Theoretical dynamics of competitors under predation

Summary Continuous population models of two prey species and a predator were explored by isocline analysis. When predator satiation and substitution between prey (with or without switching) are introduced in the models, many qualitatively different kinds of dynamic behaviour become possible. These depend in a complex but predictable way on competitive relations between prey and on predator feeding behaviour and efficiency. Under constant predation many cases of threshold responses between two or more alternate stable states are possibly; the numerical response of the predator population reduces some of the possibilities.Apparently contradictory community phenomena previously proposed, e.g. prey coexistence versus exclusion by addition of predator, exclusion versus stabilization by addition of alternate prey, are all possible as special cases. A prey which is relatively tolerant to predation can act as a keystone species, on which the existence of other prey species in the community depends, in either a positive or a negative sense. In certain conditions predator-induced obligatory mutualism between two prey species is theoretically possible.To Michael Evenari, pioneer, teacher and friend     

A stochastic model of the distribution of unequal competitors between resource patches

We present a stochastic model of individuals' movements between two patches of resources. The population is made up of two types of individual with differing competitive abilities, and two types of movements occur, with individuals moving either to increase their intake rate or at random. Several previous models have used simulations to evaluate the likely distribution of individuals. We instead derive equations for the equilibrium distribution of the population, which can be solved numerically. This avoids the need to choose an initial distribution for the population, and enables us to obtain the probability with which rare events occur. This may not be possible when simulations are used, since a rare event may not occur at all. We find that when random movements are rare, an increase in the rate of random movements out of a patch can increase the number of individuals on that patch. We consider an approximation to the model with rare random movements, which provides an explanation for this phenomenon.     

Movement between patches, unequal competitors and the ideal free distribution

Researchers have often commented on the ability of the original ideal free distribution (IFD) model to approximate observed animal distributions even though the critical assumption that competitors are of equal ability is usually violated. We provide an explanation by recognizing that animals will occasionally move between patches for reasons other than to simply maximize their resource payoffs, given perfect (i.e. ideal) information about the current payoff in each patch, and that these movements will continue to occur even after an equilibrium is reached. When such movements are incorporated into an unequal competitors IFD model, a single, stable distribution of each competitor type is predicted. This equilibrium will usually be characterized by under-matching of total competitive units relative to the distribution of resources (i.e. too few competitive units in the good patch). More importantly, it will often resemble the original, equal competitors IFD, in that total competitor numbers will come close to matching the distribution of resources. We argue that researchers claiming to have observed an IFD of equal competitors have actually observed this equilibrium distribution of unequal competitors. Our model predicts that the deviation from input-matching will usually be an under-matching of total competitor numbers relative to resources (i.e. too few competitors in the good patch). Examination of published data reveals that post-equilibrium movement between patches occurs frequently and, although the reported distributions are similar to those predicted by input-matching, under-matching is usually observed.     

Antipredator defense as a limited resource: unequal predation risk in broods of an insect with maternal care

The allocation of parental investment is a potential sourceof conflict within broods whenever offspring are able obtaindifferential access to the parental resource. Unlike the provisioningof food, parental antipredator behavior is usually considereda resource that benefits all offspring simultaneously. In thethornbug treehopper (Umbonia crassicornis), offspring formaggregations in exposed positions on host-plant stems. Theyare subject to intense predation, and maternal defense is theirprimary means of protection. I examined the distribution ofrisk within these offspring groups, using natural variationin the outcome of more than 500 predation attempts (324 recordedon videotape) by vespid wasps (Pseudopolybia compressa) on18 U. crassicornis aggregations. I found three influences onan individual offspring's risk of predation. The first wasthe presence of a defending female: as expected, offspringwere much more likely to survive contact with a wasp if thefemale was present than if the female had disappeared. Thesecond influence was position relative to other offspring: when wasps were successful in removing an individual, they almostalways removed it from the edge of the group. The third influencewas distance from the female: the closer an offspring was tothe female at the time it was contacted by a wasp, the higherits likelihood of survival. The distribution of risk is determinedlargely by the behavior of defending females and the prey-searchingbehavior of wasps. The nature of risk within these aggregations sets the stage for two forms of sibling rivalry: selfish herdbehavior and competition for access to maternal defense. Italso raises the question of how a parent should allocate defenseamong offspring when it is unable to defend them all simultaneously.     

Stage-dependent predation on competitors: consequences for the outcome of a mosquito invasion

1. Predator-mediated coexistence occurs when predation allows competitors to coexist, due to preferential consumption of a superior competitor relative to an inferior competitor. Differences between the native treehole mosquito ( Aedes triseriatus ) and the co-occurring Asian tiger mosquito ( Aedes albopictus ) in anti-predatory larval behaviours account, in part, for the greater vulnerability of this invasive species to native predatory midge ( Corethrella appendiculata ). We test the hypothesis that stage-dependent differences in the sizes of A. albopictus and A. triseriatus larvae, relative to the size-limited C. appendiculata , contribute to differential consumption and the likelihood of predator-mediated coexistence of these competitors.
2. In all instars, larvae of A. triseriatus were larger than A. albopictus of the same stage. Third and fourth instar C. appendiculata selectively consumed late-stage A. albopictus in preference to same-stage A. triseriatus . Small, early-stage prey larvae did not differ in vulnerability to predation, but large, late-stage larvae differed significantly in vulnerability to predation, probably owing to size-limited predation by fourth instar C. appendiculata. This effect was less pronounced for third instar C. appendiculata .
3. Prey size, in conjunction with anti-predatory behavioural responses, alters the probability of predator-mediated coexistence. A stage-structured predation model showed that equally vulnerable early stages reduce the range of environmental conditions (productivities) in which predator-mediated coexistence is possible, increasing the likelihood of both competitive exclusion of the resident species or failure of the invasive to establish. These results underscore the importance of stage-dependent interspecific differences in predator–prey interactions for determining how predators may affect community composition.     

Intratrophic predation in simple predator-prey models

Intratrophic predation is a phenomenon not usually considered in mathematical models of biological populations, and yet it may occur in any model where many species are considered as a single model variable. This paper demonstrates how intratrophic predation can be rationally included in a general predator-prey model, and shows that the resulting model has some desirable and intuitively plausible features. A simple asymptotic method is developed in order to investigate how intratrophic predation can affect both the position and stability of the equilibria of a model. The methods can be applied to wide classes of population models, and the conclusions drawn are of practical importance.     

The effects of background coloration and dark spots on the risk of predation in poison frog models

Protective coloration is a well-known predator avoidance strategy in prey species. Aposematic species often display a contrasting color pattern consisting of dark spots of different shapes and sizes on a bright background coloration. Both elements, background color and spots are expected to serve different purposes. While the ecological function of the bright coloration has been addressed in many studies, the question of whether the interaction with differently sized spots influences predator behavior has received less attention by researchers. In a lowland rain forest in Costa Rica we used 2700 clay models that imitated the polytypic strawberry poison frog (Oophaga pumilio) as a proxy for an aposematic prey species. We manipulated the dorsal color pattern by using a local and a non-local aposematic and a non-local cryptic background color and combined them with black spots increasing in size (none, small, medium, large). The major objective was to test if spot size alters the survival rate of differently colored models. Background coloration and spot size were significant predictors of being attacked. However, the interaction between both effects was not. During five trials predators avoided the non-local aposematic color morph and did not discriminate between local aposematic and non-local cryptic models. Spot size and attack rate were negatively linear correlated which suggests that predator selection promotes the evolution of dark spots. We further conclude that spot size matters in a contrasting color pattern and plays an important role in predator avoidance.     

Nonlinearity in the predation risk of prey mobility

Odorous waste products such as urine and faeces are unavoidable for most animals and are widely exploited by predators and their prey. Consequently, waste accumulations can be risky and prey which increase their mobility in order to disperse and dilute their waste should avoid a high predation risk until this benefit is balanced by the increasing risks of random predator encounter. This hypothesis was tested for voles (Microtus spp.) in Finland which are vulnerable to predation due to the scent and ultraviolet attractiveness of their urine. The mortality and mobility of radio-collared voles showed a U-shaped relationship, regardless of vole sex, species or population cycle phase. The low risks for prey making intermediate movements suggest that predation risk can exert strong selective pressures on prey such that they have little respite from the risk of being killed.     

The role of predation in plankton models

Models of carbon and nitrogen cycles in the ocean are a majortool in elucidating short-and long-term patterns of chemicalfluxes. Variability in space and time are usually attributedto changes in ocean physics at different scales. This paperstresses the significance of the upper (predatory) closure inthese simple nutrient-plant-herbivore models. The mathematicalform used to close the system and the values given to the parametershave very marked effects on the overall response. In particularthe major differences between North Atlantic and Pacific patternsmay depend on this aspect as much as on the physical cycles.It is shown that the selection of different closure forms infive recent modelling studies corresponds to differences inthe nutrient dynamics and plankton cycles. Thus, in general,the character of the results from these models will depend onboth the form of the mortality closure and the parameter valuesused. Our ignorance in both areas is considerable.     

Optimal diving under the risk of predation

Many air-breathing aquatic foragers may be killed by aerial or subsurface predators while recovering oxygen at the surface; yet the influence of predation risk on time allocation during dive cycles is little known in spite of numerous studies on optimal diving. We modeled diving behavior under the risk of predation at the surface. The relationship between time spent at the surface and the risk of death is predicted to influence the optimal surface interval, regardless of whether foragers accumulate energy at a constant rate while at the food patch, deplete food resources over the course of the dive, or must search for food during the dive. When instantaneous predation risk during a single surface interval decreases with time spent at the surface, a diver should increase its surface interval relative to that which maximizes energy intake, thereby increasing dive durations and reducing the number of surfacings per foraging bout. When instantaneous risk over a single surface interval does not change or increases with increasing time at the surface, divers should decrease their surface interval (and consequently their dive duration) relative to that which maximizes energy intake resulting in more dives per foraging bout. The fitness consequences of selecting a suboptimal surface interval vary with the risk function and the way divers harvest energy when at depth. Finally, predation risk during surface intervals should have important consequences for habitat selection and other aspects of the behavioral ecology of air-breathing aquatic organisms.     

Size-dependent predation risk in cryptic prey

Journal of Ethology - Visual crypsis of prey is determined by the interaction between an individual’s physical appearance to their predators and visual aspects of their environment. Physical...     

Effects of competitors and Chaoborus predation on the cladocerans of a eutrophic lake: an enclosure study

The role of large laboratory grown food competitors ofthe genus Daphnia as well as the predationimpact of Chaoborus on the cladoceran communityof an eutrophic lake was assessed in five insitu enclosure experiments. The hypothesis tested wasthat the outcome of competition and gape-limitedpredation on cladocerans is size dependent. Accordingto the generally accepted assumptions on competitionand invertebrate predation, large-bodied cladocerantaxa were expected to be less affected by competingcongeners and by Chaoborus than weresmall-bodied taxa. Effects of the predator upon anassemblage of differently sized cladoceran taxa weremuch more pronounced than effects of competition.There was a tendency of predation and competitionimpact to decrease with cladoceran size, but predationpressure was also low for some small cladocerans andhigh for some large cladocerans. The general trendswere further obscured by factors not or indirectlylinked to body size.     

Olfactory assessment of predation risk in the aquatic environment

The aquatic environment is well suited for the transmission of chemical information. Aquatic animals have evolved highly sensitive receptors for detecting these cues. Here, I review behavioural evidence for the use of chemical cues by aquatic animals for the assessment of predation risk. Chemical cues are released during detection, attack, capture and ingestion of prey. The nature of the cue released depends on the stage of the predation sequence in which cues are released. Predator odours, disturbance pheromones, injury-released chemical cues and dietary cues all convey chemical information to prey Prey use these cues to minimize their probability of being taken on to the next stage of the sequence. The evolution of specialized epidermal alarm substance cells in fishes in the superorder Ostariophysi represent an amplification of this general phenomenon. These cells carry a significant metabolic cost. The cost is offset by the fitness benefit of the chemical attraction of predators. Attempts of piracy by secondary predators interrupt predation events allowing prey an opportunity for escape. In conclusion, chemical cues are widely used by aquatic prey for risk assessment and this has resulted in the evolution of specialized structures among some taxa.     

Begging and the risk of predation in nestling birds

Theoretical models of the evolution of begging in nestling passerinesassume that begging is costly, either energetically or in termsof predation. However, few empirical measures of these costsexist. We examined whether nestling begging calls could attractpredators to nests by comparing predation rates at artificialnests with and without playbacks of tree swallow begging calls.Nests were baited with quail eggs and placed in pairs on theground or in modified nest-boxes. Nests with playbacks of beggingcalls were depredated before control nests significantly moreoften in both the ground and nest-box trials, suggesting thatpredators may use begging calls to locate nests. These resultssuggest that the risk of nest predation may be increased becauseof calling by nestlings and provide further support for theassumption that conspicuous begging is costly in terms of predation     

Direct and indirect effects of predation and predation risk in old-field interaction webs

ABSTRACT Indirect effects emerge when a change in the abundance of one species indirectly affects another by changing the abundances of intermediate species-called density-mediated indirect effects-or they arise when one species modifies how two other species interact-called trait-mediated indirect effects. I report on field experiments that evaluated how grass and herb biomass in old-field interaction webs was influenced indirectly by a spider carnivore through its interactions with a generalist and a grass-specialist grasshopper species. I manipulated interaction pathways between the spider and the plants using different combinations of the grasshopper species. I changed the modality of predator-prey interactions to isolate density-mediated from trait-mediated effects using natural spiders (predation spiders) or spiders that were prevented from subduing prey by mouthpart manipulation (risk spiders). I found that indirect effects were stronger in speciose, reticulate food webs than in linear food chains owing to a trait-mediated effect, a diet shift by herbivores in response to predation risk. Spiders alone did not have significant effects on grasshopper densities in the field experiments, removing any possibility of density-mediated indirect effects. The study illustrates that ecologists should not underestimate the importance of behavioral ecology in determining community-level interactions.     

Effects of predation on host-pathogen dynamics in SIR models

The integration of infectious disease epidemiology with community ecology is an active area of research. Recent studies using SI models without acquired immunity have demonstrated that predation can suppress infectious disease levels. The authors recently showed that incorporating immunity (SIR models) can produce a “hump”-shaped relationship between disease prevalence and predation pressure; thus, low to moderate levels of predation can boost prevalence in hosts with acquired immunity. Here we examine the robustness of this pattern to realistic extensions of a basic SIR model, including density-dependent host regulation, predator saturation, interference, frequency-dependent transmission, predator numerical responses, and explicit resource dynamics. A non-monotonic relationship between disease prevalence and predation pressure holds across all these scenarios. With saturation, there can also be complex responses of mean host abundance to increasing predation, as well as bifurcations leading to unstable cycles (epidemics) and pathogen extinction at larger predator numbers. Firm predictions about the relationship between prevalence and predation thus require one to consider the complex interplay of acquired immunity, host regulation, and foraging behavior of the predator.     

The role of higher predation in plankton population models

Zooplankton mortality in plankton population models is oftenrepresented by the so-called closure term. Recently, much attentionhas been paid to the choice of functional form used for theclosure term, primarily due to the influential paper by Steeleand Henderson (J. Plankton Res., 14, 157–172, 1992). Herewe reveal an inconsistency in the normalization of Steele andHenderson's models, and show that unforced short-term oscillations(limit cycles) can occur when a quadratic closure term is used.Furthermore, we contradict the hypothesis regarding the relationshipbetween nutrient steady-state values and the choice of closureterm: using the seven-component plankton model of Fasham (TheGlobal Carbon Cycle, Heimann,M. (ed.), pp. 457–504, 1993)with four alternative closure terms, we find the nutrient valueto depend more upon the choice of parameter values than on thechoice of closure term. However, our results agree with andstrengthen the general conclusion of Steele and Henderson'swork: that the choice of closure term can strongly influencethe dynamics of models.