Carina Müller
email: carina.mueller@wur.nl

Claire Chabanet

Gertrude G Zeinstra

Gerry Jager

Camille Schwartz

Sophie Nicklaus
email: sophie.nicklaus@inrae.fr

The sweet tooth of infancy: Is sweetness exposure related to sweetness liking in infants up to 12 months of age?

Keywords: Sweetness liking, Sweetness exposure, Children, Longitudinal, Infants, Sweetness preference, birth cohort, sugar

Table of contents

Executive summary

Background:

Infants become increasingly exposed to sweet-tasting foods in their first year of life. However, it is still unclear whether repeated exposure to sweet taste is linked to infants' sweetness liking during this period. Making use of data from the OPALINE cohort, this study aimed to examine the link between sweetness exposure and sweetness liking during two important periods in early infant feeding: at the start of complementary feeding (3-6 months) and the transition to the family table (10-12 months).

Methods:

Infants' sweetness exposure was assessed using seven-day food records which were completed by mothers every month (n=312), reporting daily consumption rates of formula/breast milk or complementary food and the type of formula milk and/or complementary foods for each feeding occasion. Infants' sweetness liking was studied in the laboratory at three, six, and twelve months of age by assessing their response to a lactose-water solution and the amount drunk of this solution compared to plain water. Linear regressions and SEM assessed associations between exposure to and liking for sweetness at six and twelve months.

Results:

Neither at six (n=182) nor at twelve months (n=197) was sweetness exposure associated with sweetness liking. While sweetness liking at three months was unrelated to liking at six months, the latter predicted sweetness liking at twelve months.

Conclusions:

These findings demonstrate no association between sweetness exposure at three to twelve months and liking at six and twelve months despite a sharp increase in sweetness exposure in that period. However, sweetness liking at six and twelve months was positively associated.

Abstract

Infants become increasingly exposed to sweet-tasting foods in their first year of life. However, it is still unclear whether repeated exposure to sweet taste is linked to infants' sweetness liking during this period. Making use of data from the OPALINE cohort, this study aimed to examine the link between sweetness exposure and sweetness liking during two important periods in early infant feeding: at the start of complementary feeding (3-6 months) and the transition to the family table (10-12 months). Infants' sweetness exposure was assessed using seven-day food records which were completed by mothers every month (n=312), reporting daily consumption rates of formula/breast milk or complementary food and the type of formula milk and/or complementary foods for each feeding occasion. Infants' sweetness liking was studied in the laboratory at three, six, and twelve months of age by assessing their response to a lactose-water solution and the amount drunk of this solution compared to plain water. Linear regressions and SEM assessed associations between exposure to and liking for sweetness at six and twelve months. Neither at six (n=182) nor at twelve months (n=197) was sweetness exposure associated with sweetness liking. While sweetness liking at three months was unrelated to liking at six months, the latter predicted sweetness liking at twelve months. These findings demonstrate no association between sweetness exposure at three to twelve months and liking at six and twelve months despite a sharp increase in sweetness exposure in that period. However, sweetness liking at six and twelve months was positively associated.

Introduction

Humans have an innate preference for sweet taste (1; 2; 3) . In childhood, the sweet taste is generally more liked than in adulthood and is preferred over all other tastes in the first 20 months of life (4; 5) . Despite the quasi-universal trait of liking sweetness, there are great inter-individual differences regarding which specific tastes and sweetness levels are liked the most [START_REF] Garneau | Sweet liker status in children and adults: Consequences for beverage intake in adults[END_REF] . A child's preferred level of sweetness may ultimately affect his or her food intake and weight, as a greater preference for sweetness has been associated with consumption of high-calorie foods and, moreover, with overweight and obesity in six-to-nine-year-old children (7; 8) . However, it remains difficult to explain how differences in sweetness liking arise [START_REF] Mennella | Flavor programming during infancy[END_REF] . Some studies argue that food and taste preferences may be linked to sex [START_REF] Yuan | Associations between infant dietary intakes and liking for sweetness and fattiness sensations in 8-to-12-year-old children[END_REF] or genetic differences [START_REF] Lehto | Predicting gender differences in liking for vegetables and preference for a variety of vegetables among 11-year-old children[END_REF] . Previously, boys were found to like sweet foods more at eight to twelve years than girls [START_REF] Yuan | Associations between infant dietary intakes and liking for sweetness and fattiness sensations in 8-to-12-year-old children[END_REF] and genotypes at the TAS2R38 taste gene locus were associated with sucrose preference and liking of sweet-tasting foods in five-to-ten-year-old children [START_REF] Lehto | Predicting gender differences in liking for vegetables and preference for a variety of vegetables among 11-year-old children[END_REF] . Further, research suggests that individuals vary in their hedonic liking response to sweetness as evidenced by differences between sweetness liker or disliker phenotypes [START_REF] Armitage | Understanding sweet-liking phenotypes and their implications for obesity: Narrative review and future directions[END_REF] and that children as well may be distributed along a continuum from sweetness likers to dislikers [START_REF] Garneau | Sweet liker status in children and adults: Consequences for beverage intake in adults[END_REF] .

In addition to sex and genetic differences, there is an ongoing discussion about whether repeated exposure to sweet taste alters the degree of sweetness liking or not (13; 14; 15; 16; 17) . Some research suggests that sweetness liking may be maintained or increased through dietary exposure to sweet-tasting foods (15; 16; 17) . For example, babies who were regularly fed sweetened water during their first months of life liked sweetened water more at six months and at two years than children who were not regularly fed sweetened water in infancy (16; 17) . However, this link was not found when sweetness liking was tested with a sweetened fruit-flavored drink instead of sweetened water at two years of age [START_REF] Beauchamp | Acceptance of sweet and salty tastes in 2-yearold children[END_REF] . This suggests that the relationship between early sweetness exposure and sweetness liking may depend on the medium used for both exposing to sweetness and measuring sweetness liking. In a recent systematic review, equivocal evidence for the presence and possible direction of a relationship between sweetness exposure and sweetness liking was found [START_REF] Appleton | Sweet taste exposure and the subsequent acceptance and preference for sweet taste in the diet: systematic review of the published literature[END_REF] . On the one hand, a higher intake of added sugars in the first year of life was related to a higher preference for sweetness at age four to seven [START_REF] Liem | Sweet and sour preferences during childhood: role of early experiences[END_REF] . Further, a higher intake of foods with added sugars during the first year of life was linked to a higher intake at age three to seven [START_REF] Foterek | Commercial complementary food consumption is prospectively associated with added sugar intake in childhood[END_REF] . On the other hand, neither added sugar consumption nor the consumption frequency of sweet foods was linked to sweetness liking in seven-to-twelve-year-old, respectively six-tonine-year-old children (8; 19) . Those findings demonstrate that the link between sweetness exposure and liking is more complex than initially indicated by earlier studies, and far from being systematically shown.

In addition to the different study results and conclusions, very limited research aims to shed light on the association between exposure to sweet taste and the degree of sweetness liking in the first 12 months of life [START_REF] Vabø | The relationship between food preferences and food choice: a theoretical discussion[END_REF] . During this time, infants go through a major dietary transition -from exclusive milk feeding, over complementary feeding to eating what is consumed by the family (21; 22) . In addition, what infants eat in those early months could influence their eating behavior in the long term, as diet quality and food preferences in infancy are related to food intake and food preferences through adolescence and early adulthood (23; 24; 25; 26; 27) . Moreover, research suggests that dietary patterns are already established by the age of 18 months and those set at two years build the root for lifelong eating habits [START_REF] Saavedra | Lessons from the feeding infants and toddlers study in North America: what children eat, and implications for obesity prevention[END_REF] . Due to the importance of the first few months for long-term eating behavior, it is important to examine this period to assess the role of or potential relationship between repeated exposure to sweet-tasting foods and the degree of sweetness liking at this crucial stage of life.

When dietary intake is no longer limited to breast or formula milk, the level of sweetness exposure starts to differ more between children (28; 29) . Hence, this study was conducted to define the role of dietary exposure to sweetness on sweetness liking during two crucial changes in early infant feeding: at three to six months (start of complementary feeding) and at ten to twelve months (transition to the family table). We predicted that higher exposure to sweetness would be associated with higher sweetness liking in those periods. Further, we hypothesized that the link between sweetness exposure and sweetness liking would be stronger at twelve than six months, as infants' sweetness exposure was found to be higher at ten to twelve compared to three to six months [START_REF] Yuan | Infant dietary exposures to sweetness and fattiness increase during the first year of life and are associated with feeding practices[END_REF] . Acknowledging that sweetness liking may already differ between infants at birth, we also investigated the associations between sweetness liking at three months and sweetness liking at six and twelve months. We hypothesized that repeated exposure would override innate sweetness preferences, so that sweetness liking at three months would have a low impact on sweetness liking at six and twelve months.

Methods

General design

We conducted secondary data analyses using the French birth cohort study "Observatoire des Préférences Alimentaires du Nourrisson et de l'Enfant" (Observatory of Infant and Child Food Preferences), OPALINE in short. Between 2005 and 2009, 312 women were recruited before their last trimester of pregnancy via leaflets and posters at doctors' and pediatricians' consulting rooms in maternity hospitals and clinics, as well as pharmacies and day-care centers. To be included in the study, parents had to be at least 18 years old and have children in good health after birth. Children's degree of sweetness liking was assessed in the laboratory at ages three, six, twelve, and twenty months (based on the expected delivery date, not the actual delivery date). In this paper, only the measurements at three, six, and twelve months are included in the analyses as the procedure at twenty months was slightly different [START_REF] Schwartz | Infant acceptance of primary tastes and fat emulsion: Developmental changes and links with maternal and infant characteristics[END_REF] . During their last trimester of pregnancy, mothers participated in interviews on sociodemographic and health characteristics. After the child's birth, mothers reported their children's birth date, sex, gestational age, and birth weight and length. Further, between birth and one year, mothers filled out twelve monthly seven-day food records at home in which they indicated the number and timing of each feeding occasion with breast or formula milk. Furthermore, they described the complementary foods they might have given, the food type (homemade food, ready-prepared baby food, readyprepared adult food, plus the brand if relevant), and texture (e.g. drained, lumpy, or thick), and whether they had added any ingredient (e.g. sugar or salt) to the foods. They were not asked to report the amount consumed by the child. Mothers also recorded special occurrences in between two monthly food records, such as the introduction of new foods. Based on the records, foods were grouped into milk, homemade foods, ready-prepared baby foods, and ready-prepared adult foods. Detailed explanations of the recording method and overall procedures used in the OPALINE study were explained previously (4; 28; 30; 31) . This study was conducted according to the guidelines laid down in the Declaration of Helsinki and all procedures involving human subjects were approved by the local ethical committee (Comité Consultatif de Protection des Personnes dans la Recherche Biomédicale de Bourgogne-ID RCB 2007-A00808-45). Written informed consent was obtained from both parents prior to the first experimental session. The protocol related to the present analysis was preregistered at https://osf.io/6tz4c. The OPALINE data can be accessed upon request.

Sweetness Exposure

Infants' exposure to sweetness (SweetExposure) was measured through the diet (based on the food records) as the cumulative frequency of the taste intensities of all consumed foods during each period of recording (28; 32; 33) . For that, all foods were linked to their sweetness intensity through existing databases (32; 33) . In short, the data sets (one for baby food and one for adult foods) included information for each food item based on the evaluation from trained panelists who tasted and rated the taste intensity on a continuous scale from zero to ten, inspired by the Spectrum method [START_REF] Munoz | The Spectrum Descriptive Analysis IVIethod. Manual on descriptive analysis testing for sensory evaluation[END_REF] . Following this method, four sweet reference solutions were used and arranged on the scale with increasing intensity to give reference intensities to the panelists to aim for standardized ratings [START_REF] Yuan | Infant dietary exposures to sweetness and fattiness increase during the first year of life and are associated with feeding practices[END_REF] . For the adult food database, the panelists conducted home-based measurements where the reference solutions were replaced by reference foods [START_REF] Munoz | The Spectrum Descriptive Analysis IVIethod. Manual on descriptive analysis testing for sensory evaluation[END_REF] . Mixed dishes were rated according to the mean of the ingredients' tastes. An extensive explanation of the sweetness intensity measurements can be found elsewhere [START_REF] Yuan | Infant dietary exposures to sweetness and fattiness increase during the first year of life and are associated with feeding practices[END_REF] . The exposure to sweetness was then calculated for each month and child by the sum of sweetness intensities of food items weighted by consumption frequencies and divided by the number of days for which the food diary was completed. Based on that, the average daily mean of SweetExposure was calculated for the three to six and ten to twelve months periods.

Sweetness Liking

Infants' degree of sweetness liking (SweetLiking) was estimated at three, six, and twelve months by comparing the infant's acceptance of a sweet solution (0.20 M lactose + water) to water. The solution was chosen because it is similar to the lactose concentration in breast milk and reflects moderate intensity [START_REF] Schwartz | Developmental changes in the acceptance of the five basic tastes in the first year of life[END_REF] . The sweet solution was prepared every three days, kept refrigerated at +4° Celsius, and used at room temperature during the sweetness liking test. The bottles contained 30 ml of the solution or water at three and six months and 50 ml at twelve months. Further, mothers reported which nipple shape and material the child was used to so that the experience during the laboratory assessment would be similar to infants' home experience. In the data collection process, liking was also assessed for the other basic tastes (sour, salty, bitter, and umami) and the researchers were blind to the order in which these tastes were tested. For this paper, only the degree of sweetness liking is reported.

Procedure

Children were tested individually in a room designed for infant testing at the Centre Européen des Sciences du Goût (Dijon, France) or the FLAVIC (FLAvour VIsion Consumer Behaviour) joint research unit (Dijon, France). Children sat in a bouncer (three and six months) or a high chair (12 months). Each of them was accompanied by one parent while one of four included researchers conducted the test. To ensure that children were in a similar hunger state at the beginning of the test, parents were asked to refrain from giving the child water, milk, or food one hour before the test. On the test day, compliance with this instruction was checked by asking the parent to report the last time the child had consumed something on that day. In videotaped sessions, children were presented with four bottles in the following order: water, sweet solution, sweet solution, and water. Each of the bottles was presented for 45 seconds by gently rubbing the nipple against the child's mouth, followed by a 15-second break before presenting the next bottle. In case the child did not drink, he/she was offered a toy. When necessary, the parent sat closer to the child, or the child was put on the parent's lap. The degree of sweetness liking was defined through three scores: the ingestion ratio and two liking ratios (liking rated by the experimenter and liking rated by the parent). Sweetness liking measures were only recorded if the child drank at least 1.0 g from the sweet solution. Otherwise, it was considered missing.

Ingestion Ratio

The first indicator for the degree of sweetness liking, the ingestion ratio (IR), was created by measuring the amount the child drank from the sweet solution bottles and the water bottles. For that, the bottles were weighed to the nearest 0.1 g (Sartorius U3600S; Sartorius AG, Göttingen, Germany) before and after each solution was presented to the child. Based on the weights, the IR was calculated by first summing the amount drunk from the two sweet solutions. This sum was then divided by the sum of amounts drunk from all four bottles so that each child could be assigned an IR between zero and one. For each of the three liking ratios, a ratio of 0.5 indicated indifference to the sweet solution relative to water. A ratio > 0.5 indicated a preference for the sweet solution relative to water and a ratio < 0.5 indicated rejection of the sweet solution relative to water.

Subjects

In this paper, data were included from 312 mothers, leading to a sample of 319 children including seven pairs of twins. Of those, information on the degree of sweetness liking was available for 153 infants at three months, 216 at six months, and 215 at twelve months. Further, of the 319 infants, information on sweetness exposure was available for 251 infants for the three to six months period and 264 for the ten to twelve months period.

For SweetLiking, missing data were considered as occurring at random because they were due to children being sick or drinking less than 1.0 g of the sweet solution on the assessment day. Similarly, missing data for SweetExposure were considered as occurring at random because they were due to incomplete food records. As many observations as possible were included for each analysis, resulting in different sample sizes for each analysis.

Statistical Analyses

Statistical analyses were performed using R, version 4.1.1 for Windows. The sweetness liking data were merged across the experimenters and sessions, as previously no difference was found in the judgment of the experimenters [START_REF] Schwartz | Developmental changes in the acceptance of the five basic tastes in the first year of life[END_REF] . Results are expressed as mean values and standard deviations. Inferences about the association between the degree of sweetness liking and sweetness exposure were made based on p-values, the size of regression coefficients, and confidence intervals.

To assess whether SweetLiking at three months differed from SweetLiking at six and twelve months and whether liking at six months differed from liking at twelve months, paired samples t-tests were conducted. Again, as many observations as possible were used for each t-test [n= 137 (difference three and six months); n= 164 (difference six and twelve months); n= 122 (difference between three and twelve months)]. In addition, another paired samples t-test was conducted to assess whether exposure to sweetness differed at three to six months compared to ten to twelve months, including all individuals with complete data on sweetness exposure at both investigated periods (n = 247).

The relationship between sweetness exposure and liking was tested using linear regressions. To reduce the number of linear regression models, we only used one of the two liking ratios, because both (LRE and LRP) measured the child's hedonic liking and correlated strongly with each other at each of the time points of assessment [three months (r(151) = .43, p<0.001); six months (r(214) = .48, p<0.001); twelve months (r(209) = .64, p<0.001)]. The LRE was chosen as it was based on the judgment of the same four experimenters, whereas the LRP was based on the judgment of each parent. All linear regression models were conducted twice, with the IR and LRE as the outcome variables. First, the link between the degree of sweetness liking (IR and LRE) at six months (12 months respectively) and exposure to sweetness at three to six months (10-12 months respectively) was tested with a bivariate linear regression. For that, all individuals with complete data on IR and LRE at six months (12 months respectively) and sweetness exposure at three to six months (10-12 months respectively) were included in the analyses. Next, multiple linear regressions were conducted by adding confounders to the bivariate models. Based on the directed acyclic graph method, the duration of exclusive breastfeeding and the mother's level of education were selected as confounders for inclusion in the regression analyses (4; 5; 28; 35; 36) . Next, an interaction term between the child's sex and sweetness exposure, as well as the main effect of sex, were introduced but removed again from the final models due to non-significance. Because missing values were judged to be at random, the bivariate analyses were performed a second time for complete cases only to assess the robustness of the results. Only individuals with available data for all four variables (SweetLiking at six months, SweetLiking at twelve months, SweetExposure at three to six months, and SweetExposure at ten to twelve months) were included in the complete case models.

Finally, to get a global picture of the relationships between exposure and liking, all available data regarding SweetLiking at three, six, and twelve months and SweetExposure at three to six and ten to twelve months were gathered in a Structural Equation Model (SEM, supplementary material Figure S1, n = 319). Compared to the linear regressions, the SEM allows for consideration of all (in)dependent variables in the same model and therefore to test relationships simultaneously [START_REF] Nunkoo | Structural equation modelling and regression analysis in tourism research[END_REF] . Structural models were estimated using the R package Lavaan 0.6-7, by full information maximum likelihood (FIML) to address missing values [START_REF] Rosseel | Lavaan: An R package for structural equation modeling and more. Version 0.5-12 (BETA)[END_REF] . All three SweetLiking variables (IR, LRE, LRP) were used for a more precise estimation of liking at each age. The first step was to check whether the construct measurement (CFA) was satisfactory concerning the latent variables (SweetLiking at three, six, and twelve months) as measured by the three indicators (observed variables IR, LRE, and LRP). More precisely, the CFA model was built, and fit criteria (CFI, TLI, and RMSEA) were used to evaluate the quality of the measurement model and convergent validity. It was checked that the estimation showed high loadings and low correlations between constructs. Next, the structural model was built. SweetLiking at three months of age was included to account for individual differences in sweetness liking that may occur during the milk feeding period before differences in sweetness exposure begin to increase. It was assessed whether SweetLiking at three months predicts SweetLiking at six months, whether SweetLiking at six months predicts SweetLiking at twelve months and whether SweetExposure at three to six months (respectively 10-12 months) predicts SweetLiking at six months (respectively 12 months).

Results

Subjects

Characteristics of the included mother-infant pairs are displayed in Table 1. The infants were on average exclusively breastfed for around three months and more than half of the infants were male (54%). The majority of mothers (89%) had a high or medium level of education. The calculated average IR was 0.56 ± 0.12 at three months, 0.58 ± 0.13 at six months, and 0.58 ± 0.18 at twelve months of age. The calculated average LRE was 0.53 ± 0.09 at three months, 0.54 ± 0.08 at six months, and 0.52 ± 0.10 at twelve months of age (Fig. 1). Hence, on average, the sweet solution was preferred over water at all time points as all the IR and LRE values were above 0. Liking Ratio (rated by the experimenter) at three, six, and twelve months.

SweetExposure

The daily exposure to sweetness increased significantly from three to six months to ten to twelve months as confirmed by the paired samples t-test [t(246) = 28.64, p<0.001, CI 95% (7.43; 8.53)]. Whereas SweetExposure was on average at 7.07 ± 2.53 during the three to six months period, it was double as high during the ten to twelve months period with an average SweetExposure of 14.71 ± 3.87 (Fig. 2). The Levene paired test showed unequal variances with more variability in sweetness exposure in the ten to twelve months period compared to the three to six months period [t(246)=6.16, p<0.001, CI 95% (0.80; 1.55)]. Neither at six months nor at twelve months, was SweetLiking (indicated by IR and LRE) associated with prior SweetExposure (Tables 2 &3). No relationship was found in the bivariate analyses between SweetLiking at six months and SweetExposure at three to six months of age. This was true for both parameters measuring SweetLiking: IR [β (95% CI): 0.006 (-0.002; 0.013)] and LRE [β (95% CI): -0.002 (-0.007; 0.003)]. This finding was supported when controlling for the duration of exclusive breastfeeding and the mothers' educational level, as well as when only including individuals for whom we had complete data on all variables (SweetExposure three to six months, SweetExposure ten to twelve months, SweetLiking six months, SweetLiking twelve months; Table 2). Moreover, the association between SweetExposure at 10-12 months and SweetLiking at 12 months was not significant: neither for the IR [β (95% CI): -0.002 (-0.008; 0.005)] nor for the LRE [β (95% CI): -0.002 (-0.006; 0.001)]. Again, this finding was supported when controlling for the duration of exclusive breastfeeding and the mothers' educational level, as well as when only including individuals for whom we had complete data on SweetExposure and SweetLiking at three to six and ten to twelve months (Table 3).

Structural Equation Model (SEM)

The preliminary measurement model showed good fit [CFI=0.99, TLI=0.98, RMSEA=0.03 (95% CI (0.00, 0.06))], with high loadings (0.56 to 0.86, all p<0.001) and low correlations between latent variables (0.07 to 0.34). The structural model also showed good fit (CFI=0.97, TLI=0.96, RMSEA=0.04), and indicated that SweetLiking at six months predicted SweetLiking at twelve months (standardized estimate=0.28, p = 0.01) (Fig. 3). However, SweetLiking at three months did not predict SweetLiking at six months (standardized estimate=0.11, p = 0.41). In this model, no effect of SweetExposure on SweetLiking was found, as previously concluded from the regression analyses.

Figure 3. SEM regression model and standardized parameters (n=319) showing the relationship between the degree of sweetness liking at three, six, and twelve months, as well as the associations between sweetness exposure at three to six months and the degree of sweetness liking at six months; and the relationship between sweetness exposure at ten to twelve months and the degree of sweetness liking at twelve months. IR: Ingestion ratio; LRE: Liking ratio rated by the experimenter; LRP: Liking ratio rated by the parent.

Discussion

To the authors' knowledge, this is the first study that investigated the relationship between exposure to sweet taste estimated over the whole diet and the degree of sweetness liking in the first year of life, during two major shifts in feeding mode (three to six months -beginning of complementary feeding; ten to twelve months -transition to the family table). In contrast to our hypothesis, no association between infant's exposure to sweet taste in the diet and their degree of sweetness liking was found, neither at the beginning of complementary feeding at six months nor the transition to the family table at twelve months. Even though, as expected, the exposure to sweet tastes increased from three to six months to ten to twelve months, the degree of sweetness liking did not change between these periods. In line with our hypothesis, sweetness liking at three months did not predict sweetness liking at six months. However, sweetness liking at six months did predict sweetness liking at twelve months.

Sweet taste exposure in infancy

Most birth cohorts focused on nutrition tend to characterize dietary macro-and micronutrient intake instead of taste exposure (39; 40) . Besides other papers investigating the OPALINE cohort, only one recent study focused on taste exposure [START_REF] Nguyen | Dietary taste patterns in early childhood: the Generation R Study[END_REF] . However, the researchers used a different method than the one used in this study and investigated a slightly older cohort (one to two years) than the age group we focused on. Hence, the level of sweetness exposure in the present study is difficult to compare to other studies for three to twelve months old infants. However, to give a reference, the level of sweetness exposure at three to six months in our study corresponds to a daily average intake of four bottles of infant formula, including one bottle with infant dry sweetened cereals. The level of sweetness exposure at 10-12 months corresponds to three bottles of infant formula, including one with dry sweetened cereals, a vegetable, meat, and starch puree with added fat, two fruit purees, and a fruit-flavored yogurt [START_REF] Yuan | Infant dietary exposures to sweetness and fattiness increase during the first year of life and are associated with feeding practices[END_REF] . In the OPALINE sample, fruits and vegetables were most often introduced first, followed by dairy products, cereal, meats, dessert, starchy foods, fish, and biscuits [START_REF] Lange | Maternal feeding practices during the first year and their impact on infants' acceptance of complementary food[END_REF] . This is comparable with what was found by the French national survey on food consumption of children up until the age of three: Besides milk, the first consumed foods were fruits, vegetables, and dairy products, followed by cereals, potatoes, meat, fish, rice, and pasta [START_REF] Chouraqui | The French national survey on food consumption of children under 3 years of age-Nutri-Bébé 2013: design, methodology, population sampling and feeding practices[END_REF] .

Relationship between sweet food consumption and sweetness liking

Previous studies draw contradictory conclusions regarding the link between exposure to sweetness, estimated by the consumption of sweet foods, and sweetness preference in childhood. On the one hand, when measuring sweetness preference using the same sweet food or drink with which sweetness exposure was estimated, the literature suggests a positive relationship between sweetness exposure and liking (16; 17; 43) . This was true for six-month-old infants who showed a heightened preference for sweetened water after regularly being fed with it during their first six months of life compared to children without regular consumption of sweetened water [START_REF] Beauchamp | Dietary experience and sweet taste preference in human infants[END_REF] . This positive relationship was also found in five-year-old children who liked a sweetened fruitflavored drink more after being exposed to it for eight days [START_REF] Liem | Sweet and sour preferences in young children and adults: role of repeated exposure[END_REF] . Those findings contradict the present results where the association between sweetness exposure and the degree of sweetness liking over the first year of life could not be proven. This may be explained by the fact that in this study the relationship between sweetness exposure and liking was analyzed by looking at the overall dietary exposure to sweet taste in the diet, whereas the papers above looked at the change in sweetness liking for the same sweet beverage the child had been exposed to. Previous studies demonstrated that the association between sweetness exposure and liking is not as straightforward when exposure and liking are tested with different mediums. For example, Beauchamp and Moran [START_REF] Beauchamp | Acceptance of sweet and salty tastes in 2-yearold children[END_REF] could not replicate the positive relationship between sweetness exposure (through sweetened water) at six months and liking when testing sweetness liking with a fruit-flavored drink instead of sweetened water at two years. However, when sweetness liking was assessed with sweetened water at this age, the association was still positive [START_REF] Beauchamp | Acceptance of sweet and salty tastes in 2-yearold children[END_REF] . Furthermore, a systematic relationship between consuming sweet products and sweetness liking in seven-to-twelve-year-old children could not be proven, as sweetness liking was only related to candy and snack consumption but not to consumption of sweet drinks, dairy, fruit, cereal, or added sugar consumption [START_REF] Divert | Relation between sweet food consumption and liking for sweet taste in French children[END_REF] . This suggests that the association between exposure and liking is largely stimulusspecific and cannot be generalized to the whole diet. As children learn through repeated exposure which foods should taste sweet [START_REF] Drewnowski | Sweetness and food preference[END_REF] , children may get used to the taste of the specific sweetened beverages which resulted in an increased liking as previously shown (16; 17; 43) . However, this is not associated with a general increase in children's preference for sweetness. This does not undermine the importance of food and flavor experiences, in particular during the first years of life, in the shaping of food preferences, but emphasizes the fact that this learning is food-specific [START_REF] Nicklaus | Eating and Drinking in Childhood[END_REF] .

No relationship between sweetness exposure and sweetness liking: Possible interpretation

We hypothesized that higher exposure to sweet tastes during infants' first year of life may result in a higher degree of sweetness liking. However, the results did not confirm this hypothesis. Apart from the possibility that this hypothesis is wrong, other aspects must be considered to interpret these findings. First, individual variations in the degree of sweetness liking at this early age may still be a result of genotypes, and not of environmental influences such as dietary exposures. This assumption is supported by a study by Mennella et al. [START_REF] Mennella | Genetic and environmental determinants of bitter perception and sweet preferences[END_REF] that found that in five-to-ten-year old children, the TAS2R38 taste gene locus was related to sucrose preferences and the liking of sweettasting foods and drinks; which was much less obvious in their mothers. Nonetheless, following this line of reasoning, sweetness liking at three months should have predicted sweetness liking at six months in our sample, yet it did not, even though sweetness was already preferred over water at three months. However, sweetness liking at six months did predict sweetness liking at twelve months. This result may be due to the fact that infants' control over swallowing behavior at three months of age was still too limited to reflect individual differences well enough, although it appeared adequate to reflect a preference for the sweetened water over plain water.

Second, sweetness exposure in this study sample may not have been varied enough to detect an effect on the degree of sweetness liking. This may be especially true because the parents in our study started to complementary feed their infants on average at the age of five and a half months, with little variability. Hence, infants may have been exposed to comparable sweetness intensity levels for most of the time in the first period due to exclusive milk feeding. In the second period when sweetness exposure varied more between infants, the duration of the exposure period (between 10 and 12 months) may have been too short, or the sweet taste intensities may not have been strong enough to detect an effect on sweetness liking. Also, Schwartz et al. [START_REF] Schwartz | À quelles saveurs les nourrissons sont-ils exposés dans la première année de vie?[END_REF] found that during the first 12 months, the taste intensities of the foods children were exposed to were relatively low, even though children mainly experienced sweet taste during the milk feeding period with an even increased sweetness exposure during the first year. Because in this study only exposure frequency to sweet tastes was assessed, but not how much of the sweet-tasting foods were consumed in each eating occasion, we cannot estimate the proportion of the overall energy intake coming from sweet-tasting foods. Hence, it must be considered that the overall sweetness intensity the infant was exposed to in the first 12 months of life was not strong enough to detect an effect on sweetness liking.

Third, the effect of sweetness exposure in infancy may affect the degree of sweetness liking only later in childhood, after a longer period of exposure to sweet-tasting foods.

Liem and Mennella [START_REF] Liem | Sweet and sour preferences during childhood: role of early experiences[END_REF] found that children from parents who regularly added sugar to the child's diet between zero and twelve months were more likely to prefer apple juice with added sugar at four to seven years. In line with this result, a diet rich in added sugars during the first 12 months was related to a higher degree of sweetness liking at three to seven years [START_REF] Foterek | Commercial complementary food consumption is prospectively associated with added sugar intake in childhood[END_REF] . In the present study, the ingestion ratio during the sweetness liking test in the twelfth month varied more between children than in the third and sixth months. In combination with the increased exposure to sweetness in the second period (10-12 months), this may hint towards the possibility of a slight impact of sweetness exposure on the degree of sweetness liking, although this link was not detected in our analyses.

Lastly, growing evidence demonstrates that hedonic responses to sweet taste differ between individuals due to sweet-liking phenotypes [START_REF] Armitage | Understanding sweet-liking phenotypes and their implications for obesity: Narrative review and future directions[END_REF] . It was found that children can be classified as either sweet likers or sweet dislikers [START_REF] Garneau | Sweet liker status in children and adults: Consequences for beverage intake in adults[END_REF] . Hence, children in our sample may also be distributed along this continuum but we did not observe bimodality in the distribution as evidenced in Figure 1. The unequal variances regarding the IR may be a hint towards the emergence of such a difference in sweetness liking in our sample. However, we expected that sweetness exposure would lead to a similar effect across the continuum of children who rather like or dislike sweetness.

Strengths, limitations and conclusion

Despite the care which was taken to account for uncontrolled factors, our study entails some limitations. First, in our study, only consumption frequencies were recorded, not portion sizes. Hence, infants with the same exposure frequencies of sweet-tasting foods but different portion sizes were assigned the same level of sweetness exposure. Thus, we cannot account for the contribution of portion size to sweetness exposure. Further, the methodological choice to measure sweetness liking may have undermined the liking value, because some infants may have not been used to the taste of sweetened water, since they were mostly fed milk during the first months of life. However, lactose was chosen to create the sweetened water solution as it is a taste infants were likely to have experienced, in particular in breast, or formula milk [START_REF] Schwartz | Developmental changes in the acceptance of the five basic tastes in the first year of life[END_REF] . In addition to that, sweetness exposure was estimated based on the food records mothers filled out. We cannot assure that mothers have filled in the food records truthfully. Further, when a sweet food (e.g. applesauce) was consumed mixed with a sour food (e.g. yogurt), the sourness of the sour food may have reduced the perceived sweetness of the sweet food, but this was not accounted for in our calculation which only reflects the average sweetness of a mixture. Lastly, similar to other cohort studies, lower educated families were under-represented in our sample as almost 90% of mothers had a high or medium level of education. A higher maternal education level is generally associated with better diet quality in mothers and children and was previously associated with higher exposure to neutral tastes in children aged one and two (41; 45; 46) . Following that, conclusions from our study are less applicable to children of lowereducated mothers. It should be mentioned that the subjective sweetness liking experience cannot be measured in a purely objective way, but only relative sweetness liking. Therefore, in our study, we chose to measure the degree of sweetness liking as a relative liking of a sweet solution (water+lactose) compared to a neutral stimulus (water). However, a strength of our study is that three proxies for relative liking were included in our analyses (IR, LRE, and LRP) to get a broader picture of relative sweetness liking instead of relative consumption only. Besides the limitations, our study contains multiple strengths. First, infants' overall exposure to sweetness was taken into account instead of focusing on the macro-nutrient intake only. For that, the overall diet was included and not only exposure to particular sweet-tasting foods.

Another strength is the longitudinal design which allowed examination of sweetness exposure and liking at multiple time points. Further, the fact that sweetness exposure was estimated based on twelve monthly seven-day food records gave an overall impression of infants' exposure to sweetness over the first year instead of only delivering a snapshot of sweetness exposure at a single time point. As sweetness exposure was averaged based on the monthly food records for each of the periods, the impact of outliers (e.g. due to special occasions such as birthdays) regarding the intake of sweet-tasting foods was minimized.

In conclusion, this study did not show a relationship between sweetness exposure and the degree of sweetness liking in infants throughout observations from the third until the twelfth month of life. Although sweetness exposure increased from the first (three to six months) to the second period (ten to twelve months), the degree of sweetness liking did not change. This was contrary to what was expected. Based on the findings, we hypothesize that, at such early age, inter-individual variations in sweetness liking may rather occur due to differences in genotypes, especially when variations in sweetness exposure between children are limited. The impact of high exposure to sweet-tasting foods in the first 12 months of life on the degree of sweetness liking later in life should be investigated longitudinally including time points in childhood up until adolescence to understand the impact of sweetness exposure on establishing (healthy) eating habits early on. Longitudinal research has shown that eating behavior learned in infancy impacts eating behavior in childhood [START_REF] Maier-Nöth | The lasting influences of early food-related variety experience: a longitudinal study of vegetable acceptance from 5 months to 6 years in two populations[END_REF] . Whether this is also true for early exposure to sweet taste remains unclear. Future studies should aim for more variability in the study sample with participants representing the whole sociodemographic continuum, to represent a variety of feeding habits, and should also consider the consumed quantities of sweet products in addition to the frequencies.

  Executive summary .................................................................................................................. Submitted paper .......................................................................................................................

  IR =(Grams Sweet Bottle 1 + Grams Sweet Bottle 2) (Grams Sweet Bottle 1 + Grams Sweet Bottle 2 + Grams Water Bottle 1 + Grams Water Bottle 2)Liking RatioFor the second and third sweetness liking indicators, the experimenters and parents rated the child's reaction to each of the four bottles on a 5-point-Likert scale (1 -strong rejection; 2 -slight rejection; 3 -neutral; 4 -slight acceptance; 5-strong acceptance). The child's overall behavior, including facial expressions, was taken into account. As a result, each of the four bottles was assigned a score between one and five. Based on those scores, the experimenter liking ratio (LRE) and parent liking ratio (LRP) were calculated similarly to the IR by summing the scores of the two sweet solutions and dividing them by the sum of all four scores. Again, ratios between zero and one were possible.LRE/LRP = (Score Sweet Bottle 1 + Score Sweet Bottle 2) (Score Sweet Bottle 1 + Score Sweet Bottle 2 + Score Water Bottle 1 + Score Water Bottle 2)

125 ( 39 )

 39 159 (50) ²Observatoire des Préférences Alimentaires du Nourrisson et de l'Enfant (Observatory of Infant and Child Food Preferences) ³Level of education: Low = High school diploma or less; Middle = Secondary education or undergraduate education; High = University or higher vocational training Sweetness liking at three, six and twelve months

5 .

 5 Paired samples t-tests confirmed that the IR did not change significantly between three and six months [t(136) = 1.14, p = 0.26, CI 95% (-0.01; 0.05)], between six and twelve months [t(163) = 1.14, p = 0.26, CI 95% (-0.01; 0.05)], and neither between three and twelve months [t(121) = 1.59, p = 0.11, CI 95% (-0.01; 0.06)]. The Levene paired test showed unequal variances with more variability regarding the IR in the twelfth month compared to the third month [t(121)=2.88, p=0.005, CI 95% (0.01; 0.06)] or sixth month [t(163)=3.80, p<0.001, CI 95% (0.02; 0.06)]. However, variances in the IR did not differ between the third and sixth month [t(136)=0.08, p=0.94, CI 95% (-0.02; 0.02)]. Similarly, paired samples t-tests confirmed that the LRE did not change significantly between three and six months [t(136) = -0.57, p = 0.57, CI 95% (-0.02; 0.01)], between six and twelve months [t(163) = -0.82, p = 0.41, CI 95% (-0.02; 0.01)], and between three and twelve months [t(121) = -0.73, p = 0.46, CI 95% (-0.03; 0.01)]. The Levene paired test indicated that the variances did not differ significantly regarding the LRE between the twelfth and third month [t(121)=-1.22, p=0.23, CI 95% (-0.03; 0.01)], between the twelfth and sixth month [t(163)=0.98, p=0.33, CI 95% (-0.01; 0.02)], or between the third and sixth month [t(136)=1.42, p=0.16, CI 95% (0.00; 0.02)].

Figure 1 .

 1 Figure 1. Children's degree of Sweetness Liking measured by the Ingestion Ratio and

Figure 2 .

 2 Figure 2. Infants' exposure to sweetness during the three to six months and the ten to twelve months periods

Table 1 :

 1 Mother and infant characteristics, OPALINE² (n=319)

	Infant characteristics
	Sex [n(%)]	Male	172 (54)
		Female	147 (46)
			Mean	SD
	Weight (kg)	At birth	3.25	0.48
		At 3 months At 6 months	5.78	0.72
		At 12 months	7.47	0.78
			9.55	0.96
	Length (cm)	At birth	49.52	4.55
		At 3 months At 6 months	60.08	2.74
		At 12 months	66.71	2.52
			74.88	2.66
	Duration of exclusive breastfeeding (months)		2.97	1.93
	Age at beginning of complementary feeding		5.46	0.84
	(months)
	Maternal characteristics		Mean	SD
	Age at delivery (years)		30.75	4.58
	Pre-pregnancy BMI (kg/m²)		22.14	3.43
	Level of education³ [n(%)]	Low		33 (11)
		Middle
		High

Table 2 :

 2 Regression models investigating the influence of sweetness exposure at three to six months on the degree of sweetness liking at six months for two sweetness liking outcome variables: Ingestion Ratio & Liking Ratio (rated by the experimenter)

					Ingestion Ratio				Liking Ratio Experimenter
		N	β	SE*	CI 95%	RSD	p	β	SE*	CI 95 %	RSD †	p
						†
	Model	18	.006 .004 -.002; .013 .128 .14	-	.002 -.007; .003 .083	.40
	1	2						.002
	Model	15	.003 .004 -.005; .011 .129 .41	-	.003 -.009; .002 .086	.18
	2	8						.004
	Model	15	.006 .004 -.002; .015 .129 .13	-	.003 -.005; .005 .079	.96
	3	0						.001

Model 1: Bivariate model [Outcome variable: SweetLiking at six months (Ingestion Ratio or Liking Ratio Experimenter); Independent variable: SweetExposure at three to six months], n=182 Model 2: Multiple linear regression model [Outcome variable: SweetLiking at six months (Ingestion Ratio or Liking Ratio Experimenter); Independent variables: SweetExposure at three to six months + duration of exclusive breastfeeding + maternal education level], n=158 Model 3: Bivariate model on complete cases (only individuals with complete information about exposure and liking at three to six and ten to twelve months) [Outcome variable: SweetLiking at six months (Ingestion Ratio or Liking Ratio Experimenter); Independent variable: SweetExposure at three to six months], n=150 * Standard error † Residual Standard error

Table 3 :

 3 Regression models investigating the influence of sweetness exposure at 10-12 months on the degree of sweetness liking at 12 months for two sweetness liking outcome variables: Ingestion Ratio & Liking Ratio (rated by the experimenter)

					Ingestion Ratio				Liking Ratio Experimenter
		N	β	SE*	CI 95%	RSD	p	β	SE*	CI 95 %	RSD †	p
						†
	Model	19	-	.003 -.008; .005 .176 .61	-	.002 -.006; .001 .100	.23
	1	7	.002					.002
	Model	16	-	.004 -.009; .005 .178 .57	-	.002 -.007; .001 .102	.10
	2	7	.002					.003
	Model	15	-	.004 -.010; .004 .171 .42	-	.002 -.006; .001 .092	.20
	3	0	.003					.002

Model 1: Bivariate model [Outcome variable: SweetLiking at 12 months (Ingestion Ratio or Liking Ratio Experimenter); Independent variable: SweetExposure at 10-12 months], n=197 Model 2: Multiple linear regression model [Outcome variable: SweetLiking at 12 months (Ingestion Ratio or Liking Ratio Experimenter); Independent variables: SweetExposure at 10-12 months + duration of exclusive breastfeeding + maternal education level], n=167 Model 3: Bivariate model on complete cases (only individuals with complete information about exposure and liking at three to six and ten to twelve months) [Outcome variable: SweetLiking at 12 months (Ingestion Ratio or Liking Ratio Experimenter); Independent variable: SweetExposure at 10-12 months], n=150 * Standard error † Residual Standard error

Acknowledgements

The authors wish to thank the children and parents who took part in the present study, and E. Szleper, V. Feyen and J. Pierard for data collection; F. Durey for her technical support. We are grateful to the OPALINE team for its general support, in particular to C. Laval, C. Lange (ChemoSens), and V. Boggio. Financial support This work was supported by the European Union's horizon 2020 research and innovation program under the Edulia project, a Marie Sklodowska-Curie Innovative Training Network program [grant agreement No. 764985], and by the financial support of the Regional Council of Burgundy, IFR92, PRNH-INRA-INSERM and the Agence Nationale de la Recherche (ANR; The French National Research Agency) under the 'Programme National de Recherche en Alimentation et Nutrition Humaine' (project ANR-06-PNRA-028, OPALINE). The present study, labelled by Vitagora® (The Taste, Nutrition and Health Innovation Pole), was supported by grants from Blédina, Nestlé, Symrise, Benjamin Delessert and Cedus. Funders were not involved in any way in the interpretation or analysis of the data.


Vincent Calcagno

; David

; Jarne

François ; Massol

Coevolution of species colonization rates controls food-chain length in spatially structured food webs

Keywords: dispersal, eco-evolutionary dynamics, habitat destruction, metacommunity, patch occupancy model

The complexity of food webs and how it depends on environmental variables is a longstanding question in ecology. Food-chain length depends on many factors, such as productive space, disturbance and spatial processes. It is not clear though how food-chain length should vary with adaptive evolutionary changes of the constitutive species. Assuming that each trophic level is subject to a competition-colonization trade-off, we model the adaptive evolution of their colonization rates and its consequences on equilibrium occupancies and food-chain length. When colonization rates are allowed to evolve, longer food chains can persist. Extinction, perturbation and habitat loss all affect the evolutionarystable colonization rates, but trade-off strength (costs of dispersal) has a major role: weaker trade-offs yield longer chains. Our results suggest a strong link between within-trophic level competition, spatial occupancies and food-chain length. Although these eco-evo dynamics partly alleviate the constraint on food-chain length in metacommunities, we show it is no magic bullet: the highest, most vulnerable, trophic levels are also those that least benefit from evolution. Our model generates qualitative predictions regarding how trait evolution affects the response of communities to disturbance and habitat loss. This highlights the importance of eco-evolutionary dynamics at metacommunity level in determining food-chain length.

Introduction

An important puzzle in ecology is how food web topology, and in particular food-chain length, is determined [START_REF] Hutchinson | Homage to Santa Rosalia, or why are there so many kinds of animals[END_REF][START_REF] Pimm | Food Webs[END_REF][START_REF] May | The structure of food webs[END_REF][START_REF] Cohen | Trophic links of community food webs[END_REF][START_REF] Stenseth | The structure of food webs predicted from optimal food selection models: an alternative to Pimm's stability hypothesis[END_REF][START_REF] Cohen | Dynamic basis of food web organization[END_REF][START_REF] Williams | Simple rules yield complex food webs[END_REF][START_REF] Williams | Limits to trophic levels and omnivory in complex food webs: Theory and data[END_REF]. Food-chain length is a measure of the number of feeding links between resources and top predators (e.g. [START_REF] Sabo | Food chains in freshwaters[END_REF]. Ecological theory has long tried to understand what limits this length [START_REF] Hutchinson | Homage to Santa Rosalia, or why are there so many kinds of animals[END_REF][START_REF] May | Will a large complex system be stable?[END_REF][START_REF] Hastings | Length and evolutionary stability of food chains[END_REF][START_REF] Pimm | Food Webs[END_REF][START_REF] Menge | Community regulation: variation in disturbance, competition, and predation in relation to environmental stress and recruitment[END_REF]. For instance, the energetic constraint hypothesis [START_REF] Hutchinson | Homage to Santa Rosalia, or why are there so many kinds of animals[END_REF] invokes imperfect transfers of energy and resources along food chains, the dynamics constraint hypothesis (May, 1972, Pimm and[START_REF] Pimm | Number of trophic levels in ecological communities[END_REF] argues that long food chains are more vulnerable to perturbation than short ones, and the community area hypothesis combines the diversity-area relationship obtained by the theory of island biogeography [START_REF] Macarthur | The Theory of Island Biogeography[END_REF] with the link scaling law [START_REF] Cohen | Trophic links of community food webs[END_REF] to predict a concave increase in food-chain length with habitat area [START_REF] Cohen | Community area and food-chain length: theoretical predictions[END_REF]. Recent empirical studies have identified three major determinants of food-chain length: productive space (i.e. ecosystem size × productivity), disturbance, and ecosystem size [START_REF] Post | The long and short of food-chain length[END_REF]. While confirming the roles of resource limitation and perturbation, these results argue against single explanations, and also stress the need to incorporate space in theoretical models. Indeed, despite ample evidence that food-chain length correlates with habitat area or ecosystem size [START_REF] Schoener | Food webs from the small to the large[END_REF][START_REF] Cohen | Community area and food-chain length: theoretical predictions[END_REF], Post et al., 2000[START_REF] Takimoto | Ecosystem size, but not disturbance, determines food-chain length on islands of the Bahamas[END_REF], spatial processes are still understudied in theoretical models of food webs [START_REF] Holt | Food webs in space: On the interplay of dynamic instability and spatial processes[END_REF][START_REF] Amarasekare | Spatial dynamics of foodwebs[END_REF]. [START_REF] Calcagno | Constraints on food chain length arising from regional metacommunity dynamics[END_REF] extended the model of [START_REF] Holt | Food webs in space: On the interplay of dynamic instability and spatial processes[END_REF] to provide predictions under a range of conditions encompassing top-down effects of any sorts and habitat selection effects, while [START_REF] Pillai | Metacommunity theory explains the emergence of food web complexity[END_REF] studied the effect of colonization rates on the complexity of food webs at the metacommunity level. More recently, [START_REF] Wang | Metapopulation capacity determines food chain length in fragmented landscapes[END_REF] reanalyzed a similar ecological model of spatial food chains in order to study how metacommunity dynamics should influence maximum food-chain length. They rendered the model spatially realistic and provided some empirical support for its predictions in a butterflyparasitoid system. The spatial structure of populations, on the other hand, has inspired one of the most prolific research lines in evolutionary biology, namely the evolution of dispersal (for reviews, [START_REF] Bowler | Causes and consequences of animal dispersal strategies: relating individual behaviour to spatial dynamics[END_REF][START_REF] Ronce | How does it feel to be like a rolling stone? Ten questions about dispersal evolution[END_REF][START_REF] Duputié | An empiricist's guide to theoretical predictions on the evolution of dispersal[END_REF]. Indeed, there has been an early realization that spatial structure, beyond its population dynamical consequences, also imposed strong selection pressures, and that the key parameter in this context, the colonization, dispersal, or migration rate, could be shaped by evolutionary adaptation. A range of selective forces should act on the dispersal rate, and determine its evolutionarily stable (ES) value, depending among others on patch size, connectivity, spatio-temporal environmental variability and dispersal costs. In the case of metapopulation occupancy models, following the seminal work of [START_REF] Levins | Some demographic and genetic consequences of environmental heterogeneity for biological control[END_REF], [START_REF] Slatkin | Competition and regional coexistence[END_REF], [START_REF] Hastings | Disturbance, coexistence, history, and competition for space[END_REF], [START_REF] Hanski | Coexistence of competitors in patchy environment[END_REF], [START_REF] Tilman | Competition and biodiversity in spatially structured habitats[END_REF] and others, one can translate a purely ecological statement of the problem ("what is the occupancy of competing species when they obey a competitioncolonization trade-off?", [START_REF] Calcagno | Coexistence in a metacommunity: the competition-colonization trade-off is not dead[END_REF]) into an evolutionary question ("how should this competition-colonization trade-off drive the evolution of colonization rates of coexisting species?", Aubrée et al. 2020), and thence investigate the eco-evolutionary dynamics of adaptation of colonization rates in a metacommunity. The purpose of this article is to connect these two important aspects of spatially structured communities, namely the ecological limit they impose on food-chain length on the one hand, and the evolutionary dynamics of dispersal on the other hand, and to determine how they could interact and influence one another. In [START_REF] Calcagno | Constraints on food chain length arising from regional metacommunity dynamics[END_REF], two distinct constraints on food-chain length arising from metacommunity structure were identified. First, finite colonization rates limit predator occupancy to a subset of prey-occupied sites. Second, extinction rates accumulate along food chains. Both processes thus concur to decrease maximal and average food-chain length in metacommunities. However, in an eco-evolutionary dynamics framework, the evolution of colonization rates, in response to competition within trophic levels, will affect the first constraint (by either increasing or decreasing colonization rates), and hence will likely change trophic level occupancies and food-chain length. Here, we investigate this question theoretically by plugging an adaptive dynamics-based model of colonization evolution into the food-chain metacommunity model of [START_REF] Calcagno | Constraints on food chain length arising from regional metacommunity dynamics[END_REF]. This model allows us to assess how habitat availability and extinction and perturbation rates select for colonization rates, and how this selection changes prediction between a metacommunity that evolves and one that does not. The parameters of the competition-colonization trade-off provide us with another lever quantifying the strength of intra-trophic level competition. Ultimately, this model allows us to predict how food-chain length changes with environmental variables in response to selection on colonization rates.

Model and Methods

Spatial food chain model

We use a model of spatial food chain identical to that in [START_REF] Calcagno | Constraints on food chain length arising from regional metacommunity dynamics[END_REF], and very close to that of [START_REF] Wang | Metapopulation capacity determines food chain length in fragmented landscapes[END_REF]. It is best formulated in terms of the dynamics of i q , the fraction of patches that contain trophic level i, and thus all the lower trophic levels too, regardless of the presence/absence of upper trophic levels (Fig. 1). These dynamics can be expressed in a way similar to Levins' classical metapopulation model:

  1 () i i i i i i i dq c q q q e q dt         (1)
where for the first trophic level (i=1), 0 qh  is the proportion of habitat (patches) available (level 0 is therefore not counted in food-chain length). As a simple example, a fully developed set of equations is described in Supplementary Material for a two-level trophic chain. This equation assumes that patches experience perturbation at rate µ, which causes all trophic levels to disappear simultaneously (perturbation-driven extinction). An additional fraction of extinctions, called the effective extinction rate i e  , is experienced independently by each trophic level, and incorporates a basal extinction rate e, potentially modified by bottom-up and top-down effects. Bottom-up effects reflect the fact that if a given trophic level goes extinct in a patch, all upper trophic levels must go extinct too. Top-down effects represent how the presence of upper trophic levels may increase the extinction rate of the focal trophic level (parameter TD e ), for instance through a reduction of local population size.

We assume that in the fraction of sites that contain the i+1 trophic level (

1 / ii qq  
) top-down effects increase the extinction rate by a constant. Applying this rule to all trophic levels, this yields i e  to be expressed as 1 ( 1)( ) /

TD TD i i e i e e e q q

    

(see [START_REF] Calcagno | Constraints on food chain length arising from regional metacommunity dynamics[END_REF][START_REF] Wang | Metapopulation capacity determines food chain length in fragmented landscapes[END_REF].

Evolutionary dynamics of colonization rate

The above model has been thoroughly studied for arbitrary, fixed, colonization rates of the different trophic levels [START_REF] Calcagno | Constraints on food chain length arising from regional metacommunity dynamics[END_REF]. In this article, we further let colonization rate values evolve under the effect of natural selection (the basal extinction rates and the strength of top-down effects are fixed). Metapopulation structure is known to impose strong selection pressures on dispersal, and hence on the colonization rate [START_REF] Duputié | An empiricist's guide to theoretical predictions on the evolution of dispersal[END_REF]. Dispersal is selected for by the presence of empty available patches [START_REF] Comins | Evolutionarily stable dispersal strategies[END_REF], and, for low enough population sizes, kin competition. On the other hand, dispersal is counter-selected by competitive trade-offs, i.e. the fact that high dispersal rates come at the expense of local growth and/or competitive strength, which is the case when dispersal is costly (Supplementary Material). We here use a simple representation of these evolutionary dynamics, that can be derived from competition-colonization trade-offs [START_REF] Calcagno | Diversity spurs diversification in ecological communities[END_REF], or alternatively from spatially structured population models (Supplementary Material). It incorporates the three selective forces listed above. The derivation yields the following equation for the dynamics of i c :

  10 2 i G i i i i dc V q q c q dt         
(2) is a parameter representing the genetic variance in colonization (from a quantitative genetics perspective, Lande 1979; see Dieckmann & Law 1996 for an alternative interpretation). The other two evolutionary parameters describe the strength of the trade-off between local competitiveness and colonization (Supplementary Material).  is the probability that immigrants replace residents when they have the same colonization rate (between 0 and 1), and 0  is the (negative) slope quantifying how much increasing colonization rate comes at the expense of decreased local competitiveness (i.e. there is a cost of dispersal). The first two terms in the brackets represent positive selection for dispersal caused by the presence of empty available patches (fraction As shown in Supplementary Material, eq. ( 2) admits a unique positive equilibrium in the cases of interest; this singular strategy is always convergence stable, and is an evolutionarily stable strategy (ESS) provided one condition is met by the trade-off function.

1 ii qq   ),
The ESS is attained when the selective forces for and against colonization cancel out.

Computing equilibria and maximum food-chain length

The dynamics of (1) can be used directly, with fixed colonization rates, to compute foodchain length in the absence of evolution (Calcagno et al. 2010;[START_REF] Wang | Metapopulation capacity determines food chain length in fragmented landscapes[END_REF]). To introduce evolution, we study the coupled dynamics of eq. ( 1) and (2), using the common simplification that eq. (1) was at equilibrium, i.e. that metapopulation dynamics was faster than evolutionary dynamics. Given the nature of the ecological and evolutionary attractors, the assumption is not expected to have important consequences [START_REF] Sanchez | Two-time scales in spatially structured models of population dynamics: a semigroup approach[END_REF]. For numerical examples with small numbers of trophic levels, we numerically integrated eq. ( 2) through time, keeping eq. ( 1) at equilibrium. For larger numbers of trophic levels and to compute maximum food-chain length, we assumed eq. ( 2) was at equilibrium (ESS), and implemented an iterative algorithm allowing to jointly solve eq. ( 1) and ( 2) (see Supplementary Material for details on the algorithm). Using this algorithm, we computed the maximum food-chain length, defined as the maximum number of trophic levels that can persist, where persistence is defined as having equilibrium occupancy greater than some small threshold level ϵ. In practice, we used 10 -3 , meaning that any trophic level should occupy at equilibrium at least one patch in one thousand in order to persist. In all figures, we used the following reference parameter values, unless stated otherwise or a parameter was systematically varied: , , , , .

Results

The evolution of dispersal in a spatial food chain

Fig. 2a-b presents results for the simplest possible case with only two trophic levels: one prey and one predator. In the figure, the basal extinction rate is gradually increased, causing the occupancy of the two trophic levels to decline, eventually going extinct one after the other. This basically mimics a continuous degradation of the environment which becomes harsher and harsher in time, as expected for example if the taxa are challenged by climate change or anthropisation. In the absence of evolution, the figure was parameterized in order to replicate the results of [START_REF] Wang | Metapopulation capacity determines food chain length in fragmented landscapes[END_REF]'s figure 1, thus including top-down control of the predator. In that case, our mathematical model faithfully reproduces these spatially realistic simulation results. Occupancy decreases markedly for the higher trophic level, which disappears at rather low extinction rates. The lower trophic level can maintain itself at much larger extinction rates. Due to the absence of trait dynamics, he colonization ratio (c/e) curves remain identical, until the higher trophic level disappears. Fig. 2c-h shows the impact of evolution on these results. Important quantitative and qualitative differences emerge. If evolution is slow (Fig. 1c-d), i.e. if parameter G V is low in eq. ( 2), evolution has little impact, and does not significantly "delay" the extinction of the predator (i.e. allows it to survive at higher values of e). Despite the predator evolving higher colonization rate when approaching extinction, eventually outpacing the increase in extinction rate (i.e. the colonization ratio c/e increases), this is not sufficient to prevent extinction. Following the predator's extinction however, the prey manages to persist despite the continuous increase in extinction rate, through a gradual increase in its colonization rate, and thus its colonization ratio c/e (Fig. 2d). Its occupancy declines, but the decline is mitigated by evolution, preventing extinction in the range of extinction rates considered. When evolution is faster, the predator can evolve sufficiently to delay its extinction (Fig. 2ef), and ultimately it also manages to escape extinction (albeit at low occupancy), just like the prey (Fig. 2g-h). Note that when the prey is not threatened with extinction, evolution in the prey can initially decrease its equilibrium occupancy, which is detrimental to predator persistence and counteracts the effects of evolution in the latter. From eq. ( 2), it can be seen that as a species approaches extinction, 0 i q  , i c always increases, acting to counteract extinction in all cases. However, comparing among trophic levels when they are on the verge of extinction ( i q  ), one can deduce that (i) the positive selection pressure caused by available habitat is lower for higher trophic levels (since 1 i q  decreases with i), and (ii) the negative selection pressure caused by local competition is stronger (since the colonization rate i c will generally be increasing with trophic position). Both effects make selection for larger colonization rates less efficient at higher trophic levels, providing a rationale for the results shown in Fig. 2. Overall, the evolution of colonization rate is beneficial to species persistence and thus foodchain length. Higher trophic levels will be selected for larger colonization rates than lower trophic levels. However, while all trophic levels are selected for higher colonization when approaching extinction, the intensity of the effect increases with trophic level, putting a higher evolutionary challenge on higher trophic levels. Furthermore, evolution at low trophic levels, when they are not threatened by extinction, is often detrimental to the persistence of upper trophic levels. For these two reasons, the beneficial effects of evolution are not as effective as one might expect to promote food-chain length. Basically, a fast evolution of predators is more efficient at maintaining the integrity of the food chain than a fast evolution of their prey; fast evolution in prey becomes necessary to maintain the system only in conditions where the prey would be threatened even in the absence of predation. Since results go in the same direction with fast and slow evolution and since assuming the ESS allows for much easier mathematical analysis and faster computing (Supplementary Material), in the following we will consider fast evolution only, and compare results with the "no evolution" scenario. Our results can be taken as giving an upper bound on the potential consequence of evolution on food-web dynamics, and capturing the two extreme possible situations, most actual situations probably falling somewhere in between them.

Maximum food-chain length under habitat degradation

We considered two forms of habitat degradation: (i) an increase in extinction rate (as in the previous section), and (ii) habitat destruction (i.e. a decrease in the fraction of available patches h; see equation [1]). As expected, increasing the extinction rate decreases the maximum food-chain length in the absence of evolution (Fig. 3a, see also [START_REF] Calcagno | Constraints on food chain length arising from regional metacommunity dynamics[END_REF][START_REF] Wang | Metapopulation capacity determines food chain length in fragmented landscapes[END_REF]). In the presence of evolution, however, the decline is much reduced. This is caused by an increase in the colonization rate of the upper trophic levels, which are selected for high values, even though this does not suffice to overcome the increasing extinction rate and the reduced occupancy of lower trophic levels (Fig. 3b). Note that, with or without evolution, the decline of maximum food-chain length with extinction rate always has an overall convex shape (rapid loss of many trophic levels followed by gradual loss of the remaining levels as extinction rate increases). When destroying habitat patches (reducing h), the same tendency is observed: evolution allows longer food chains to persist, compared to the reference case with no evolution (Fig. 3c). Note, however, that all trophic levels jointly evolve higher colonization rates, even the lower ones (Fig. 3d). This is because decreasing h affects the first trophic level just as strongly as the others, unlike increasing the extinction rate, which has a disproportionately stronger effect on the higher trophic levels. We also remark a qualitative impact of evolution: the decline of food-chain length with habitat destruction follows a convex sequence in the absence of evolution (first many losses, then more gradual losses), as it does when manipulating extinction rate. However, with evolution, increasing habitat destruction causes a concave declining sequence of food-chain length, with two trophic levels (out of four) going extinct when habitat destruction attains values of 0.8-1.0 (Fig. 3c).

The consequences of trade-off intensity

Increasing the intensity of the trade-off between colonization and local competitiveness (i.e. decreasing the basal competitiveness of immigrants  and/or making the slope 0  more negative) increases the negative selection pressure on the colonization rates (eq. 2), and should thus select for lower values of the latter. This should in turn negatively affect maximum food-chain length. This is indeed what we find (Fig. 4a), except that parameter  has very little impact. The latter result is consistent with [START_REF] Calcagno | Diversity spurs diversification in ecological communities[END_REF]. If the tradeoff slope is very shallow, colonization rates are free to evolve to quite high values, which allows much longer food chains to persist (Fig. 4b). Conversely, if the slope is very negative, selection favours low colonization values, especially at lower trophic levels, at the expense of population persistence and food-chain length (Fig. 4b). Costs of dispersal (trade-off intensity) are therefore a critical aspect for predicting the consequences of dispersal evolution for food-chain length.

The relationship between food-chain length and the proportion of empty patches

As demonstrated by [START_REF] Calcagno | Constraints on food chain length arising from regional metacommunity dynamics[END_REF] and [START_REF] Wang | Metapopulation capacity determines food chain length in fragmented landscapes[END_REF], in the absence of evolution, a negative correlation is expected between food-chain length and the fraction of empty patches. In other words, long food chains can be observed only if the total occupancy is high enough, as shown in Fig. 5. When varying the extinction rate e, we again find that evolution changes the pattern quantitatively, but not quantitatively (Fig. 5a-b). Things are different when the amount of habitat destruction varies: in this case, we observe concave negative relationships between food-chain length and the fraction of empty patches, but only with evolution. Without evolution, we observe the classic convex relationships observed otherwise or, at best, linear relationships (Fig. 5c-d). Such a qualitative difference in the shape of the relationships could be looked for in empirical or experimental data in order to infer the action of evolutionary dynamics. Interestingly, this difference is reminiscent of the one we have observed between food-chain length and habitat destruction (Fig. 3c-d). We checked that varying other parameters (specifically the perturbation rate µ) could not produce concave relationships, with or without evolution (Supplementary Fig. 2). It therefore seems that habitat destruction has a specific action that brings up a qualitative difference between evolved and unevolved food chains. Specifically, with evolution, relationships that are otherwise convex can be turned concave.

Discussion

As previous studies have shown, metacommunity dynamics impose an intrinsic constraint on food-chain length, and the persistence of long food-chains in spatially structured habitats thus requires specific conditions [START_REF] Holt | Food webs in space: On the interplay of dynamic instability and spatial processes[END_REF][START_REF] Calcagno | Constraints on food chain length arising from regional metacommunity dynamics[END_REF]. Higher trophic levels are vulnerable to extinction from multiple processes, and, paraphrasing Robert May, they must arguably deploy "devious strategies" in order to persist. The most obvious strategy in this context is the adoption of systematically higher colonization rates by higher trophic levels, but there are also other strategies, such as behavioural ones [START_REF] Calcagno | Constraints on food chain length arising from regional metacommunity dynamics[END_REF]. As shown here, the evolutionary dynamics of colonization rates, i.e. the evolution of dispersal at individual trophic levels, is yet another way to alleviate the constraint on foodchain length. Natural selection does favour larger colonization rates at upper trophic levels and an evolutionary increase in colonization rate can, if fast enough, allow the persistence of longer food chains than when species traits are constant. The selection pressures imposed on colonization rates by trophic relationships and spatial structure cause evolutionary responses that can sustain the persistence of more trophic levels in the face of habitat degradation, such as increased disturbances or habitat destruction. It would seem at first glance that such eco-evolutionary dynamics could be the ultimate devious strategy, by allowing the colonization rates of species to evolve larger values as needed. They could potentially alleviate any limit on food-chain length, as spatial persistence is ensured provided a sufficiently large colonization rate. This would be similar to evolutionary rescue, in another context and at a larger scale. However, our results show that things are not so simple. Indeed, when all trophic levels are allowed to evolve in such a way, two factors limit the efficiency of evolution in rescuing food-chain length. First, the lowest trophic levels, which are typically not facing the greatest danger of spatial extinction, experience little selection for increased colonization as their effective extinction rates are low. Quite the opposite, they can readily be selected for lower colonization rates, because of intraspecific competition or, equivalently, costs of dispersal. Such a negative selection pressure lowers their spatial occupancy, directly jeopardizing the persistence of the superior trophic levels. Second, the strength of selection for larger colonization rates typically declines, all else being equal, as trophic level increases. This is because positive selection declines as the fraction of hospitable patches decreases, while at the same time, the larger colonization rates that higher trophic levels must adopt increase the strength of selection against dispersal caused by intraspecific competition (see the gradient equation [2]). Combined, these two factors make eco-evolutionary dynamics at lower trophic levels potentially detrimental to maximum food-chain length, and not so effective at rescuing higher trophic levels. In short, even if very efficient, evolutionary dynamics is not the silver bullet to ensure the persistence of higher trophic levels. This is why, even with no particular constraint on the speed or extent of adaptive evolution, eco-evolutionary dynamics does not totally suppress the spatial constraint on maximum food-chain length. Even when it permits longer food-chains to persist, the higher trophic levels are typically kept at low spatial occupancies, thus vulnerable to environmental perturbations or other random events.

In the evolutionary context we have considered here, the question of understanding what devious strategies higher trophic levels must deploy to persist remains, though the range of available strategies is more precisely defined. Theoretically, factors that could favour the persistence of longer food-chains are: (i) higher trophic levels have faster evolution rates, or (ii) competition-colonization trade-off intensities are weaker at higher trophic levels. These two possibilities remain to be investigated empirically. We can nonetheless remark that one of the components affecting trade-off intensity is local population size (Supplementary Material). The larger the local population size, the less steep the trade-off, all else being equal. Since we would quite often expect higher trophic levels to have smaller local population sizes, this should make 0  more negative as trophic level goes up. If so, this would be yet another factor detrimental to food-chain length under eco-evolutionary dynamics. Regarding heterogeneity in evolution rates among trophic levels, the good news is that, if evolution proceeded more quickly in prey than predators or vice versa for all traits under selection, such a heterogeneity should leave a clear mark on the population dynamics series of both predator and prey [START_REF] Yoshida | Rapid evolution drives ecological dynamics in a predator-prey system[END_REF][START_REF] Hiltunen | A newly discovered role of evolution in previously published consumer-resource dynamics[END_REF], thus providing us with an empirical test of this hypothesis. We obviously did not impose any restriction on the range of colonization rates that could evolve. This may be unrealistic and other selective forces or constraints could of course interfere with the effects presented here. For instance, colonization rates may have upper bounds (see Supplementary Material for an example resulting from maximum reproductive investment). If the upper bound is low enough, this could constrain the possibility of at least some trophic levels to persist through the evolution of greater colonization rates. Large colonization rates are especially selected for at higher trophic levels, so the latter would need to have less stringent bounds. One direct way to test our predictions is to use an experimental approach, with suitable biological systems such as ciliates or other microorganisms in which both dispersal and competition have been thoroughly studied [START_REF] Fox | Effects of intra-and interspecific interactions on species responses to environmental change[END_REF][START_REF] Pennekamp | Dispersal propensity in Tetrahymena thermophila ciliates-A reaction norm perspective[END_REF]) and for which the definition of trophic levels, patches and dispersal are simple to establish. More generally, we might use observational data from the field to evaluate whether some of the qualitative patterns / trends we have identified here actually occursthese patterns could indeed be diagnostic of whether the type of eco-evolutionary dynamics modelled are at play or not. Of course, natural communities and food chains experience processes and contingencies left out in models (e.g. autocorrelation and/or clustering of perturbations, species occurring at more than one trophic level). This would often complicate the task, but datasets such as the one used in [START_REF] Wang | Metapopulation capacity determines food chain length in fragmented landscapes[END_REF] exist and are extremely useful in this context, especially if they extend to three or more trophic levels. The patterns reported in Fig. 3 and 5 appear especially valuable for empirical assessments. Indeed, we found that among systems differing in their level of habitat destruction, either spontaneously or upon experimental manipulation , the maximum food-chain length declines in a generically convex manner in the absence of eco-evolutionary dynamics, whereas it could have a concave decline with such dynamics (Fig. 3c). Such a concave shape is never observed without evolutionary dynamics, and is not observed when manipulating the extinction rate. The existence of a concave relationship would therefore be a strong indication that ecoevolutionary dynamics are at play. Alternatively, the correlation between total occupancy (and thus the fraction of unoccupied patches) and maximum food-chain length offers the same prediction (Fig. 5): it could assume a concave shape only with eco-evolutionary dynamics, not in their absence, and only if habitat destruction is the underlying varying parameter. A concave shape is observed upon varying the extinction rate e or the perturbation rate µ (Supplementary Fig. 2). It thus seems that datasets or experiments documenting the impact of habitat destruction on maximum food-chain length and overall occupancy offer great promises to evaluate the importance of eco-evolutionary dynamics in shaping food webs. Our results were derived in a simple spatially homogeneous and mean-field patchoccupancy model. Interestingly, such a simple model faithfully reproduces the results presented in [START_REF] Wang | Metapopulation capacity determines food chain length in fragmented landscapes[END_REF], who used stochastic simulations of a spatially realistic model. This gives additional credence in the predictions we derived here. Our results could be extended in many different ways, possibly including more complex food-web topologies ("how would omnivory affect model predictions?"), introducing several species per trophic level (leading to the study of apparent predation at the scale of the metacommunity) or even using trophic level-specific definitions of a patch (e.g. [START_REF] Mccann | The dynamics of spatially coupled food webs[END_REF]), but they reveal some fundamental ways in which the evolution of dispersal and spatial food-webs dynamics are interconnected. In any case, they suggest a lot is to be gained from bringing more ecoevolutionary dynamics into the realm of food-web ecology.

Author contributions

The initial idea of this work originated from FM during his PhD thesis with PJ and PD. VC and FM designed and conducted the research. VC and FM wrote the initial manuscript, all co-authors contributed to manuscript preparation. Acknowledgments VC acknowledges funding from INRAE, PJ, PD and FM from the CNRS. All authors acknowledge funding from ANR (project AFFAIRS 12-ADAP-005 to PD). VC and FM are thankful to CESAB, Montpellier, for hosting a work session. FM also thanks D. Gravel and various people at ISA and EDYSAN for feedback. VC dedicates the derivation of the function from a spatially structured population model to the dearly missed Isabelle Oliveri, who hinted at it in a split sentence in 2005, as he was doing his PhD under her supervision.

Conflicts of interest

The authors declare no conflict of interest.

Figure legends Figure 1.

A graphical illustration of the spatial food chain model. The habitat consists of many interconnected patches. Each patch can be colonized by one or more trophic levels. The first trophic level can colonize any empty available habitat patch, whereas the second trophic level can only colonize patches where the first trophic level is found, etc. Each trophic level can disappear from a patch at some basal extinction rate e, and local extinction of one trophic level causes the local extinction of all upper trophic levels. Patches can also undergo catastrophic perturbation events, at rate μ, causing all trophic levels to be removed at once. The dynamical variables of interest in eq. ( 1) are the q i , i.e. the proportion of patches occupied by the i-th trophic level (and possibly upper trophic levels too), as illustrated at the bottom of the figure. ). The two trophic levels initially had colonization rates c = 10; without evolution they retained these values throughout, whereas with evolution the values gradually changed according to eq. ( 2). Other parameters were at default values, except μ = 0 and e TD = 2 e. Figure 3. Maximum food-chain length under habitat deterioration. (a-b) The effect of increasing the extinction rate on maximum food-chain length (a), without evolution (orange) and with evolution (blue). In the case of evolution, the colonization ratio values at each trophic level are shown in (b). (c-d) Same as (a-b), except that the level of habitat destruction (1-h) was increased instead of e. Initially (i.e. for e=0 or h=1), species have the same colonization rates in the two scenarios (with or without evolution), set at the corresponding ES values. These values do not change in the no evolution scenario, whereas they changed in the other scenario. Figure 4. Consequences of varying the competitive trade-off intensity. (a) A contour plot of maximum food-chain length, with evolution, as a function of the two competitive trade-off parameters (ɸ; y-axis) and (Ѱ 0 ; log scale, x-axis; -100 < Ѱ 0 < -0.01). (b) For a fixed ɸ = 0.5 (corresponding to the dotted line in panel a), the colonization ratios of the different trophic levels as a function of Ѱ 0 . Figure 5. The relationship between food-chain length and the fraction of empty patches without evolution (left panels) and with evolution (right panels). (a-b) Each dot represents a different parameter value, where the extinction rate varies between 0.01 and 100, under three different values of Ѱ 0 . (c-d) Each dot represents a different parameter value, where the habitat destruction level 1-h varies between 0 and 1, under three values of Ѱ 0 . In all panels, the three values of Ѱ 0 were -1 (gray dots), -0.1 (orange dots) and -0.01 (blue dots). As in Fig. 3, species had colonization rates set at the ES values for the initial parameter value, and these values remained constant in the no evolution scenarios, whereas they adapted in the evolution scenarios. Points were slightly jittered vertically for better readability.



  negative selection on colonization rate caused by local competition. More specifically, the  term represents the (weak) positive selection caused by kin competition (Supplementary Material), whereas the term involving 0 represents the counter-selection imposed by competitive trade-offs and costs of dispersal.

Figure 2 .

 2 Figure legends Figure 1.A graphical illustration of the spatial food chain model. The habitat consists of many interconnected patches. Each patch can be colonized by one or more trophic levels. The first trophic level can colonize any empty available habitat patch, whereas the second trophic level can only colonize patches where the first trophic level is found, etc. Each trophic level can disappear from a patch at some basal extinction rate e, and local extinction of one trophic level causes the local extinction of all upper trophic levels. Patches can also undergo catastrophic perturbation events, at rate μ, causing all trophic levels to be removed at once. The dynamical variables of interest in eq. (1) are the q i , i.e. the proportion of patches occupied by the i-th trophic level (and possibly upper trophic levels too), as illustrated at the bottom of the figure. Figure 2. Increasing extinction rate in a system with two trophic levels. (a-b) No evolution. The extinction rate is gradually increased from its baseline value (e=1). The equilibrium occupancies of the prey (blue) and the predator (green) gradually decline until extinction (a), as the colonization ratios (c/e) decline with the increase in e (b). These results very closely reproduce Wang et al. (2021) fig. 1 results. (c-d) Introducing evolution at low speed relative to the change in e ( ). (e-f) Introducing evolution at an intermediate speed relative to the change in e ( ). (g-h) Introducing evolution at a large speed relative to the change in e (). The two trophic levels initially had colonization rates c = 10; without evolution they retained these values throughout, whereas with evolution the values gradually changed according to eq. (2). Other parameters were at default values, except μ = 0 and e TD = 2 e. Figure3. Maximum food-chain length under habitat deterioration. (a-b) The effect of increasing the extinction rate on maximum food-chain length (a), without evolution (orange) and with evolution (blue). In the case of evolution, the colonization ratio values at each trophic level are shown in (b). (c-d) Same as (a-b), except that the level of habitat destruction (1-h) was increased instead of e. Initially (i.e. for e=0 or h=1), species have the same colonization rates in the two scenarios (with or without evolution), set at the corresponding ES values. These values do not change in the no evolution scenario, whereas they changed in the other scenario. Figure 4. Consequences of varying the competitive trade-off intensity. (a) A contour plot of maximum food-chain length, with evolution, as a function of the two competitive trade-off parameters (ɸ; y-axis) and (Ѱ 0 ; log scale, x-axis; -100 < Ѱ 0 < -0.01). (b) For a fixed ɸ = 0.5 (corresponding to the dotted line in panel a), the colonization ratios of the different trophic levels as a function of Ѱ 0 .Figure 5. The relationship between food-chain length and the fraction of empty patches without evolution (left panels) and with evolution (right panels). (a-b) Each dot represents a different parameter value, where the extinction rate varies between 0.01 and 100, under three different values of Ѱ 0 . (c-d) Each dot represents a different parameter value, where the habitat destruction level 1-h varies between 0 and 1, under three values of Ѱ 0 . In all panels,

  Figure 2 595

Figure 5

 5 Figure 5