Suboptimal foraging theory: How inaccurate predictions and approximations can make better models of adaptive behavior

Optimal foraging theory (OFT) is based on the ecological concept that organisms select behaviors that convey future fitness, and on the mathematical concept of optimization: finding the alternative that provides the best value of a fitness measure. As implemented in, e.g., state-based dynamic modeling, OFT is powerful for one key problem of modern ecology: modeling behavior as a tradeoff among competing fitness elements such as growth, risk avoidance, and reproductive output. However, OFT is not useful for other modern problems such as representing feedbacks within systems of interacting, unique individuals: when we need to model foraging by each of many individuals that interact competitively or synergistically, optimization is impractical or impossible-there are no optimal behaviors. For such problems we can, however, still use the concept of future fitness to model behavior, by replacing optimization with less precise (but perhaps more realistic) techniques for ranking alternatives. Instead of simplifying the systems we model until we can find "optimal" behavior, we can use theory based on inaccurate predictions, coarse approximations, and updating to produce good behavior in more complex and realistic contexts. This "state- and prediction-based theory" (SPT) can, for example, produce realistic foraging decisions by each of many unique, interacting individuals when growth rates and predation risks vary over space and time. Because SPT lets us address more natural complexity and more realistic problems, it is more easily tested against more kinds of observation and more useful in management ecology. A simple foraging model illustrates how SPT readily accommodates complexities that make optimization intractable. Other models use SPT to represent contingent decisions (whether to feed or hide, in what patch) that are tradeoffs between growth and predation risk, when both growth and risk vary among hundreds of patches, vary unpredictably over time, depend on characteristics of the individuals, are subject to feedbacks from competition, and change over the daily light cycle. Modern ecology demands theory for tradeoff behaviors in complex contexts that produce feedbacks; when optimization is infeasible, we should not be afraid to use approximate fitness-seeking methods instead.

From theory to practice in pattern-oriented modelling: identifying and using empirical patterns in predictive models

To robustly predict the effects of disturbance and ecosystem changes on species, it is necessary to produce structurally realistic models with high predictive power and flexibility. To ensure that these models reflect the natural conditions necessary for reliable prediction, models must be informed and tested using relevant empirical observations. Pattern-oriented modelling (POM) offers a systematic framework for employing empirical patterns throughout the modelling process and has been coupled with complex systems modelling, such as in agent-based models (ABMs). However, while the production of ABMs has been rising rapidly, the explicit use of POM has not increased. Challenges with identifying patterns and an absence of specific guidelines on how to implement empirical observations may limit the accessibility of POM and lead to the production of models which lack a systematic consideration of reality. This review serves to provide guidance on how to identify and apply patterns following a POM approach in ABMs (POM-ABMs), specifically addressing: where in the ecological hierarchy can we find patterns; what kinds of patterns are useful; how should simulations and observations be compared; and when in the modelling cycle are patterns used? The guidance and examples provided herein are intended to encourage the application of POM and inspire efficient identification and implementation of patterns for both new and experienced modellers alike. Additionally, by generalising patterns found especially useful for POM-ABM development, these guidelines provide practical help for the identification of data gaps and guide the collection of observations useful for the development and verification of predictive models. Improving the accessibility and explicitness of POM could facilitate the production of robust and structurally realistic models in the ecological community, contributing to the advancement of predictive ecology at large.

Two hundred years of zooplankton vertical migration research

Vertical migration is a geographically and taxonomically widespread behaviour among zooplankton that spans across diel and seasonal timescales. The shorter-term diel vertical migration (DVM) has a periodicity of up to 1 day and was first described by the French naturalist Georges Cuvier in 1817. In 1888, the German marine biologist Carl Chun described the longer-term seasonal vertical migration (SVM), which has a periodicity of ca. 1 year. The proximate control and adaptive significance of DVM have been extensively studied and are well understood. DVM is generally a behaviour controlled by ambient irradiance, which allows herbivorous zooplankton to feed in food-rich shallower waters during the night when light-dependent (visual) predation risk is minimal and take refuge in deeper, darker waters during daytime. However, DVMs of herbivorous zooplankton are followed by their predators, producing complex predator-prey patterns that may be traced across multiple trophic levels. In contrast to DVM, SVM research is relatively young and its causes and consequences are less well understood. During periods of seasonal environmental deterioration, SVM allows zooplankton to evacuate shallower waters seasonally and take refuge in deeper waters often in a state of dormancy. Both DVM and SVM play a significant role in the vertical transport of organic carbon to deeper waters (biological carbon sequestration), and hence in the buffering of global climate change. Although many animal migrations are expected to change under future climate scenarios, little is known about the potential implications of global climate change on zooplankton vertical migrations and its impact on the biological carbon sequestration process. Further, the combined influence of DVM and SVM in determining zooplankton fitness and maintenance of their horizontal (geographic) distributions is not well understood. The contrasting spatial (deep versus shallow) and temporal (diel versus seasonal) scales over which these two migrations occur lead to challenges in studying them at higher spatial, temporal and biological resolution and coverage. Extending the largely population-based vertical migration knowledge base to individual-based studies will be an important way forward. While tracking individual zooplankton in their natural habitats remains a major challenge, conducting trophic-scale, high-resolution, year-round studies that utilise emerging field sampling and observation techniques, molecular genetic tools and computational hardware and software will be the best solution to improve our understanding of zooplankton vertical migrations.

Computational animal welfare: towards cognitive architecture models of animal sentience, emotion and wellbeing

To understand animal wellbeing, we need to consider subjective phenomena and sentience. This is challenging, since these properties are private and cannot be observed directly. Certain motivations, emotions and related internal states can be inferred in animals through experiments that involve choice, learning, generalization and decision-making. Yet, even though there is significant progress in elucidating the neurobiology of human consciousness, animal consciousness is still a mystery. We propose that computational animal welfare science emerges at the intersection of animal behaviour, welfare and computational cognition. By using ideas from cognitive science, we develop a functional and generic definition of subjective phenomena as any process or state of the organism that exists from the first-person perspective and cannot be isolated from the animal subject. We then outline a general cognitive architecture to model simple forms of subjective processes and sentience. This includes evolutionary adaptation which contains top-down attention modulation, predictive processing and subjective simulation by re-entrant (recursive) computations. Thereafter, we show how this approach uses major characteristics of the subjective experience: elementary self-awareness, global workspace and qualia with unity and continuity. This provides a formal framework for process-based modelling of animal needs, subjective states, sentience and wellbeing.

A framework and standardized terminology to facilitate the study of predation-risk effects

The very presence of predators can strongly influence flexible prey traits such as behavior, morphology, life history, and physiology. In a rapidly growing body of literature representing diverse ecological systems, these trait (or "fear") responses have been shown to influence prey fitness components and density, and to have indirect effects on other species. However, this broad and exciting literature is burdened with inconsistent terminology that is likely hindering the development of inclusive frameworks and general advances in ecology. We examine the diverse terminology used in the literature, and discuss pros and cons of the many terms used. Common problems include the same term being used for different processes, and many different terms being used for the same process. To mitigate terminological barriers, we developed a conceptual framework that explicitly distinguishes the multiple predation-risk effects studied. These multiple effects, along with suggested standardized terminology, are risk-induced trait responses (i.e., effects on prey traits), interaction modifications (i.e., effects on prey-other-species interactions), nonconsumptive effects (i.e., effects on the fitness and density of the prey), and trait-mediated indirect effects (i.e., the effects on the fitness and density of other species). We apply the framework to three well studied systems to highlight how it can illuminate commonalities and differences among study systems. By clarifying and elucidating conceptually similar processes, the framework and standardized terminology can facilitate communication of insights and methodologies across systems and foster cross-disciplinary perspectives.

Movement rule selection through eco-genetic modeling: Application to diurnal vertical movement

Agent-based, spatially-explicit models that incorporate movement rules are used across ecological disciplines for a variety of applications. However, appropriate movement rules may be difficult to implement due to the complexity of an individual's response to both proximate and ultimate cues, as well as the difficulty in directly assessing how organisms choose to move across their environment. Environmental cues may be complex and dynamic, and therefore, movement responses may require tradeoffs between preferred levels of different environmental variables (e.g., temperature, light level, and prey availability). Here, we present an approach to determine appropriate movement rules by setting them as heritable traits in an eco-genetic modeling framework and allowing movement rules to evolve during the model rather than setting them a priori. We modeled yellow perch, Perca flavescens, movement in a simulated environment and allowed perch to move in response to high-resolution vertical gradients in temperature, dissolved oxygen, light, predators, and prey. Evolving movement rules ultimately increased fish growth and survival over generations in our model, indicating that evolving movement rules led to improved individual performance. We found that emergent movement rules were consistent across trials, with evolved movement rules incorporating different weights of these environmental factors and the most rapid selection on temperature preference. This case study presents a flexible method using eco-genetic modeling to determine appropriate movement rules that can be applied to diverse scenarios in spatially-explicit ecological modeling.

Eco-genetic model to explore fishing-induced ecological and evolutionary effects on growth and maturation schedules

Eco-genetic individual-based models involve tracking the ecological dynamics of simulated individual organisms that are in part characterized by heritable parameters. We developed an eco-genetic individual-based model to explore ecological and evolutionary interactions of fish growth and maturation schedules. Our model is flexible and allows for exploration of the effects of heritable growth rates (based on von Bertalanffy and biphasic growth patterns), heritable maturation schedules (based on maturation reaction norm concepts), or both on individual- and population-level traits. In baseline simulations with rather simple ecological trade-offs and over a relatively short time period (<200 simulation years), simulated male and female fish evolve differential genetic growth and maturation. Further, resulting patterns of genetically determined growth and maturation are influenced by mortality rate and density-dependent processes, and maturation and growth parameters interact to mediate the evolution of one another. Subsequent to baseline simulations, we conducted experimental simulations to mimic fisheries harvest with two size-limits (targeting large or small fish), an array of fishing mortality rates, and assuming a deterministic or stochastic environment. Our results suggest that fishing with either size-limit may induce considerable changes in life-history trait expression (maturation schedules and growth rates), recruitment, and population abundance and structure. However, targeting large fish would cause more adverse genetic effects and may lead to a population less resilient to environmental stochasticity.

Size-selective fishing gear and life history evolution in the Northeast Arctic cod

Industrial fishing has been identified as a cause for life history changes in many harvested stocks, mainly because of the intense fishing mortality and its size-selectivity. Because these changes are potentially evolutionary, we investigate evolutionarily stable life-histories and yield in an energy-allocation state-dependent model for Northeast Arctic cod Gadus morhua. We focus on the evolutionary effects of size-selective fishing because regulation of gear selectivity may be an efficient management tool. Trawling, which harvests fish above a certain size, leads to early maturation except when fishing is low and confined to mature fish. Gillnets, where small and large fish escape, lead to late maturation for low to moderate harvest rates, but when harvest rates increase maturation age suddenly drops. This is because bell-shaped selectivity has two size-refuges, for fish that are below and above the harvestable size-classes. Depending on the harvest rate it either pays to grow through the harvestable slot and mature above it, or mature small below it. Sustainable yield on the evolutionary time-scale is highest when fishing is done by trawling, but only for a small parameter region. Fishing with gillnets is better able to withstand life-history evolution, and maintains yield over a wider range of fishing intensities.

The emotion system promotes diversity and evolvability

Studies on the relationship between the optimal phenotype and its environment have had limited focus on genotype-to-phenotype pathways and their evolutionary consequences. Here, we study how multi-layered trait architecture and its associated constraints prescribe diversity. Using an idealized model of the emotion system in fish, we find that trait architecture yields genetic and phenotypic diversity even in absence of frequency-dependent selection or environmental variation. That is, for a given environment, phenotype frequency distributions are predictable while gene pools are not. The conservation of phenotypic traits among these genetically different populations is due to the multi-layered trait architecture, in which one adaptation at a higher architectural level can be achieved by several different adaptations at a lower level. Our results emphasize the role of convergent evolution and the organismal level of selection. While trait architecture makes individuals more constrained than what has been assumed in optimization theory, the resulting populations are genetically more diverse and adaptable. The emotion system in animals may thus have evolved by natural selection because it simultaneously enhances three important functions, the behavioural robustness of individuals, the evolvability of gene pools and the rate of evolutionary innovation at several architectural levels.

Effects of the emotion system on adaptive behavior

A central simplifying assumption in evolutionary behavioral ecology has been that optimal behavior is unaffected by genetic or proximate constraints. Observations and experiments show otherwise, so that attention to decision architecture and mechanisms is needed. In psychology, the proximate constraints on decision making and the processes from perception to behavior are collectively described as the emotion system. We specify a model of the emotion system in fish that includes sensory input, neuronal computation, developmental modulation, and a global organismic state and restricts attention during decision making for behavioral outcomes. The model further includes food competition, safety in numbers, and a fluctuating environment. We find that emergent strategies in evolved populations include common emotional appraisal of sensory input related to fear and hunger and also include frequency-dependent rules for behavioral responses. Focused attention is at times more important than spatial behavior for growth and survival. Spatial segregation of the population is driven by personality differences. By coupling proximate and immediate influences on behavior with ultimate fitness consequences through the emotion system, this approach contributes to a unified perspective on the phenotype, by integrating effects of the environment, genetics, development, physiology, behavior, life history, and evolution.

Trait-mediated trophic interactions: is foraging theory keeping up?

Many ecologists believe that there is a lack of foraging theory that works in community contexts, for populations of unique individuals each making trade-offs between food and risk that are subject to feedbacks from behavior of others. Such theory is necessary to reproduce the trait-mediated trophic interactions now recognized as widespread and strong. Game theory can address feedbacks but does not provide foraging theory for unique individuals in variable environments. 'State- and prediction-based theory' (SPT) is a new approach that combines existing trade-off methods with routine updating: individuals regularly predict future food availability and risk from current conditions to optimize a fitness measure. SPT can reproduce a variety of realistic foraging behaviors and trait-mediated trophic interactions with feedbacks, even when the environment is unpredictable.

Optimal resource allocation to survival and reproduction in parasitic wasps foraging in fragmented habitats

Expansion and intensification of human land use represents the major cause of habitat fragmentation. Such fragmentation can have dramatic consequences on species richness and trophic interactions within food webs. Although the associated ecological consequences have been studied by several authors, the evolutionary effects on interacting species have received little research attention. Using a genetic algorithm, we quantified how habitat fragmentation and environmental variability affect the optimal reproductive strategies of parasitic wasps foraging for hosts. As observed in real animal species, the model is based on the existence of a negative trade-off between survival and reproduction resulting from competitive allocation of resources to either somatic maintenance or egg production. We also asked to what degree plasticity along this trade-off would be optimal, when plasticity is costly. We found that habitat fragmentation can indeed have strong effects on the reproductive strategies adopted by parasitoids. With increasing habitat fragmentation animals should invest in greater longevity with lower fecundity; yet, especially in unpredictable environments, some level of phenotypic plasticity should be selected for. Other consequences in terms of learning ability of foraging animals were also observed. The evolutionary consequences of these results are discussed.

Simulating Species Richness Using Agents with Evolving Niches, with an Example of Galápagos Plants

I sought to evolve plant species richness patterns on 22 Galápagos Islands, Ecuador, as an exploration of the utility of evolutionary computation and an agent-based approach in biogeography research. The simulation was spatially explicit, where agents were plant monocultures defined by three niche dimensions, lava (yes or no), elevation, and slope. Niches were represented as standard normal curves subjected to selection pressure, where neighboring plants bred if their niches overlapped sufficiently, and were considered the same species, otherwise they were different species. Plants that bred produced seeds with mutated niches. Seeds dispersed locally and longer distances, and established if the habitat was appropriate given the seed's niche. From a single species colonizing a random location, hundreds of species evolved to fill the islands. Evolved plant species richness agreed very well with observed plant species richness. I review potential uses of an agent-based representation of evolving niches in biogeography research.

Individual-based ecology of coastal birds

Conservation objectives for non-breeding coastal birds (shorebirds and wildfowl) are determined from their population size at coastal sites. To advise coastal managers, models must predict quantitatively the effects of environmental change on population size or the demographic rates (mortality and reproduction) that determine it. As habitat association models and depletion models are not able to do this, we developed an approach that has produced such predictions thereby enabling policy makers to make evidence-based decisions. Our conceptual framework is individual-based ecology, in which populations are viewed as having properties (e.g. size) that arise from the traits (e.g. behaviour, physiology) and interactions of their constituent individuals. The link between individuals and populations is made through individual-based models (IBMs) that follow the fitness-maximising decisions of individuals and predict population-level consequences (e.g. mortality rate) from the fates of these individuals. Our first IBM was for oystercatchers Haematopus ostralegus and accurately predicted their density-dependent mortality. Subsequently, IBMs were developed for several shorebird and wildfowl species at several European sites, and were shown to predict accurately overwinter mortality, and the foraging behaviour from which predictions are derived. They have been used to predict the effect on survival in coastal birds of sea level rise, habitat loss, wind farm development, shellfishing and human disturbance. This review emphasises the wider applicability of the approach, and identifies other systems to which it could be applied. We view the IBM approach as a very useful contribution to the general problem of how to advance ecology to the point where we can routinely make meaningful predictions of how populations respond to environmental change.

In silico evolution of functional morphology: A test on bone tissue biomechanics

Evolutionary algorithms (EAs) use Darwinian principles--selection among random variation and heredity--to find solutions to complex problems. Mostly used in engineering, EAs gain growing interest in ecology and genetics. Here, we assess their usefulness in functional morphology, introducing finite element modelling (FEM) as a simulated mechanical environment for evaluating the 'fitness' of randomly varying structures. We used this method to identify biomechanical adaptations in bone tissue, a long-lasting problem in skeletal morphology. The algorithm started with a bone tissue model containing randomly distributed vascular spaces. The EA randomly mutated the distribution of vascular spaces, and selected the new structure if its mechanical resistance was increased. After some thousands of generations, organized phenotypes emerged, containing vascular canals and sinuses, mimicking real bone tissue organizations. This supported the hypothesis that natural bone microstructures can result from biomechanical adaptation. Despite its limited faithfulness to reality, we discuss the ability of the EA+FEM method to assess adaptation in a dynamic evolutionary framework, which is not possible in the real world because of the generation times of macro-organisms. We also point out the interesting potential of EAs to simulate not only adaptation, but also concurrent evolutionary phenomenons such as historical contingency.

Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth

We used evolutionary programming to model innate migratory pathways of wildebeest in the Serengeti Mara Ecosystem, Tanzania and Kenya. Wildebeest annually move from the southern short-grass plains of the Serengeti to the northern woodlands of the Mara. We used satellite images to create 12 average monthly and 180 10-day surfaces from 1998 to 2003 of percentage rainfall and new vegetation. The surfaces were combined in five additive and three multiplicative models, with the weightings on rainfall and new vegetation from 0% to 100%. Modeled wildebeest were first assigned random migration pathways. In simulated generations, animals best able to access rainfall and vegetation were retained, and they produced offspring with similar migratory pathways. Modeling proceeded until the best pathway was stable. In a learning phase, modeling continued with the ten-day images in the objective function. The additive model, influenced 25% by rainfall and 75% by vegetation growth, yielded the best agreement, with a multi-resolution comparison to observed densities yielding 76.8% of blocks in agreement (kappa = 0.32). Agreement was best for dry season and early wet season (kappa = 0.22-0.57), and poorest for the late wet season (0.04). The model suggests that new forage growth is a dominant correlate of wildebeest migration.

Modelling the many-wrongs principle: the navigational advantages of aggregation in nomadic foragers

We develop a simple individual-based model to gain an understanding of the drivers of aggregation behaviour in nomadic foragers. The model incorporates two key elements influencing nomadic foragers in variable environments: uncertainty regarding the location of food sources and variability in the spatio-temporal distribution of ephemeral food sources. A genetic algorithm is used to evolve parameters describing an individual's movement and aggregation strategy. We apply the aggregation model to a case study of the Bornean bearded pig (Sus barbatus). Bearded pigs are ideal for considering the foraging advantages of aggregation, because they are highly mobile and exhibit a variety of aggregation strategies, ranging from solitary and sedentary to mass aggregation and wide ranging migration. Our model demonstrates the "many-wrongs principle", and shows that environmental variability, uncertainty in the location of food sources, and local population density drive aggregation behaviour.