level on vulnerability, resilience and robustness of agricultural systems[END_REF].

 Apart from modelling and quantifying the diversity-food security relationships, more focus on the pathways from diversification to food security should be researched. The most researched pathway is perhaps through consumption of own production but there might also be marketbased agricultural diversification [START_REF] Bellon | To diversify or not to diversify, that is the question. Pursuing agricultural development for smallholder farmers in marginal areas of Ghana[END_REF]. Consumption versus income-generating pathways are for example discussed for India in [START_REF] Gillespie | The Agriculture-Nutrition Disconnect in India What Do We Know? IFPRI Discuss[END_REF].

 There are noticeable gaps in understanding the relationship between diversity and food security; on the national / global scale. On a national scale for example it would be interesting to know if the prevalence of mal-or undernutrition change when the country decreased the number of commodities produced nationally?

In conclusion agricultural diversity can be beneficial for food security, but it is not the only available strategy to promote food security. Where diversification is also the cheapest strategy in terms of monetary and labour costs it can be an appealing and effective option to improve agricultural practices and profits. Therefore, holistic study designs considering the natural, social and economic aspects of agricultural and food systems are best suited to represent interactions between them and understand the complex effects of diversification.

Figure 1

 1 Figure 1 Publication selection process used in this review.

Figure 2

 2 Figure 2 Number of studies using different measures of diversity (left) and different food security indicators (right) used in reviewed publications (N=88). Studies that use multiple metrics are counted multiple times accordingly.

  144) £ C = count, BP = Berger Parker index, H' = Shannon Diversity index, SID = Simpson Diversity index, BI = Berry index, RE = Relative Entropy, NFD = Nutritional Functional Diversity, SC = cropping system or farming typology, CE = Composite Entropy Index Table 5 Summary of studies examining the association between diversity and food access. Description of relationship * § CSI = Coping Strategy Index, DSR = Dietary Species Richness, FCS = Food consumption score, FVS = Food Variety Score, HDDS = Household Dietary Diversity Score, HFIAS = Household Food Insecurity Access Scale, HHS = Household Hunger Scale, MAHFP = Months of Adequate Household Food Provisioning, M-HDDS = Modified Household Dietary Diversity Score (recall period and/or number and type of food groups modified), M-HFIAP = Modified Household Food Insecurity of Access Prevalence.

  (ns) £ C = count; H' = Shannon diversity index, SID = Simpson diversity index, β = regression coefficient § WAZ = weight-for-age z-score, HAZ = height-for-age z-score, WHZ = weight-for-height z score, MUAC= middle upper arm circumference for age z score, BMI = Body mass index, IDDS = Individual Dietary Diversity Score, IFCI = Infant and Child Feeding Index, IYCDDS = Infant and Young Child Dietary Diversity, MDD = Minimum dietary diversity, MDD-C=Minimum Dietary Diversity of Children, MDD-W = Minimum Dietary Diversity for Women, MPA = Mean Probability of Adequacy of Micronutrient Intake, NAR = Nutrient Adequacy Ratio, NAR-mean = mean nutrient adequacy ratio, WDDS = Women's Dietary Diversity Score, WDDS-10 = 10-Food Group Women's Dietary Diversity Score.



  The food dimension and indicators representing that dimension should be clearly stated and explained. Where possible researchers should use established indicators. They have often been tested or validated in several case studies and were developed and discussed by a commission of experts. If new indicators are introduced, they should be validated and compared with existing ones.

  These are selected references fulfilling the criteria of this literature review except for year of publication and cited in section 6 in[START_REF] Altieri | Agroecology and the design of climate change-resilient farming systems[END_REF] on agrobiodiversity and vulnerability, section 2 in Frison et al. 2011 on productivity and stability, Table 1 in Di Falco 2012 and Table 1 in Lin 2011.

	Resistance to pest infestation	Within-field crop genetic	Zhu et al. 2000 (China), Kahn
	through biological control	diversity reduces pest	et al. 1998 (Kenya) cited in
		infestation and disease	Altieri et al. 2015
		severity
	Resistance to heat and water	Shade trees in agroforestry	Lin 2007 (Mexico) cited in
	stress through shade control	reduce water stress for coffee	Altieri et al. 2015
		plants compared to systems
		with fewer shade trees.
		Finding	Reference*
	Variability of crop yield and	Crop variety richness reduces	Di Falco et al. 2007 (Ethiopia),
	income	the within-household variance	Di Falco & Chavas 2009
		of yields above a certain	(Ethiopia), Smale et al. 1998
		diversity level	(Pakistan), Widawsky &
			Rozelle 1998 (China) cited in Di
			Falco 2012
	Resistance to water stress	Landraces yield higher than	Ceccarelli 1996 (Syria) cited in
	after a short-term external	modern cultivars in water	Frison et al. 2011; Natarajan
	shock (water shortage)	stress conditions and have less	and Willey 1996 (India) cited in
		yield variability between stress	Altieri et al. 2015
		and no stress conditions; Grain
		yield decrease in stress
		condition was smaller in
		replacement intercropping
		system than in sole crops
	Resistance to erosion after a	Fewer arable land loss due to	Holt-Giménez 2002
	short-term external shock	landslides in agroecological	(Nicaragua), Philpott et al.
	(hurricane)	plots compared to	2009 (Mexico) cited in Altieri
		conventionally managed plots	et al. 2015

*

Table 3

 3 Summary of studies examining the association between diversity and food availability. 425

	Reference	Country	Sample size	Method	Indicator of diversity	Indicator of food availability	Description of
							relationship*
				Cropping system, farm or household scale
	Chimonyo et	Malawi	6 field	Field experiments	Crop diversity (SC) -maize	Crop yield (maize grown in	Positive
	al., 2019		experiments, 5		intercropped compared to	sequence with soybeans,
			seasons, 6		maize sole crop	peanut or peanut-pigeon pea)
			cropping			Crop yield (maize intercropped	Negative
			systems			with pigeonpea)
	Douxchamps	Burkina Faso,	600 hh	Stepwise multiple	Crop diversity (SC)	Land productivity (type IV	Positive
	et al., 2016	Ghana, Senegal		linear regression		intensified farming)	(β=0.812)
						Land productivity (type I	Neutral (ns)
						subsistence farming)
						Land productivity (type II	Neutral (ns)
						diversified farming)
						Land productivity (type III	Neutral (ns)
						extensive farming)
	Dzanku and	Ghana	416 hh	Random effects	Crop diversity (SID)	Household food supply	Neutral (ns)
	Sarpong,			model		adequacy
	2011
	Hondrade et	Philippines	6 farmers' fields	Field experiments	Crop diversity (SC) -rice-	Crop yield	Mixed
	al., 2017		in 3 seasons and		mungbean intercropping		depending on
			8 cropping		compared to rice		year and
			treatments		monoculture		proportion of
							intercropped
							rows
	Isaacs et al.,	Rwanda	2 cropping	Field experiments	Crop diversity (SC) -maize-	Crop yield	Negative (d =
	2016		systems planted		bean intercropping compared		0.9-1.7 t/ha)
			by 13 farmers		to sole bean crop
			association
	Islam et al.,	Bangladesh	2 seasons, 4	Field experiment	Crop diversity (SC) -four crops Crop yield	Positive (d =

Table 4

 4 Summary of studies examining the association between diversity and stability. The magnitude of the relationships cannot be compared directly across studies as the methods and indicators used differ. The type of regression model, number and types of crops and livestock species for example will all influence the result. The table shows selected results from each study as assumed relevant to the topic of this review.

	Reference Country Sample size Method	Indicator of	Indicator	Description of
				diversity	of stability	relationship*
	Chimonyo	Malawi 6 field	Field	Crop	Inter-site	Positive (d = -
	et al., 2019	experiments,	experiments	diversity (SC)	CV of crop	0.98-4.87%
		5 seasons, 6		-fertilized	yield: (1)	compared to
		cropping		sole maize		fertilized sole
		systems with		compared to		maize)
		6 maize		(1) rotation	Inter-site	Negative (d =
		cropping		with soybean	CV of crop	+3.4%
		systems		and peanut-	yield: (2)	compared to
				pigeon pea,		fertilized sole
				(2) rotation		maize)
				with peanut,	Inter-site	Negative (d =
				(3)	CV of crop	+6% compared
				intercropped	yield: (3)	to fertilized
				with pigeon		sole maize)
				pea
	Kassie et	Malawi 1,925 hh	Multinomial	Crop	Crop yield	Positive
	al., 2015	with 2,937	endogenous	diversity (SC)	skewness	(adoption
		maize plots	switching	-maize-	as a proxy	effect = 0.67
			treatment	legume	for risk
			regression	rotation or	exposure
			using	intercropping
	Snapp et	Malawi > 1,000 farm	Field	Crop	Inter-site	Positive (d = -1-
	al. 2010	sites	experiment	diversity (SC)	variability	2%)
				-unfertilized	of system
				sole maize	grain yield
				compared to	(CV): (1)
				(1) rotation	Inter-site	Positive (d = -8-
				with peanut,	variability	14% compared
				(2) rotation	of system	to unfertilized
				with annual	grain yield	sole maize)
				and semi-	(CV): (2)
				perennial	Inter-site	Mixed
				legumes, (3)	variability
				intercropped	of system
				with pigeon	grain yield
				pea	(CV): (3)
	*

d = difference, SC =cropping system, CV = Coefficient of variation

Table 5

 5 Summary of studies examining the association between diversity and food access.

	Reference	Country	Sample	Method	Indicator of diversity £	Indicator of access §	Description of relationship *
			size
					Village to regional scale
	Akerele and	Nigeria	1,148 hh	Fixed effects model	Farming diversity (C, BI,	Share of expenditure of	Positive (β=0.0423-0.1187)
	Shittu, 2017				RE)	food item in the total
						food budget (BI)
					Farming diversity (C, BI,	Share of expenditure of	Positive (β=0.0541-0.2354)
					RE)	food item in the total
						food budget (RE)
	KC et al., 2016	Nepal	1,466 hh	Probit model	Crop diversity (C)	More than or less/equal	Positive (β=0.0525)
						12 mths food sufficiency
					Livestock diversity (C)	More than or less/equal	Positive (β=0.0910
						12 mths food sufficiency
	Brüssow et al.,	Tanzania	900 farms	Propensity Score	Crop diversity (C)	FCS	Positive (ATT=3.51)
	2017			(nearest neighbour)		Household per capita	Positive (ATT=103.3g)
				matching		protein intake
						MAHFP	Negative (ATT= -1.48)
						CSI	Neutral (ns)
						Household per capita	Neutral (ns)
						energy intake
						Household net income	Neutral (ns)
						from crop production
	De Jager et al.,	Ghana	329 hh	Poisson regression	Crop diversity (C)	Household self-	Positive (β=0.1)
	2018			model	Crop diversity (H')	sufficiency (no. food groups)	Positive (β=0.7)
				Linear mixed model	Crop diversity (C)	Household self-	Positive (β=6.2-6.4)
					Crop diversity (H')	sufficiency (quantity	Positive (β=23.4-26.4)

Table 5

 5 Summary of studies examining the association between diversity and food access.

	Reference	Country	Sample	Method	Indicator of diversity £	Indicator of access §	Description of relationship *
			size
						nutrients)
	Jones, 2017b	Malawi	2,526 hh	Generalized estimating	Crop diversity (C)	HDDS	Positive (β= 0.08-0.13)
				equations
	Kasem and	Thailand	245 hh	Interviews, calculated	Crop diversity (SC) -	Net income from	Positive (d = 55,447 Baht/year)
	Thapa, 2011			income from farm gate	diversified rice cropping	agriculture per hh
				prices and input prices	system compared to rice
					monoculture
	Kissoly et al.,	Tanzania	899 hh	Poisson regression	Production diversity (C)	M-HDDS	Positive (β=0.022-0.030)
	2018			model
	Koppmair et al.,	Malawi	408 hh	Simple linear regression Production diversity (C)	HDDS	Positive (β=0.124)
	2017
				Linear regression with	Crop diversity (C)	HDDS	Neutral (ns)
				Poisson estimator
	Kumar et al.,	Zambia	3,340 hh	Ordered logit model	Production diversity (C)	M-HDDS	Positive (β=0.387)
	2015				Crop diversity (C)	M-HDDS	Positive (β=0.250)
					Farming diversity (C)	M-HDDS	Positive (β=0.451)
	Ladha et al., 2016 India,	4 locations,	Field experiment	Crop diversity (multiple	Income from crop sales Positive (d = 1,029 US$/ha)
		Bangladesh	six		cropping index in %)
			seasons, 2
			years
	Limbu et al.,	Tanzania	6	Field experiment	Production diversity (SC)	Annual net cash flow	Positive (d = 57.43 USD)
	2017		vegetable		-integrated fish-
			plots, 4 fish		vegetable system
			ponds		compared to non-
					integrated system
					Production diversity (SC)		Neutral (ns)

Table 5

 5 Summary of studies examining the association between diversity and food access.

	Reference	Country	Sample	Method	Indicator of diversity £	Indicator of access §	Description of relationship *
			size
					-integrated vegetable
					system compared to
					non-integrated system
	M'Kaibi et al.,	Kenya	525 hh	Spearman rank	Agricultural biodiversity	HDDS	Positive (F = 14.791)
	2017			correlation, ANOVA	(C)	HFIAS	Positive (rho= -0.136)
	M'Kaibi et al.,	Kenya	525 hh	Spearman rank order	Agricultural biodiversity	HFIAS	Positive (rho= -0.10)
	2015			correlations	(C)
	Makate et al.,	Zimbabwe	~600 hh	Multiple linear	Crop diversity (SID-	Income from agriculture Positive (β=3.498)
	2016			regression	binary)	FSC	Positive (β=0.638)
						HDDS	Positive (β=3.545)
				Probit regression model		HFIAS (Binary)	Neutral (ns)
	Murendo et al.,	Zimbabwe	2,815 hh	Multiple linear	Farming diversity (C)	M-HDDS	Positive (IRR=1.03)
	2018			regression	Crop diversity (C)	M-HDDS	Positive (IRR=1.04)
					Livestock diversity (C)	M-HDDS	Positive (IRR=1.03)
	N'Danikou et al.,	Mali	180 hh	Correlation analysis	Agricultural biodiversity	Food insecurity index	Negative (r = -0.22)
	2017				(C)	based on CSI
	Ng'endo et al.,	Kenya	30 hh	Spearman rank order	Farming diversity (C)	HDDS	Neutral (ns)
	2016			correlation	Farming diversity (H')		Neutral (ns)
					Farming diversity (SID)		Neutral (ns)
					Farming diversity (NFD)		Neutral (ns)
					Farming diversity (C)	FSC	Neutral (ns)
					Farming diversity (H')		Neutral (ns)
					Farming diversity (SID)		Neutral (ns)
					Farming diversity (NFD)		Neutral (ns)
	Ng'Endo et al.,	Kenya	30 hh	Pearson correlation	Agrobiodiversity (C)	HHS	Neutral (ns)

Table 5

 5 Summary of studies examining the association between diversity and food access.

	Reference	Country	Sample	Method	Indicator of diversity £	Indicator of access §	Description of relationship *
			size
	2015				Agrobiodiversity (H')		Neutral (ns)
					Agrobiodiversity (SID)		Neutral (ns)
	Nkomoki et al.,	Zambia	400 hh	Correlation analysis	Crop diversity (Binary)	FCS	Positive
	2018					HHS	Positive
	Parvathi, 2018	Laos	556 hh	Fixed effects regression	Farming diversity (C)	FSC	Mixed: Positive (β=6.59);
				model			Negative (β=0.145) for squared
							farm diversity
	Passarelli et al.,	Ethiopia	373 hh	Simultaneous equation	Production diversity (C)	HDDS	Neutral (ns)
	2018			models		Income from agriculture Negative (β=-0.838)
		Tanzania	402 hh			HDDS	Neutral (ns)
						Income from agriculture Neutral (ns)
	Pradhan et al.,	India	3 years	Field experiment	Crop diversity (SC) -	Profit	Positive (d = 359-527 USD/ha)
	2018		experiment		Additive crop rotation
					design with maize
	Romeo et al.,	Kenya	1,353 hh	Ordinary Least Squares	Farming diversity, incl.	M-HDDS	Positive (β=0.195-0.317)
	2016			multivariate regression	purchased and gifted	Share of food	Positive (β=0.006-0.01)
					food (C)	expenditure (SID)
						Share of food	Positive (β=0.025-0.039)
						expenditure (H')
	Sibhatu et al.,	Indonesia	674 hh	Multivariate regression	Farming diversity (C)	M-HDDS	Positive (β=0.054)
	2015a	Kenya	397 hh	with Poisson estimator			Neutral (ns)
	Sibhatu and	Indonesia	672 hh	Regression model with	Production diversity (C)	M-HDDS	Neutral (ns)
	Qaim, 2018a			Probit estimator for M-		Household per capita	Neutral (ns)
				HDDS, regression model		energy consumption
				with ordinary least		Household	Neutral (ns)
				squares for others		micronutrient
						adequacy-mean, zinc,
						iron, VitA

Table 5

 5 Summary of studies examining the association between diversity and food access.

	Reference	Country	Sample	Method	Indicator of diversity £	Indicator of access §	Description of relationship *
			size
					Farming diversity (C)	M-HDDS	Positive (ME=0.155)
						Household per capita	Positive (ME=300.4)
						energy consumption,
						Household calorie	Positive (ME=0.078)
						adequacy
						Household	Positive (ME=0.067)
						micronutrient
						adequacy-mean
						Household nutrient	Positive (ME=0.065)
						adequacy -zinc
						Household nutrient	Positive (ME=0.065)
						adequacy -iron
						Household nutrient	Positive (ME=0.071)
						adequacy -VitA
		Kenya	393 hh		Production diversity (C)	M-HDDS	Positive (ME=0.067-0.070)
						Household per capita	Neutral (ns)
						energy consumption,
						Household	Neutral (ns)
						micronutrient
						adequacy-mean, zinc,
						iron, VitA
					Farming diversity (C)	M-HDDS	Positive (ME=0.045)
						Household per capita	Neutral (ns)
						energy consumption
						Household	Neutral (ns)
						micronutrient adequacy
		Uganda	417 hh		Production diversity (C)	HDDS	Positive (ME=0.316-0.334)
						Household per capita	Neutral (ns)

Table 5

 5 Summary of studies examining the association between diversity and food access.

	Reference	Country	Sample	Method	Indicator of diversity £	Indicator of access §	Description of relationship *
			size
						energy consumption
						Household	Neutral (ns)
						micronutrient
						adequacy-mean, zinc,
						iron, VitA
					Farming diversity (C)	HDDS	Positive (ME=0.194-0.198)
						Household per capita	Positive (ME=83.035)
						energy consumption
						Household calorie	Positive (ME=0.030)
						adequacy
						Household mean	Positive (ME=0.025)
						nutrient adequacy
						Household zinc	Positive (ME=0.024)
						adequacy
						Household -VitA	Positive (ME=0.030)
						adequacy
						Household -iron	Neutral (ns)
						adequacy
	Traoré et al.,	Mali	258 hh	Linear mixed model	Crop diversity (C)	FSC	Positive (β=1.47)
	2018					HDDS	Positive (β=0.29)
	Valencia et al.,	Brazil	75 farmers Correlation analysis	Farming diversity (C)	HDDS	Positive (r2=0.06)
	2019
	Vanek et al.,	Bolivia	297 hh	Stepwise multiple linear	Crop diversity (C)	HFIAS	Positive (β= -0.584)
	2016			regression		HDDS	Neutral (ns)
	Whitney et al.,	Uganda	102 hh	Projection to Latent	Agrobiodiversity (H')	HDDS	Neutral (uncorrelated)

Table 5

 5 Summary of studies examining the association between diversity and food access.

	Reference	Country	Sample	Method	Indicator of diversity £	Indicator of access §	Description of relationship *
			size
	2018			Structures (PLS)	Agrobiodiversity (C)		Positively correlated
				regression analysis
	Williams et al.,	Sri Lanka	50 hh	Bivariate tests	Agrobiodiversity (H')	FCS	Neutral (ns)
	2018
	Ritzema et al.,	Cambodia	631 hh	Multivariate stepwise	Crop diversity (C)	M-HDDS	Neutral (ns)
	2019			regression	Livestock diversity (C)		Neutral (ns)
		Lao	365 hh		Crop diversity (C)		Neutral (ns)
					Livestock diversity (C)		Positive (β=0.049)
		Vietnam	310 hh		Crop diversity (C)		Neutral (ns)
					Livestock diversity (C)		Positive (β=0.068)
	Bellon et al.,	Ghana	637 hh	Linear regression	Crop diversity (SID)	Income from agriculture Positive (β=0.425)
	2020					Value of products for	Positive (β=0.175)
						own consumption
	Tesfaye and	Uganda	4,523 hh	Fixed-effects	Crop diversity (C)	M-HDDS	Positive (β=0.153-0.158,
	Tirivayi, 2020			instrumental variable			IRR=1.008)
				regressions, Fixed-	Crop diversity (H')		Positive (β=0.619-1.317,
				effects Poisson model,			IRR=1.051)
				Ordinary least squares	Crop diversity (CE)		Positive (β=1.195-4.682,
				regression			IRR=1.135)
					Crop diversity (BP)		Positive (β=0.162-0.648,
							IRR=1.012)
	Bezner Kerr et	Malawi	425 hh	Multivariate regression Crop diversity (C)	HFIAS (binary)	Neutral (ns)
	al., 2019					M-HDDS	Neutral (ns)
	Huluka and	Ethiopia	306 hh	Probit and simple linear	Crop diversity (C)	HDDS	Positive (β=0.2921-0.3132)
	Wondimagegnhu,			regression
	2019

Table 5

 5 Summary of studies examining the association between diversity and food access.

	Reference	Country	Sample	Method	Indicator of diversity £	Indicator of access §	Description of relationship *
			size
					National scale
	Asfaw et al., 2018 Niger	3,344 hh	Quantile regression	Crop diversity (C)	Household per capita	Positive (β=0.0209-0.0337)
						energy intake
					Crop diversity (BP)	Household per capita	Positive (β=0.0504-0.0263)
						energy intake
					Crop diversity (H')	Household per capita	Positive (β=0.0604-0.0249)
						energy intake
	Ayenew et al.,	Nigeria	6,089 hh	Fixed effect model (FE),	Farming diversity (C)	M-HDDS	Positive (β=0.016 for FE and
	2018			Random effect model			0.025 for RE)
				(RE)
	Birthal et al.,	India	51,770 h	Multiple linear	Crop diversity (SC) -	Likelihood of being	Negative (β= -0.0691 -0.0282)
	2015			regression, Instrumental	system with or without	under the poverty line
				variable (IV) regression	high-value crops
	Das and Ganesh-	India	26,951 hh	Multivariate regression Crop diversity (C)	Income from agriculture Positive (β=0.290-0.293);
	Kumar, 2018						Negative for squared counts
							(β=-0.07)
					Livestock diversity (C)	Income from agriculture Positive (β=1.232); Negative for
							squared counts (β=-0.27)
	Dillon et al., 2015 Nigeria	~5,000 hh	Ordinary least squares	Crop diversity (C)	M-HDDS	Positive (β=0.037 for OLS and
				(OLS) regression and			β=0.24 for IV)
				Instrumental variables
				(IV) regression
	Ecker, 2018	Ghana	11,217 hh	Fixed effect model	Crop diversity (C)	M-HDDS	Mixed: Positive (β=0.111-0.178
							for all hh, β=0.148 for non-poor
							hh); Neutral (ns) for poor hh
					Crop diversity (SID)		Mixed: Positive (β=0.309-0.551
							for all hh, β=0.396 for non-poor

Table 5

 5 Summary of studies examining the association between diversity and food access.

	Reference	Country	Sample	Method	Indicator of diversity £	Indicator of access §	Description of relationship *
			size
							hh); Neutral (ns) for poor hh
	Islam et al., 2018 Bangladesh 6,040 hh	Pooled and random	Crop diversity (C)	HDDS	Positive (β=0.019)
				effects model, Poisson
				regression
	Jones et al., 2014 Malawi	6,623 hh	Multiple linear	Crop diversity (C)	M-HDDS	Positive (β=0.23)
				regression		FSC	Positive (β =0.81)
					Crop diversity (SID)	M-HDDS	Positive (β=0.68)
						FSC	Neutral (ns)
					Farming diversity (C)	M-HDDS	Positive (β=0.20)
						FSC	Positive (β=0.71)
	Mofya-Mukuka	Zambia	14,212 hh	Poisson regression and	Crop diversity (SID)	Farm income	Positive (β=0.9142)
	and			Ordinary least squares		FSC	Positive (β=0.646-0.702)
	Hichaambwa,			regression		MAHFP	Positive (β=0.727-0.741)
	2018			Poisson regression		HDDS	Positive (β=0.284)
	Sauer et al., 2018 Zambia	5,381 hh	Two-stage least squares	Crop diversity (SC) -	MAHFP	Neutral (ns)
				regression	cereal-legume	HDDS	Positive (β=9.918)
					intercropping yes/no
	Sibhatu et al.,	Indonesia,	8,230 hh	Multivariate regression	Farming diversity (C)	M-HDDS	Positive (β=0.009)
	2015a	Kenya,		with Poisson estimator
		Ethiopia,
		Malawi
		Ethiopia	2,045 hh				Neutral (ns)
		Malawi	5,114 hh				Positive (β=0.015); Negative (β=-
							3.2e-04) for squared C
	Snapp and Fisher,	Malawi	9,291 hh	Poisson regression,	Crop diversity (C) -	M-HDDS	Positive (IRR=1.019)
	2015			Ordinary least squares	crops intercropped with	FSC	Negative(β=-0.189)
				regression	maize
					Crop diversity (C) -non-M-HDDS	Positive (IRR=1.019)

Table 5

 5 Summary of studies examining the association between diversity and food access.

	Reference	Country	Sample	Method	Indicator of diversity £	Indicator of access §	Description of relationship *
			size
					maize crops	FSC	Positive (β=0.333)
	Somé and Jones,	Burkina	10,860 hh	Mixed linear regression	Crop diversity (C)	HDDS	Positive (β=0.085)
	2018	Faso		model
	Thapa et al.,	Nepal	8,066 hh	Ordinary least squares	Crop diversity (value	Probability of being	Positive (β=-0.002 --0.004)
	2018			regression, two-stage	share of high-value	poor
				least squares regression	crops cultivated)
					Crop diversity (binary) -	Poverty head-count	Positive (d = 9.18 %)
					growers and non-	ratio
					growers of high-value
					crops
	Fraval et al., 2019 Burkina	7,708 hh	Logistic regression	Crop production	M-HFIAP	Positive (β=0.10)
		Faso;		model	diversity (C)
		Democratic			Livestock production		Positive (β=0.32)
		Republic of			diversity (C)
		Congo		Negative binomial	Crop production	M-HDDS	Mixed: Positive (β=0.03);
		Ethiopia;		regression	diversity (C)		Neutral for M-HDDS and crop
		Kenya;					diversity in best period (ns)
		Malawi;			Livestock production		Positive (β=0.05)
		Mali;			diversity (C)
		Tanzania;
		Uganda;
		Zambia
	Zanello et al.,	Afghanistan 14,079 hh	Ordinary least squares	Crop diversity (C)	FSC	Positive (β=0.862-1.852)
	2019			(OLS) regression,	Livestock diversity (C)		Positive (β=2.322-3.
				Instrumental variable
				(IV) regression

Table 6

 6 Summary of studies examining the association between diversity and utilization.

	Reference	Country	Sample	Method	Indicator of diversity £	Indicator of utilization §	Description of relationship *
			size
				Village to regional scale
	Adubra et	Mali	4,790 hh,	Logistic regression,	Production diversity (C)	MDD-W	Positive (OR = 1.12)
	al., 2019		5,046	simple linear regression		WDDS-10	Positive (β=0.10)
			mother-
			child pairs
	Azupogo et	Ghana	642	Multiple linear regression Farming diversity (C)	Haemoglobin	Positive (β=0.59)
	al., 2019		children			concentration (6-9 yrs)
			aged 6-17			Haemoglobin	Neutral (ns)
			years			concentration (6-17 yrs)
	Bellon et	Benin	880 hh	Generalized method of	Agrobiodiversity (C)	MDD-W	Positive (β=0.036)
	al., 2016			moments for parameter
				estimation
	Boedecker	Benin	120 women ANOVA	Agrobiodiversity (Binary)	WDDS	Positive (d=0.6)
	et al., 2014					Individual's nutrient	Neutral (ns)
						consumption
	De Jager et	Ghana	329 hh	Linear mixed model,	Crop diversity (C)	IYCDDS	Neutral (ns)
	al., 2018			quasi-binomial regression		MPA	Neutral (ns)
					Crop diversity (H')	IYCDDS	Neutral (ns)
						MPA	Neutral (ns)
	Gelli et al.,	Malawi	1,199 hh,	Multilevel regression	Crop diversity (C)	HAZ (6-24 mths)	Positive (DID=0.44)
	2018		304	models using difference-		Prevalence of stunting (6-	Negative (DID=-17%)
			children	in-difference estimator		24 mths)
			aged 6-24			10 other relationships	Neutral (ns)
			mths, 1,248			with HAZ, WHZ, WAZ,
			children			prevalence of stunting,
			36-72			prevalence of wasting,
			mths)			prevalence of
						underweight

Table 7

 7 Synthesis table summarizing the diversity-food security relationships found in literature on three levels of data collection.Code for symbols: ++ more than half of relationships are positive; < small sample size

	Food security dimension

Author contribution and acknowledgements KW, FA, CG and CR had the idea for this review article and were supported by the CSIRO-INRA Linkage scheme. KW designed the search syntax and pre-selected publications based on the initial abstract screening. All authors either reviewed the pre-selected publications, extracted data from the included publications and/or wrote parts of the manuscript with KW. KW and JPD reviewed and cleaned data for the synthesis tables describing the magnitude of the observed effects and details of methods. All authors read and reviewed the full articles included in the review after initial screening to assess their relevance and contributed to revising the manuscript multiple times before submission.