Size and scaling of predator-prey dynamics

We propose a scaled version of the Rosenzweig–MacArthur model using both Type I and Type II functional responses that incorporates the size dependence of interaction rates. Our aim is to link the energetic needs of organisms with the dynamics of interacting populations, for which survival is a result of a game-theoretic struggle for existence. We solve the scaled model of predator–prey dynamics and predict population level characteristics such as the scaling of coexistence size ranges and the optimal predator–prey size ratio. For a broad class of such models, the optimal predator–prey size ratio given available prey of a fixed size is constant. We also demonstrate how scaling predictions of prey density differ under resource limitation vs. predator drawdown. Finally, we show how evolution of predator size can destabilize population dynamics, compare scaling of predator–prey cycles to previous work, as well as discuss possible extensions of the model to multispecies communities.     

The influence of size-dependent life-history traits on the structure and dynamics of populations and communities

Individual organisms often show pronounced changes in body size throughout life with concomitant changes in ecological performance. We synthesize recent insight into the relationship between size dependence in individual life history and population dynamics. Most studies have focused on size‐dependent life‐history traits and population size‐structure in the highest trophic level, which generally leads to population cycles with a period equal to the juvenile delay. These cycles are driven by differences in competitiveness of differently sized individuals. In multi‐trophic systems, size dependence in life‐history traits at lower trophic levels may have consequences for both the dynamics and structure of communities, as size‐selective predation may lead to the occurrence of emergent Allee effects and the stabilization of predator–prey cycles. These consequences are linked to that individual development is density dependent. We conjecture that especially this population feedback on individual development may lead to new theoretical insight compared to theory based on unstructured or age‐dependent models. Density‐dependent individual development may also cause individuals to realize radically different life histories, dependent on the state and dynamics of the population during their life and may therefore have consequences for individual behaviour or the evolution of life‐history traits as well.     

The evolution of traits that determine ability in competitive contests

Summary We analyse mathematical models of the evolution of a trait that determines ability in contest competition. We assume that the value of the competitive trait affects two different components of fitness, one measuring the benefit of winning contests and the other measuring the cost of developing the competitive trait. Unlike previous analyses, we include the population dynamical consequences of larger competitive trait values. Exaggeration of the competitive trait reduces the mean probability of survival during the non-competitive stage of the life cycle. The resulting lower population density reduces competition and, therefore, reduces the advantages of greater competitive ability. Models without population dynamics often predict dimorphism in the competitive trait when resource possession is decided by interactions with many other individuals. If the competition involves a contest with a single other individual, models without population dynamics often predict cycles of increase and collapse in the trait or a continual increase, possibly resulting in extinction. When population dynamics are included, both of these results become less likely and a single stable trait value becomes more likely. Population dynamics also make it possible to have dimorphism when individuals have a single pairwise contest and alternative stable trait values when an individual has many contests. Increases in the value of the resource being contested may increase or decrease the evolutionarily stable size of the trait. Competition between very differently sized species will often decrease size in the larger species (character convergence).     

Ontogenetic symmetry and asymmetry in energetics

Body size ( $\equiv $ 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.     

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.     

Cooperation driven by mutations in multi-person Prisoner's Dilemma

The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be considered as isolated events. For this case, and assuming simple trigger strategies and many iterations per game, we analyse the rate of convergence to the evolutionarily stable populations. We find that for some values of the payoff parameters of the Prisoner's Dilemma this rate is so low that the assumption, that mutations in the population are infrequent on that time-scale, is unreasonable. Furthermore, the problem is compounded as the group size is increased. In order to address this issue, we derive a deterministic approximation of the evolutionary dynamics with explicit, stochastic mutation processes, valid when the population size is large. We then analyse how the evolutionary dynamics depends on the following factors: mutation rate, group size, the value of the payoff parameters, and the structure of the initial population. In order to carry out the simulations for groups of more than just a few individuals, we derive an efficient way of calculating the fitness values. We find that when the mutation rate per individual and generation is very low, the dynamics is characterized by populations which are evolutionarily stable. As the mutation rate is increased, other fixed points with a higher degree of cooperation become stable. For some values of the payoff parameters, the system is characterized by (apparently) stable limit cycles dominated by cooperative behaviour. The parameter regions corresponding to high degree of cooperation grow in size with the mutation rate, and in number with the group size. For some parameter values, we find more than one stable fixed point, corresponding to different structures of the initial population.     

Adaptive plasticity in ontogenetic niche shifts stabilizes consumer-resource dynamics

Ontogenetic niche shifts, changes in the diet or habitats of organisms during their ontogeny, are widespread among various animal taxa. Ontogenetic niche shifts introduce stage structure in a population with different stages interacting with different communities and can substantially affect their dynamics. In this article, I use mathematical models to test the hypothesis that adaptive plasticity in the timing of ontogenetic niche shifts has a stabilizing effect on consumer-resource dynamics. Adaptive plasticity allows consumers in one ontogenetic niche to perform an early shift to the next ontogenetic niche if the resource density of the first niche is low. The early shift will reduce predation by the consumer on the scarce resource. On the other hand, adaptive plasticity allows consumers to delay their shift to the next niche if the resource density of the first niche is high. The delayed shift will increase the predation on the abundant resource. As a result, the scarce resource will tend to increase, and the abundant resource will tend to decrease. This causes density-dependent negative feedback in the resource dynamics, which stabilizes the consumer-resource dynamics. To test this hypothesis, I compare three consumer-resource models differing in terms of mechanisms controlling the timing of the ontogenetic niche shift: the fixed-age model assumes that the age at which the ontogenetic niche shift occurs is fixed; the fixed-size model assumes that the size at the shift is fixed; and the adaptive plasticity model assumes that the timing of the shift is such that the individual fitness of the consumer is maximized. I show that only the adaptive plasticity model has a locally stable equilibrium and that the stabilizing effect is due to the density-dependent negative feedback in the resource dynamics. I discuss the ontogenetic niche shifts of lake fish in light of the obtained result.     

Group size structure affects patterns of aggression in larval salamanders

The potential importance of intrapopulation phenotypic variabilityto population-level ecology has been demonstrated in both theoreticaland field studies. One way to connect individuals to the dynamicsof populations they compose is to study behavioral response(an individual-level characteristic) to variability in conspecificphenotypes (a population-level characteristic). We examinedeffects of variation in size of individuals on patterns of aggressionin larval tiger salamanders (Ambystoma tigrinum nebulosum) byobserving aggressive behavior in groups of three larvae in alaboratory experment. We assessed effects of variability insize of conspecifics independently of mean larval size and larvaldensity Overall levels of aggression were generally higher ingroups in which all individuals were similprly sized than ingroups of variably sized individuals. Medium-sized individualsexhibited significantly higher levels of aggression and wereattacked significantly more often when in groups consistingonly of similarly sized larvae as compared to groups composedof larvae representing a wider range of body sizes. Activitylevels of larvae were also generally lower when all individualswere the same size, resulting in a negative correlation betweenactivity and levels of iggressititi. These results suggest thatgioups of similarly sized individuals experience a more aggressivesocial environment than groups of variably sized individuals,and they suggest a promising avenue of research for connectingindividual behavioral and physiological responses to size structure(phenotypic variability) with population dynamics.     

Dwarfs and Giants: Cannibalism and Competition in Size-Structured Populations

Cannibals and their victims often share common resources and thus potentially compete. Smaller individuals are often competitively superior to larger ones because of size-dependent scaling of foraging and metabolic rates, while larger ones may use cannibalism to counter this competition. We study the interplay between cannibalism and competition using a size-structured population model in which all individuals consume a shared resource but in which larger ones may cannibalize smaller conspecifics. In this model, intercohort competition causes single-cohort cycles when cannibalism is absent. Moderate levels of cannibalism reduce intercohort competition, enabling coexistence of many cohorts. More voracious cannibalism, in combination with competition, produces large-amplitude cycles and a bimodal population size distribution with many small and few giant individuals. These coexisting "dwarfs" and "giants" have very different life histories, resulting from a reversal in importance of cannibalism and competition. The population structure at time of birth determines whether individuals suffer severe cannibalism, with the few survivors reaching giant sizes, or whether they suffer intense intracohort competition, with all individuals remaining small. These model results agree remarkably well with empirical data on perch population dynamics. We argue that the induction of cannibalistic giants in piscivorous fish is a population-dynamic emergent phenomenon that requires a combination of size-dependent cannibalism and competition.     

Some patterns of spatial-ontogenetic structure in populations of tuber orchids

Population dynamics, density, and aggregation size of tuberoid orchids have been identified based on mapping, electronic maps constructed with “point processes,” and Ripley function and pair-correlation function. Discrete and discrete-continuous types of spatial structure dominate in populations in optimal ecological conditions. The bounded aggregations of levels I (radius 0.45–0.75 m) and II (radius 1.2–2.5 m) are formed at 3 to 7.5 m². The spatial pattern depends on generative specimens which are related with the “group effect.” The microloci have full ontogenetic structure and may be regarded as elemental populations. They form larger aggregations of levels III and IV with random spatial distribution and continuous bounds. Aggregations of higher level are not formed under worse ecological conditions. Random spatial distribution and incomplete ontogenetic spectrum of microloci are indicators of critical population status.     

Feeding across the food web: The interaction between diet,movement and body size in estuarine crocodiles (Crocodylus porosus)

The estuarine crocodile (Crocodylus porosus) is an apex predator across freshwater, estuarine and coastal environments. The impact of a changing C. porosus population upon the ecosystem is unknown, but due to large ontogenetic changes in body mass (>1000‐fold) their impact may be wide reaching and substantial. Here we investigated the relationship between diet, movement and body size in a population of C. porosus inhabiting a tidal river in northern Australia. Subcutaneous acoustic transmitters and fixed underwater receivers were used to determine the activity space and movement patterns of 42 individuals (202–451 cm in total length). There was no size‐related spatial partitioning among different sized crocodiles. Large individuals (snout–vent length (SVL): 160 cm < SVL < 188.5 cm) did, however, exhibit a much larger activity space than other size classes. Diet and individual specialization was assessed using the composition of stable carbon (δ¹³C) and nitrogen (δ¹⁵N) isotopes in tissues with different turnover rates. There was a quadratic relationship between body size and δ¹⁵N, suggesting that medium‐sized individuals (110 cm < SVL < 160 cm) incorporated a greater proportion of high trophic prey into their diets than small (SVL < 110 cm) or large individuals (SVL > 160 cm). Tissue δ¹³C composition on the other hand was positively correlated with body size, indicating that different size classes were trophically linked to primary producers in different habitats. Individual‐level analyses showed that small crocodiles were generalist feeders while medium and large size classes specialized on particular prey items within the food webs they fed. The findings further our understanding of ontogenetic variation in C. porosus diet, and suggest that change in C. porosus population size or demographics may be influential at various levels across the local food web.     

Stage-structured ontogeny in resource populations generates non-additive stabilizing and de-stabilizing forces in populations and communities

Demographic heterogeneity influences how populations respond to density dependent intraspecific competition and trophic interactions. Distinct stages across an organism's development, or ontogeny, are an important example of demographic heterogeneity. In consumer populations, ontogenetic stage structure has been shown to produce categorical differences in population dynamics, community dynamics and even species coexistence compared to models lacking explicit ontogeny. The study of consumer–resource interactions must also consider the ontogenetic stage structure of the resource itself, particularly plants, given their fundamental role at the basis of terrestrial food webs. We incorporate distinct ontogenetic stages of plants into an adaptable multi-stage consumer–resource modeling framework that facilitates studying how stage specific consumers shape trophic dynamics at low trophic levels. We describe the role of density dependent demographic rates in mediating the dynamics of stage-structured plant populations. We then investigate how these demographic rates interact with consumer pressure to influence stability and coexistence in multiple stage-specific consumer–resource interactions. Results detail how density dependent effects across distinct ontogenetic stages in plant development produce non-additivity in the drivers of dynamic stability both in single populations and in consumer–resource settings, challenging the ubiquity of certain traditional ecological dynamic paradigms. We also find categorical differences in the population variability induced by herbivores consuming separate plant stages. Consumer–resource models, such as plant–herbivore interactions, often average out demographic heterogeneity in populations. Here, we show that explicitly including plant demographic heterogeneity through ontogeny yields distinct dynamic expectations for both plants and herbivores compared to traditional consumer–resource formulations. Our results indicate that efforts to understand the demographic effect of herbivores on plant populations may need to also consider the effects of plant demographics on herbivores and the reciprocal relationship between them.     

Resource diversity promotes among‐individual diet variation,but not genomic diversity,in lake stickleback

Many generalist species consist of specialised individuals that use different resources. This within‐population niche variation can stabilise population and community dynamics. Consequently, ecologists wish to identify environmental settings that promote such variation. Theory predicts that environments with greater resource diversity favour ecological diversity among consumers (via disruptive selection or plasticity). Alternatively, niche variation might be a side‐effect of neutral genomic diversity in larger populations. We tested these alternatives in a metapopulation of threespine stickleback. Stickleback consume benthic and limnetic invertebrates, focusing on the former in small lakes, the latter in large lakes. Intermediate‐sized lakes support generalist stickleback populations using an even mixture of the two prey types, and exhibit greater among‐individual variation in diet and morphology. In contrast, genomic diversity increases with lake size. Thus, phenotypic diversity and neutral genetic polymorphism are decoupled: trophic diversity being greatest in intermediate‐sized lakes with high resource diversity, whereas neutral genetic diversity is greatest in the largest lakes.     

Cyclomorphosis in natural populations of Daphnia cephalata King

SUMMARY. Daphnia cephalata King is a major component of the zooplankton in freshwater ponds of eastern Australia. Phenotypic variation in head shape both within and between populations is striking. Some of this variation is ontogenetic, but among individuals of similar size head length still varies by a factor of two. The causes of this variation have been investigated by analysing head size in thirty-four populations of D. cephalata over a 17-month period. An annual cycle in crest size, apparently related to seasonal changes in mean temperature, was evident when the data were pooled. Large differences in head size were commonly observed, however, among samples collected simultaneously. Some of this variation was correlated with local differences in resource availability, which were due, in part, to local variation in Daphnia density. Other consistent interpopulation differences in head size were related to stable environmental differences among sites and probably also to genetic differences among populations.     

Evolution of cooperation under -person snowdrift games

In the animal world, performing a given task which is beneficial to an entire group requires the cooperation of several individuals of that group who often share the workload required to perform the task. The mathematical framework to study the dynamics of collective action is game theory. Here we study the evolutionary dynamics of cooperators and defectors in a population in which groups of individuals engage in N-person, non-excludable public goods games. We explore an N-person generalization of the well-known two-person snowdrift game. We discuss both the case of infinite and finite populations, taking explicitly into consideration the possible existence of a threshold above which collective action is materialized. Whereas in infinite populations, an N-person snowdrift game (NSG) leads to a stable coexistence between cooperators and defectors, the introduction of a threshold leads to the appearance of a new interior fixed point associated with a coordination threshold. The fingerprints of the stable and unstable interior fixed points still affect the evolutionary dynamics in finite populations, despite evolution leading the population inexorably to a monomorphic end-state. However, when the group size and population size become comparable, we find that spite sets in, rendering cooperation unfeasible.     

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.     

Cannibals and parasites: conflicting regulators of bimodality in high latitude Arctic char, Salvelinus alpinus

Unexploited populations of Arctic char (Salvelinus alpinus) sampled in autonomous lake ecosystems in northern Svalbard demonstrate extraordinary catch curves with age and size frequency distributions characterized by discrete bimodality. Analyses of size‐age relationship, summer diet and food‐related intestinal parasite intensities of modal char groups revealed a pattern of discrete ontogenetic niche shifts. Life‐history changes at age 10–15 and size 200–300 mm/50–300 g involved shifting from an initial mode of small‐sized, slow‐growing and sexually mature individuals feeding on micro‐crustaceans and aquatic insects (Chironomidae, Trichoptera), to a terminal mode of large‐sized and fast‐growing cannibals. Cannibalism, however, was found to result in accumulation of cestodan parasites, of which Diphyllobothrium ditremum increases age‐related mortality rates and may be lethal at 1500–2000 plerocercoids. Genetically allopatric populations with cannibalism demonstrated a female‐biased sex ratio, primarily in the initial mode, suggesting sexual asynchrony in their ontogeny. By contrast, a small population of large‐sized, non‐cannibalistic Arctic char feeding exclusively on the large amphipod Gammaracanthus lacustris, demonstrated unimodal size and age frequency distribution, faster growth, an excess of males and lower parasite burden. Seasonal prey shortage and slow juvenile growth in association with fitness components favoring large body size is a suggested mechanism for inducing cannibalism. Although not the basic cause of bimodality as such, it is concluded that ontogenetic niche shift by cannibalism reinforces discrete age modal divergence resulting in the numerical preponderance of large‐sized individuals in these marginal char populations. Cannibalism is thus considered an important strategy for survival of landlocked Arctic char in the High Arctic. As a conflicting cost to the more efficient use of available energy by larger individuals, the accumulation of cestodan parasites in cannibals, however, will reduce the survival rate of old individuals and accelerate their termination within this modal group.     

Individual variability and population regulation: a model of the significance of within-generation density dependence

Most models of theoretical population ecology consider population density as a state variable and thus ignore the fact that populations are composed not of identical average individuals but of individuals which are usually different. However, this individual variability may be important for population regulation. We therefore analysed an individual-based population model which explicitly describes within-generation processes, i.e. individual growth, starvation, and resource dynamics. The results show that if population dynamics are dominated by slow changes in resource level, the population size in the model undergoes wide oscillation, often leading to extinction. If, on the other hand, fast within-generation processes predominate, such as starvation and sudden drops in resource levels, the population fluctuates to a limited extent around an average. Within-generation density dependence may thus be an important mechanism which is largely ignored in classic time-discrete state-variable models. We conclude that the individual-based approach provides important insights into the hierarchical organization of population dynamics, i.e. the relationship between fast processes at the individual level and slower processes at the population level.     

Individual size variation and population stability in a seasonal environment: a discrete-time model and its calibration using grasshoppers

Much recent literature is concerned with how variation among individuals (e.g., variability in their traits and fates) translates into higher-level (i.e., population and community) dynamics. Although several theoretical frameworks have been devised to deal with the effects of individual variation on population dynamics, there are very few reports of empirically based estimates of the sign and magnitude of these effects. Here we describe an analytical model for size-dependent, seasonal life cycles and evaluate the effect of individual size variation on population dynamics and stability. We demonstrate that the effect of size variation on the population net reproductive rate varies in both magnitude and sign, depending on season length. We calibrate our model with field data on size- and density-dependent growth and survival of the generalist grasshopper Melanoplus femurrubrum. Under deterministic dynamics (fixed season length), size variation impairs population stability, given naturally occurring densities. However, in the stochastic case, where season length exhibits yearly fluctuations, size variation reduces the variance in population growth rates, thus enhancing stability. This occurs because the effect of size variation on net reproductive rate is dependent on season length. We discuss several limitations of the current model and outline possible routes for future model development.     

Population variation and individual maximum size in two leech populations: energy extraction from cannibalism or niche widening?

The theory of cannibal dynamics predicts a link between population dynamics and individual life history. In particular, increased individual growth has, in both modeling and empirical studies, been shown to result from a destabilization of population dynamics. We used data from a long-term study of the dynamics of two leech (Erpobdella octoculata) populations to test the hypothesis that maximum size should be higher in a cycling population; one of the study populations exhibited a delayed feedback cycle while the other population showed no sign of cyclicity. A hump-shaped relationship between individual mass of 1-year-old leeches and offspring density the previous year was present in both populations. As predicted from the theory, the maximum mass of individuals was much larger in the fluctuating population. In contrast to predictions, the higher growth rate was not related to energy extraction from cannibalism. Instead, the higher individual mass is suggested to be due to increased availability of resources due to a niche widening with increased individual body mass. The larger individual mass in the fluctuating population was related to a stronger correlation between the densities of 1-year-old individuals and 2-year-old individuals the following year in this population. Although cannibalism was the major mechanism regulating population dynamics, its importance was negligible in terms of providing cannibalizing individuals with energy subsequently increasing their fecundity. Instead, the study identifies a need for theoretical and empirical studies on the largely unstudied interplay between ontogenetic niche shifts and cannibalistic population dynamics.