Simplifying a physiologically structured population model to a stage-structured biomass model

A nonautonomous model for the interaction between a size-structured consumer and an unstructured resource

In this paper, we propose and analyze a nonautonomous model that describes the dynamics of a size-structured consumer interacting with an unstructured resource. We prove the existence and uniqueness of the solution of the model using the monotone method based on a comparison principle. We derive conditions on the model parameters that result in persistence and extinction of the population via the upper-lower solution technique. We verify and complement the theoretical results through numerical simulations.

Pathogens stabilize or destabilize depending on host stage structure

A common assumption is that pathogens more readily destabilize their host populations, leading to an elevated risk of driving both the host and pathogen to extinction. This logic underlies many strategies in conservation biology and pest and disease management. Yet, the interplay between pathogens and population stability likely varies across contexts, depending on the environment and traits of both the hosts and pathogens. This context-dependence may be particularly important in natural consumer-host populations where size- and stage-structured competition for resources strongly modulates population stability. Few studies, however, have examined how the interplay between size and stage structure and infectious disease shapes the stability of host populations. Here, we extend previously developed size-dependent theory for consumer-resource interactions to examine how pathogens influence the stability of host populations across a range of contexts. Specifically, we integrate a size- and stage-structured consumer-resource model and a standard epidemiological model of a directly transmitted pathogen. The model reveals surprisingly rich dynamics, including sustained oscillations, multiple steady states, biomass overcompensation, and hydra effects. Moreover, these results highlight how the stage structure and density of host populations interact to either enhance or constrain disease outbreaks. Our results suggest that accounting for these cross-scale and bidirectional feedbacks can provide key insight into the structuring role of pathogens in natural ecosystems while also improving our ability to understand how interventions targeting one may impact the other.

Life-history responses to temperature and seasonality mediate ectotherm consumer-resource dynamics under climate warming

Climate warming is altering life cycles of ectotherms by advancing phenology and decreasing generation times. Theoretical models provide powerful tools to investigate these effects of climate warming on consumer-resource population dynamics. Yet, existing theory primarily considers organisms with simplified life histories in constant temperature environments, making it difficult to predict how warming will affect organisms with complex life cycles in seasonal environments. We develop a size-structured consumer-resource model with seasonal temperature dependence, parameterized for a freshwater insect consuming zooplankton. We simulate how climate warming in a seasonal environment could alter a key life-history trait of the consumer, number of generations per year, mediating responses of consumer-resource population sizes and consumer persistence. We find that, with warming, consumer population sizes increase through multiple mechanisms. First, warming decreases generation times by increasing rates of resource ingestion and growth and/or lengthening the growing season. Second, these life-history changes shorten the juvenile stage, increasing the number of emerging adults and population-level reproduction. Unstructured models with similar assumptions found that warming destabilized consumer-resource dynamics. By contrast, our size-structured model predicts stability and consumer persistence. Our study suggests that, in seasonal environments experiencing climate warming, life-history changes that lead to shorter generation times could delay population extinctions.

Plastic energy allocation toward life-history functions in a consumer-resource interaction : Analyzing the temporal patterns of the consumer-resource dynamics

Various environmental alterations resulting from the current global change compromise the persistence of species in their habitual environment. To cope with the obvious risk of extinction, plastic responses provide organisms with rapid acclimatization to new environments. The premise of plastic rescue has been theoretically studied from mathematical models in both deterministic and stochastic environments, focusing on analyzing the persistence and stability of the populations. Here, we evaluate this premise in the framework of a consumer-resource interaction considering the energy investment towards reproduction vs. maintenance as a plastic trait according to positive/negative variation of the available resource. A basic consumer-resource mathematical model is formulated based on the principle of biomass conversion that incorporates the energy allocation toward vital functions of the life-cycle of consumer individuals. Our mathematical approach is based on the impulsive differential equations at fixed moments considering two impulsive effects associated with the instants at which consumers obtain environmental information and when energy allocation strategy change occurs. From a preliminary analysis of the non-plastic temporal dynamics, namely when the energy allocation is constant over time and without experiencing changes concerning the variation of resources, both the persistence and stability of the consumer-resource dynamic are dependent on the energy allocation strategies belonging to a set termed stability range. We found that the plastic energy allocation can promote a stable dynamical pattern in the consumer-resource interaction depending on both the magnitude of the energy allocation change and the time lag between environmental sensibility instants and when the expression of the plastic trait occurs.

Linking multi-level population dynamics: state, role, and population

The dynamics of an ecological community can be described at different focal scales of the species, such as individual states or the population level. More detailed descriptions of ecological dynamics offer more information, but produce more complex models that are difficult to analyze. Adequately controlling the model complexity and the availability of multiple descriptions of the concerned dynamics maximizes our understanding of ecological dynamics. One of the central goals of ecological studies is to develop links between multiple descriptions of an ecological community. In this article, starting from a nonlinear state-level description of an ecological community (generalized McKendrick-von Foerster model), role-level and population-level descriptions (Lotka-Volterra model) are derived in a consistent manner. The role-level description covers a wider range of situations than the population-level description. However, using the established connections, it is demonstrated that the population-level description can be used to predict the equilibrium status of the role-level description. This approach connects state-, role-, and population-level dynamics consistently, and offers a justification for the multiple choices of model description.

Smaller species but larger stages: Warming effects on inter- and intraspecific community size structure

Global warming can alter size distributions of animal communities, but the contribution of size shifts within versus between species to such changes remains unknown. In particular, it is unclear if expected body size shrinkage in response to warming, observed at the interspecific level, can be used to infer similar size shifts within species. In this study, we compare warming effects on interspecific (relative species abundance) versus intraspecific (relative stage abundance) size structure of competing consumers by analyzing stage‐structured bioenergetic food web models consisting of one or two consumer species and two resources, parameterized for pelagic plankton. Varying composition and temperature and body size dependencies in these models, we predicted interspecific versus intraspecific size structure across temperature. We found that warming shifted community size structure toward dominance of smaller species, in line with empirical evidence summarized in our review of 136 literature studies. However, this result emerged only given a size–temperature interaction favoring small over large individuals in warm environments. In contrast, the same mechanism caused an intraspecific shift toward dominance of larger (adult) stages, reconciling disparate observations of size responses within and across zooplankton species in the literature. As the empirical evidence for warming‐driven stage shifts is scarce and equivocal, we call for more experimental studies on intraspecific size changes with warming. Understanding the global warming impacts on animal communities requires that we consider and quantify the relative importance of mechanisms concurrently shaping size distributions within and among species.

Effects of Warming on Intraguild Predator Communities with Ontogenetic Diet Shifts

AbstractSpecies interactions mediate how warming affects community composition via individual growth and population size structure. While predictions on how warming affects composition of size- or stage-structured communities have so far focused on linear (food chain) communities, mixed competition-predation interactions, such as intraguild predation, are common. Intraguild predation often results from changes in diet over ontogeny ("ontogenetic diet shifts") and strongly affects community composition and dynamics. Here, we study how warming affects a community of intraguild predators with ontogenetic diet shifts, consumers, and shared prey by analyzing a stage-structured bioenergetics multispecies model with temperature- and body size-dependent individual-level rates. We find that warming can strengthen competition and decrease predation, leading to a loss of a cultivation mechanism (the feedback between predation on and competition with consumers exerted by predators) and ultimately predator collapse. Furthermore, we show that the effect of warming on community composition depends on the extent of the ontogenetic diet shift and that warming can cause a sequence of community reconfigurations in species with partial diet shifts. Our findings contrast previous predictions concerning individual growth of predators and the mechanisms behind predator loss in warmer environments and highlight how feedbacks between temperature and intraspecific size structure are important for understanding such effects on community composition.

Should we account for mesozooplankton reproduction and ontogenetic growth in biogeochemical modeling?

Mesozooplankton play a key role in marine ecosystems as they modulate the transfer of energy from phytoplankton to large marine organisms. In addition, they directly influence the oceanic cycles of carbon and nutrients through vertical migrations, fecal pellet production, respiration, and excretion. Mesozooplankton are mainly made up of metazoans, which undergo important size changes during their life cycle, resulting in significant variations in metabolic rates. However, most marine biogeochemical models represent mesozooplankton as protists-like organisms. Here, we study the potential caveats of this simplistic representation by using a chemostat-like zero-dimensional model with four different Nutrient-Phytoplankton-Zooplankton configurations in which the description of mesozooplankton ranges from protist-type organisms to using a size-based formulation including explicit reproduction and ontogenetic growth. We show that the size-based formulation strongly impacts mesozooplankton. First, it generates a delay of a few months in the response to an increase in food availability. Second, the increase in mesozooplankton biomass displays much larger temporal variations, in the form of successive cohorts, because of the dependency of the ingestion rate to body size. However, the size-based formulation does not affect smaller plankton or nutrient concentrations. A proper assessment of these top-down effects would require implementing our size-resolved approach in a 3-dimensional biogeochemical model. Furthermore, the bottom-up effects on higher trophic levels resulting from the significant changes in the temporal dynamics of mesozooplankton could be estimated in an end-to-end model coupling low and high trophic levels.

Evolution of Reproduction Periods in Seasonal Environments

AbstractMany species are subject to seasonal cycles in resource availability, affecting the timing of their reproduction. Using a stage-structured consumer-resource model in which juvenile development and maturation are resource dependent, we study how a species' reproductive schedule evolves, dependent on the seasonality of its resource. We find three qualitatively different reproduction modes. First, continuous income breeding (with adults reproducing throughout the year) evolves in the absence of significant seasonality. Second, seasonal income breeding (with adults reproducing unless they are starving) evolves when resource availability is sufficiently seasonal and juveniles are more efficient resource foragers. Third, seasonal capital breeding (with adults reproducing partly through the use of energy reserves) evolves when resource availability is sufficiently seasonal and adults are more efficient resource foragers. Such capital breeders start reproduction already while their offspring are still experiencing starvation. Changes in seasonality lead to continuous transitions between continuous and seasonal income breeding, but the change between income and capital breeding involves a hysteresis pattern, such that a population's evolutionarily stable reproduction pattern depends on its initial one. Taken together, our findings show how adaptation to seasonal environments can result in a rich array of outcomes, exhibiting seasonal or continuous reproduction with or without energy reserves.

Infection pathology and competition mediate host biomass overcompensation from disease

Predators can increase the biomass of their prey, particularly when prey life stages differ in competitive ability and predation is stage specific. Akin to predators, parasites influence host population sizes and engage in stage-structured interactions, yet whether parasites can increase host population biomass remains relatively unexplored. Using a stage-structured consumer-resource model and a mesocosm experiment with snails and castrating trematodes, we examined responses of host biomass to changes in infection prevalence under variation in host pathology and resource competition. Equilibrium adult host biomass increased with infection prevalence in the model when parasites castrated hosts and adults were superior competitors to juveniles. Juvenile biomass increased with infection prevalence whether parasites caused mortality or castration, but only when juveniles were superior competitors. In mesocosms, increases in infection by castrating trematodes reduced snail egg production, juvenile abundance, and adult survival. At high competition, juvenile growth and total biomass increased with infection prevalence due to competitive release. At low competition, juvenile biomass decreased with infection due to reduced reproduction. These results highlight how disease-induced biomass overcompensation depends on infection pathology, resource availability, and competitive interactions within and between host life stages. Considering such characteristics may benefit biocontrol efforts using parasites.

False Exclusion: A Case to Embed Predator Performance in Classical Population Models

We argue that predator-prey dynamics, a cornerstone of ecology, can be driven by insufficiently explored aspects of predator performance that are inherently prey dependent: that is, these have been falsely excluded. Classical (Lotka-Volterra-based) models tend to consider only prey-dependent ingestion rate. We highlight three other prey-dependent responses and provide empirically derived functions to describe them. These functions introduce neglected nonlinearities and threshold behaviors into dynamic models, leading to unexpected outcomes: specifically, as prey abundance increases predators (1) become less efficient at using prey; (2) initially allocate resources toward survival and then allocate resources toward reproduction; and (3) are less likely to die. Based on experiments using model zooplankton, we explore the consequences of including these functions in the classical structure and show that they alter qualitative and quantitative dynamics of an empirically informed generic predator-prey model. Through bifurcation analysis, our revised structure predicts (1) predator extinctions, where the classical structure allows persistence; (2) predator survival, where the classical structure drives predators toward extinction; and (3) greater stability through smaller amplitude of cycles, relative to the classical structure. Then, by exploring parameter space, we show how these responses alter predictions of predator-prey stability and competition between predators. In light of our results, we suggest that classical assumptions about predator responses to prey abundance should be reevaluated.

A physiologically-structured fish population model with size-dependent foraging

A previous physiologically-structured model for a fish population based on individual-level characteristics is studied. The foraging rate is generalized to include a size-dependent functional response and the energy distribution of adults is generalized to permit both reproduction and growth. Equilibria are determined and their stability studied along with a discussion of harvesting strategies. The model with these generalizations is shown to give different predictions than the original model regarding age distribution of fish and harvesting strategies.

Cannibalism prevents evolutionary suicide of ontogenetic omnivores in life-history intraguild predation systems

The majority of animal species are ontogenetic omnivores, that is, individuals of these species change or expand their diet during life. If small ontogenetic omnivores compete for a shared resource with their future prey, ecological persistence of ontogenetic omnivores can be hindered, although predation by large omnivores facilitates persistence. The coupling of developmental processes between different life stages might lead to a trade-off between competition early in life and predation later in life, especially for ontogenetic omnivores that lack metamorphosis. By using bioenergetic modeling, we study how such an ontogenetic trade-off affects ecological and evolutionary dynamics of ontogenetic omnivores. We find that selection toward increasing specialization of one life stage leads to evolutionary suicide of noncannibalistic ontogenetic omnivores, because it leads to a shift toward an alternative community state. Ontogenetic omnivores fail to re-invade this new state due to the maladaptiveness of the other life stage. Cannibalism stabilizes selection on the ontogenetic trade-off, prevents evolutionary suicide of ontogenetic omnivores, and promotes coexistence of omnivores with their prey. We outline how ecological and evolutionary persistence of ontogenetic omnivores depends on the type of diet change, cannibalism, and competitive hierarchy between omnivores and their prey.

Size-based ecological interactions drive food web responses to climate warming

Predicting climate change impacts on animal communities requires knowledge of how physiological effects are mediated by ecological interactions. Food-dependent growth and within-species size variation depend on temperature and affect community dynamics through feedbacks between individual performance and population size structure. Still, we know little about how warming affects these feedbacks. Using a dynamic stage-structured biomass model with food-, size- and temperature-dependent life history processes, we analyse how temperature affects coexistence, stability and size structure in a tri-trophic food chain, and find that warming effects on community stability depend on ecological interactions. Predator biomass densities generally decline with warming - gradually or through collapses - depending on which consumer life stage predators feed on. Collapses occur when warming induces alternative stable states via Allee effects. This suggests that predator persistence in warmer climates may be lower than previously acknowledged and that effects of warming on food web stability largely depend on species interactions.

Meeting Yield and Conservation Objectives by Harvesting Both Juveniles and Adults

Sustainable yields that are at least 80% of the maximum sustainable yield are sometimes referred to as "pretty good yields" (PGY). The range of PGY harvesting strategies is generally broad and thus leaves room to account for additional objectives besides high yield. Here, we analyze stage-dependent harvesting strategies that realize PGY with conservation as a second objective. We show that (1) PGY harvesting strategies can give large conservation benefits and (2) equal harvesting rates of juveniles and adults is often a good strategy. These conclusions are based on trade-off curves between yield and four measures of conservation that form in two established population models, one age-structured model and one stage-structured model, when considering different harvesting rates of juveniles and adults. These conclusions hold for a broad range of parameter settings, although our investigation of robustness also reveals that (3) predictions of the age-structured model are more sensitive to variations in parameter values than those of the stage-structured model. Finally, we find that (4) measures of stability that are often quite difficult to assess in the field (e.g., basic reproduction ratio and resilience) are systematically negatively correlated with impacts on biomass and size structure, so that these later quantities can provide integrative signals to detect possible collapses.

Selection of trilateral continuums of life history strategies under food web interactions

The study of life history strategies has a long history in ecology and evolution, but determining the underlying mechanisms driving the evolution of life history variation and its consequences for population regulation remains a major challenge. In this study, a food web model with constant environmental conditions was used to demonstrate how multi-species consumer–resource interactions (food-web interactions) can create variation in the duration of the adult stage, age of maturation, and fecundity among species. The model included three key ecological processes: size-dependent species interactions, energetics, and transition among developmental stages. Resultant patterns of life history variation were consistent with previous empirical observations of the life history strategies of aquatic organisms referred to as periodic, equilibrium, and opportunistic strategies (trilateral continuums of life history strategies). Results from the simulation model suggest that these three life history strategies can emerge from food web interactions even when abiotic environmental conditions are held constant.

Predicting phenological shifts in a changing climate

Phenological shifts constitute one of the clearest manifestations of climate warming. Advanced emergence is widely reported in high-latitude ectotherms, but a significant number of species exhibit delayed, or no change in, emergence. Here we present a mechanistic theoretical framework that reconciles these disparate observations and predicts population-level phenological patterns based solely on data on temperature responses of the underlying life history traits. Our model, parameterized with data from insects at different latitudes, shows that peak abundance occurs earlier in the year when warming increases the mean environmental temperature, but is delayed when warming increases the amplitude of seasonal fluctuations. We find that warming does not necessarily lead to a longer activity period in high-latitude species because it elevates summer temperatures above the upper limit for reproduction and development. Our findings both confirm and confound expectations for ectotherm species affected by climate warming: an increase in the mean temperature is more detrimental to low-latitude species adapted to high mean temperatures and low-amplitude seasonal fluctuations; an increase in seasonal fluctuations is more detrimental to high-latitude species adapted to low mean temperatures and high-amplitude fluctuations.

Predator Persistence through Variability of Resource Productivity in Tritrophic Systems

The trophic structure of species communities depends on the energy transfer between trophic levels. Primary productivity varies strongly through time, challenging the persistence of species at higher trophic levels. Yet resource variability has mostly been studied in systems with only one or two trophic levels. We test the effect of variability in resource productivity in a tritrophic model system including a resource, a size-structured consumer, and a size-specific predator. The model complies with fundamental principles of mass conservation and the body-size dependence of individual-level energetics and predator-prey interactions. Surprisingly, we find that resource variability may promote predator persistence. The positive effect of variability on the predator arises through periods with starvation mortality of juvenile prey, which reduces the intraspecific competition in the prey population. With increasing variability in productivity and starvation mortality in the juvenile prey, the prey availability increases in the size range preferred by the predator. The positive effect of prey mortality on the trophic transfer efficiency depends on the biologically realistic consideration of body size-dependent and food-dependent functions for growth and reproduction in our model. Our findings show that variability may promote the trophic transfer efficiency, indicating that environmental variability may sustain species at higher trophic levels in natural ecosystems.

Temperature-dependent body size effects determine population responses to climate warming

Current understanding of animal population responses to rising temperatures is based on the assumption that biological rates such as metabolism, which governs fundamental ecological processes, scale independently with body size and temperature, despite empirical evidence for interactive effects. Here, we investigate the consequences of interactive temperature- and size scaling of vital rates for the dynamics of populations experiencing warming using a stage-structured consumer-resource model. We show that interactive scaling alters population and stage-specific responses to rising temperatures, such that warming can induce shifts in population regulation and stage-structure, influence community structure and govern population responses to mortality. Analysing experimental data for 20 fish species, we found size-temperature interactions in intraspecific scaling of metabolic rate to be common. Given the evidence for size-temperature interactions and the ubiquity of size structure in animal populations, we argue that accounting for size-specific temperature effects is pivotal for understanding how warming affects animal populations and communities.

Seasonal reproduction leads to population collapse and an Allee effect in a stage-structured consumer-resource biomass model when mortality rate increases

Many populations collapse suddenly when reaching low densities even if they have abundant food conditions, a phenomenon known as an Allee effect. Such collapses can have disastrous consequences, for example, for loss of biodiversity. In this paper, we formulate a stage-structured consumer-resource biomass model in which adults only reproduce at the beginning of each growing season, and investigate the effect of an increasing stage-independent background mortality rate of the consumer. As the main difference with previously studied continuous-time models, seasonal reproduction can result in an Allee effect and consumer population collapses at high consumer mortality rate. However, unlike the mechanisms reported in the literature, in our model the Allee effect results from the time difference between the maturation of juveniles and the reproduction of adults. The timing of maturation plays a crucial role because it not only determines the body size of the individuals at maturation but also influences the duration of the period during which adults can invest in reproductive energy, which together determine the reproductive output at the end of the season. We suggest that there exists an optimal timing of maturation and that consumer persistence is promoted if individuals mature later in the season at a larger body size, rather than maturing early, despite high food availability supporting rapid growth.

A Parent-Offspring Trade-Off Limits the Evolution of an Ontogenetic Niche Shift

Many free-living animal species, including the majority of fish, insects, and amphibians, change their food and habitat during their life. Even though these ontogenetic changes in niche are common, it is not well understood which ecological conditions have favored the evolution of these shifts. Using an adaptive dynamics approach, we show that it is evolutionarily advantageous to switch to an alternative food source in the course of ontogeny when this results in a higher intake rate for the switching consumers. Individuals are, however, not able to specialize on this new food source when this negatively affects the performance early in life on the original food source. Selection on these early life stages is so strong that in species with a complete diet shift, evolution results in large juveniles and adults that are maladapted to the alternative food source while their offspring are specialized on the original food source when young. These outcomes suggest strong selection to decouple the different life stages, such that they can maximize their performance on different food sources independently from each other. Metamorphosis could be a way to decouple the different life stages and therefore evolve in species that feed on multiple food sources during their life.

Approximation of a physiologically structured population model with seasonal reproduction by a stage-structured biomass model

Seasonal reproduction causes, due to the periodic inflow of young small individuals in the population, seasonal fluctuations in population size distributions. Seasonal reproduction furthermore implies that the energetic body condition of reproducing individuals varies over time. Through these mechanisms, seasonal reproduction likely affects population and community dynamics. While seasonal reproduction is often incorporated in population models using discrete time equations, these are not suitable for size-structured populations in which individuals grow continuously between reproductive events. Size-structured population models that consider seasonal reproduction, an explicit growing season and individual-level energetic processes exist in the form of physiologically structured population models. However, modeling large species ensembles with these models is virtually impossible. In this study, we therefore develop a simpler model framework by approximating a cohort-based size-structured population model with seasonal reproduction to a stage-structured biomass model of four ODEs. The model translates individual-level assumptions about food ingestion, bioenergetics, growth, investment in reproduction, storage of reproductive energy, and seasonal reproduction in stage-based processes at the population level. Numerical analysis of the two models shows similar values for the average biomass of juveniles, adults, and resource unless large-amplitude cycles with a single cohort dominating the population occur. The model framework can be extended by adding species or multiple juvenile and/or adult stages. This opens up possibilities to investigate population dynamics of interacting species while incorporating ontogenetic development and complex life histories in combination with seasonal reproduction.

Some directions in ecological theory

The role of theory within ecology has changed dramatically in recent decades. Once primarily a source of qualitative conceptual framing, ecological theories and models are now often used to develop quantitative explanations of empirical patterns and to project future dynamics of specific ecological systems. In this essay, I recount my own experience of this transformation, in which accelerating computing power and the widespread incorporation of stochastic processes into ecological theory combined to create some novel integration of mathematical and statistical models. This stronger integration drives theory towards incorporating more biological realism, and I explore ways in which we can grapple with that realism to generate new general theoretical insights. This enhanced realism, in turn, may lead to frameworks for projecting ecological responses to anthropogenic change, which is, arguably, the central challenge for 21st-century ecology. In an era of big data and synthesis, ecologists are increasingly seeking to infer causality from observational data; but conventional biometry provides few tools for this project. This is a realm where theorists can and should play an important role, and I close by pointing towards some analytical and philosophical approaches developed in our sister discipline of economics that address this very problem. While I make no grand prognostications about the likely discoveries of ecological theory over the coming century, you will find in this essay a scattering of more or less far-fetched ideas that I, at least, think are interesting and (possibly) fruitful directions for our field.

Fishing-induced life-history changes degrade and destabilize harvested ecosystems

Fishing is widely known to magnify fluctuations in targeted populations. These fluctuations are correlated with population shifts towards young, small, and more quickly maturing individuals. However, the existence and nature of the mechanistic basis for these correlations and their potential ecosystem impacts remain highly uncertain. Here, we elucidate this basis and associated impacts by showing how fishing can increase fluctuations in fishes and their ecosystem, particularly when coupled with decreasing body sizes and advancing maturation characteristic of the life-history changes induced by fishing. More specifically, using an empirically parameterized network model of a well-studied lake ecosystem, we show how fishing may both increase fluctuations in fish abundances and also, when accompanied by decreasing body size of adults, further decrease fish abundance and increase temporal variability of fishes’ food resources and their ecosystem. In contrast, advanced maturation has relatively little effect except to increase variability in juvenile populations. Our findings illustrate how different mechanisms underlying life-history changes that may arise as evolutionary responses to intensive, size-selective fishing can rapidly and continuously destabilize and degrade ecosystems even after fishing has ceased. This research helps better predict how life-history changes may reduce fishes’ resilience to fishing and ecosystems’ resistance to environmental variations.

Stability patterns for a size-structured population model and its stage-structured counterpart

In this paper we compare a general size-structured population model, where a size-structured consumer feeds upon an unstructured resource, to its simplified stage-structured counterpart in terms of equilibrium stability. Stability of the size-structured model is understood in terms of an equivalent delayed system consisting of a renewal equation for the consumer population birth rate and a delayed differential equation for the resource. Results show that the size- and stage-structured models differ considerably with respect to equilibrium stability, although the two models have completely identical equilibrium solutions. First, when adult consumers are superior foragers to juveniles, the size-structured model is more stable than the stage-structured model while the opposite occurs when juveniles are the superior foragers. Second, relatively large juvenile (adult) mortality tends to stabilise (destabilise) the size-structured model but destabilise (stabilise) the stage-structured model. Third, the stability pattern is sensitive to the adult-offspring size ratio in the size-structured model but much less sensitive in the stage-structured model. Finally, unless the adult-offspring size ratio is sufficiently small, the stage-structured model cannot satisfactorily capture the dynamics of the size-structured model. We conclude that caution must be taken when the stage-structured population model is applied, although it can consistently translate individual life history and stage-specific differences to the population level.

Alternative stable states in a stage-structured consumer-resource biomass model with niche shift and seasonal reproduction

We formulate and analyze a stage-structured consumer-resource biomass model, in which consumers reproduce in a pulsed event at the beginning of a growing season and furthermore go through a niche shift during their life history. We show that the resulting semi-discrete model can exhibit two stable states that can be characterized as a development-controlled state and a reproduction-controlled state. Varying resource availabilities and varying the extent of the niche shift determines whether juveniles or adults are more limited by their resource(s) and can lead to switches between the alternative stable states. Furthermore, we quantify the persistence of the consumer population and the occurrence of the two alternative stable states as a function of resource availabilities and extent of the niche shift. All the results show that irrespective of the type of reproduction of the consumers (continuous or seasonal), the stage-structured model will exhibit alternative stable states as long as development of the juvenile stage and reproduction of the adult stage are both resource-dependent.

Regime shifts in exploited marine food webs: detecting mechanisms underlying alternative stable states using size-structured community dynamics theory

Many marine ecosystems have undergone ‘regime shifts’, i.e. abrupt reorganizations across trophic levels. Establishing whether these constitute shifts between alternative stable states is of key importance for the prospects of ecosystem recovery and for management. We show how mechanisms underlying alternative stable states caused by predator–prey interactions can be revealed in field data, using analyses guided by theory on size-structured community dynamics. This is done by combining data on individual performance (such as growth and fecundity) with information on population size and prey availability. We use Atlantic cod (Gadus morhua) and their prey in the Baltic Sea as an example to discuss and distinguish two types of mechanisms, ‘cultivation-depensation’ and ‘overcompensation’, that can cause alternative stable states preventing the recovery of overexploited piscivorous fish populations. Importantly, the type of mechanism can be inferred already from changes in the predators' body growth in different life stages. Our approach can thus be readily applied to monitored stocks of piscivorous fish species, for which this information often can be assembled. Using this tool can help resolve the causes of catastrophic collapses in marine predatory–prey systems and guide fisheries managers on how to successfully restore collapsed piscivorous fish stocks.

Effects of temperature on intraspecific competition in ectotherms

Understanding how temperature influences population regulation through its effects on intraspecific competition is an important question for which there is currently little theory or data. Here we develop a theoretical framework for elucidating temperature effects on competition that integrates mechanistic descriptions of life-history trait responses to temperature with population models that realistically capture the variable developmental delays that characterize ectotherm life cycles. This framework yields testable comparative predictions about how intraspecific competition affects reproduction, development, and mortality under alternative hypotheses about the temperature dependence of competition. The key finding is that ectotherm population regulation in seasonal environments depends crucially on the mechanisms by which temperature affects competition. When competition is strongest at temperatures optimal for reproduction, effects of temperature and competition act antagonistically, leading to more complex dynamics than when competition is temperature independent. When the strength of competition increases with temperature past the optimal temperature for reproduction, effects of temperature and competition act synergistically, leading to dynamics qualitatively similar to those when competition is temperature independent. Paradoxically, antagonistic effects yield a higher population floor despite greater fluctuations. These findings have important implications for predicting effects of climate warming on population regulation. Synergistic effects of temperature and competition can predispose populations to stochastic extinction by lowering minimum population sizes, while antagonistic effects can increase the potential for population outbreaks through greater fluctuations in abundance.

Size-dependent diffusion promotes the emergence of spatiotemporal patterns

Spatiotemporal patterns, indicating the spatiotemporal variability of individual abundance, are a pronounced scenario in ecological interactions. Most of the existing models for spatiotemporal patterns treat species as homogeneous groups of individuals with average characteristics by ignoring intraspecific physiological variations at the individual level. Here we explore the impacts of size variation within species resulting from individual ontogeny, on the emergence of spatiotemporal patterns in a fully size-structured population model. We found that size dependency of animal's diffusivity greatly promotes the formation of spatiotemporal patterns, by creating regular spatiotemporal patterns out of temporal chaos. We also found that size-dependent diffusion can substitute large-amplitude base harmonics with spatiotemporal patterns with lower amplitude oscillations but with enriched harmonics. Finally, we found that the single-generation cycle is more likely to drive spatiotemporal patterns compared to predator-prey cycles, meaning that the mechanism of Hopf bifurcation might be more common than hitherto appreciated since the former cycle is more widespread than the latter in case of interacting populations. Due to the ubiquity of individual ontogeny in natural ecosystems we conclude that diffusion variability within populations is a significant driving force for the emergence of spatiotemporal patterns. Our results offer a perspective on self-organized phenomena, and pave a way to understand such phenomena in systems organized as complex ecological networks.

Bifurcation analysis in a stage-structured predator–prey model with maturation delay

In this paper, we investigate the impact of maturation delay on the positive equilibrium solutions in a stage-structured predator–prey system. By analyzing the characteristic equation we derive the conditions for the emergence of Hopf bifurcation. By applying the normal form and the center manifold argument, the direction as well as the stability of periodic solutions bifurcating from Hopf bifurcation is explored. Results show that maturation delay can change the nature of the positive equilibrium solutions, and the loss of equilibrium stability occurs as a consequence of Hopf bifurcation. When Hopf bifurcation takes place, periodic solution arises and is further demonstrated to be asymptotically stable. In addition, the periodic solutions appear only for intermediate maturation delay, that is, there exists a delay window, outside of which the positive equilibrium is locally stable. Furthermore, numerical analysis shows that Hopf bifurcation is favored by a superior competition for adult predators to juveniles, a smaller mortality on juvenile and/or adult predators, and a higher resource carrying capacity. Interestingly, increasing food carrying capacity can lead to the emergence of irregular chaotic dynamics and regular limit cycles.

When does fishing lead to more fish? Community consequences of bottom trawl fisheries in demersal food webs

Bottom trawls are a globally used fishing gear that physically disturb the seabed and kill non-target organisms, including those that are food for the targeted fish species. There are indications that ensuing changes to the benthic invertebrate community may increase the availability of food and promote growth and even fisheries yield of target fish species. If and how this occurs is the subject of ongoing debate, with evidence both in favour and against. We model the effects of trawling on a simple ecosystem of benthivorous fish and two food populations (benthos), susceptible and resistant to trawling. We show that the ecosystem response to trawling depends on whether the abundance of benthos is top-down or bottom-up controlled. Fishing may result in higher fish abundance, higher (maximum sustainable) yield and increased persistence of fish when the benthos which is the best-quality fish food is also more resistant to trawling. These positive effects occur in bottom-up controlled systems and systems with limited impact of fish feeding on benthos, resembling bottom-up control. Fishing leads to lower yields and fish persistence in all configurations where susceptible benthos are more profitable prey. Our results highlight the importance of mechanistic ecosystem knowledge as a requirement for successful management.

Symmetry breaking in ecological systems through different energy efficiencies of juveniles and adults

Ontogenetic development is a fundamental aspect of the life history of all organisms and has major effects on population and community dynamics. We postulate a general conceptual framework for understanding these effects and claim that two potential energetics bottlenecks at the level of the individual organism--the rate by which it develops and the rate by which it reproduces--form a fundamental route to symmetry-breaking in ecological systems, leading to ontogenetic asymmetry in energetics. Unstructured ecological theory, which ignores ontogenetic development, corresponds to a limiting case only, in which mass-specific rates of biomass production through somatic growth and reproduction, and biomass loss through mortality, are independent of body size (ontogenetic symmetry). Ontogenetic symmetry results in development and reproduction being limited to the same extent by food density. In all other cases, symmetry-breaking occurs. Ontogenetic asymmetry results in increases in juvenile, adult, or even total biomass in response to mortality. At the community level, this gives rise to alternative stable states via predator-induced shifts in prey size distributions. Ontogenetic asymmetry furthermore leads to two distinct types of cycles in population dynamics, depending on whether development or reproduction is most energy limited. We discuss the mechanisms giving rise to these phenomena and the empirical support for them. We conclude that the concepts of ontogenetic symmetry and ontogenetic asymmetry form a novel and general organizing principle on which future ecological theory should be developed.

Stabilizing effect of cannibalism in a two stages population model

In this paper we build a prey-predator model with discrete weight structure for the predator. This model will conserve the number of individuals and the biomass and both growth and reproduction of the predator will depend on the food ingested. Moreover the model allows cannibalism which means that the predator can eat the prey but also other predators. We will focus on a simple version with two weight classes or stage (larvae and adults) and present some general mathematical results. In the last part, we will assume that the dynamics of the prey is fast compared to the predator's one to go further in the results and eventually conclude that under some conditions, cannibalism can stabilize the system: more precisely, an unstable equilibrium without cannibalism will become almost globally stable with some cannibalism. Some numerical simulations are done to illustrate this result.

Dynamics and management of stage-structured fish stocks

With increasing fishing pressures having brought several stocks to the brink of collapse, there is a need for developing efficient harvesting methods that account for factors beyond merely yield or profit. We consider the dynamics and management of a stage-structured fish stock. Our work is based on a consumer-resource model which De Roos et al. (in Theor. Popul. Biol. 73, 47-62, 2008) have derived as an approximation of a physiologically-structured counterpart. First, we rigorously prove the existence of steady states in both models, that the models share the same steady states, and that there exists at most one positive steady state. Furthermore, we carry out numerical investigations which suggest that a steady state is globally stable if it is locally stable. Second, we consider multiobjective harvesting strategies which account for yield, profit, and the recovery potential of the fish stock. The recovery potential is a measure of how quickly a fish stock can recover from a major disturbance and serves as an indication of the extinction risk associated with a harvesting strategy. Our analysis reveals that a small reduction in yield or profit allows for a disproportional increase in recovery potential. We also show that there exists a harvesting strategy with yield close to the maximum sustainable yield (MSY) and profit close to that associated with the maximum economic yield (MEY). In offering a good compromise between MSY and MEY, we believe that this harvesting strategy is preferable in most instances. Third, we consider the impact of harvesting on population size structure and analytically determine the most and least harmful harvesting strategies. We conclude that the most harmful harvesting strategy consists of harvesting both adults and juveniles, while harvesting only adults is the least harmful strategy. Finally, we find that a high percentage of juvenile biomass indicates elevated extinction risk and might therefore serve as an early-warning signal of impending stock collapse.

Interspecific resource competition effects on fisheries revenue

In many fisheries multiple species are simultaneously caught while stock assessments and fishing quota are defined at species level. Yet species caught together often share habitat and resources, resulting in interspecific resource competition. The consequences of resource competition on population dynamics and revenue of simultaneously harvested species has received little attention due to the historical single stock approach in fisheries management. Here we present the results of a modelling study on the interaction between resource competition of sole (Solea solea) and slaice (Pleuronectus platessa) and simultaneous harvesting of these species, using a stage-structured population model. Three resources were included of which one is shared with a varied competition intensity. We find that plaice is the better competitor of the two species and adult plaice are more abundant than adult sole. When competition is high sole population biomass increases with increasing fishing effort prior to plaice extinction. As a result of this increase in the sole population, the revenue of the stocks combined as function of effort becomes bimodal with increasing resource competition. When considering a single stock quota for sole, its recovery with increasing effort may result in even more fishing effort that would drive the plaice population to extinction. When sole and plaice compete for resources the highest revenue is obtained at effort levels at which plaice is extinct. Ignoring resource competition promotes overfishing due to increasing stock of one species prior to extinction of the other species. Consequently, efforts to mitigate the decline in one species will not be effective if increased stock in the other species leads to increased quota. If a species is to be protected against extinction, management should not only be directed at this one species, but all species that compete with it for resource as well.

Community-level consequences of cannibalism

Ecological interactions determine the structure and dynamics of communities and their responses to the environment. Understanding the community-level effects of ecological interactions, such as intra- and interspecifc competition, predation, and cannibalism, is therefore central to ecological theory and ecosystem management. Here, we investigate the community-level consequences of cannibalism in populations with density-dependent maturation and reproduction. We model a stage-structured consumer population with an ontogenetic diet shift to analyze how cannibalism alters the conditions for the invasion and persistence of stage-specific predators and competitors. Our results demonstrate that cannibalistic interactions can facilitate coexistence with other species at both trophic levels. This effect of cannibalism critically depends on the food dependence of the demographic processes. The underlying mechanism is a cannibalism-induced shift in the biomass distribution between the consumer life stages. These findings suggest that cannibalism may alter the structure of ecological communities through its effects on species coexistence.

Ontogenetic symmetry and asymmetry in energetics

Body size (≡ biomass) is the dominant determinant of population dynamical processes such as giving birth or dying in almost all species, with often drastically different behaviour occurring in different parts of the growth trajectory, while the latter is largely determined by food availability at the different life stages. This leads to the question under what conditions unstructured population models, formulated in terms of total population biomass, still do a fair job. To contribute to answering this question we first analyze the conditions under which a size-structured model collapses to a dynamically equivalent unstructured one in terms of total biomass. The only biologically meaningful case where this occurs is when body size does not affect any of the population dynamic processes, this is the case if and only if the mass-specific ingestion rate, the mass-specific biomass production and the mortality rate of the individuals are independent of size, a condition to which we refer as "ontogenetic symmetry". Intriguingly, under ontogenetic symmetry the equilibrium biomass-body size spectrum is proportional to 1/size, a form that has been conjectured for marine size spectra and subsequently has been used as prior assumption in theoretical papers dealing with the latter. As a next step we consider an archetypical class of models in which reproduction takes over from growth upon reaching an adult body size, in order to determine how quickly discrepancies from ontogenetic symmetry lead to relevant novel population dynamical phenomena. The phenomena considered are biomass overcompensation, when additional imposed mortality leads, rather unexpectedly, to an increase in the equilibrium biomass of either the juveniles or the adults (a phenomenon with potentially big consequences for predators of the species), and the occurrence of two types of size-structure driven oscillations, juvenile-driven cycles with separated extended cohorts, and adult-driven cycles in which periodically a front of relatively steeply decreasing frequencies moves up the size distribution. A small discrepancy from symmetry can already lead to biomass overcompensation; size-structure driven cycles only occur for somewhat larger discrepancies.