An Overlooked Consequence of Dietary Mixing: A Varied Diet Reduces Interindividual Variance in Fitness

The influence of immune challenges on the mean and variance in reproductive investment: a meta-analysis of the terminal investment hypothesis

Finding the optimal balance between survival and reproduction is a central puzzle in life-history theory. The terminal investment hypothesis predicts that when individuals encounter a survival threat that compromises future reproductive potential, they will increase immediate reproductive investment to maximise fitness. Despite decades of research on the terminal investment hypothesis, findings remain mixed. We examined the terminal investment hypothesis with a meta-analysis of studies that measured reproductive investment of multicellular iteroparous animals after a non-lethal immune challenge. We had two main aims. The first was to investigate whether individuals, on average, increase reproductive investment in response to an immune threat, as predicted by the terminal investment hypothesis. We also examined whether such responses vary adaptively on factors associated with the amount of reproductive opportunities left (residual reproductive value) in the individuals, as predicted by the terminal investment hypothesis. The second was to provide a quantitative test of a novel prediction based on the dynamic threshold model: that an immune threat increases between-individual variance in reproductive investment. Our results provided some support for our hypotheses. Older individuals, who are expected to have lower residual reproductive values, showed stronger mean terminal investment response than younger individuals. In terms of variance, individuals showed a divergence in responses, leading to an increase in variance. This increase in variance was especially amplified in longer-living species, which was consistent with our prediction that individuals in longer-living species should respond with greater individual variation due to increased phenotypic plasticity. We find little statistical evidence of publication bias. Together, our results highlight the need for a more nuanced view on the terminal investment hypothesis and a greater focus on the factors that drive individual responses.

Dietary-based developmental plasticity affects juvenile survival in an aquatic detritivore

Developmental plasticity is ubiquitous in natural populations, but the underlying causes and fitness consequences are poorly understood. For consumers, nutritional variation of juvenile diets is probably associated with plasticity in developmental rates, but little is known about how diet quality can affect phenotypic trajectories in ways that might influence survival to maturity and lifetime reproductive output. Here, we tested how the diet quality of a freshwater detritivorous isopod (Asellus aquaticus), in terms of elemental ratios of diet (i.e. carbon : nitrogen : phosphorus; C : N : P), can affect (i) developmental rates of body size and pigmentation and (ii) variation in juvenile survival. We reared 1047 individuals, in a full-sib split-family design (29 families), on either a high- (low C : P, C : N) or low-quality (high C : P, C : N) diet, and quantified developmental trajectories of body size and pigmentation for every individual over 12 weeks. Our diet contrast caused strong divergence in the developmental rates of pigmentation but not growth, culminating in a distribution of adult pigmentation spanning the broad range of phenotypes observed both within and among natural populations. Under low-quality diet, we found highest survival at intermediate growth and pigmentation rates. By contrast, survival under high-quality diet survival increased continuously with pigmentation rate, with longest lifespans at intermediate growth rates and high pigmentation rates. Building on previous work which suggests that visual predation mediates the evolution of cryptic pigmentation in A. aquaticus, our study shows how diet quality and composition can generate substantial phenotypic variation by affecting rates of growth and pigmentation during development in the absence of predation.

Global associations between macronutrient supply and age-specific mortality

Animal experiments have demonstrated that energy intake and the balance of macronutrients determine life span and patterns of age-specific mortality (ASM). Similar effects have also been detected in epidemiological studies in humans. Using global supply data and 1,879 life tables from 103 countries, we test for these effects at a macrolevel: between the nutrient supplies of nations and their patterns of ASM. We find that macronutrient supplies are strong predictors of ASM even after correction for time and economic factors. Globally, signatures of undernutrition are evident in the effects of low supply on life expectancy at birth and high mortality across ages, even as recently as 2016. However, in wealthy countries, the effects of overnutrition are prominent, where high supplies particularly from fats and carbohydrates are predicted to lead to high levels of mortality. Energy supplied at around 3,500 kcal/cap/d minimized mortality across ages. However, we show that the macronutrient composition of energy supply that minimizes mortality varies with age. In early life, 40 to 45% energy from each of fat and carbohydrate and 16% from protein minimizes mortality. In later life, replacing fat with carbohydrates to around 65% of total energy and reducing protein to 11% is associated with the lowest level of mortality. These results, particularly those regarding fats, accord both with experimental data from animals and within-country epidemiological studies on the association between macronutrient intake and risk of age-related chronic diseases.

Illustrating the importance of meta-analysing variances alongside means in ecology and evolution

Meta-analysis is increasingly used in biology to both quantitatively summarize available evidence for specific questions and generate new hypotheses. Although this powerful tool has mostly been deployed to study mean effects, there is untapped potential to study effects on (trait) variance. Here, we use a recently published data set as a case study to demonstrate how meta-analysis of variance can be used to provide insights into biological processes. This data set included 704 effect sizes from 89 studies, covering 56 animal species, and was originally used to test developmental stress effects on a range of traits. We found that developmental stress not only negatively affects mean trait values, but also increases trait variance, mostly in reproduction, showcasing how meta-analysis of variance can reveal previously overlooked effects. Furthermore, we show how meta-analysis of variance can be used as a tool to help meta-analysts make informed methodological decisions, even when the primary focus is on mean effects. We provide all data and comprehensive R scripts with detailed explanations to make it easier for researchers to conduct this type of analysis. We encourage meta-analysts in all disciplines to move beyond the world of means and start unravelling secrets of the world of variance.

Dietary macronutrient content, age-specific mortality and lifespan

Protein and calorie restrictions extend median lifespan in many organisms. However, studies suggest that among-individual variation in the age at death is also affected. Ultimately, both of these outcomes must be caused by effects of nutrition on underlying patterns of age-specific mortality (ASM). Using model life tables, we tested for effects of dietary macronutrients on ASM in mice ( Mus musculus). High concentrations of protein and fat relative to carbohydrates were associated with low life expectancy and high variation in the age at death, a result caused predominantly by high mortality prior to middle age. A lifelong diet comprising the ratio of macronutrients self-selected by mouse (in early adulthood) was associated with low mortality up until middle age, but higher late-life mortality. This pattern results in reasonably high life expectancy, but very low variation in the age at death. Our analyses also indicate that it may be possible to minimize ASM across life by altering the ratio of dietary protein to carbohydrate in the approach to old age. Mortality in early and middle life was minimized at around one-part protein to two-parts carbohydrate, whereas in later life slightly greater than equal parts protein to carbohydrate reduced mortality.

Debris ingestion and nutritional niches in estuarine and reef green turtles

Little attention has been drawn toward the effects of marine debris ingestion in relation to nutrient acquisition and fitness consequences. We tested whether anthropogenic debris ingestion influence the nutritional niches of endangered green turtles (Chelonia mydas) in estuarine and reef habitats on the Brazilian coast. Our results showed that estuarine turtles consumed diets with lower proportional wet mass composition of protein (P) and water (W) than their reef conspecifics. The amounts of debris, mostly plastics, retrieved from the digestive tracts of estuarine turtles were higher compared with those individuals from reefs. The realized nutritional niche from estuarine turtles was subject to the debris density in the environment, lack of benthic food resources available and the surface foraging behavior, likely preventing them from reaching their nutritional goals and resulting in lower fitness. The study provides critical information for the management and conservation of ecologically threatened individuals, populations, and their natural habitats.

Nutritional quality modulates trait variability

Background

Trait based functional and community ecology is en vogue. Most studies, however, ignore phenotypical diversity by characterizing entire species considering only trait means rather than their variability. Phenotypical variability may arise from genotypical differences or from ecological factors (e.g., nutritionally imbalanced diet), and these causes can usually not be separated in natural populations. We used a single genotype from a parthenogenetic model system (the oribatid mite Archegozetes longisetosus Aoki) to exclude genotypical differences. We investigated patterns of dietary (10 different food treatments) induced trait variation by measuring the response of nine different traits (relating to life history, morphology or exocrine gland chemistry).

Results

Nutritional quality (approximated by carbon-to-nitrogen ratios) influenced all trait means and their variation. Some traits were more prone to variation than others. Furthermore, the “threshold elemental ratio”- rule of element stoichiometry applied to phenotypic trait variation. Imbalanced food (i.e. food not able to fully meet the nutritional demands of an animal) led to lower trait mean values, but also to a higher variation of traits.

Conclusion

Imbalanced food led not only to lower trait value averages, but also to higher trait variability. There was a negative relationship between both parameters, indicating a direct link of both, average trait levels and trait variation to nutritional quality. Hence, variation of trait means may be a predictor for general food quality, and further indicate trade-offs in specific traits an animal must deal with while feeding on imbalanced diets.

Electronic supplementary material

The online version of this article (10.1186/s12983-018-0297-2) contains supplementary material, which is available to authorized users.

Exploring Interactions between the Gut Microbiota and Social Behavior through Nutrition

Microbes influence a wide range of host social behaviors and vice versa. So far, however, the mechanisms underpinning these complex interactions remain poorly understood. In social animals, where individuals share microbes and interact around foods, the gut microbiota may have considerable consequences on host social interactions by acting upon the nutritional behavior of individual animals. Here we illustrate how conceptual advances in nutritional ecology can help the study of these processes and allow the formulation of new empirically testable predictions. First, we review key evidence showing that gut microbes influence the nutrition of individual animals, through modifications of their nutritional state and feeding decisions. Next, we describe how these microbial influences and their social consequences can be studied by modelling populations of hosts and their gut microbiota into a single conceptual framework derived from nutritional geometry. Our approach raises new perspectives for the study of holobiont nutrition and will facilitate theoretical and experimental research on the role of the gut microbiota in the mechanisms and evolution of social behavior.

Strategies for calibrating models of biology

Computational and mathematical modelling has become a valuable tool for investigating biological systems. Modelling enables prediction of how biological components interact to deliver system-level properties and extrapolation of biological system performance to contexts and experimental conditions where this is unknown. A model's value hinges on knowing that it faithfully represents the biology under the contexts of use, or clearly ascertaining otherwise and thus motivating further model refinement. These qualities are evaluated through calibration, typically formulated as identifying model parameter values that align model and biological behaviours as measured through a metric applied to both. Calibration is critical to modelling but is often underappreciated. A failure to appropriately calibrate risks unrepresentative models that generate erroneous insights. Here, we review a suite of strategies to more rigorously challenge a model's representation of a biological system. All are motivated by features of biological systems, and illustrative examples are drawn from the modelling literature. We examine the calibration of a model against distributions of biological behaviours or outcomes, not only average values. We argue for calibration even where model parameter values are experimentally ascertained. We explore how single metrics can be non-distinguishing for complex systems, with multiple-component dynamic and interaction configurations giving rise to the same metric output. Under these conditions, calibration is insufficiently constraining and the model non-identifiable: multiple solutions to the calibration problem exist. We draw an analogy to curve fitting and argue that calibrating a biological model against a single experiment or context is akin to curve fitting against a single data point. Though useful for communicating model results, we explore how metrics that quantify heavily emergent properties may not be suitable for use in calibration. Lastly, we consider the role of sensitivity and uncertainty analysis in calibration and the interpretation of model results. Our goal in this manuscript is to encourage a deeper consideration of calibration, and how to increase its capacity to either deliver faithful models or demonstrate them otherwise.

Sex differences in life history, behavior, and physiology along a slow-fast continuum: a meta-analysis

The pace-of-life syndrome (POLS) hypothesis predicts that behavior and physiology covary with life history. Evidence for such covariation is contradictory, possibly because systematic sources of variation (e.g. sex) have been neglected. Sexes often experience different selection pressures leading to sex-specific allocation between reproduction and self-maintenance, facilitating divergence in life-history. Sex-specific differences in means and possibly variances may therefore play a key role in the POLS framework. We investigate whether sexes differ in means and variances along the fast-slow pace-of-life continuum for life history and physiological and behavioral traits. In addition, we test whether social and environmental characteristics such as breeding strategy, mating system, and study environment explain heterogeneity between the sexes. Using meta-analytic methods, we found that populations with a polygynous mating system or for studies conducted on wild populations, males had a faster pace-of-life for developmental life-history traits (e.g., growth rate), behavior, and physiology. In contrast, adult life-history traits (e.g., lifespan) were shifted towards faster pace-of-life in females, deviating from the other trait categories. Phenotypic variances were similar between the sexes across trait categories and were not affected by mating system or study environment. Breeding strategy did not influence sex differences in variances or means. We discuss our results in the light of sex-specific selection that might drive sex-specific differences in pace-of-life and ultimately POLS.

Collective foraging in spatially complex nutritional environments

Nutrition impinges on virtually all aspects of an animal's life, including social interactions. Recent advances in nutritional ecology show how social animals often trade-off individual nutrition and group cohesion when foraging in simplified experimental environments. Here, we explore how the spatial structure of the nutritional landscape influences these complex collective foraging dynamics in ecologically realistic environments. We introduce an individual-based model integrating key concepts of nutritional geometry, collective animal behaviour and spatial ecology to study the nutritional behaviour of animal groups in large heterogeneous environments containing foods with different abundance, patchiness and nutritional composition. Simulations show that the spatial distribution of foods constrains the ability of individuals to balance their nutrient intake, the lowest performance being attained in environments with small isolated patches of nutritionally complementary foods. Social interactions improve individual regulatory performances when food is scarce and clumpy, but not when it is abundant and scattered, suggesting that collective foraging is favoured in some environments only. These social effects are further amplified if foragers adopt flexible search strategies based on their individual nutritional state. Our model provides a conceptual and predictive framework for developing new empirically testable hypotheses in the emerging field of social nutrition.This article is part of the themed issue 'Physiological determinants of social behaviour in animals'.

Dietary restriction increases variability in longevity

Nutritional environments, particularly those experienced during early life, are hypothesized to affect longevity. A recent cross-taxa meta-analysis found that, depending upon circumstance, average longevity may be increased or decreased by early-life dietary restriction. Unstudied are the effects of diet during development on among-individual variance in longevity. Here, we address this issue using emerging methods for meta-analysis of variance. We found that, in general, standard deviation (s.d.) in longevity is around 8% higher under early-life dietary restriction than a standard diet. The effects became especially profound when dietary insults were experienced prenatally (s.d. increased by 29%) and/or extended into adulthood (s.d. increased by 36.6%). Early-life dietary restriction may generate variance in longevity as a result of increased variance in resource acquisition or allocation, but the mechanisms underlying these largely overlooked patterns clearly warrant elucidation.

Using plant nutrient landscapes to assess Anthropocene effects on insect herbivores

Global climate change will dramatically affect insect herbivores through changes in plant quality. Linking how multiple climate factors affect plant macronutrient content may be the most accurate way to understand the response of insect herbivores. Studies should embrace the complexity of interacting climate factors in natural systems and characterize shifts in multidimensional plant nutrient landscapes. This nutrient landscape simplifies interpretation of climate effects, although selection of appropriate currencies, scale, and interactions with allelochemicals present challenges. By assessing climate change through the filter of nutrient landscapes we could gain an understanding of how complex interacting climate change drivers affect the 'buffet' available to different insect herbivores.

Meta-evaluation of meta-analysis: ten appraisal questions for biologists

Meta-analysis is a statistical procedure for analyzing the combined data from different studies, and can be a major source of concise up-to-date information. The overall conclusions of a meta-analysis, however, depend heavily on the quality of the meta-analytic process, and an appropriate evaluation of the quality of meta-analysis (meta-evaluation) can be challenging. We outline ten questions biologists can ask to critically appraise a meta-analysis. These questions could also act as simple and accessible guidelines for the authors of meta-analyses. We focus on meta-analyses using non-human species, which we term 'biological' meta-analysis. Our ten questions are aimed at enabling a biologist to evaluate whether a biological meta-analysis embodies 'mega-enlightenment', a 'mega-mistake', or something in between.

You are what you eat: diet shapes body composition, personality and behavioural stability

BACKGROUND

Behavioural phenotypes vary within and among individuals. While early-life experiences have repeatedly been proposed to underpin interactions between these two hierarchical levels, the environmental factors causing such effects remain under-studied. We tested whether an individual's diet affected both its body composition, average behaviour (thereby causing among-individual variation or 'personality') and within-individual variability in behaviour and body weight (thereby causing among-individual differences in residual within-individual variance or 'stability'), using the Southern field cricket Gryllus bimaculatus as a model. We further asked whether effects of diet on the expression of these variance components were sex-specific.

METHODS

Manipulating both juvenile and adult diet in a full factorial design, individuals were put, in each life-stage, on a diet that was either relatively high in carbohydrates or relatively high in protein. We subsequently measured the expression of multiple behavioural (exploration, aggression and mating activity) and morphological traits (body weight and lipid mass) during adulthood.

RESULTS

Dietary history affected both average phenotype and level of within-individual variability: males raised as juveniles on high-protein diets were heavier, more aggressive, more active during mating, and behaviourally less stable, than conspecifics raised on high-carbohydrate diets. Females preferred more protein in their diet compared to males, and dietary history affected average phenotype and within-individual variability in a sex-specific manner: individuals raised on high-protein diets were behaviourally less stable in their aggressiveness but this effect was only present in males. Diet also influenced individual differences in male body weight, but within-individual variance in female body weight.

DISCUSSION

This study thereby provides experimental evidence that dietary history explains both heterogeneous residual within-individual variance (i.e., individual variation in 'behavioural stability') and individual differences in average behaviour (i.e., 'personality'), though dietary effects were notably trait-specific. These findings call for future studies integrating proximate and ultimate perspectives on the role of diet in the evolution of repeatedly expressed traits, such as behaviour and body weight.

Meta-analysis of variance: an illustration comparing the effects of two dietary interventions on variability in weight

New meta-analysis methods from evolutionary biology allow us to ask how treatments affect variability, as opposed to just the average. Using these methods we demonstrate that low carbohydrate ad libitum diets may have more variable outcomes than calorie restricted diets.

Meta-analysis, which drives evidence-based practice, typically focuses on the average response of subjects to a treatment. For instance in nutritional research the difference in average weight of participants on different diets is typically used to draw conclusions about the relative efficacy of interventions. As a result of their focus on the mean, meta-analyses largely overlook the effects of treatments on inter-subject variability. Recent tools from the study of biological evolution, where inter-individual variability is one of the key ingredients for evolution by natural selection, now allow us to study inter-subject variability using established meta-analytic models. Here we use meta-analysis to study how low carbohydrate (LC) ad libitum diets and calorie restricted diets affect variance in mass. We find that LC ad libitum diets may have a more variable outcome than diets that prescribe a reduced calorie intake. Our results suggest that whilst LC diets are effective in a large proportion of the population, for a subset of individuals, calorie restricted diets may be more effective. There is evidence that LC ad libitum diets rely on appetite suppression to drive weight loss. Extending this hypothesis, we suggest that between-individual variability in protein appetite may drive the trends that we report. A priori identification of an individual’s target intake for protein may help define the most effective dietary intervention to prescribe for weight loss.

The Effect of Diet Mixing on a Nonselective Herbivore

The balanced-diet hypothesis states that a diverse prey community is beneficial to consumers due to resource complementarity among the prey species. Nonselective consumer species cannot differentiate between prey items and are therefore not able to actively regulate their diet intake. We thus wanted to test whether the balanced-diet hypothesis is applicable to nonselective consumers. We conducted a laboratory experiment in which a nonselective model grazer, the freshwater gastropod Lymnaea stagnalis, was fed benthic green algae as single species or as a multi-species mixture and quantified the snails’ somatic growth rates and shell lengths over a seven-week period. Gastropods fed the mixed diet were found to exhibit a higher somatic growth rate than the average of the snails fed single prey species. However, growth on the multi-species mixture did not exceed the growth rate obtained on the best single prey species. Similar results were obtained regarding the animals’ shell height increase over time. The mixed diet did not provide the highest growth rate, which confirms our hypothesis. We thus suggest that the balanced-diet hypothesis is less relevant for non-selective generalist consumers, which needs to be considered in estimates of secondary production.

Individuality in nutritional preferences: a multi-level approach in field crickets

Selection may favour individuals of the same population to differ consistently in nutritional preference, for example, because optimal diets covary with morphology or personality. We provided Southern field crickets (Gryllus bimaculatus) with two synthetic food sources (carbohydrates and proteins) and quantified repeatedly how much of each macronutrient was consumed by each individual. We then quantified (i) whether individuals were repeatable in carbohydrate and protein intake rate, (ii) whether an individual's average daily intake of carbohydrates was correlated with its average daily intake of protein, and (iii) whether short-term changes in intake of carbohydrates coincided with changes in intake of protein within individuals. Intake rates were individually repeatable for both macronutrients. However, individuals differed in their relative daily intake of carbohydrates versus proteins (i.e., 'nutritional preference'). By contrast, total consumption varied plastically as a function of body weight within individuals. Body weight-but not personality (i.e., aggression, exploration behaviour)-positively predicted nutritional preference at the individual level as large crickets repeatedly consumed a higher carbohydrate to protein ratio compared to small ones. Our finding of level-specific associations between the consumption of distinct nutritional components demonstrates the merit of applying multivariate and multi-level viewpoints to the study of nutritional preference.

Dietary choice for a balanced nutrient intake increases the mean and reduces the variance in the reproductive performance of male and female cockroaches

Sexual selection may cause dietary requirements for reproduction to diverge across the sexes and promote the evolution of different foraging strategies in males and females. However, our understanding of how the sexes regulate their nutrition and the effects that this has on sex‐specific fitness is limited. We quantified how protein (P) and carbohydrate (C) intakes affect reproductive traits in male (pheromone expression) and female (clutch size and gestation time) cockroaches (Nauphoeta cinerea). We then determined how the sexes regulate their intake of nutrients when restricted to a single diet and when given dietary choice and how this affected expression of these important reproductive traits. Pheromone levels that improve male attractiveness, female clutch size and gestation time all peaked at a high daily intake of P:C in a 1:8 ratio. This is surprising because female insects typically require more P than males to maximize reproduction. The relatively low P requirement of females may reflect the action of cockroach endosymbionts that help recycle stored nitrogen for protein synthesis. When constrained to a single diet, both sexes prioritized regulating their daily intake of P over C, although this prioritization was stronger in females than males. When given the choice between diets, both sexes actively regulated their intake of nutrients at a 1:4.8 P:C ratio. The P:C ratio did not overlap exactly with the intake of nutrients that optimized reproductive trait expression. Despite this, cockroaches of both sexes that were given dietary choice generally improved the mean and reduced the variance in all reproductive traits we measured relative to animals fed a single diet from the diet choice pair. This pattern was not as strong when compared to the single best diet in our geometric array, suggesting that the relationship between nutrient balancing and reproduction is complex in this species.

Adaptive collective foraging in groups with conflicting nutritional needs

Collective foraging, based on positive feedback and quorum responses, is believed to improve the foraging efficiency of animals. Nutritional models suggest that social information transfer increases the ability of foragers with closely aligned nutritional needs to find nutrients and maintain a balanced diet. However, whether or not collective foraging is adaptive in a heterogeneous group composed of individuals with differing nutritional needs is virtually unexplored. Here we develop an evolutionary agent-based model using concepts of nutritional ecology to address this knowledge gap. Our aim was to evaluate how collective foraging, mediated by social retention on foods, can improve nutrient balancing in individuals with different requirements. The model suggests that in groups where inter-individual nutritional needs are unimodally distributed, high levels of collective foraging yield optimal individual fitness by reducing search times that result from moving between nutritionally imbalanced foods. However, where nutritional needs are highly bimodal (e.g. where the requirements of males and females differ) collective foraging is selected against, leading to group fission. In this case, additional mechanisms such as assortative interactions can coevolve to allow collective foraging by subgroups of individuals with aligned requirements. Our findings indicate that collective foraging is an efficient strategy for nutrient regulation in animals inhabiting complex nutritional environments and exhibiting a range of social forms.

Social Network Analysis and Nutritional Behavior: An Integrated Modeling Approach

Animals have evolved complex foraging strategies to obtain a nutritionally balanced diet and associated fitness benefits. Recent research combining state-space models of nutritional geometry with agent-based models (ABMs), show how nutrient targeted foraging behavior can also influence animal social interactions, ultimately affecting collective dynamics and group structures. Here we demonstrate how social network analyses can be integrated into such a modeling framework and provide a practical analytical tool to compare experimental results with theory. We illustrate our approach by examining the case of nutritionally mediated dominance hierarchies. First we show how nutritionally explicit ABMs that simulate the emergence of dominance hierarchies can be used to generate social networks. Importantly the structural properties of our simulated networks bear similarities to dominance networks of real animals (where conflicts are not always directly related to nutrition). Finally, we demonstrate how metrics from social network analyses can be used to predict the fitness of agents in these simulated competitive environments. Our results highlight the potential importance of nutritional mechanisms in shaping dominance interactions in a wide range of social and ecological contexts. Nutrition likely influences social interactions in many species, and yet a theoretical framework for exploring these effects is currently lacking. Combining social network analyses with computational models from nutritional ecology may bridge this divide, representing a pragmatic approach for generating theoretical predictions for nutritional experiments.