domain: sde sdu

text:
Daniel Raucoules
email: d.raucoules@brgm.fr

Fabrizio Tomaro

Michael Foumelis

Caterina Negulescu

Marcello De Michele

Bertrand Aunay

LANDSLIDE OBSERVATION FROM ALOS-2/PALSAR-2 DATA (IMAGE CORRELATION TECHNIQUES AND SAR INTERFEROMETRY). APPLICATION TO SALAZIE CIRCLE LANDSLIDES (LA RÉUNION ISLAND)

Keywords: InSAR, ALOS-2, Landslide

In the presented study our purpose is to show the interest of space-borne high-resolution L-band Synthetic Aperture Radar (SAR) images (ALOS-2/PALSAR2 data in SM1 mode) for mapping deformation of slow landslides. The methods we combined are sub-pixel correlation offset tracking techniques and differential SAR interferometry. Hell-bourg and Grand Ilet landslides (our test cases) are located on La Réunion Island in the Indian Ocean with motions up to about 1 m/y. The produced deformation maps resulted better than those obtained in previous studies with C or X band SAR data or with current Sentinel-1 data as L-band data are less affected by the vegetated cover than X-or C-band data. Finally, the possibility of deriving 3D mapping of the displacement by combining ascending and descending acquisitions (each one provides 2 components of the deformation: line of sight and azimuth) is investigated.

INTRODUCTION

Landslides are one of the geo-hazards with the most impact in terms of socioeconomic costs. Displacement monitoring of slope motions is therefore required to prevent and mitigate landslide risk. The Salazie Circles on La Réunion Island (Indian Ocean) are affected by several landslides, including two major ones affecting the municipalities of Grand Ilet and Hell-bourg (Figure 1). The Hell-Bourg landslide is divided into three main panels, with average velocities increasing northward from 0.8 to 1.33 m/y [START_REF] Belle | The application of an innovative inverse model for understanding and predicting landslide movements (Salazie cirque landslides, Reunion Island)[END_REF]. A previous study based on SAR Interferometry presented in [START_REF] Delacourt | Observation of a large-scale landslide in La Reunion Island using differential SAR interferometry[END_REF] focused on the Hell-bourg landslide and showed the promise of using L-band data for interferometric purposes in the study area by comparing C-band RADARSAT (C-band) results and JERS-1 L-band data. The advantages of L-band data were twofold: due to the partially vegetated cover, L-band interferograms were significantly less affected by temporal decorrelation than those produced with RADARSAT data and the longer wavelengths are more adapted for the expected displacement ranges (several dm/y).

METHODS

Used techniques

In this study, we propose to use offset tracking based on local image correlation and Differential SAR interferometry (DInSAR) to derive deformation maps. For details on these techniques the reader can refer to [START_REF] Wakabayashi | Glacier flow estimation by SAR image correlation[END_REF][START_REF] Hanssen | Radar Interferometry: Data Interpretation and Error Analysis[END_REF]. Processing was carried out using GAMMA interferometric software.

The final idea is to combine ascending and descending acquisition modes offset estimates and Line of Sight displacements estimates in order to obtain a better representation of the phenomenon. The procedure for combining the different components of the displacement is detailed in [START_REF] Raucoules | Timevariable 3D ground displacements from high-resolution SAR subpixel image correlation: Application to La Valette landslide (South French Alps)[END_REF].

Data

Table 1 lists the ALOS-2/PALSAR2 acquisitions available for this study.

Table 1: ALOS 2-PALSAR 2 data

Ascending data is acquired in SM3 (3.8m azimuth sampling) mode while Descending acquisitions are in SM1 (1.8m). SM1 data are therefore more suitable for offset tracking techniques (whose performances depend on reolution).

RESULTS

Deformation mapping

The following figures illustrate the main results obtained during this study. They consist in displacement rates (figures 2 and 4) obtained by stacking of interferograms and offsets estimated and their evolution (Figure 3)

Comparison with C band data

Comparison with SENTINEL 1 interferogram stacks has been carried out. Due to the expected poor coherence on the test area, we processed only SENTINEL 1 interferograms with time spans shorter than 18 days in order to reduce the impact of temporal decorrelation. All the available SENTINEL 1 images available on the area during the period (end 2014-2016) were included in the computation. Results are presented on figures 5 and 6. Noteworthy is the fact that the main landslides of the area are identified on both interferogram stacks. However, the Sentinel-1 appears affected by temporal decorrelation even with very short time-spans reducing their interest (in particular for delimitating the landslides boundaries and panels.

CONCLUSION

These results show the interest of the specific characteristics of the ALOS-2/PALSAR-2 sensor for monitoring landslides in the context of La Reunion or similar (tropical climate, partly vegetated/partly urbanized cover). The interest comes both from the sensor's frequency (L band being appropriate for vegetated covers) and the fine resolution (increasing offset tracking performances). In further works we plan to deeper investigate the correlation of the observed displacements with the surface consequences (damages) occurred during the studied period.

Figure 1 :

 1 Figure 1: location of Salazie Circle (yellow frame)

Figure 2 :

 2 Figure 2: stack of offsets estimated along azimuth direction in pixel/yr (1 pixel=1.8m) Remark: As shown on figure 2, the Hellbourg landslide has an important South-North horizontal component (about 7 times larger than the vertical component). The consequence is that a simple decomposition between vertical and horizontal components based only on Line-of-Sight from ascending and descending acquisition would fail (the resulting vertical component estimate would be incorrect).

Figure 3 :

 3 Figure 3: Evolution of Grand Ilet and Hell-Bourg Landslides observed using the ascending PALSAR 2 dataset (phase in radians).

Figure 4 :

 4 Figure 4: comparison Ascending (left) Descending (right) interferogram stacks on Hellbourg and Grand Ilet (cumulated phase in radians).Finally Figure5shows a decomposition of the observed displacement on Hellbourg landslide.

Figure 5 :

 5 Figure 5: Hellbourg Landslide. Upper left: South North component of the displacement, Upper Right: East-west, Lower: vertical.

Figure 4 :

 4 Figure 4 : ALOS-2/PALSAR-2 interferogram stack (ascending mode) main landslides are located.

Figure 5 :

 5 Figure 5 : Sentinel-1 interferogram stack (asecending mode)

ACKNOWLEDGEMENT

The authors wish to thank CNES (project KALIDEOS and Dr. Philippe Durand) for providing the ALOS-2 data on La Réunion Island.


domain: shs sdv info

text:
Laurence Bernard

Hélène Fougere

T Larsen

José Pires

Diets supplemented with various lipid sources differently affect selected milk metabolites concentrations in cows and goats

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

Diets supplemented with various lipid sources differently affect selected milk metabolites concentrations in cows and goats

Laurence Bernard 1 , Hélène Fougère 1 , Torben Larsen 2 , José Pires 1 1 Université d'Auvergne, INRA, Vetagro Sup, UMR12133 Herbivores, St Genès-Champanelle, France. 2 Department of Animal Science, Aarhus University, Tiele, Denmark

Abstract

Previous research has shown that animal husbandry factors such as diet composition and intake can alter milk content of selected metabolites (Larsen et al., 2016). Our objectives were to determine the effects of species (cow vs goat) and dietary lipid supplements known to largely impact milk fat content at least in cows, on selected metabolites and enzymes in milk. Twelve Holstein cows and 12 Alpine goats, all multiparous, nonpregnant and at 86 ± 24.9 and 61 ± 1.8 DIM respectively, were fed a basal diet (45% forage + 55% concentrate) not supplemented (CTL) or supplemented with corn oil plus wheat starch (COS; 5% diet dry matter (DM)), marine algae powder (MAP; 1.5% diet DM), or hydrogenated palm oil (HPO; 3% diet DM) in a replicated 4×4 Latin square design with 28-d experimental periods. Data on intake and milk production were reported in Fougere et al. (2018). B-hydroxybutyrate (BHBA), isocitrate, glucose, glucose-6-phosphate, glutamate, cholesterol, choline, free amino acid group, urea, alkaline phosphatase and lactate dehydrogenase were analysed (Larsen et al., 2016(Larsen et al., , 2017) ) on morning milk samples collected on d24 of each experimental period.

Production data from this experiment is reported elsewhere (Fougère et al., 2018). In cows, milk fat content was lowered by COS and MAP (-45% and -22% respectively; p<0.001) and increased by HPO (+13%; p<0.001) compared with CTL, whereas in goats only MAP decreased milk fat content (-15%; p<0.001) compared to CTL. Energy and protein balance were positive for all treatments in both species.

Regarding milk metabolites and enzymes, irrespective of diet, cow milk was richer in alkaline phosphatase and glucose compared to goats (16 and 3 times more respectively, p < 0.01), whereas goat milk contained more urea and glucose-6-phosphate compared to cows (1.9 and 5.3 times more respectively, p < 0.01). In cows, COS decreased BHBA and choline (-25 and -24% respectively; p < 0.001) compared to CTL whereas no effects were observed in goats. COS and MAP increased milk isocitrate compared to CTL in cows, but decreased isocitrate concentrations in goat milk. In cows, milk choline was correlated with milk fat content (r=0.693, p=0.001), and lactate dehydrogenase was correlated with milk somatic cells count (r=0.839, p=0.001) but not in goats.

We provide evidence of different milk metabolite responses according to species and diets. Metabolites or enzymes secreted in milk may be indicators of specificities of lipid metabolism among ruminant species, and may contribute to a better understanding of mechanisms regarding milk fat secretion processes.

  Fougère, H., C. Delavaud, and L. Bernard. 2018. Diets supplemented with starch and corn oil, marine algae, or hydrogenated palm oil differentially modulate milk fat secretion and composition in cows and goats: A comparative study. Journal of dairy science 101(9):8429-8445. Larsen, T., L. Alstrup, and M. R. Weisbjerg. 2016. Minor milk constituents are affected by protein concentration and forage digestibility in the feed ration. Journal of Dairy Research 83(1):12-19.


Aphid triggered immunity in melon: key determinants for durable resistance to virus and aphids"

published or not. The documents may come

Aphid triggered immunity in melon: key determinants for durable resistance to virus and aphids

polymorphisms have been identified in the Vat cluster. The Vat gene structure suggests a functioning so called effector-triggered immunity (ETI), with separate recognition and response phases. During the recognition phase, the VAT protein is thought to interact (likely indirectly) with an aphid effector introduced by aphid salivation within the plant cells. A few hours later, several miRNAs are upregulated in Vat plants. Peroxidase activity increases, and callose and lignin are deposited in the walls of the cells adjacent to the stylet path, disturbing aphid behavior. In aphids feeding on Vat plants, the levels of miRNAs are modified. At the plant level, resistance to aphids is quantitative (aphids escape the plant and display low rates of reproduction). 'Aphid-ETI' has qualitative and local effect against non circulative viruses (CMV, ZYMV, WMV) and but quantitative effect against circulative virus such as CABYVs.

Durability of ETI is highly variable. At population level, 'Aphid-ETI' reduces aphid density and genetic diversity, and durability of the 'Aphid-ETI' strongly depends on the agroecosystem. Some clones are adapted to Vat resistance, putatively either by introducing a polymorphic effector not triggering ETI, or by adapting to the defenses they triggered.

Comment citer ce document : Boissot, N. ( 2018). Aphid triggered immunity in melon: key determinants for durable resistance to virus and aphids. Presented at Cucurbitaceae 2018, Davis, USA (2018-11-12 -2018-11-15).

Several ways to enhance 'Aphid-ETI' durability will be proposed. 'Aphid-ETI' against viruses decreases the intensity of Cucumber Mosaic Virus (CMV) and Cucurbit aphid-borne yellows virus (CABYV) epidemics. Laboratory experiments strongly suggested that non circulative viruses cannot adapt to 'Aphid-ETI' and therefore durability of 'Aphid-ETI' against CMV is predicted long. Field experiments combined to modelling suggested that highly durable resistance against CABYV could be obtained by combining within a same melon genotype the Vat gene with recessive genes conferring resistance to CABYV. Extension of those results to any other circulative viruses will be discussed.


Serge Garcia
email: serge.garcia@inra.fr.

Claudio Petucco
email: claudio.petucco@inra.fr

Bo Jellesmark Thorsen

Suzanne Elizabeth Vedel

Modelling the choice between and the costs of multiple-use vs. specialized forest management

Keywords: Forest, multiple-use vs. specialized management, household production model, cost function, corner solution, recursive mixed system

Forests provide ecosystem services jointly with timber production. In some cases, private forest owners implement management actions in order to enhance the provision of such services. They may get direct benefits from this decision such as private amenity values or effects on (e.g., hunting), they may have altruist traits in their utility function for providing public goods (e.g., biodiversity conservation, carbon sequestration), or they may be incited for by a public authority and compensated for the costs. Specifically, this paper focuses on the decision of setting aside forest land. It raises the more general question of the efficiency of multiple-use vs. specialized management of forest lands. We propose an econometric analysis to identify factors of the set-aside choice and to measure the impact of this decision on forest management costs. A flexible cost function is modelled and estimated for both types of management. The percentages of old/mature deciduous and old/mature coniferous forests are used as biodiversity and carbon indicators. Results show that the set-aside choice depends on the landowners' income and on their socio-economic characteristics.

Set-aside decision has a significant and positive impact on the management costs. This implies that the additional private and public benefits achieved from

Introduction

Beside timber and non-timber products (e.g., game, cork, mushrooms), forest ecosystems provide a large number of non-marketed services such as recreational services, carbon sequestration, water regulation and biodiversity preservation. Consideration of non-timber forest goods and services and multiple-use forestry has a long tradition in the forest economics literature [START_REF] Gregory | An economic approach to the multiple use. Forest Science 1 (1)[END_REF][START_REF] Hagenstein | A Theoretical Method for Examining Forest Land-Use Alternatives[END_REF]. However, following [START_REF] Hartman | Harvesting decision when a standing forest has value[END_REF] numerous studies analysed the forest as a multifunctional system. Since the standard framework introduced by Faustmann (1849) establishing the correct expression for the net present value of perpetual forest rotations, the optimal harvest age has been analysed in numerous variations where the forest provide a flow of valuable services in addition to the value of the timber growth, and many economic studies analyse forestry under a multiple-use forest management regime [START_REF] Bowes | Multiple use management of public forest lands[END_REF].

Earlier studies have considered mostly the management of forests at the stand level. Later contributions to the multiple-use forest management literature considered forest levels and the interaction between stands (e.g., [START_REF] Vincent | Efficient multiple-use forestry may require land-use specialization[END_REF][START_REF] Swallow | Spatial and temporal specialization in forest ecosystem management under sole ownership[END_REF][START_REF] Swallow | Spatial interactions in multiple use forestry and substitution and wealth effects for the single stand[END_REF][START_REF] Boscolo | Nonconvexities in the production of timber, biodiversity, and carbon sequestration[END_REF][START_REF] Zhang | Multiple-use forestry vs. forestland-use specialization revisited[END_REF]. As explained by [START_REF] Boscolo | Nonconvexities in the production of timber, biodiversity, and carbon sequestration[END_REF], fixed logging costs and administrative constraints on logging regulations can create non-convexities in forestry production sets that include timber and non-timber products. The most efficient management approach for jointly producing timber and nontimber products is not clear: Is management of forests at the landscape level, where forest stands are completely or partially specialized in the production of timber and non-timber products, preferable? Or rather a uniform management that treats all stands identically? Economic studies, and especially empirical ones, should still investigate this issue to provide new insights relevant for assessing the potential welfare gains of observed practices like specialized and multiple-use forest management.

In this paper, we focus on the choice of multiple-use forestry vs. forest-use specialization in order to assess potential complementarity or competition relationships between different ecosystem services (ES) as reflected in the costs of forest management. Specifically, we empirically study the decision of setting aside forest land. Untouched forest can be recommended for biodiversity conservation and carbon sequestration as public goods, and be a part of public conservation programmes. However, forest owners could also set aside because they get private benefits from amenity values or indirect effects through hunting for instance. They might also have altruist traits in their utility function for providing public goods. We carry out an econometric analysis to identify factors of the choice of setting aside forest land and to measure the impact of this decision on forest management costs.

Multiple uses can be modelled by joint production approaches. The joint production framework makes it possible to analyse synergies and trade-offs between different goods and services, but it is a relatively complex framework because forest management, ecosystem functions and forest owners' objectives are interlinked. Our approach is based on the behaviour of non-industrial private forest (NIPF) owners and offers an adequate way to study joint production in a context where landowners attach importance to standing timber and the amenity values it provides. It has been shown that NIPF forest management is characterised by owners' multiple objectives relatively to management by industrial landowners (Newman and Wear, 1993). In this literature, models of the NIPF owner behaviour include amenities consumption [START_REF] Binkley | Timber supply from nonindustrial forests: a microeconomic analysis of landowner behavior[END_REF]Hyberg and Holthausen, 1989;[START_REF] Max | A behavioral model of timber supply[END_REF]; among others). Thus, our economic modelling of the decision to specialise a part of the forest for biodiversity conservation and carbon sequestration is based on a household production approach.

From this framework, we derive a cost function integrating set-aside decisions along with decisions on the timber output. Knowing the cost structure of multifunctional forest management is important for several reasons. It is first a powerful tool for forest owners to use in the management of their forestlands and to help them adapt their practices to different exogenous shocks. It is also directly connected with forest policy and the efficiency of economic instruments in favour of the provision of ES. Indeed, it is important to understand which factors influence the implementation of these instruments among landowners in order to be able to assess appropriately the costs and benefits of ES conservation. Finally, it is useful for assessing the cost-effectiveness of different economic instruments and mandatory regulations.

Nevertheless, there is a lack of empirical studies on forest management costs when both timber and objectives on ES are analysed. Puttock (2005) estimated costs for integrated harvesting and other forest management activities applying the marginal cost and the joint production frameworks. The objective was to analyse the cost of producing fuel wood from different integrated harvesting systems. [START_REF] Bair | Regional cost information for private timberland conversion and management[END_REF] identified the costs of private timber management practices and studied the way these practices influence forest management and affect the future timber supply. Other studies using cost approaches aimed to assess the cost of specific ES, such as [START_REF] Moulton | Production economics of private forestry: A comparison of industrial and non-industrial forest owners[END_REF] or [START_REF] Nielsen | Mitigating climate change through afforestation: New cost estimates for the United States[END_REF], who provided cost estimates for carbon sequestration through afforestation. Recently, Heshmatol Vaezin et al. (2014) and [START_REF] Hily | Assessing the cost-effectiveness of a biodiversity conservation policy: A bio-econometric analysis of Natura 2000 contracts in forest[END_REF] estimated cost functions for biodiversity conservation implemented through the EU Natura 2000 policy. This article uses a cost function analysis and presents an empirical application from a survey on NIPF owners in Denmark5 to give new insights on the consequences of alternative management approaches on forestlands, including e.g. biodiversity preservation and carbon sequestration objectives. We used two indicators which can be interpreted as proxies for the biological richness and the carbon sequestration in our study: the percentages of old/mature deciduous and old/mature coniferous forests. Indeed, the biologically richest forests in Denmark are linked to old deciduous forests.6 Moreover, old growth forests have been shown to be global carbon sinks [START_REF] Luyssaert | Old-growth forests as global carbon sinks[END_REF].

In our econometric approach, we deal with possible selection bias related to the decision to set aside a part of the forestland and with the endogeneity of harvested timber volume, by simultaneously estimating a set of equations using a recursive mixed-process model. Indeed, we have different kinds of dependent variables (i.e., continuous, binary and censored) appearing as explanatory variables in other equations.

Even though this study focuses on multifunctional forests, our approach could be applied to other ecosystems such as agriculture. In the next section, we present our database obtained from a survey on Danish NIPF owners and propose a first analysis of forest management costs according to the set-aside decision. Section 3 presents the econometric strategy from the economic modelling that accounts for the endogeneity of both the decision of setting aside and its impact on timber harvesting decisions. Section 4 describes the different econometric results while the last section discusses these results in the light of the debate on specialization vs. multiple-use management of forests.

Data and first empirical analysis

Data

The data we used in this study was obtained using an online survey of Danish forest owners, which was carried out at a national level in the period from June-August 2012. Forest landowners were randomly selected from a contact list obtained from the National Forest Inventory and a systematic stratification based on forest property size classes was implemented for selecting forest owners. We contacted forest owners through an official university letter including a leaflet with brief information on the survey and statements of support from the Danish Forest Owner Association. The letter included the name of the website where they could log-on to fill out a questionnaire online constructed using the software SurveyXact. Completing the questionnaire, the forest owners obtained the possibility to win a prize (3 × DKK1000 voucher to be spent in groceries stores).

The questionnaire was designed based on experience from previous studies on landowners (Boon et al. 2004, Broch and[START_REF] Broch | Using choice experiments to investigate the policy relevance of heterogeneity in farmer agri-environmental contract preferences[END_REF]. The questionnaire included questions regarding the landowners' forest property features, the forest management, cost and revenues as well as the forest landowners' socio-economic characteristics. The questionnaire also included a choice experiment which has been analysed in other studies (see [START_REF] Vedel | Forest owners' willingness to accept contracts for ecosystem service provision is sensitive to additionality[END_REF]. After testing the questionnaire within a focus group of forest landowners, the questions related to costs and revenues where revised and simplified in order to make them less burdensome to answer. Specifically, respondents were asked to state the gross cost/expenditures for their largest forest holding during the previous year (2011), including cost of harvesting, administration and taxes and excluding interest expenditures. Moreover, they were asked to report the harvested volume during that same year from that same forest and whether or not they had set aside at least 5% of their forest land as untouched. In Denmark, there exist nature protection programmes with targeted actions including securing specific forests with the designation of a share of forested areas for biodiversity. The forest owner is obliged to have forest on his land and to re-establish forest stands (e.g., clear cut) within a reasonable time period following (Danish Parliament, 2013).

A total of 1,429 forest owners were contacted and reminder letters were sent to the ones who had not replied during the three-four weeks following the first letter. Overall, 308 questionnaires were returned. Respondent who did not state their gross annual cost were eventually excluded from the analysis, leaving a sample of 136 forest owners. This sample of 136 owners in total owned approximately 45,000 hectares of forest land. This corresponds to around 10 % of the privately owned forest area in Denmark.

Forest management costs

Our objective is to study the difference in costs related to different management of forests (i.e., multiple-use vs. specialised management) for biodiversity conservation and carbon sequestration. For this purpose, we observe landowners who set aside a fixed fraction of their forestland and others who do not. In our simplified setting, we consider that NIPF owners use their forest to produce and harvest timber, referred to as , and to benefit from non-timber or forest amenity values of various sorts, referred to as . The production of the NIPF owner/household is a transformation function of different inputs, including the land , and produced marketed good .

An important feature of forest management is that it implies long-term decisions. Even when the problem is examined from cross-section data as in this study, we cannot ignore the capital structure of forest production and the temporal dimension of production decisions. This is why the analysis must account for the forest characteristics (e.g., forest cover type, age of forest stands, the percentage of non-productive land). At this stage of production, the owner is characterized by cost-minimizing behaviour with respect to the transformation defined above. The owner i's (short-run) cost function can simply be written as:

, , , , , , All models fit very well the data with several significant coefficients, such as those of firstorder and quadratic terms, with the expected signs, as well as a high R-squared (from 0.58 to 0.61). For instance, a value of 0.3 for the coefficient of VOL means that an increase of 1% of harvest increases the cost of only 0.3% and seems to indicate the existence of economies of scales in timber harvesting. Moreover, the negative sign of the coefficient associated with the variable PCON indicates that a higher percentage of deciduous trees (the dropped residual variable) increase forest management costs. Across the three models the percentage of nonproductive land (PNOP) tends to decrease forest management costs in accordance with the expected lower management activity.

In model ( 2), the coefficient associated with the variable SASIDE is significantly positive at the 1% level, indicating that the set-aside decision correlates with increased forest management costs. Moreover, our ecosystem services indicators (e.g. for biodiversity and carbon indicators), which are the variables POLDDEC and POLDCON, have a significant impact on management costs: Managing the likely biological richest forest (a forest with a higher percentage of old deciduous trees) tends to be less costly, whereas carbon sequestration through e.g. old coniferous trees seems to correlate with higher cost at forest level. In model

(3), the coefficients associated with the cross terms SASIDE × VOL and SASIDE × SIZE are not significantly different from zero at the 10% level. This means we find no interaction between the decision to set aside and timber harvesting or forest size, respectively, in terms of costs.

Thus, the above results suggest that the decision to set aside seems to have an impact on forest management costs. One may wonder whether the structure of technology could differ across owners who have or have not decided to set aside a part of his/her forest property. To do that, we estimated two different cost functions for each of the two sub-samples of forest properties. Table A2 in Appendix presents these estimation results and shows some significant difference between parameters (like those of VOL and SIZE) according to the cost function, but with a lower quality of fit to the data. Several econometric issues deserve to be studied because they could bias the results and the interpretation of a rough cost analysis if not taken into account. First, we found that the decision of setting aside had an impact on management costs in the forest. But we do not know if this decision is correlated with unobserved heterogeneity of owners regarding management of their forests or not. For instance, forest owners can decide to set aside a part of their property because they have no specific means to implement efficient forestry on this parcel. Second, we can think that the decision to set aside could have an impact on the harvested volume of timber if the part of productive forest declared untouched is important for production. We thus could think about two different and switching regimes, reflected in the decision to reserve a part of forest for biodiversity conservation or other non-timber uses or not.

Moreover, forest landowners in our dataset are NIPF owners, who has been shown to have diverse motivations and non-income objectives (see e.g., [START_REF] Binkley | Timber supply from nonindustrial forests: a microeconomic analysis of landowner behavior[END_REF][START_REF] Max | A behavioral model of timber supply[END_REF][START_REF] Dennis | An economic analysis of harvest behavior: Integrating forest and ownership characteristics[END_REF]. We thus propose an econometric analysis based on a household production model to simultaneously identify factors of the choice of setting aside forestland and to measure the impact of this decision on forest management costs. In the following section, we model the preferences of forest owners by deriving a household production model.

Econometric strategy for estimating NIPF landowners' decision and its impact on costs

The model of decision to set aside

As explained above, NIPF owners can voluntary set aside a fixed fraction of their forest property to e.g. conserve biodiversity and/or for carbon sequestration or other non-timber services. We assume that the NIPF owners maximising their utility of choosing whether or not to set aside a fixed fraction of their forest. U * refers to as the (stochastic) indirect utility function, which we assume to be unobserved. Indirect utility V depends on the expected net revenues of the productive forest " (depending on the cost function and timber prices), on the levels of amenities and on the forest owner's individual characteristics Y (e.g., income, age, management objectives):

# * = % [" , | ' ] + ( , (2)
where ( is the error term.

We choose a simple linear function for the stochastic utility function, so that we can write it econometric form as:

# * = ) * + ( , (3)
where includes the determinants X of the cost function, as well as the forest owner's individual characteristics ' and the forest characteristics . The vector ) denotes the set of parameters associated to , to be estimated.

We assume that the forest owner seeks to maximize his/her expected utility. Thus, the forest owner compares this expected indirect utility when setting aside a share of his forestland 7 (i.e., specialisation) # * + , with the indirect utility without setting aside (i.e., multiple-use management on the total forestland) # * . The forest owner decides to setting aside if # * + ≥ # * . Based on the difference in utilities, we can write the implicit utility of the decision to setting aside as:

- * = # * + -# * .

(4)

The econometric strategy

In our econometric analysis, we encounter several econometric problems so that we cannot conduct ordinary least squares regression on different functions separately. First, we have to account for the possibly endogenous nature of the choice of setting aside forest land in order to avoid a problem of selection bias. In fact, setting aside a part of forest could be influenced by past levels of timber harvesting and expected differences in harvesting according to the two regimes (Set-aside vs. No set-aside). Simultaneously, the decision to set aside could 7 The indirect utility when setting aside a share of forestland may account for the subsidy awarded by the government.

impact timber harvesting. Second, the timber harvest variable can also be a source of endogeneity in the cost function because unobserved cost heterogeneity can interact with harvest levels. Moreover, the nature of the data leads us to model the harvest function as a "corner solution" problem, since a large proportion of the observations are equal to zero (47 out of 136 observations). Following [START_REF] Maddala | Switching regression models with exogenous and endogenous switching, Proceedings of the business and economic statistics section[END_REF], we use a switching regression model with endogenous switching, in which harvested volume is explicitly estimated as a supply function

Given that # * is unobservable, what we observe is a dummy variable -(=1 if setting aside, 0 otherwise), which directly depend on the unobserved utility - * :

-= 0 1, if ) * ≥ ( 0, if ) * < ( , ( 5
)
which allows us to estimate the parameters ) through a probit model. In particular, we consider that the landowner choice is determined by harvest differences between the two regimes (Set-aside or No set-aside) and other factors:

- * = 5 + - + 67 + ( , (6)
where - * is the latent variable for unobserved forest owners' utility with the corresponding binary variable -. 7 is a vector of variables that influence landowner choice and ( is an error term. The term +captures the harvest differences between setting aside and no setting aside management. 8 The two different cost functions are defined as:

No set-aside: * = A * B + C (7)

Set-aside:

+ * = A + * B + + C + (8)
Equations ( 7) and ( 8) constitute standard censored Tobit models, where = * if * > 0, and = 0 otherwise. In our framework where harvested volume is the output in the cost function (1), we have ≡ clnvol = ln 1 + (LM . X is the vector of explanatory variables and A the associated coefficients to be estimated.

The model to be estimated consists of the set-aside choice (6), harvest equations ( 7) and ( 8), and cost function (1).

We assume that ( are correlated with C and N + , and possibly with the error term of the cost function and that they are distributed as a multivariate normal distribution with mean zero vector and the following covariance matrix: 8) with S T set equal to unit, in order to identify ) (probit model). Moreover the correlation parameter S U V U W is set to zero since sub-samples for equations ( 7) and ( 8) do not overlap.

O = P Q Q Q R S T S TU V S TU W S XT S Y V S U V U W S XY V S U W S XY W S X Z [ [ [ \ (
The estimation of the complete model consisting of four equations, which is assumed to have a recursive structure, is estimated in only one step by maximum likelihood, using the Conditional Mixed Process programme (CMP) developed by [START_REF] Roodman | Estimating fully observed recursive mixed-process models with cmp[END_REF].

Results

The model to be estimated is a recursive mixed system as it is composed of several equations with different structures along with linear regressions and continuous variables, some being non-linear (such as the set-aside decision which is modelled as a probit), others being censored (i.e., the timber supply functions modelled as standard Tobits). Moreover, our model includes a switching regression since it incorporates two timber supply functions estimated from two subsamples according to the switching rule of setting aside or not. Finally, the model is recursive because some endogenous variables appear on the right-hand sides as observed: the harvested volume (VOL, in log) and the binary decision to set aside (SASIDE)

in the cost function. The system is estimated by full-information maximum likelihood method and estimation results are presented in Table 3. Whereas estimation results of the simultaneous equation model are presented in a whole table, we prefer to discuss each equation in turn and thus discuss results on the set-aside decision to begin, and then the timber harvest and cost functions, for clarity. However, to begin, observing the more general results is useful to assess the relevance of the model. In particular, the significance of several of the correlation coefficients confirms the links between equations, especially concerning unobserved heterogeneity. More specifically, the choice of a switching regression for the timber supply functions is validated by the coefficient S TY W found as significantly different from zero. The size of forest being controlled in the regression, this means that when forest owners decide to set aside a part of their forest, timber harvesting is more intensive or more regular on the part not enrolled in the set-aside program. We also find a negative and significant correlation between the set-aside and cost equations (i.e., the parameter S XT ). This means that the variable SASIDE is endogenous in the cost equation and that there exist unobservable heterogeneity decreasing management costs when a part of forest is set aside. Similarly, there is a negative and significant correlation (S XY W ) between the disturbances of the harvest equation in Set-aside Regime and the cost equation, leading to conclude that unobserved factors explain lower costs by increasing harvesting when setting aside is adopted.

The set-aside decision

The upper part of Table 3 presents the probit estimates from the set-aside decision model.

Estimation results suggest that besides some forest management and forest property features, the set-aside decision is also influenced by the landowners' socio-economic characteristics, as well as their motivations for owning a forest. Among the landowners' characteristics, we observe that the likelihood of setting aside a share of the property increases with the landowners' income (significant at the 10% level). Moreover, the decision is influenced by the age of the forest owner and his/her education level. Younger forest owners with a lower level of education tend to decide to set aside forest more often than other forest owners.

Considering the forest owners motivations, respondents assigning great and very great

importance to learn about nature as a reason for owning a forest have higher likelihood to set aside part of their forest land. Similarly, respondents who express some interest in owning a forest for gaining income from hunting, greenery etc. seem to have a higher likelihood of subtracting part of the forest from the timber production compared with respondents who have not expressed these objectives. On the contrary, landowners owning a forest with the greatest interest for a long-term financial investment have a lower likelihood of setting aside compared with respondents who have not expressed this motive. Finally, forest owners assigning great importance in helping supply recreational areas for the public have lower willingness to set aside part of their forest land.

Regarding the forest property features, the results show that the probability of setting aside increases with the percentage of coniferous trees in the forestland. Interestingly, the probability of setting aside is lower if the forest estate is surrounded by forestland compared to other land uses. The negative sign of the parameter associated with the total size of the forest (in log) owned by the respondents suggests that owners are less likely to set aside forestland if they own a large property, but it is significant only at the 10% level. Finally, we notice that the percentages of old deciduous and coniferous forests have no effect on the setaside decision and conclude that forests with high potential for biodiversity and carbon sequestration are not the target of forest owners.

The timber supply and cost functions

Turning to the switching regression of timber harvesting, we find that the price of timber positively increases the timber harvesting in No Set-aside Regime, as expected. Similarly, the size of forest land implies a higher harvesting. We also find that membership of a forest association increases harvesting regardless of the regime. In Set-aside Regime, the size of forest has a significant and positive impact on timber harvesting. Moreover, the significantly positive coefficient associated with the variable PCON shows that harvesting levels are higher in forest with a higher part of coniferous. Also, timber harvesting is lower in forests with a high percentage of old and mature coniferous stands (supposed to be reserved for carbon sequestration). Finally, we find no significant change in harvesting for properties with old deciduous forests.

In the cost equation, we find several significant parameters with the expected sign, such as for the variables VOL, SIZE and VOL × VOL. We also find that a forest with a higher proportion of coniferous trees is less costly than forests where deciduous trees predominate.

The same applies for when the percentage of non-productive forest increases, probably because labour is much less important in this part of the forest owner's property. While it was found that deciduous forests generated higher management costs, the significantly negative sign of POLDDEC indicates that costs are decreasing when deciduous trees are old and mature. However, our estimation shows that management costs increase significantly when coniferous trees are old and mature (POLDCON). We also find that costs significantly decrease when the forest owner is a member of a forest association.

The impact of set-aside decision on management costs is tested by directly introducing the variable in the cost equation. We find a positive and highly significant impact on the costs.

Moreover, we measure the effect on the marginal cost of harvesting by crossing the variable VOL with the dummy variable SASIDE. The coefficient associated with this new variable is non-significant. This seems to indicate that harvesting and reserving a part of forest for biodiversity and carbon sequestration are independent in terms of management costs.

However we find a significant and positive sign for the coefficient of the interaction term VOL × POLDDEC. This result seems to reject the hypothesis of complementarity of costs between timber production and biodiversity conservation, thus meaning the existence of a trade-off between timber and biodiversity.

Concluding Discussion

The results from the probit equation showed that the landowners' motivations as well as their socioeconomic characteristics are relevant predictors of their decision of setting aside forest or not for the provision of non-timber services, e.g. biodiversity protection or carbon sequestration. This is consistent with our theoretical model and seems to confirm the hypothesis that NIPF owners are utility-maximisers in a broader sense than implied by the assumption of profit-maximisation [START_REF] Binkley | Timber supply from nonindustrial forests: a microeconomic analysis of landowner behavior[END_REF][START_REF] Max | A behavioral model of timber supply[END_REF][START_REF] Dennis | An economic analysis of harvest behavior: Integrating forest and ownership characteristics[END_REF]Hyberg and Holthausen, 1989;Newman and Wear, 1993). This is in line with a significant amount of empirical literature on NIPF landowners' decision making [START_REF] Amacher | Econometric analyses of nonindustrial forest landowners: Is there anything left to study[END_REF]Beach et al., 2005).

By looking at the factors reducing the likelihood of setting aside, we observe that it decreases when a higher percentage of broadleaves are present on the property. This result may be explained by the different site productivities. Since broadleaved trees generally are grown in areas with good soil fertility, we may expect a higher opportunity cost of setting aside forestland on sites covered by broadleaves, and hence a lower likelihood of observing this decision.

Regarding the forest owner income, we observed a significant and positive relationship with the set-aside decision. This is in line with previous findings in which a negative relationship was found between the likelihood of harvesting and the landowner's income (Hyberg and Holthausen, 1989;Denis, 1989). This suggests that forest owners' utility of providing biodiversity conservation and/or carbon sequestration or enjoying amenity values from set-aside decision, is increasing with their income. Of course, this result depends on the share of the total income that is generated by the forest property. We tested this variable in the model, but it did not turn out to be significant, hence we leave it out to improve the model performance.

Turning to the production part of the model (i.e., timber supply and cost functions estimation), our results bring new insights on the efficiency of multiple-use forest management and the forest owners' behaviour concerning timber supply. The first important result is the structural difference between the timber supplies according to the type of management (multiple-use vs. specialised management). Our results clearly show a more intensive timber harvesting in the case of specialised management and that is quite independent of price levels. It would seem that when the forest owners are engaged in a program in which they have set aside 5% of their forest land as untouched, then they allow themselves to make more intensive timber harvesting on the remaining lands.

The second important result is that there is a high and significant extra annual overhead cost in specialising a part of forest for biodiversity conservation and carbon sequestration.

However, this result is lessened by more intensive harvesting making it possible to exploit scale economies in the case of setting aside. Another result is the absence of interaction between harvesting and specialised management in terms of costs, indicating an equal marginal cost of harvesting whatever the type of management chosen. However, the positive interaction between harvesting and old deciduous forests seems to show the existence of trade-off between timber production and e.g. biodiversity conservation. But, at the same time the greatest gains in biodiversity are connected with old areas with deciduous trees (indigenous to the area). Hence, from a social planner point of view setting aside deciduous forest for biodiversity preservation would be more cost-efficient.

These results can be discussed in light of the debate on specialisation vs. multiple-use management paradigms. In other words, our model seems to suggest that forest management costs are higher in the case of specialised management. Moreover, this type of management seems to correlate with the forest owner harvesting more on remaining forest lands and even independently of timber prices. At the same time, we find an average cost scale elasticity lower than one, making it possible to exploit some economies of scale, and we show that increasing harvest in the case of specialised management reduces overall cost. Apart from these scale economies, our results suggest that forest management costs are generally lower in multiple-use forest management than in specialised management properties. This observation suggests that the additional benefits achieved from specialized relative to multiple-use management should exceed this cost premium, also from the forest owner's utility point of view.

Appendix

Table 1 . Descriptive statistics

 1 In Table1, we report descriptive statistics for the variables used in the analysis. Means and standard deviations are presented for the whole sample and for two different subsamples, i.e.

	Total	Set-aside Regime	No set-aside Regime
	(N=136)	(N=78)	(N=58)

Set-aside Regime vs. No set-aside Regime. The price variable was obtained by dividing the annual timber revenues by the annual timber volume produced. This value was available only for about 50% of the sample. Prices were hence predicted through a hedonic price model. The model and the estimated coefficients are presented in Appendix A.

Table 2 . Cost function estimation

 2

		Model (1)	Model (2)	Model (3)
	Variable	COST (in log) COST (in log) COST (in log)
	VOL (in log)	0.324***	0.348***	0.469***
		(0.0940)	(0.0921)	(0.124)
	SIZE (in log)	0.666***	0.671***	0.502**
	VOL × VOL SIZE × SIZE VOL × SIZE	(0.155) 0.158** (0.0726) -0.206** (0.0822) 0.0192 (0.0414)	(0.152) 0.155** (0.0707) -0.190** (0.0804) 0.00692 (0.0406)	(0.198) 0.150** (0.0707) -0.137 (0.0878) 0.000292 (0.0408)
	PCON	-2.643***	-3.181***	-3.097***
		(0.895)	(0.895)	(0.895)
	PNOP	-1.151	-1.690**	-1.671**

Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 3 . Estimation results of the complete model

 3

	Equation	Variable	Coefficient	Standard Error
	SASIDE
		INCOME(in log)	0.587*	(0.345)

Table A1 . Hedonic price model (dependent variable: Timber price in log)

 A1

	Variable		Coef.	Std. Err.
	SIZE (in log)		0.098	0.071
	PDEC		1.068**	0.411
	Certification of forest (y/n)		0.800**	0.331
	Membership of at least one forest organisation (y/n)	0.568**	0.283
	Neighbouring land: agriculture (y/n)		-0.402	0.364
	Constant		4.627***	0.369
	F(5,61)		7.060
	Prob > F		0.000
	R-squared		0.367
	Adj R-squared		0.315
	Notes: N = 67. *** p<0.01, ** p<0.05, * p<0.1
	Table A2. Separated Translog cost function
	estimations
	Variable	Cost (in log) Cost (in log)
		No set-aside	Set-aside
	VOL (in log)	0.701***	0.171*
		(0.211)	(0.0917)
	SIZE (in log)	0.285	0.839***
	VOL × VOL SIZE × SIZE VOL × SIZE	(0.290) 0.314* (0.163) -0.249 (0.159) -0.0475 (0.0801)	(0.157) 0.0901 (0.0694) 0.00263 (0.121) -0.0421 (0.0515)
	PCON	-3.093**	-2.578**
		(1.516)	(1.060)
	PNOP	-1.455	-1.425
		(1.478)	(0.882)
	POLDDEC	-3.633	-1.455
		(2.761)	(2.042)
	POLDCON	2.254	3.677
		(2.353)	(2.371)
	Constant	1.427	2.077***
		(1.017)	(0.697)
	Observations	58	78
	R-squared	0.522	0.702
	Standard errors in parentheses *** p<0.01, ** p<0.05,
	* p<0.1

[START_REF] Jacobsen | Assessing costs of multifunctional NATURA 2000 management restrictions in continuous cover beech forest management[END_REF] investigate the possible financial losses from placing some Natura 2000 management restrictions such as setting aside of individual trees for aging and natural decay.

See http://www.prinsengineering.com/biodiv_dk.htm. PRINS Engineering specialised in digital remote sensing and GIS has participated in the framework of the ESA / EU program to a project intended to support the monitoring and mapping of biological rich forest areas in several countries, including Denmark.

Some, but not all, of the variables in X may also appear in Z.

The research leading to these results has received funding from the European Union's Seventh Framework Program (FP7/2007-2013) under grant agreement NEWFOREX (no.243950). This work was supported by a grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" program (ANR-11-LABX-0002-01, Lab of Excellence ARBRE).


domain: math info sdv

text:
Julie Hurel

Mathieu Roland

Sophie Schbath

Stéphanie Bougeard

Mauro Petrillo

Fabrice Touzain

Detection of unknown genetically modified organisms (GMO) by statistical analysis of high-throughput sequencing data

Potential GMO reads

Trimming

INTRODUCTION

European legislation requires the reporting of GMOs in food products when their proportion is higher than 0.9%. In recent years, not described GMOs have been produced whose sequence is unknown making them not detectable by current PCR approaches. To date, no detection method have been described for the detection of unknown GMOs. The method was developed using two sets of raw reads of the bacteria Bacillus Subtilis : the first related to a genetically modified genome and the second to a wild bacteria.

Blast Pangenome

A pangenome groups most of the different genes present in the same species. Two Blastn 4 are performed on the pangenome of Bacillus Subtilis one on the coding sequences (CDS) and one on the whole genome. This pangenome involves 35 different strains of Bacillus Subtilis. The sequences selected by Blast alignment have an identity percentage greater than 98% and an alignment coverage percentage greater than 80%.

Distance Calculation

The insert sequences of an unknown GMO have a different vocabulary from that of the wild genome from which it is derived. A genome has its own vocabulary, consisting of words. Each word is a set of nucleotides with predefined length such as "ATGCCT". We search over-represented or rare words using R'mes 5 in the wild genome to define specificities of its vocabulary and highlight the vocabulary of an insert that shows different word proportions. This difference is evaluated through a distance calculation between the words vector of all CDS of the wild genome and the words vector of each candidate GMO insert CDS. The distance between a CDS of the wild genome and all the CDS of the wild genome -almost similar -will be close to 0 while the distance between all CDS of the wild genome and an insert CDS will be higher. We use Bray-Curtis distance 6 (BC) after comparison with alternative distances and employ two types of calculation : one based on proportions of short words, the other based on frequencies of long words over-expressed in wild genome.

Machine Learning

A machine learning step is implemented to discriminate CDS of GMO inserts. The learning datasets correspond to the wild CDS found in sample (Wild CDS ref.

2) and to a databank of known GMOs (known filtered GMO inserts). This databank contains only filtered sequences that don't belong to the species of the wild genome. The sequences of candidates GMO inserts not matching pangenome after the two Blasts are used as prediction data (Potential GMO inserts). The variables retained for this learning are the Bray-Curtis distance, the CDS length, the average of the R'mes words exceptionality scores, the over-represented words density per nucleotide (sum of the counts of over-represented words divided by the length of the CDS), the GC percentage and the codon usage.

RESULTS

12 machine learning methods were tested using the Caret package 7 . The parameters of each method were optimized by cross-validation. The performance of these methods was then compared on the basis of a second cross-validation to obtain the most efficient methods in terms of predicting sequences of GMO inserts (highest sensitivity and specificity). We retained Random Forest method for Machine Learning. It preserves most of the GMO inserts. Based on searched properties of the wild genome, we cannot exclude to find in results genes coming from recent horizontal gene transfer instead of GMO insert.

Potential GMO inserts

Alignment Blast 4

CDS Pangenome

Potential GMO inserts

Alignment Blast 4

Potential GMO inserts

Add to wild CDS ref.

CDS unaligned

CDS aligned

CDS aligned

CDS unaligned

Whole genome Pangenome

Aim : Highlight the sequences of inserts representing a tiny part of the genome if the unknown genome submitted is indeed a GMO.

MATERIAL AND METHODS

Cleaning pipeline

Conclusion : On a GM Bacillus Subtilis, most of the inserts are found. On a wild Bacillus Subtilis, we obtained only one false positive.

  Li H. and Durbin R. Fast and accurate short read alignment with Burrows-Wheeler Transform. Bioinformatics, 25:1754-60, 2009. [2] Nurk, Bankevich and al. SPAdes: A new genome assembly algorithm and its applications to single-cell sequencing. Journal of Computational Biology, 19(5): 455-477, 2012. [3] Seemann T. Prokka: rapid prokaryotic genome annotation. Bioinformatics, 30(14):2068-9, 2014. [4] Altschul, S.F., Gish, W., Miller, W., Myers, E.W. & Lipman, D.J. Basic local alignment search tool J. Mol. Biol. 215:403-410, 1990. [5] Schbath S. and Hoebeke M. R'MES: a tool to find motifs with a significantly unexpected frequency in biological sequences. In Advances in genomic sequence analysis and pattern discovery. Science, Engineering, and Biology Informatics, vol. 7, World Scientific. 2011. [6] Ricotta C. and Podani J. On some properties of the Bray-Curtis dissimilarity and their ecological meaning. Ecol. Complex, 31:201-205, 2017. [7] Max Kuhn and al. Caret: Classification and Regression Training. 2017. R package version 6.0-78. https://CRAN.R-project.org/package=caret.


M Donner

R Gohier

H De Vries

What types of circular business models for creating value from agro-waste?

Keywords: circular economy, business models, agro-waste management, value creation

. The circular economy is enabled by novel business models.

The objective of this research is to identify and characterise different types of business models that create value from agricultural waste and by-products via cascading or closing loops.

. From a business perspective, valorising agrowaste requires a reverse logistics, a new vision of customer-supplier relationships, new forms of organization and new marketing strategies, at the crossroads of various value chains.

 divide sustainable business models into eight archetypes which describe the main type of business model innovation: technological, social or organisational. According to Fielt (2013), a characterisation of each business model type should include specific classification criteria (e.g. level of innovation) and business model framework elements, such as customer, value proposition, organisational structure, economics and/or other value dimensions.

).

These six cases represent six types of circular business models for creating value from agro-waste and by-products. They differ in their way of value creation (from lower to higher value) and/or in their organisational form as shown in figure 1: biogas plant (case 1), upcycling entrepreneurship (case 4), environmental biorefinery (case 6), support structure (case 5), agricultural cooperative (case 3) and agropark (case 2).

Figure 1. Typology of circular business models for valorising agro-waste and by-products.

The typology shows the diversity but also a complementarity of circular business models that create value from agro-waste and by-products. The classification is useful because it advances the conceptual understanding of business models and may provide practical recommendations for other businesses, investors and resource or equipment suppliers in understanding the positioning and long-term perspectives of the business. Although the analysis identifies different circular business models, the results represent only the first step to create a value cascading model in which agricultural resources use is optimised. The typical agricultural characteristics (heterogeneity, fluctuating volumes of resources, flexibility in production) still need to be integrated to create synergies and ensure that the highest value is achieved, and the environmental impact over the whole life cycle is minimized.

Table 1 .

 1 Cases analysed.

		Case 1	Case 2	Case 3	Case 4	Case 5	Case 6
	Type of organisational structure	Farmer with a biogas plant	Agribusiness park	Union of wine cooperatives	University spin-off	Local cluster of different stakeholders	Eco-industrial cluster
	Resources and transformation process	Pig manure & vegetables; anaerobic digestion	Combined heat electricity and water recirculation systems	By-products from wine; extraction process	Cow manure and wine; anaerobic digestion	Organic urban food and agro-waste; anaerobic digestion	Cereals and sugar cane by-products; full scale biorefinery
	Value proposition	Heat, electricity, fertilizer	Heat, electricity	Compost, ingredients for food & pharma industries	Electricity, fertilisers, PHA for bio-materials	Biogas, network	Plant proteins
	Key partners	Local farmers	Vegetable producers (greenhouses) and traders	Cooperatives and research	Cooperative, two other universities	Local authorities, enterprises and research	Agrofood enterprises, research
	Customers	Public supplier, households and wholesaler	Data-centres use greenhouses electricity and produce heat for	Enterprises	Feed-in of electricity	Local enterprises	Enterprises
	Strategic approach	Enlarge product portfolio for mixed market sectors	Networking, economies of scale	Innovation, mixed market sectors	Innovation, upscaling, pilot-scale demonstration, consultancy	Networking, niche strategy (organic)	New markets for large volumes of unused by-products

Acknowledgement: This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 688338.


Jean-Michel Marin

Christian Robert

Approximating the marginal likelihood in mixture models

Keywords: Bayesian model choice, conjugate prior, Rao-Blackwellisation, Markov Chain Monte Carlo (MCMC)

 that it truly approximates the marginal densities once the label switching issue has been solved.

Introduction

Model choice is a central issue in mixture modelling because of the nonparametric nature of mixtures [START_REF] Marin | Bayesian modelling and inference on mixtures of distributions[END_REF][START_REF] Frühwirth-Schnatter | Finite Mixture and Markov Switching Models[END_REF]. Indeed, while a distribution with a density of the form

f k (x|θ k ) = k i=1 p k i g(x|µ k i ) , p k i > 0 , k i=1 p k i = 1 , (1)
where the densities g are known and the corresponding parameters µ k i 's are unknown, is a welldefined object (with θ k = (p k 1 , . . . , p k k , µ k 1 , . . . , µ k k ), it occurs that, in most settings, the number of components k is uncertain and is an integral part of the inferential goals. This is true for classification as well as for estimation purposes, especially because of the weakly informative nature of mixtures: due to the representation of those distributions as sums of components g(x|µ k i ), samples from f k (x|θ k ) provide relatively little information about each of the components, in the sense that there always is a positive probability that no point in the sample has been generated from a particular component.

Evaluating the number k of components from a sample x = (x 1 , . . . , x n ) from ( 1) is therefore a quite relevant issue in the setting of mixtures and a standard Bayesian approach is to consider the 4 jean-michel.marin@inria.fr and xian@ceremade.dauphine.fr 1 problem from a model choice perspective, i.e. to consider that each value of k defines a different model, with density

f k (x|θ k ) = n i=1 f k (x i |θ k )
and corresponding parameter θ k , and to compute the corresponding Bayes factors

B π k,k+1 (x) = f k (x|θ k )π k (θ k ) dθ k f k+1 (x|θ k+1 )π k+1 (θ k+1 ) dθ k+1 = m k (x) m k+1 (x)
for all pairs (k, k + 1) of interest. Obviously, there exist different Bayesian solutions for the approximation of B π k,k+1 (x) and this is well-documented in the literature (see, e.g., [START_REF] Chen | Monte Carlo Methods in Bayesian Computation[END_REF][START_REF] Frühwirth-Schnatter | Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques[END_REF]. One possible solution is to derive the posterior probabilities of the different values of k (that are proportional to the m k (x)'s) by an reversible jump MCMC algorithm as in [START_REF] Richardson | On Bayesian analysis of mixtures with an unknown number of components (with discussion)[END_REF]. But we consider however that there is a fundamental inefficiency in using a random walk like the reversible jump MCMC algorithm on a structure-the collection of mixture distributions with an unknown number of components-made of a rather small number of terms (since k is usually bounded): the resulting inherent randomness does not seem pertinent in a finite state space. For one thing, the proposed values of the parameters θ k at each step of a reversible jump MCMC algorithm are less likely to be accepted than in a regular Gibbs sampling scheme because of (a) the introduction of an additional proposal to move between models and between the parameters of those models, rather than relying on the exact full conditionals of the true target distribution, (b) the comparison not only of values of the parameters within a model but in connection with the relative likelihoods of different models which, by its very nature, forces the corresponding Markov chain to remain more often in the more probable models and thus slows down the exploration of the less probable models, and (c) the lack of connection between the adjacent elements of the Markov chain since the parameter space changes at every step. This is of course arguable, as defended in [START_REF] Richardson | On Bayesian analysis of mixtures with an unknown number of components (with discussion)[END_REF] who maintain the opposite point of view that using a reversible jump algorithm improves the mixing of the Markov chain within each model. (This is certainly true from a probabilistic perspective, namely that two consecutive values of θ k are less correlated than in a Gibbs scheme because there is an arbitrary large number of intermediate simulations between those two values, but this does not answer the criticism that a proper exploration of each model, i.e. of each value of k, requires in the end a much larger number of simulations than the sum of the numbers of simulations requested by the approximation of each posterior distribution π k (θ k |x), not to mention the additional level of complexity in designing efficient reversible jumps algorithms, see [START_REF] Brooks | Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions (with discussion)[END_REF] Exploring each model/case separately by MCMC and then producing an approximation of the corresponding marginal densities is therefore more reasonable if those marginals can be correctly approximated. Once a sample from the posterior distribution π k (θ k |x) has been produced, there are again many alternatives for approximating the marginals m k (x), as discussed in, for instance, [START_REF] Frühwirth-Schnatter | Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques[END_REF] or [START_REF] Chopin | Contemplating evidence: properties, extensions of, and alternatives to nested sampling[END_REF], but the central point of this note is to stress the point already made in [START_REF] Berkhof | A Bayesian approach to the selection and testing of mixture models[END_REF] that a proper approximation can be found when using a simple correction to [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] marginal likelihood approximation, since this solution has somehow been overlooked in the literature, maybe due to the original controversy surrounding [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] proposal. We recall in Section 2 the basis of [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] approximation and the difficulties surrounding its implementation to the mixture problem, before presenting in Section 3 our correction and demonstrating in Section 4 how this correction recovers the true marginal densities.

2 The original proposal [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] method for approximating a marginal (likelihood) is a direct application of Bayes' theorem: given

x ∼ f k (x|θ k ) and θ k ∼ π k (θ k ), we have that m k (x) = f k (x|θ k ) π k (θ k ) π k (θ k |x) ,
for all θ's (since both the lhs and the rhs of this equation are constant in θ). Therefore, if an arbitrary value of θ, θ * say, is selected and if a good approximation to π(θ|x) can be constructed, π(θ|x) say, [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] approximation to the marginal likelihood is

mk (x) = f k (x|θ * k ) π k (θ * k ) πk (θ * k |x)
.

(2)

In the special setting of mixtures of distributions, [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] approximation is particularly attractive as there exists a natural approximation to π k (θ k |x), based on the Rao-Blackwell [START_REF] Gelfand | Sampling based approaches to calculating marginal densities[END_REF]

estimate πk (θ * k |x) = 1 T T t=1 π k (θ * k |x, z (t) k ) ,
where the z

(t)
k 's are the latent variables simulated by the MCMC sampler. (We recall that the natural Gibbs sampler in this setting [START_REF] Diebolt | Estimation des paramètres d'un mélange par échantillonnage bayésien[END_REF] is based on two steps: (i) the simulation of the latent variables z ik that correspond to the component indicators, conditional on the parameter θ k , and (ii) the simulation of the parameter θ k , conditional on the latent variables z ik . When conjugate priors are used for θ k , step (ii) can be implemented in one block, see [START_REF] Diebolt | Estimation des paramètres d'un mélange par échantillonnage bayésien[END_REF]Robert, 1990, Casella et al., 2004.) The estimate πk (θ * k |x) is a parametric unbiased approximation of π k (θ * k |x) that converges with rate O( √ T ). This Rao-Blackwell approximation obviously requires the full conditional density π k (θ * k |x, z) to be available in closed form (constant included), but this is the case when the component densities g(x|µ i ) are within an exponential family and when conjugate priors on the µ i 's are used.

To be efficient, [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] method requires (a) a central choice of θ * k but, since in the case of mixtures, the likelihood is computable, θ * k can be chosen as the MCMC approximation to the MAP or to the ML estimator, and (b) a good approximation to π k (θ k |x). This later requirement is the core of [START_REF] Neal | Erroneous results in "Marginal likelihood from the Gibbs output[END_REF] criticism in the case of mixtures: while, at a formal level, πk (θ * k |x) is a converging approximation of π k (θ k |x) by virtue of the ergodic theorem, this convergence result relies on the fact that the chain (z (t) k ) converges to its stationarity distribution. Unfortunately, in the case of mixtures, as shown in [START_REF] Celeux | Computational and inferential difficulties with mixtures posterior distribution[END_REF], the Gibbs sampler rarely converges in essence because of the (lack of) label switching phenomenon (see also [START_REF] Jasra | Markov Chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling[END_REF]. In short, due to the lack of identifiability of mixture models (since the components remain invariant under permutations of their indices), the posterior distribution is generaly multimodal and, in the case of an exchangeable prior, it is also exchangeable. Therefore, when the Gibbs output fails to reproduce the exchangeability predicted by the theory, namely when it remains concentrated around one (or a subset) of the k! modes of the posterior distribution, the approximation πk (θ * k |x) is untrustworthy and Neal (1999) demonstrated via a numerical experiment that (2) is significantly different from the true value m k (x) in that case. [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] tried to overcome this difficulty by using a constrained parameter set based on an identifiability constraint, but such constraints are notorious for slowing down the corresponding MCMC sampler and, more importantly, for failing to isolate a single mode of the posterior distribution [START_REF] Celeux | Computational and inferential difficulties with mixtures posterior distribution[END_REF].

The fix

There is, however, an easy remedy to this problem, as already demonstrated in [START_REF] Berkhof | A Bayesian approach to the selection and testing of mixture models[END_REF]. Since, when the prior distribution is exchangeable over the components of the mixture, the posterior distribution is also exchangeable, this means that

π k (θ k |x) = π k (σ(θ k )|x) = 1 k! σ∈S π k (σ(θ k )|x)
for all σ's in S k , set of all permutations of {1, . . . , k}. (The notation σ(θ * k ) indicates the transform of θ * k where components are switched according to the permutation σ.) In other words, the distribution of interest is invariant over all permutations and the data brings no information about an ordering of the components. The lack of symmetry in an approximation πk (θ * k |x) is therefore purely ancillary and integrating out this factor of randomness by recovering the label switching symmetry a posteriori can only reduce the variability of the approximation, by a standard Rao-Blackwell argument. We thus propose replacing πk (θ

* k |x) in (2) above with πk (θ * k |x) = 1 T k! σ∈S k T t=1 π k (σ(θ * k )|x, z (t) k ) .
Note that this solution is taking advantage of the symmetry predicted by the theory, following the general principles stated in [START_REF] Kong | A theory of statistical models for Monte Carlo integration[END_REF].

The modified πk (θ * k |x) is shown (through examples) in the next section to recover the missing mass lost in the lack of exploration of the k! modes of the posterior density, rightly pointed out by [START_REF] Neal | Erroneous results in "Marginal likelihood from the Gibbs output[END_REF]. When the Gibbs sampler starts exploring more than one mode of the posterior density, there is no loss in using the symmetrised estimator πk (θ * k |x) (except for the additional computing time). In the case of "perfect symmetry", both estimators are identical, which is a good indicator of proper mixing. In other cases, a difference between both estimators points out a lack of mixing, at least from the point of view of exchangeability, and it may call for additional simulations with different starting points. The major question in such cases is to ascertain whether or not the Gibbs sampler has completely explored at least one major mode of the posterior distribution. As shown in [START_REF] Marin | Bayesian modelling and inference on mixtures of distributions[END_REF], there may also exist secondary modes where a standard Gibbs sampler gets trapped. In such occurrences, even a symmetrised estimate of π k (θ k |x) fails to produce a proper approximation of m k (x), but this goes undetected. This is however unrelated with the original difficulty of [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] approximation and trapping modes can be detected by using tempering devices or other simulation algorithms like Population Monte Carlo [START_REF] Douc | Convergence of adaptive mixtures of importance sampling schemes[END_REF]. (We indeed point out that the approximation (2) can also be used in a setup where a sample θ 115.68 -103.35 -102.66 -101.93 -102.88 -105.48 -108.44 Table 1: Estimations of the marginal likelihoods by the symmetrised Chib's approximation (based on 10 5 Gibbs iterations and, for k > 5, 100 permutations selected at random in S k ). (Source: [START_REF] Lee | Bayesian inference on mixtures of distributions[END_REF]

Illustration

In this example, we consider the benchmark galaxy dataset (Roeder, 1992, Mengersen and[START_REF] Mengersen | Testing for mixtures: A Bayesian entropic approach (with discussion)[END_REF], that represents the distribution of the radial speeds of n = 82 galaxies as a mixture of k normal distributions with both mean and variance unknown. In this case, label switching mostly does not occur. If we compute log mk (x) using only the original estimate, with θ * k chosen as the MAP estimator, the (logarithm of the) estimated marginal likelihood is mk (x) = -105.1396 for k = 3 (based on 10 3 simulations), while introducing the permutations leads to mk (x) = -103.3479. As already noted by [START_REF] Neal | Erroneous results in "Marginal likelihood from the Gibbs output[END_REF], the difference between the original [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] approximation and the true marginal likelihood is close to log(k!) (only) when the Gibbs sampler remains concentrated around a single mode of the posterior distribution. In the current case, we have that -116.3747 + log(2!) = -115.6816 exactly! (We also checked this numerical value against a brute-force estimate obtained by simulating from the prior and averaging the likelihood, up to fourth digit agreement.) A similar result holds for k = 3, with -105.1396 + log(3!) = -103.3479. Both Neal (1999) and Frühwirth-Schnatter ( 2004) also pointed out that the log(k!) difference was unlikely to hold for larger values of k as the modes were getting less separated on the posterior surface and thus the Gibbs sampler was more likely to explore in parts several modes. For k = 4, we get for instance that the original [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] approximation is -104.1936, while the average over permutations gives -102.6642. Similarly, for k = 5, the difference between -103.91 and -101.93 is less than log(5!). The log(k!) difference cannot therefore be used as a direct correction for [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] approximation because of this difficulty in controlling the amount of overlap. But it is altogether unnecessary since using the permutation average resolves the difficulty. Table 1 shows that the prefered value of k for the galaxy dataset and the current choice of prior distribution is k = 5.

When the number of components k grows too large for all permutations in S k to be considered in the average, a (random) subsample of permutations can be simulated to keep the computing time to a reasonable level when keeping the identity as one of the permutations, as in Table 1 for k = 6, 7. (See [START_REF] Berkhof | A Bayesian approach to the selection and testing of mixture models[END_REF] for another solution.) Note also that the discrepancy between the original [START_REF] Chib | Marginal likelihood from the Gibbs output[END_REF] approximation and the average over permutations is a good indicator of the mixing properties of the Markov chain, if a further convergence indicator is requested.

Acknowledgements

Both authors are grateful to Kerrie Mengersen for helpful discussions on this topic. This work had been supported by the Agence Nationale de la Recherche (ANR, 212, rue de Bercy 75012 Paris) through the 2006-2008 project Adap'MC.