Allometric scaling enhances stability in complex food webs

Classic local stability theory predicts that complex ecological networks are unstable and are unlikely to persist despite empiricists' abundant documentation of such complexity in nature. This contradiction has puzzled biologists for decades. While some have explored how stability may be achieved in small modules of a few interacting species, rigorous demonstrations of how large complex and ecologically realistic networks dynamically persist remain scarce and inadequately understood. Here, we help fill this void by combining structural models of complex food webs with nonlinear bioenergetic models of population dynamics parameterized by biological rates that are allometrically scaled to populations' average body masses. Increasing predator–prey body mass ratios increase population persistence up to a saturation level that is reached by invertebrate and ectotherm vertebrate predators when being 10 or 100 times larger than their prey respectively. These values are corroborated by empirical predator–prey body mass ratios from a global data base. Moreover, negative effects of diversity (i.e. species richness) on stability (i.e. population persistence) become neutral or positive relationships at these empirical ratios. These results demonstrate that the predator–prey body mass ratios found in nature may be key to enabling persistence of populations in complex food webs and stabilizing the diversity of natural ecosystems.     

How predator incursions affect critical patch size: the role of the functional response

Understanding the impact of habitat edges provides a key to deciphering how community dynamics change as functions of habitat structure and spatial scale. Motivated by studies of predation on bird nests in forest fragments and other cases of "cross-boundary subsidies," we present results from a partial differential equation model in which a patch-resident prey species suffers incidental mortality from a generalist predator species residing in the surrounding matrix habitat. We demonstrate that predator intrusions have the potential to induce critical patch size effects for the prey species, even when the prey's dynamics would otherwise preclude such effects. We also demonstrate that the existence of critical patch size effects depends on the functional response of the predator, with Lotka-Volterra and Type II functional responses generating the effect (but not Type III). We conclude by discussing how predator-induced critical patch size effects can influence opportunities for regionwide persistence of the prey by altering the fraction and spatial distribution of meaningful patches within a metapopulation.     

The role of prey taxis in biological control: a spatial theoretical model

We study a reaction-diffusion-advection model for the dynamics of populations under biological control. A control agent is assumed to be a predator species that has the ability to perceive the heterogeneity of pest distribution. The advection term represents the predator density movement according to a basic prey taxis assumption: acceleration of predators is proportional to the prey density gradient. The prey population reproduces logistically, and the local population interactions follow the Holling Type II trophic function. On the scale of the population, our spatially explicit approach subdivides the predation process into random movement represented by diffusion, directed movement described by prey taxis, local prey encounters, and consumption modeled by the trophic function. Thus, our model allows studying the effects of large-scale predator spatial activity on population dynamics. We show under which conditions spatial patterns are generated by prey taxis and how this affects the predator ability to maintain the pest population below some economic threshold. In particular, intermediate taxis activity can stabilize predator-pest populations at a very low level of pest density, ensuring successful biological control. However, very intensive prey taxis destroys the stability, leading to chaotic dynamics with pronounced outbreaks of pest density.     

Influence of intra‐ and interspecific variation in predator–prey body size ratios on trophic interaction strengths

1. Predation is a pervasive force that structures food webs and directly influences ecosystem functioning. The relative body sizes of predators and prey may be an important determinant of interaction strengths. However, studies quantifying the combined influence of intra‐ and interspecific variation in predator–prey body size ratios are lacking.
2. We use a comparative functional response approach to examine interaction strengths between three size classes of invasive bluegill and largemouth bass toward three scaled size classes of their tilapia prey. We then quantify the influence of intra‐ and interspecific predator–prey body mass ratios on the scaling of attack rates and handling times.
3. Type II functional responses were displayed by both predators across all predator and prey size classes. Largemouth bass consumed more than bluegill at small and intermediate predator size classes, while large predators of both species were more similar. Small prey were most vulnerable overall; however, differential attack rates among prey were emergent across predator sizes. For both bluegill and largemouth bass, small predators exhibited higher attack rates toward small and intermediate prey sizes, while larger predators exhibited greater attack rates toward large prey. Conversely, handling times increased with prey size, with small bluegill exhibiting particularly low feeding rates toward medium–large prey types. Attack rates for both predators peaked unimodally at intermediate predator–prey body mass ratios, while handling times generally shortened across increasing body mass ratios.
4. We thus demonstrate effects of body size ratios on predator–prey interaction strengths between key fish species, with attack rates and handling times dependent on the relative sizes of predator–prey participants.
5. Considerations for intra‐ and interspecific body size ratio effects are critical for predicting the strengths of interactions within ecosystems and may drive differential ecological impacts among invasive species as size ratios shift.

     

Climate change and cyclic predator–prey population dynamics in the high Arctic

The high Arctic has the world's simplest terrestrial vertebrate predator–prey community, with the collared lemming being the single main prey of four predators, the snowy owl, the Arctic fox, the long-tailed skua, and the stoat. Using a 20-year-long time series of population densities for the five species and a dynamic model that has been previously parameterized for northeast Greenland, we analyzed the population and community level consequences of the ongoing and predicted climate change. Species' responses to climate change are complex, because in addition to the direct effects of climate change, which vary depending on species' life histories, species are also affected indirectly due to, e.g., predator–prey interactions. The lemming–predator community exemplifies these complications, yet a robust conclusion emerges from our modeling: in practically all likely scenarios of how climate change may influence the demography of the species, climate change increases the length of the lemming population cycle and decreases the maximum population densities. The latter change in particular is detrimental to the populations of the predators, which are adapted to make use of the years of the greatest prey abundance. Therefore, climate change will indirectly reduce the predators' reproductive success and population densities, and may ultimately lead to local extinction of some of the predator species. Based on these results, we conclude that the recent anomalous observations about lack of cyclic lemming dynamics in eastern Greenland may well be the first signs of a severe impact of climate change on the lemming–predator communities in Greenland and elsewhere in the high Arctic.     

Strategies of aphidophagous predators: lessons for modelling insect predator–prey dynamics

Both theoretical and empirical evidence indicate that in systems where insect predators have longer developmental times than their prey the predators have little impact on the abundance of their prey. In assessing the 'effectiveness' of a predator for biological control one should take into account that selection maximizes predator fitness, not its effctiveness as a biocontrol agent. Therefore, predators that have a long developmental time relative to their prey are unlikely to be the best biocontrol agents. If these results can be generalized to other predator–prey systems, then it is clear that an understanding of predator–prey dynamics can only be achieved by studying predators.     

Spatial co-occurrence networks predict the feeding histories of polyphagous arthropod predators at field scales

In agricultural systems, polyphagous beetles and spiders are abundant components of the beneficial arthropod community. Although data on the dietary ranges of these groups is increasing, remarkably little is understood regarding how individuals interact with their prey at small spatial scales. We demonstrate the utility of a spatially-explicit network model that integrates predator behaviour using predator-prey co-occurrences. Three co-occurrence matrices, one each for June, July and August, were generated using Vortis suction sample data collected from an 80 point grid imposed on a field of winter wheat. Heuristic predator-prey linkages, based on positive spatial co-occurrence, were imposed on these three matrices to create networks. It was found that primary consumers were highly aggregated and showed a strong tendency to co-occur. This contrasted with patterns of predator–predator or predator–prey co-occurrences that either aggregated to their prey or were weak and more scattered. These patterns could not be explained by either competition for resources or body size differences. Procrustean methods indicated that the networks were temporally dynamic, consistently achieving rates of turnover >60%. A negative relationship was found between decreasing predator–prey co-occurrence in the network and the number of prey positives in the guts of those predators. For large polyphagous beetles, the closer they were to their prey at the field scale, the more likely they were to have eaten them. This simple underlying relationship suggests that spatial co-occurrence networks can be used to predict feeding behaviour and could make a valuable contribution to food web structuring.     

Scaling up population dynamic processes in a ladybird–aphid system

Here, we study how scaling up to the metapopulation level affects predictions of a population dynamics model motivated by an aphidophagous predator–aphid system. The model incorporates optimization of egg distribution in predatory females, cannibalism among their offspring, and self-regulation of the prey population. These factors determine the within-year dynamics of the system and translate the numbers of prey and predator individuals at the beginning of the season into their numbers at the end of the season at the level of one patch—one suitable host plant or a group of these. At the end of each season, all populations of prey and all populations of predators are mixed (this simulates aphid host-alternation and ladybird migration to hibernation sites), and then redistributed at the beginning of the next season. Prey individuals are distributed at random among the patches as a “prey rain”, while adult predators that survived from the previous season optimize the distribution of their offspring, in that they prefer patches with sufficient amount of prey and absence of other predators. This redistribution followed by within-season dynamics is then iterated over many seasons. We look at whether small-scale trends in population dynamics predicted by this model are consistent with large-scale outcomes. Specifically, we show that even on the metapopulation scale, the impact of predators on prey metapopulation is relatively low. We further show how the dates of predator arrival to and departure from the system affect the qualitative behaviour of the model predictions.     

Joint evolution of predator body size and prey-size preference

We studied the joint evolution of predator body size and prey-size preference based on dynamic energy budget theory. The predators’ demography and their functional response are based on general eco-physiological principles involving the size of both predator and prey. While our model can account for qualitatively different predator types by adjusting parameter values, we mainly focused on ‘true’ predators that kill their prey. The resulting model explains various empirical observations, such as the triangular distribution of predator–prey size combinations, the island rule, and the difference in predator–prey size ratios between filter feeders and raptorial feeders. The model also reveals key factors for the evolution of predator–prey size ratios. Capture mechanisms turned out to have a large effect on this ratio, while prey-size availability and competition for resources only help explain variation in predator size, not variation in predator–prey size ratio. Predation among predators is identified as an important factor for deviations from the optimal predator–prey size ratio.     

Modelling the dynamic spatio-temporal response of predators to transient prey patches in the field

The spatio-temporal dynamics of two aphid species ( Metopolophium dirhodum and Sitobion avenae ) and a generalist predator ( Pterostichus melanarius ) were observed in a field-scale study using a grid of 256 sampling locations with a 12-m spacing. Using Spatial Analysis by Distance Indices we demonstrate that populations show ephemeral spatial pattern at the field scale. We observed a positive, lagged beetle response to this aphid pattern; conversely, the aphids displayed a negative, lagged response to beetle spatial pattern. Examination of the local structure of the spatio-temporal dynamics revealed a strong response by the beetle population to aphid patches. The temporal structure of spatial associations between the species shows a strong correspondence with those from a conceptual model of predator–prey spatial interaction. The spatially coupled dynamics were sufficiently strong for the predator to have a negative effect on the intrinsic rate of increase of their prey.     

Flow‐mediated predator–prey dynamics influence fish populations in a tropical river

相似文献   

The ecology of fear and inverted biomass pyramids

In inverted biomass pyramids (IBPs) prey are outnumbered by their predators when measured by biomass. We investigate how prey should behave in the face of danger from higher predator biomass, and how anti-predator behavior (in the form of vigilance) can, in turn, affect the predator–prey system. In this study, we incorporate anti-predator behaviors into a Lotka–Volterra predator–prey model in the form of fixed and facultative vigilance. Facultative vigilance models behavior as a dynamic foraging game, allowing us to assess optimal behavioral responses in the context of IBPs using a dynamical fitness optimization approach. We model vigilance as a tradeoff between safety and either the prey's maximum growth rate or its carrying capacity. We assess the population dynamics of predators and prey with fear responses, and investigate the role fear plays on trophic structure. We found that the ecology of fear plays an important role in predator–prey systems, impacting trophic structure and the occurrence of IBPs. Fixed vigilance works against IBP structure by always reducing the predator–prey biomass ratio at equilibrium with increasing levels of vigilance. Facultative vigilance can actually promote IBPs, as prey can now adjust their vigilance levels to cope with increased predation and the costs associated with vigilance. This is especially true when the effectiveness of vigilance is low and predators are very lethal. In general, these trends are true whether the costs of vigilance are felt on the prey's maximum growth rate or its carrying capacity. Just as the ecology of fear, when first introduced, was used to explain why top carnivores are rare in terrestrial systems, it can also be used to understand how big fierce predators can be common in IBPs.     

Evolution of anti-predator traits in response to a flexible targeting strategy by predators

Anti-predator benefits increase with vigilance rate and group size in many species of animal, while simultaneously resource intake rates usually decrease. This implies that there is an optimal group size and vigilance rate that will maximize individual fitness. While this basic theory of vigilance has been modelled and tested extensively, it has often been assumed that the predator represents a 'fixed-risk' such that groups of prey are essentially independent entities that exert little or no effect on one another either directly or indirectly. We argue that this is an over-simplification, and propose that the behaviour of one group of prey will likely affect the fitness of another local group of prey if the predator preferentially attacks the most vulnerable group-rather than attack both with constant rates. Using a numerical simulation model, we make the first examination of this game and allow the prey to dynamically evolve both optimal group size distributions between two habitats and vigilance rates in response to a predator with a preference for whichever group is the more vulnerable. We show that the density of prey in the population and the sensitivity of a predator to differences in prey vulnerability are likely to drive the dynamics of such a game. This novel approach to vigilance theory opens the door to several challenging lines of future research, both experimental and theoretical.     

Predator functional response changed by induced defenses in prey

Functional responses play a central role in the nature and stability of predator-prey population dynamics. Here we investigate how induced defenses affect predator functional responses. In experimental communities, prey (Paramecium) expressed two previously undocumented inducible defenses--a speed reduction and a width increase--in response to nonlethal exposure to predatory Stenostomum. Nonlethal exposure also changed the shape of the predator's functional response from Type II to Type III, consistent with changes in the density dependence of attack rates. Handling times were also affected by prey defenses, increasing at least sixfold. These changes show that induced changes in prey have a real defensive function. At low prey densities, induction led to lower attack success; at high prey densities, attack rates were actually higher for induced prey. However, induction increased handling times sufficiently that consumption rates of defended prey were lower than those of undefended prey. Modification of attack rate and handling time has important potential consequences for population dynamics; Type III functional responses can increase the stability of population dynamics and persistence because predation on small populations is low, allowing a relict population to survive. Simulations of a predator-prey population dynamic model revealed the stabilizing potential of the Type III response.     

Irreversible prey diapause as an optimal strategy of a physiologically extended Lotka–Volterra model

We propose an optimal control framework to describe intra-seasonal predator–prey interactions, which are characterized by a continuous-time dynamical model comprising predator and prey density, as well as the energy budget of the prey over the length of a season. The model includes a time-dependent decision variable for the prey, representing the portion of the prey population in time that is active, as opposed to diapausing (a state of physiological rest). The predator follows autonomous dynamics and accordingly it remains active during the season. The proposed model is a generalization of the classical Lotka–Volterra predator–prey model towards non-autonomous dynamics that furthermore includes the effect of an energy variable. The model has been inspired by a specific biological system of predatory mites (Acari: Phytoseiidae) and prey mites (so-called fruit-tree red spider mites) (Acari: Tetranychidae) that feed on leaves of apple trees—its parameters have been instantiated based on laboratory and field studies. The goal of the work is to understand the decisions of the prey mites to enter diapause (a state of physiological rest) given the dynamics of the predatory mites: this is achieved by solving an optimization problem hinging on the maximization of the prey population contribution to the next season. The main features of the optimal strategy for the prey are shown to be that (1) once in diapause, the prey does not become active again within the same season and hence diapause is an irreversible process; (2) for the vast majority of parameter space, the portion of prey individuals entering diapause within the season does not decrease in time; (3) with an increased number of predators, the optimal population strategy for the prey is to start diapause earlier and to enter diapause more gradually. This optimal population strategy will be studied for its ESS properties in a sequel to the work presented in this article.     

Feedback between size balance and consumption strongly affects the consequences of hatching phenology in size‐dependent predator–prey interactions

In many size‐dependent predator–prey systems, hatching phenology strongly affects predator–prey interaction outcomes. Early‐hatched predators can easily consume prey when they first interact because they encounter smaller prey. However, this process by itself may be insufficient to explain all predator–prey interaction outcomes over the whole interaction period because the predator–prey size balance changes dynamically throughout their ontogeny. We hypothesized that hatching phenology influences predator–prey interactions via a feedback mechanism between the predator–prey size balance and prey consumption by predators. We experimentally tested this hypothesis in an amphibian predator–prey model system. Frog tadpoles Rana pirica were exposed to a predatory salamander larva Hynobius retardatus that had hatched 5, 12, 19 or 26 days after the frog tadpoles hatched. We investigated how the salamander hatch timing affected the dynamics of prey mortality, size changes of both predator and prey, and their subsequent life history (larval period and size at metamorphosis). The predator–prey size balance favoured earlier hatched salamanders, which just after hatching could successfully consume more frog tadpoles than later hatched salamanders. The early‐hatched salamanders grew rapidly and their accelerated growth enabled them to maintain the predator‐superior size balance; thus, they continued to exert strong predation pressure on the frog tadpoles in the subsequent period. Furthermore, frog tadpoles exposed to the early‐hatched salamanders were larger at metamorphosis and had a longer larval period than other frog tadpoles. These results suggest that feedback between the predator‐superior size balance and prey consumption is a critical mechanism that strongly affects the impacts of early hatching of predators in the short‐term population dynamics and life history of the prey. Because consumption of large nutrient‐rich prey items supports the growth of predators, a similar feedback mechanism may be common and have strong impacts on phenological shifts in size‐dependent trophic relationships.     

Heterogeneous landscapes and the role of refuge on the population dynamics of a specialist predator and its prey

How, and where, a prey species survives predation by a specialist predator during low phases of population fluctuations or a cycle, and how the increase phase of prey population is initiated, are much-debated questions in population and theoretical ecology. The persistence of the prey species could be due mainly to habitats that act as refuges from predation and/or due to anti-predatory behaviour of individuals. We present models for the former conjecture in two (and three) habitat systems with a specialist predator and its favoured prey. The model is based on dispersal of prey between habitats with high reproductive output but high risk of predation, and less productive habitats with relatively low risk of predation. We illustrate the predictions of our model using parameters from one of the most intriguing vertebrate predator–prey systems, the multi-annual population cycles of boreal voles and their predators. We suggest that cyclic population dynamics could result from a sequence of extinction and re–colonization events. Field voles (Microtus agrestis), a key vole species in the system, can be hunted to extinction in their preferred meadow habitat, but persist in sub-optimal wet habitats where their main predator, the least weasel (Mustela nivalis nivalis) has a low hunting efficiency. Re–colonization of favourable habitats would occur after the predator population crashes. At the local scale, the model suggests that the periodicity and amplitude of population cycles can be strongly influenced by the relative availability of risky and safe habitats for the prey. Furthermore, factors like intra-guild predation may lead to reduced predation pressure on field voles in sub-optimal habitats, which would act as a refuge for voles during the low phase of their population cycles. Elasticity analysis suggested that our model is quite robust to changes in most parameters but sensitive to changes in the population dynamics of field voles in the optimal grassland habitat, and to the maximum predation rate of weasels.     

Rapid contemporary evolution and clonal food web dynamics

Character evolution that affects ecological community interactions often occurs contemporaneously with temporal changes in population size, potentially altering the very nature of those dynamics. Such eco-evolutionary processes may be most readily explored in systems with short generations and simple genetics. Asexual and cyclically parthenogenetic organisms such as microalgae, cladocerans and rotifers, which frequently dominate freshwater plankton communities, meet these requirements. Multiple clonal lines can coexist within each species over extended periods, until either fixation occurs or a sexual phase reshuffles the genetic material. When clones differ in traits affecting interspecific interactions, within-species clonal dynamics can have major effects on the population dynamics. We first consider a simple predator–prey system with two prey genotypes, parametrized with data from a well-studied experimental system, and explore how the extent of differences in defence against predation within the prey population determine dynamic stability versus instability of the system. We then explore how increased potential for evolution affects the community dynamics in a more general community model with multiple predator and multiple prey genotypes. These examples illustrate how microevolutionary ‘details’ that enhance or limit the potential for heritable phenotypic change can have significant effects on contemporaneous community-level dynamics and the persistence and coexistence of species.     

Scaling up the functional response for spatially heterogeneous systems

Scale transition theory is a framework for predicting regional population dynamics from local process functions and estimates of spatial heterogeneity. Using this framework, we estimated regional scale functional responses for a benthic predator–prey system in the Baltic Sea. Functional responses were based on laboratory experiments or field observations of stomach contents, and prey densities measured at a local scale (0.1 m²) or a regional scale (300 km²). Laboratory data overestimated consumption at high prey densities, whereas predictions based on local scale data tallied closely with consumption observed at the regional scale. The predicted regional functional response was different for increasing and decreasing prey densities, reflecting that predator and prey densities, as well as the covariance between them, exhibit oscillatory dynamics. We conclude that it is important to validate laboratory data with small-scale field observations and that scale transition is a powerful tool for scaling-up process functions in heterogeneous systems.     

Dynamics of predator and modular prey: effects of module consumption on stability of prey–predator system

In traditional models of predator–prey population dynamics, it is usually assumed that consumed prey are immediately removed from the population. However, in plant–herbivore interactions, damaged plants are generally alive after attacks by herbivores. This can result in successive or simultaneous attacks by multiple predators on a single prey item (here, the term prey is expanded to include plants). We constructed a mathematical model with two time scales, taking into account predation processes within a generation, considering post‐predation survival and the modularity of prey. We assumed that a prey item can be divided into modules and that it can be fed on by multiple predators or parasitized by multiple parasites at the same time. The model includes two essential factors: the modularity of prey for predators (n) and the detaching/attaching ratio of predators to prey (ε). Based on the formulae, we revealed a general property of realistic dynamics in plant–herbivore and host–parasite interactions. The analysis showed that the model could be approximated by models with the type I, type II or Beddington–DeAngelis functional responses by taking appropriate limits to the situations. When modularity is low or the detaching/attaching ratio is high, population dynamics tend to be stabilized. These stabilizing effects may be related to interference competition among predator individuals or increases in free prey modules and free predator individuals. In the limit of high modularity, the ratio of the attached prey modules to the total prey modules becomes negligible and the dynamics tend to be destabilized. However, if quantity and quality of prey modules are negatively correlated, the equilibrium is likely to be stabilized at high modularity as long as it remains feasible. These results suggest that considering post‐predation survival and modularity of prey is crucial to understand predator–prey interactions.