Age-dependent predation is not a simple process. I. Continuous time models

The stability of models of age-dependent predation in continuous time with predators exhibiting a functional response are analyzed. A number of new features of biological importance emerge that are not present in simpler models. These include limits to the length of juvenile periods (both upper and lower) for stability, and the possibility that increases or decreases in any of the model parameters can be stabilizing or destabilizing. Hence, increased delays are not necessarily destabilizing. The variance in the length of the juvenile period is shown to be an important factor determining stability. Additionally, the relative stability of predation only on juveniles or only on adults is compared.     

Can spatial variation alone lead to selection for dispersal?

The stability of models of age-dependent predation in continuous time with predators exhibiting a functional response are analyzed. A number of new features of biological importance emerge that are not present in simpler models. These include limits to the length of juvenile periods (both upper and lower) for stability, and the possibility that increases or decreases in any of the model parameters can be stabilizing or destabilizing. Hence, increased delays are not necessarily destabilizing. The variance in the length of the juvenile period is shown to be an important factor determining stability. Additionally, the relative stability of predation only on juveniles or only on adults is compared.     

Models of ontogenetic allometry in cladoceran morphology studies

Ontogenetic variation of morphological traits in cladocerans is usually analysed by a simple allometry function. We found that common cyclomorphic and inducible traits in Bosmina and Daphnia sometimes deviate from simple allometry, however. Consequently, simple allometric analysis may at times be inadequate since important aspects of the ontogenetic development may not be revealed. We suggest that other allometric models should be used more extensively in ontogenetic studies of cladocerans morphology. Especially, complex allometric functions may help analyse the effects of size-selective predation on morphological defence traits when predators prefer prey of intermediate size. Guest editor: Piet Spaak Cladocera: Proceedings of the 7th International Symposium on Cladocera     

What is the role of predation on stability of natural communities? A theoretical investigation.

A basic question in ecology concerns the role of species interaction on dynamics of natural communities. In this framework, ecologists have considered predation, competition, mutualism, the three most important interactions, highlighting their specific effects on distribution and abundance of species, providing knowledge about phenomena like coexistence and extinction. This paper seeks to identify the effects of predation on stability of natural communities by mathematical models. Simple multispecies community models, organized in trophic levels, are analyzed by means of a qualitative technique, loop analysis, combined with a computer calculation procedure. Results do not support the hypothesis of predation as a stabilizing factor. Rather, the outcomes of the analysis suggest that predation may or may not stabilize a community. This depends on the predator's behaviour and on the network of the community.     

Does Sex-Selective Predation Stabilize or Destabilize Predator-Prey Dynamics?

Background

Little is known about the impact of prey sexual dimorphism on predator-prey dynamics and the impact of sex-selective harvesting and trophy hunting on long-term stability of exploited populations.

Methodology and Principal Findings

We review the quantitative evidence for sex-selective predation and study its long-term consequences using several simple predator-prey models. These models can be also interpreted in terms of feedback between harvesting effort and population size of the harvested species under open-access exploitation. Among the 81 predator-prey pairs found in the literature, male bias in predation is 2.3 times as common as female bias. We show that long-term effects of sex-selective predation depend on the interplay of predation bias and prey mating system. Predation on the ‘less limiting’ prey sex can yield a stable predator-prey equilibrium, while predation on the other sex usually destabilizes the dynamics and promotes population collapses. For prey mating systems that we consider, males are less limiting except for polyandry and polyandrogyny, and male-biased predation alone on such prey can stabilize otherwise unstable dynamics. On the contrary, our results suggest that female-biased predation on polygynous, polygynandrous or monogamous prey requires other stabilizing mechanisms to persist.

Conclusions and Significance

Our modelling results suggest that the observed skew towards male-biased predation might reflect, in addition to sexual selection, the evolutionary history of predator-prey interactions. More focus on these phenomena can yield additional and interesting insights as to which mechanisms maintain the persistence of predator-prey pairs over ecological and evolutionary timescales. Our results can also have implications for long-term sustainability of harvesting and trophy hunting of sexually dimorphic species.     

Incorporating spatial variation in density enhances the stability of simple population dynamics models

Simple discrete time models of population growth admit a wide variety of dynamic behaviors, including population cycles and chaos. Yet studies of natural and laboratory populations typically reveal their dynamics to be relatively stable. Many explanations for the apparent rarity of unstable or chaotic behavior in real populations have been developed, including the possible stabilizing roles of migration, refugia, abrupt density-dependence, and genetic variation in sensitivity to density. We develop a theoretical framework for incorporating random spatial variation in density into simple models of population growth, and apply this approach to two commonly used models in ecology: the Ricker and Hassell maps. We show that the incorporation of spatial density variation into both these models has a strong stabilizing influence on their dynamic behavior, and leads to their exhibiting stable point equilibria or stable limit cycles over a relatively much larger range of parameter values. We suggest that one reason why chaotic population dynamics are less common than the simple models indicate is, these models typically neglect the potentially stabilizing role of spatial variation in density.     

Density- and frequency-dependent predation of artificial bird nests

Predators are often expected to vary their relative predation rates according to the frequency of prey types in the environment (frequency-dependent predation). The underlying cause for this must lie in some dependency of absolute predation rates on the density of prey types in the environment (density-dependent predation). However, frequency-dependent predation may either be caused by 'simple' density-dependent predation, in which the absolute predation rate on a given prey type depends purely on the density of that type, or by more complex responses in which absolute rates depend also on the density of other prey types. It is usually difficult to distinguish the underlying cause of frequency-dependent predation, because frequencies tend to change as densities change. Here, we describe the results of an experiment conducted to disentangle these phenomena under two prey richness (low and high) conditions. We used artificial bird nests (placed on shrubs and on saplings) baited with quail eggs placed in natural forests as models of natural bird nests. Our results indicate that both the absolute and relative predation rates on the prey types may vary in complex ways. Predation rates depend on a complex interaction between the prey's own density, other prey density and the diversity of prey in the environment. Neglecting to include, or consider, these complexities into analyses may lead to erroneous conclusions in studies of absolute or relative predation rates.     

Permanence in an Intraguild Predation Model with Prey Switching

Intraguild predation, a form of omnivory that can occur in simple food webs when one species preys on and competes for limiting resources with another species, can have either a stabilizing effect (McCann and Hastings in Proc. R. Soc. Lond. B 264:1249-1254, 1997) or a destabilizing effect (Holt and Polis in Am. Nat. 149:745-764, 1997), depending on the assumptions of the system. Another type of behavior that has been observed in simple food web experiments (Murdoch in Ecol. Monogr. 39:335-354, 1969) is prey switching. Prey switching can occur when the predator prefers the most abundant prey. This has also been shown to be capable of having either a stabilizing effect or a destabilizing effect and even possibly lead to predator extinction (VanLeeuwen et al. in Ecology 88:1571-1581, 2007). Therefore, it is clear that incorporating prey switching into an intraguild predation model could lead to unexpected consequences. In this paper, we propose and explore such a model.     

From chaos to chaos. An analysis of a discrete age-structured prey–predator model

Discrete age-structured density-dependent one-population models and discrete age-structured density-dependent prey–predator models are considered. Regarding the former, we present formal proofs of the nature of bifurcations involved as well as presenting some new results about the dynamics in unstable and chaotic parameter regions. Regarding the latter, we show that increased predation may act both as a stabilizing and a destabilizing effect. Moreover, we find that possible periodic dynamics of low period, either exact or approximate, may not be generated by the predator, but it may be generated by the prey. Finally, what is most interesting from the biological point of view, is that given that the prey, in absence of the predator, exhibits periodic or almost periodic oscillations of low period, then the introduction of the predator does not alter this periodicity in any substantial way until the stabilizing effect of increased predation becomes so strong that a stable equilibrium is achieved. Received: 16 June 2000 / Revised version: 18 January 2001 / Published online: 12 October 2001     

Post-reproductive life span and demographic stability

Recent field studies suggest that it is common in nature for animals to outlive their reproductive viability. Post-reproductive life span has been observed in a broad range of vertebrate and invertebrate species. But post-reproductive life span poses a paradox for traditional theories of life history evolution. The commonly cited explanation is the “grandmother hypothesis”, which applies only to higher, social mammals. We propose that post-reproductive life span evolves to stabilize predator-prey population dynamics, avoiding local extinctions. In the absence of senescence, juveniles would be the most susceptible age class. If juveniles are the first to disappear when predation pressure is high, this amplifies the population’s risk of extinction. A class of older, senescent individuals can help shield the juveniles from predation, stabilizing demographics and avoiding extinction. If, in addition, the life history is arranged so that the older individuals are no longer fertile, the stabilizing effect is further enhanced.     

Separable models in age-dependent population dynamics

A class of population models is considered in which the parameters such as fecundity, mortality and interaction coefficients are assumed to be age-dependent. Conditions for the existence, stability and global attractivity of steady-state and periodic solutions are derived. The dependence of these solutions on the maturation periods is analyzed. These results are applied to specific single and multiple population models. It is shown that periodic solutions cannot occur in a general class of single population age-dependent models. Conditions are derived that determine whether increasing the maturation period has a stabilizing effect. In specific cases, it is shown that any number of switches in stability can occur as the maturation period is increased. An example is given of predator-prey model where each one of these stability switches corresponds to a stable steady state losing its stability via a Hopf bifurcation to a periodic solution and regaining its stability upon further increase of the maturation period.     

Effect of the canopy complexity of trees on the rate of predation of insects

The effect of the complexity of tree canopies on the effectiveness of biological control of tree‐dwelling insect herbivores by predators has been neglected. A complex canopy provides a greater variety of resources than a simple canopy, which may result in an increase in the abundance of both herbivores and predators in complex canopies and a higher predation rate. On the other hand, it may be more difficult to locate prey in trees with a complex canopy, which may lower the predation rate. The main aim of this study is to determine the relationship between predation rate and canopy complexity. We have used a system consisting of lime trees, larvae of blowflies as prey and naturally occurring predators (mainly birds and ants). The complexity of the canopy of 12 of the lime trees was reduced by pruning, and the predation rate was determined by recording the fate of prey pinned on each of the trees for 30 min several times during the course of a year. The predation rate was negatively associated with canopy complexity. We compare these results with those reported in the literature and contrary to the widely held view conclude that a negative relationship between predation rate and canopy complexity is a common phenomenon and can be expected to be reported in studies not only on ambush but also on predators that actively search for prey.     

Optimal intraguild foraging and population stability

This article explores effects of adaptive intraguild predation on species coexistence and community structure in three species' food webs. Two Lotka-Volterra models that assume a trade-off between competition and predation strength are considered in detail. The first model does not explicitly model resource dynamics and is considered with both nonadaptive and adaptive intraguild predation; in the latter case predators choose their diet in order to maximize their instantaneous population growth rate. The second model includes resource population dynamics. Effects of adaptive intraguild predation on the community structure along a gradient in environment productivity are analyzed and compared with some experimental results of protist food webs. Conditions under which intraguild predation is adaptive are discussed for both models. It is proved that if intraguild predators are perfect optimizers then intraguild predation should decrease with increasing environmental productivity and adaptive intraguild predation is a stabilizing factor provided environmental productivity is high enough.     

Habitat loss alters effects of intransitive higher-order competition on biodiversity: a new metapopulation framework

Recent studies have suggested that intransitive competition, as opposed to hierarchical competition, allows more species to coexist. Furthermore, it is recognized that the prevalent paradigm, which assumes that species interactions are exclusively pairwise, may be insufficient. More importantly, whether and how habitat loss, a key driver of biodiversity loss, can alter these complex competition structures (and therefore species coexistence) remain unclear. We thus present a new, simple yet comprehensive metapopulation framework that can account for any competition pattern and more complex higher-order interactions (HOIs) among species. We find that competitive intransitivity increases community diversity and that HOIs generally enhance this effect. Essentially, intransitivity promotes species richness by preventing the dominance of a few species, unlike the hierarchical competition, while HOIs facilitate species coexistence through stabilizing community fluctuations. However, variation in species’ vital rates and habitat loss can weaken or even reverse such higher-order effects, as their interaction can lead to a more rapid decline in competitive intransitivity under HOIs. Thus, it is essential to correctly identify the most appropriate interaction model for a given system before models are used to inform conservation efforts. Overall, our simple model framework provides a more parsimonious explanation for biodiversity maintenance than the existing theory.     

Is predation capable of interacting with other community processes on rocky reefs?*

Recent ecological studies have postulated some indirect effects of predation, which are thought to arise by a variety of interactions propagating through the many vertical and horizontal links in food webs. Such theoretical explanations have been invoked by some empirical studies that demonstrated surprising or unexpected results in field experiments. Studies of intertidal and subtidal portions of temperate rocky reefs provide some of the best examples of such indirect effects of predation. Rarely, however, have the actual mechanisms involved been elucidated. To do this requires independent evidence of how processes that are only indirectly linked to predation are affected by a variety of predation regimes. This paper speculates on how factors such as competition, mutualism, desiccation, wave action and variation in recruitment on seashores might interact with predation, both during and subsequent to predatory events. I present evidence from experiments with predatory whelks in New South Wales, Australia, to emphasize the plausibility of these speculations. Predation on local seashores indirectly benefited algae by removing small grazers, providing bare space for larger grazers and living space for cryptic animals, and interacted synergistically with barnacle recruitment to increase turnover of the prey population. These studies indicate the value of elucidating experimentally the mechanisms by which indirect effects are proposed to occur. Only by demonstrating that the effects work as hypothesized can they be pronounced unambiguously as particular indirect effects. Without such evidence, other possibilities (either more simple or more complex) need to he investigated.     

You can’t run but you can hide: refuge use in frog tadpoles elicits density-dependent predation by dragonfly larvae

The potential role of prey refuges in stabilizing predator–prey interactions is of longstanding interest to ecologists, but mechanisms underlying a sigmoidal predator functional response remain to be fully elucidated. Authors have disagreed on whether the stabilizing effect of prey refuges is driven by prey- versus predator-centric mechanisms, but to date few studies have married predator and prey behavioural observations to distinguish between these possibilities. We used a dragonfly nymph–tadpole system to study the effect of a structural refuge (leaf litter) on the predator’s functional response, and paired this with behavioural observations of both predator and prey. Our study confirmed that hyperbolic (type II) functional responses were characteristic of foraging predators when structural cover was low or absent, whereas the functional response was sigmoidal (type III) when prey were provided with sufficient refuge. Prey activity and refuge use were density independent across cover treatments, thereby eliminating a prey-centric mechanism as being the genesis for density-dependent predation. In contrast, the predator’s pursuit length, capture success, and handling time were altered by the amount of structure implying that observed shifts in density-dependent predation likely were related to predator hunting efficiency. Our study advances current theory by revealing that despite fixed-proportion refuge use by prey, presence of a prey refuge can induce density-dependent predation through its effect on predator hunting strategy. Ultimately, responses of predator foraging decisions in response to changes in prey availability and search efficiency may be more important in producing density-dependent predation than the form of prey refuge use.     

Dynamics of animal movement in an ecological context: dragonfly wing damage reduces flight performance and predation success

Much of our understanding of the control and dynamics of animal movement derives from controlled laboratory experiments. While many aspects of animal movement can be probed only in these settings, a more complete understanding of animal locomotion may be gained by linking experiments on relatively simple motions in the laboratory to studies of more complex behaviours in natural settings. To demonstrate the utility of this approach, we examined the effects of wing damage on dragonfly flight performance in both a laboratory drop–escape response and the more natural context of aerial predation. The laboratory experiment shows that hindwing area loss reduces vertical acceleration and average flight velocity, and the predation experiment demonstrates that this type of wing damage results in a significant decline in capture success. Taken together, these results suggest that wing damage may take a serious toll on wild dragonflies, potentially reducing both reproductive success and survival.     

Prey behavior, age-dependent vulnerability, and predation rates

Variation in the temporal pattern of vulnerability can provide important insights into predator-prey relationships and the evolution of antipredator behavior. We illustrate these points with a system that has coyotes (Canis latrans) as a predator and two species of congeneric deer (Odocoileus spp.) as prey. The deer employ different antipredator tactics (aggressive defense vs. flight) that result in contrasting patterns of age-dependent vulnerability in their probability of being captured when encountered by coyotes. We use long-term survival data and a simple mathematical model to show that (1) species differences in age-dependent vulnerability are reflected in seasonal predation rates and (2) seasonal variation in prey vulnerability and predator hunt activity, which can be associated with the availability of alternative prey, interact to shape seasonal and annual predation rates for each prey species. Shifting hunt activity from summer to winter, or vice versa, alleviated annual mortality on one species and focused it on the other. Our results indicate that seasonal variation in prey vulnerability and hunt activity interact to influence the impact that a predator has on any particular type of prey. Furthermore, these results indicate that seasonal variation in predation pressure is an important selection pressure shaping prey defenses.     

A coupled plankton system with instantaneous and delayed predation

We present two simple plankton population models: one has instantaneous predation, another has delayed predation. The models consist of two coupled differential equations representing the interaction between phytoplankton and herbivorous zooplankton with additional effect of zooplankton predation by a constant fish population. We study the dynamical behaviour and investigate the conditions to guarantee the coexistence of two species, and address the stability and bifurcation under different density of fish, with or without the maturation time delay. Analytical methods and numerical simulations are used to obtain information about the qualitative behaviour of the models.     

A coupled plankton system with instantaneous and delayed predation

We present two simple plankton population models: one has instantaneous predation, another has delayed predation. The models consist of two coupled differential equations representing the interaction between phytoplankton and herbivorous zooplankton with additional effect of zooplankton predation by a constant fish population. We study the dynamical behaviour and investigate the conditions to guarantee the coexistence of two species, and address the stability and bifurcation under different density of fish, with or without the maturation time delay. Analytical methods and numerical simulations are used to obtain information about the qualitative behaviour of the models.