Access to nutrients is a key factor governing development, reproduction and ultimately fitness. Within social groups, contest-competition can fundamentally affect nutrient access, potentially leading to reproductive asymmetry among individuals. Previously, agent-based models have been combined with the Geometric Framework of nutrition to provide insight into how nutrition and social interactions affect one another. Here, we expand this modelling approach by incorporating evolutionary algorithms to explore how contest-competition over nutrient acquisition might affect the evolution of animal nutritional strategies. Specifically, we model tolerance of nutrient excesses and deficits when ingesting nutritionally imbalanced foods, which we term ‘nutritional latitude’; a higher degree of nutritional latitude constitutes a higher tolerance of nutritional excess and deficit. Our results indicate that a transition between two alternative strategies occurs at moderate to high levels of competition. When competition is low, individuals display a low level of nutritional latitude and regularly switch foods in search of an optimum. When food is scarce and contest-competition is intense, high nutritional latitude appears optimal, and individuals continue to consume an imbalanced food for longer periods before attempting to switch to an alternative. However, the relative balance of nutrients within available foods also strongly influences at what levels of competition, if any, transitions between these two strategies occur. Our models imply that competition combined with reproductive skew in social groups can play a role in the evolution of diet breadth. We discuss how the integration of agent-based, nutritional and evolutionary modelling may be applied in future studies to further understand the evolution of nutritional strategies across social and ecological contexts.
Access to nutrients is one of the most influential factors affecting reproductive development and ultimately fitness (e. g. [1–4]). A range of factors can influence nutrient access, but for many organisms interactions with conspecifics are pivotal. Group living animals in particular face a complex trade-off between access to foods that provide them with a balanced diet, social interactions that enhance fitness via benefits of group cohesion, and competition [5]. Contest-competition, for example, where individuals directly engage one another for access to nutrients, is a source of inter-individual variance that can lead to clear dominance hierarchies [6,7]. In the extreme, contests may even lead to a reproductive division of labour, with only those individuals at the top of the hierarchy being able to access enough nutrients, and at the right balance, to reproduce [8–10]. The effects that competition over food access can have on inter-individual variation in reproduction are well known in arthropods. For example, colonies of social spiders (e. g. Stegodyphus sp.) tend to be characterised by body size asymmetries and reproductive skews [11–15]. As a result of contest-competition over food access, only larger females are able to attain enough of the right nutrients to reproduce [8,13]. It has even been proposed that the reproductive asymmetries that arise from competition over nutrients may constitute a reproductive division of labour, in which non-reproductive spiders provide alloparental care ([8,16] c. f. [14,17]). In the burying beetle, Nicrophorus vespilloides, females compete for access to carcasses, which in turn leads to a dominance hierarchy where reproduction is skewed in favour of the dominant female [18]. Experimental data indicate that access to appropriate nutrition is the main factor determining reproductive output and also impacts performance in dominance interactions [18,19]. Although there is no such direct evidence in cooperative breeding vertebrates, correlative studies in mongooses (Mungos mungo) and meerkats (Suricata suricatta) show that subordinate females breed more frequently in periods of food abundance [20,21]. These results highlight the importance of contest competition as a potentially major ecological factor shaping the evolution of nutritional and social traits in animal groups. In recent years, a new understanding of interactions between an organism’s nutritional requirements and its environment has been gained using the state-space models of the Geometric Framework (GF) [22–24]. In the GF, nutrients are represented by a Cartesian coordinate system, which is referred to as the nutrient space [23]. In the simple case of a nutrient plane, the GF represents two food components (e. g. , the macronutrients protein and carbohydrate) on x and y axes (Fig. 1). The optimal amount and blend of nutrients that the animal requires over a specified period in its life are represented by a coordinate or region within the nutrient space called the Intake Target (IT; [23]). Foods are represented by ‘food rails’, which are radials through the nutrient space with a slope that reflects the ratio of macronutrients present within the food (Fig. 1). As an individual eats, its nutritional state (x, y coordinate) moves through the nutrient space in parallel with the rail of the food it consumes. A high quality food may be considered one with a food rail that will guide an individual’s nutritional state to the IT from its current state (Fig. 1); i. e. , one that is nutritionally balanced. When confined to nutritionally imbalanced foods, the animal needs to resolve the trade-off between over-ingesting some nutrients and under-ingesting others. The strategy that it adopts in this situation, known as the ‘rule of compromise’, is expected to vary within and between species depending on the relative costs of ingesting excesses and deficits of the different nutrients [23,25]. Recently, the GF has been combined with Agent-Based Models (ABMs; simulations representing each individual explicitly, sometimes named individual-based models in ecological fields [26]) to successfully demonstrate how social interactions and nutritional strategies affect one another [5]. With regard to the influence of competition on the emergence of reproductive asymmetries, Lihoreau et al. [5] link classic models of contest competition (outlined by Bonabeau et al. [27]) with the GF in an ABM. In that model, access to each food rail is limited, and individuals must displace competitors via dominance interactions before feeding. Performance in dominance interactions is a function of the individual’s fitness, which in turn is negatively correlated with the distance between an individual’s nutritional state and the IT. Reproductive asymmetry arises as individuals who ‘get lucky’ and are able to feed on high quality foods early experience a ‘winner effect’ (see [28]). That is, a loop of positive feedback ensues whereby better-nourished individuals continue to perform well in dominance interactions and monopolise high quality foods. Ultimately, only certain individuals attain enough nutrients at the right balance to breed, a model outcome that is consistent with observations of reproductive skew in some social animals (e. g. spiders [8,13] and burying beetles [18,19]). Interestingly, this model also clearly demonstrates how early stochasticity in nutrient access can lead to the emergence of a self-organised social structure from an initially homogeneous group [5,29]. The aforementioned mechanistic model, however, does not consider the optimal nutritional strategy that individuals should adopt. When feeding on a poor quality food, an individual may choose to stop eating and seek an alternative. However, the individual risks incurring costs; e. g. , the time spent attempting, but ultimately failing, to gain access to alternative better foods. Under some circumstances it is thus conceivable that an individual could get its nutritional state closer to the IT by consuming a poor quality food, rather than by frequently searching for better balanced alternatives. Ultimately, the optimal strategy for leaving a suboptimal food may be dependent on the level of competition and the kinds of food in the environment. The incorporation of evolutionary and genetic components into GF based ABMs has been identified as a promising method with which to understand how ecological factors interact with nutritional strategies [5,23,30]. Here, we present the first such model, which we used to explore how intra-specific competition might affect the evolution of animals’ nutritional strategies. In the model by Lihoreau et al. [5], an individual’s nutritional strategy was governed by the fixed global parameter K, which we refer to here as ‘nutritional latitude’. When eating a food that will not guide its nutritional state to the IT an individual has some probability of leaving, which is both a function of the balance of nutrients in the food being consumed, and K. Here, a high K means an individual is likely to consume the same imbalanced food until reaching a point of nutritional compromise (at which point it then seeks an alternative). In contrast, a low K corresponds to a low probability that an individual will continue feeding on a food rail that will not guide its nutritional state directly to the IT. Individuals with extremely high or low values of K may, thus, be thought of as nutrient generalists or specialists, respectively (sensu Raubenheimer and Simpson [31]; we note that K as we model it here is equivalent to 1—K in Lihoreau et al. [5]). In this study, we couple nutritional latitude with an evolutionary algorithm, whereby an individual’s K is governed by an individual-level, heritable and mutable value. Each generation consists of 150 individuals that must attain a certain level of fitness (i. e. , nutritional state) within a fixed number of model iterations for it to be considered fit enough to breed. Fitness-proportionate selection then operates among those individuals fit enough to breed, with proximity to the IT (optimal point of nutrient intake in the nutrient space) determining this fitness. We allowed K to evolve over 1000 generations under varying levels of competition and in differing nutritional environments (i. e. , different abundance and nutritional compositions of food). In doing so, we aimed to explore the effects of contest competition and the number and composition of foods in the nutritional environment on the evolution of individual nutritional strategies.
We began by exploring the effect of intensity of competition on the evolution of nutritional latitude in 2- and 3-food environments. We performed 30 model runs under varying intensities of competition (c, which is bounded at 0 and 1; all parameters are outlined in Table 1, and their mode of action is described in Models). From each model run we recorded the population mean nutritional latitude (K, also bounded at 0 and 1) after 1000 generations. We first looked at the effects of competition in environments containing one nutritionally balanced food, and two imbalanced but complementary foods (i. e. , those which between them subtend a region of the nutrient space containing the IT). For the latter two complementary foods we varied the extent of their nutritional imbalance (Fig. 2). In these environments when c = 0, K was stable at a range of values (Fig. 2). The high variance in stable values of K suggests that no one level of nutritional latitude is optimal where competition is weak, but most low levels are equally fit. In the face of increasing c, K was relatively stable up to a point. With mildly imbalanced foods at c = 0. 7, and with extremely imbalanced foods at c = 0. 67, K increased sharply to above 0. 91 (Fig. 2). In both 3-food environments, increases in K were accompanied by declines in the variance of evolved K (Fig. 2). For example, in the environment with mildly imbalanced foods the 2. 5th and 97. 5th percentiles of K were 0. 14 and 0. 47, respectively with c = 0, but were 0. 69 and 0. 88 when c = 0. 73 (Fig. 2A). Thus, selection for a high level of nutritional latitude is strong at moderate to high c, with a further sharp decrease at extremely high levels of c (i. e. , > 0. 85), largely being driven by a change in the lower 2. 5th percentile of K (Fig. 2). At very high c the population could not support itself as no individuals could fulfil the fitness requirements to be considered in breeding condition by the end of the simulation (Fig. 2). We next considered competition in a 2-food environment, containing one balanced and one imbalanced food, the latter of which varied in the degree of nutritional imbalance (Fig. 3). With a mildly imbalanced food, absent or weak competition selected for a lower K (and lower variance; Fig. 3A) than in 3-food environments (Fig. 2). Thus, selection for low nutritional latitude was stronger in this 2-food environment than in the 3-food environments. That being said, in the 2-food environment with a mildly imbalanced food and low c, K was stable, before transitioning to high K under moderate to high c (Fig. 3A), as was the case in 3-food environments (Fig. 2). In the 2-food environment that contained a balanced and a severely imbalanced food, nutritional latitude showed a quite different profile from that previously observed. Increasing c in this environment selected for low nutritional latitude (and very low variance in K), reaching a minimum value of K = 0. 06 at c = 0. 625 (Fig. 3B). These results clearly indicate the importance of access to a complementary food to correct the nutritional state associated with consuming large amounts of a severely nutritionally imbalanced food (see S1 File for additional discussion). As part of experiment 1, we also looked at environments containing two nutritionally imbalanced but complementary foods. In these environments, the response of K to increasing c resembled that in 3-food environments (see S1 File). In our model, the parameter η (see Details in Models and Table 1) is the power of the relative nutritional states (fitness; F) of the ith and jth individuals to predict the outcome of a dominance interaction between these individuals. Given that we are largely concerned with species for which ability in dominance interactions is strongly correlated with nutritional state (see Lihoreau et al. [5]), in the above results η is assumed to be high (η = 25). We now explore the effects of the intensity of competition (c) in scenarios where there is greater stochasticity in the outcome of contests over food; η = 20 and η = 10. Where η was set at a lower levels, increasing the intensity of competition had the same qualitative effect on the evolution of nutritional latitude (K) as described above; i. e. at low c a range of low levels of nutritional latitude appear optimal, but a transition to high K is favoured at c greater than 0. 733 (Figs. 2 and 6). However, at lower levels of η the intensity of competition that lead to population extinction was decreased. With η = 10 the population could not consistently sustain itself above values of c of 0. 833 (Fig. 6B). In an equivalent nutritional environment with η = 25 the population could not consistently sustain itself above values of c = 0. 8667 (Fig. 2). These results indicate that having a stable dominance hierarchy, which is based on nutritional state can allow the population to better survive poor nutritional environments. We further discuss the biological implications of this finding below (see Future Directions in Discussion). In the results described above, selection acts via two mechanisms. First, only those individuals able to attain fitness greater than 0. 5 within 500 iterations are assumed to be in good enough condition to breed. Second, among those individuals fit enough to breed, fitness-proportionate selection operates [32]. The sensitivity of our results to this general selection mechanism was assessed by running the model with an alternative mechanism, truncated selection [29]. In this instance, the first 10% of the population to attain fitness over a cut-off are assigned as parents for the next generation. In our experiments cut-offs of 0. 5 and 0. 9 were assessed. Under truncated selection extinctions do not occur as the population is given a flexible amount of time to reach the fitness cut-off. We evaluated the effects of truncated selection on the model’s output in a 3-food environment with severely imbalanced foods (such an environment produced results typical of most other environments; Fig. 2B). In the absence of competition (c = 0) there was little or no selection on nutritional latitude: mean K = 0. 5 with large variance (Fig. 7). However, low and moderate levels of competition selected for very low nutritional latitude (Fig. 7). As was the case under our general selection mechanism, a transition to increased nutritional latitude was still favoured under moderate to high competition (Fig. 7). However, K was not increased to anywhere near as high a level as under an equivalent nutritional environment with our general selection mechanism (Figs. 2 and 7). Finally, at very high levels of competition a return to low K was favoured (Fig. 7). The contrasting results of experiments 1 and 4 clearly illustrate that the mode of selection affects how nutritional strategies respond to contest competition. The implications of this finding for the biological interpretation of our model are discussed below (see Future Directions in Discussion).
We developed an ABM that combines principles of the GF with an evolutionary algorithm to explore how contest competition may affect the evolution of animal nutritional strategies. Specifically, we modelled the extent to which individuals consume nutritionally imbalanced foods that will not guide them directly to their intake target (nutritional latitude, K). In most of the nutritional environments we modelled, no competition and weak to moderate competition favoured low consumption of a suboptimal food. However, given that we observed high variance in stable values of K, it seems likely that there is no single optimal strategy. Rather, any fairly low level of nutritional latitude performs well. In contrast, moderate to severe competition appears to favour the consumption of more of an imbalanced food before seeking an alternative, than when competition is weak (i. e. , they evolve increased nutritional latitude), potentially even consuming that food until reaching the point of nutritional compromise (see [23]). The balance of nutrients in the foods available also influences the optimal level of nutritional latitude. For example, in a 2-food environment that contained one highly imbalanced and one balanced food, a very low level of nutritional latitude was favoured regardless of competition (Fig. 3B). Thus, considering the nutritional composition as well as the amount of available foods is essential if we are to understand the role of competitive interactions in shaping the evolution of nutritional strategies. Our model suggests that in social groups where the availability of nutrients is highly variable, plastic nutritional latitude should be adaptive so that individuals can alter their strategy in response to the intensity of competition. Several biological systems are well suited to empirical exploration of this idea. In social spiders, experimental evidence suggests that access to lipids governs reproductive asymmetry [13]. The manipulation described by Salomon et al. [13] (creating prey that vary in lipid content) could be employed, and then the behaviour of marked individuals within these groups observed (such as described in Whitehouse and Lubin [12]). An alternative model is the house cricket (Acheta domesticus), a species with well-studied nutritional requirements [33–38]. Males are known to compete with one another for food; moreover, sexual selection likely results in reproductive asymmetry, with larger males most likely able to meet the energy requirements for intra-sexual competition [39–43]. Contest-competition and aggression over food and mate access are also observable phenomena in male fruit flies (Drosophila melanogaster; [44,45]). This species also offers numerous other advantages including, being a model organism in genetics, being well studied with regards to its nutritional requirements and fitness consequences of nutritional imbalance and being suitable for artificial selection [1,2, 46–48]. Using our ABM it will be possible to generate predictions for any number of nutritional scenarios specific to the model organisms described above. For example, considering spiders one may wish to explore a situation in which as food becomes scarce (i. e. , competition increases in intensity), certain food rails appear only sporadically [49,50]. At the inter-species level our model suggests a role for contest competition and reproductive skew in shaping the evolution of dietary breadth. Specifically, consistent intense competition for access to a food containing a limiting nutrient, which results in reproductive skew, can select for high nutritional latitude, hence contributing to nutritional generalism. This hypothesis could be tested in a comparative nutrition framework (e. g. , [31]), focussing on the intensity of contest competition and reproductive skew within groups of social generalists and specialists. Such approaches have, in the past, proved useful for studying the evolutionary mechanisms underlying dietary breadth, specifically suggesting that nutritional heterogeneity may lead to the adoption of specialist/generalist-specific rules of compromise ([23]; further discussed in Future Directions.). Additional to insights into evolving nutritional strategies, our model supports predictions that contest competition over foods can lead to dominance hierarchies and reproductive asymmetries in social groups, because dominant individuals monopolise key nutrients for reproduction [5,8, 13]. Contests for limited food can cause between-individual variance in reproductive output, regardless of the level of nutritional latitude or the nutritional environment. Given an apparent link between limited resources and alloparental care [51], contest competition over nutrients may be a mechanism forcing groups of animals on to the continuum from cooperative breeding, where helpers occasionally provide care to the offspring of breeders, to eusociality, characterised by a complete division of labour [52]. We note that our models represent a scenario in which individuals are unable to leave the group, even when competition becomes strong, due to some unstated ecological constraint. If future models explicitly focus on how nutrition and contest competition contribute to the evolution of sociality, they will likely want to vary the strength of constraints that keep individuals within the group. Our models highlight some interesting relationships between nutrition, individual-level fitness and mean population fitness. Specifically, these models show that where individual nutritional state is a strong predictor of performance in dominance interactions (here η) and in turn reproductive asymmetry (i. e. a high variance in fitness), the population is better able to survive when nutrients are severely limiting. Accordingly, previous theoretical and experimental studies in social spiders have also suggested a strong dominance hierarchy ensures that the colony is able to survive resource poor periods, as at least a few females are able to monopolise enough nutrients to breed [8,11]. We also note that the spread of high nutritional latitude under strong competition bears some similarities to an evolutionary “tragedy of the commons” [53], because once the strategy becomes highly prevalent the mean fitness of the population becomes depressed to a lower level than might be the case if all (or the vast majority of) individuals to maintain low nutritional latitude. Our evolutionary model could be further expanded to give a more detailed representation of specific biological systems. First, we assumed that the fitness payoffs surrounding the IT are symmetrical. Geometric nutritional studies have shown that in some instances the fitness landscapes associated with the intake of nutrients may be asymmetrical [25]. A case in point is the predatory ground beetle (Anchomenus doralis), where a female’s egg production displays an asymmetrical response to protein and lipid intake when mapped as a response landscape onto a protein-lipid nutrient-space [54]. Models considering the effects that asymmetrical fitness landscapes have on the evolution of nutritional strategies themselves, and in turn the consequences for social structure, are particularly exciting avenues of investigation. Second, geometric nutritional studies also demonstrate that different species follow different rules of compromise (the extent to which they consume excesses of one nutrient relative to the IT to gain another which is limiting in the diet). The model described here conforms to what is known as the ‘nearest distance’ rule of compromise [23]: individuals seek to attain a nutritional state that minimises the Euclidean distance from the IT (see Models). Some species, such as the migratory locust (Locusta migratoria), appear to conform to such a rule of compromise when confined to a single food [31]. However, other rules of compromise are also followed. For example, the desert locust (Schistocera gregaria) follows what is known as an ‘equal distance’ rule of compromise, eating more of an imbalanced diet, over-consuming the excess nutrient to a greater degree (and under-consuming the deficient nutrient to a lesser degree) than L. migratoria, under the same no-choice experiment [31]. Evidence from this and other examples using the comparative approach suggests that the adoption of these two different rules of compromise closely associates with dietary breadth, with nutrient specialists adopting the nearest distance rule we implement here [23]. The study of the co-evolution of nutritional rules of compromise, dietary breadth, fitness-landscapes and other nutritional strategies (e. g. nutritional latitude) remains largely theoretical [23,25]. However, with the increasing application of nutritional geometry to a wider range of species, both in the lab and in the field, the comparative studies required to untangle the co-evolution between the aforementioned traits should soon be possible [23]. Within the selection mechanism implemented here, individuals must first attain a certain nutritional state to breed. Amongst those individuals with a high enough fitness to breed, relative fitness (determined by proximity to the IT) then governs overall representation in the subsequent generation (i. e. , fitness proportionate selection; [32]). Thus, what we term the ‘general’ selection mechanism is most analogous to systems where reproductive asymmetries arise when resources become limiting. This mechanism of selection is typical of experimental outcomes in some social systems. For instance, female social spiders that do not attain enough nutrients (lipids) to reach a mature size at the end of the season are not capable of breeding, and larger individuals produce more offspring ([8,13,55–57] c. f. [15]). We also explored the effects of truncated selection on the model output. Whilst these two selection regimes produced some broadly similar results, there were also differences; namely, with truncated selection there was a lack of selection on nutritional latitude in the absence of competition, but low nutritional latitude was favoured under even weak competition. Truncated selection is most analogous to social systems, where dominance hierarchies and reproductive asymmetries are always present, regardless of food availability. For example, in eusocial wasps (Polistes; the inspiration for the original manifestation of the contest competition model we implement [27]) linear hierarchies form amongst females, with reproduction limited to the individual at the top (or the top few; [58]). For such species, where reproduction is always limited to a few individuals (perhaps those best able to track the IT), a model operating truncated selection may be most appropriate. Additionally, it occurs to us that artificial selection experiments can use truncated selection; i. e. , the top few performing individuals are selected for breeding (e. g. [59]). In the future, geometric ABMs such as ours may be used to generate predictions for selection experiments on nutritional strategies. However, those models should explicitly incorporate truncated selection as other modes of selection may produce inaccurate predictions. The models described here make simplifying assumptions about within population variation in nutritional requirements and the effects of nutritional state on fitness. For example, we only consider a single sex although sex differences in nutritional requirements may be ubiquitous (e. g. [60]). Such assumptions seem justifiable on the basis of the biological systems that we are interested in. Considering sex specifically, the relationship between contest competition, reproductive asymmetry and nutritional state is often only profound (or well understood) in one sex. For example, in populations of social spiders female sex ratio bias tends to be very strong and males seem largely absent [13,14]. Thus it seems reasonable to assume that males play a relatively minor role in competition over nutrient access. When modelling the relationship between nutritional state and other social phenomenon (e. g. collective behaviour and communal feeding [5]), however, it may be more realistic to model such variation. To incorporate this variation, rather than modelling a single intake target as we do here, one could include a bi-modal distribution of intake targets representing the differential requirements of each sex and individual heterogeneity simultaneously. In this instance, the combination of evolutionary algorithms, ABMs and the GF has allowed us to produce testable experimental predictions for how intra-specific competition affects the evolution of nutritional latitude and dietary breadth. The wider application of this integrated approach could be applied to assess how other nutritional strategies and ecological factors interact [30]. For instance, Lihoreau et al. [5] explore how collective decision-making can optimise the nutritional decisions of entire groups, a phenomenon that may be applicable to animals exhibiting a range of social interactions [61–63]. By expanding that model with an evolutionary algorithm, it would be possible to generate predictions for how nutritional strategies and social phenomenon co-evolve. The next step in combining evolutionary algorithms with GF-based ABMs will be to use spatially explicit models [30]. In this way researchers will be able to model the evolution of nutritional strategies in complex environments that are closely representative of real world ecosystems. Models were programmed in the software Netlogo [64]. Graphs were created and statistical calculations performed with R version 3. 1. 1 [65]. The model is described following the overview, design and details format of ABM description as widely recommended [66–68]. The code for the model can be found in S2 File.
Getting enough nutrients and at the right balance is among the primary challenges that an animal has to overcome. Animals that live in groups have the added complexity of competition among individuals over foods. We used an evolutionary simulation to explore how the intensity of such competition interacts with the composition of available foods to influence the strategies that an animal should use to meet its nutritional requirements. We found that two general strategies emerged. When competition was weak, animals that only locate and consume foods with an ideal balance of nutrients were favoured. However, when competition was strong, a strategy with which animals meet their nutritional requirements by eating large amounts of nutritionally imbalanced, but complementary, foods was optimal. These results implicate a role for competition for foods between animals within social groups in shaping dietary breadth. Evolutionary simulations such as those described here are important for understanding how different species evolve to meet their nutritional requirements in a range of ecological circumstances.
Evolving Nutritional Strategies in the Presence of Competition: A Geometric Agent-Based Model