Can predation cause the 10-year hare cycle?

Summary We relate causes of mortality of snowshoe hares to density of hares over an 8-year period that included a peak in numbers. We then use simulation modeling to examine whether these density-dependent relationships could produce changes in hare density similar to those observed in our study are in Yukon, Canada.Predation during winter was the largest source of mortality for snowshoe hares at Kluane, Yukon during 1978–84. There was a one-year lag in the response of winter predation mortality rate to hare density. There was a two-year lag in the response of winter mortality not caused by predators to hare density.A simple simulation model with density-dependent predation produced 8–11 year cycles only within a narrow range of parameters that are inconsistent with data from the Kluane region. However, a simulation model that predicted winter mortality rates using a delayed density-dependent numerical response and a Type II functional response by predators, produced 8–11 year cycles within the range of parameter values measured in our study. Yet another simulation model that predicted both summer and winter mortality rates using a delayed density-dependent numerical response and a Type II functional response by predators, did not produce 8–11 year cycles within the range of parameter values measured in our study. Lack of data on juvenile mortality may be one reason for this result.     

Simulating density-dependent relationships in south Texas northern bobwhite populations

Density dependence influences northern bobwhite (Colinus virginianus) reproduction and overwinter mortality. However, the functional forms of these density-dependent relationships or the factors that influence them during the annual life cycle events of this bird are not clear. We used a systems analysis approach with a compartment model based on difference equations (Δt = 3 months) for bobwhites in South Texas to simulate population behavior using 16 different functional forms of density-dependent production and overwinter mortality. During the reproductive season, a weak linear density-dependent relationship resulted in the longest population persistence (up to 100.0 yr), whereas a reverse-sigmoid density-dependent relationship had the worst population persistence (2.5–3.5 yr). Regarding overwinter mortality, a sigmoid or weak linear density-dependent relationship and a weak linear or no density-dependent reproduction relationship had the longest population persistence (87.5–100.0 yr). Weak linear density-dependent reproduction with either sigmoid or weak linear overwinter mortality produced stable fall population trends. Our results indicated that density dependence may have a greater influence on overwinter survival of bobwhites than previously thought. Inclusion of density-dependent functional relationships that represent both density-dependent reproduction and overwinter mortality, were critical for our simulation model to function properly. Therefore, integrating density-dependent relationships for both reproductive and overwinter periods of the annual cycle of bobwhite life history events is essential for conducting realistic bobwhite population simulation analyses that can be used to test different management scenarios in an integrated and interdisciplinary manner. © 2012 The Wildlife Society.     

Coexistence of species in a defensive switching model

We consider a simple mathematical model of two-predators and one-prey system which has the defensive switching property of predation-avoidance. We assume that the prey remains vigilant against relatively abundant predator species and guards against it by switching to another (relatively rare) predator species. We analyze how the intensity of defensive switching affects the stability of the model system. It is seen that the system generally has a stable three species coexisting equilibrium state. In the special case that the intensity of defensive switching equals one and the two predators have the same mortality rates, it is shown that the system asymptotically settles to a Volterra's oscillation in three-dimensional space. It is observed that a sufficiently small or sufficiently large value of intensity of defensive switching can make the system unstable. Finally, it is shown that the handling time may have a stabilizing effect on predator-prey systems with defensive switching.     

Consequences of size structure in the prey for predator-prey dynamics: the composite functional response

1. Current formulations of functional responses assume that the prey is homogeneous and independent of intraspecific processes. Most prey populations consist of different coexisting size classes that often engage in asymmetrical intraspecific interactions, including cannibalism, which can lead to nonlinear interaction effects. This may be important as the size structure with the prey could alter the overall density-dependent predation rates. 2. In a field experiment with damselfly and dragonfly larvae, 16 treatments manipulated the density of a small prey stage, the presence of large conspecific prey and the presence of heterospecific predators. 3. Size structure in the prey (i.e. when both prey stages were present) decreased the impact of the predator on overall prey mortality by 25-48% at mid and high prey densities, possibly due to density-dependent size-structured cannibalism in the prey. The predation rates on small prey stages were determined by the interaction of large prey and predators. Predation rates increased with prey density in the absence of large prey, but predation rates were constant across densities when large conspecifics were present. 4. The functional response for unstructured prey followed a Holling type III model, but the predation rate for size-structured prey was completely different and followed a complex pattern that could not be explained with any standard functional response. 5. Using additional laboratory experiments, a mortality model was developed and parameterized. It showed that the overall prey mortality of size-structured prey can be adequately predicted with a composite functional response model that modelled the individual functional responses of each prey stage separately and accounted for their cannibalistic interaction. 6. Thus, treating a prey population as a homogeneous entity will lead to erroneous predictions in most real-world food webs. However, if we account for the effects of size structure and the intraspecific interactions on functional responses by treating size classes as different functional groups, it is possible to reliably predict the dynamics of size-structured predator-prey systems.     

Extinction and permanence of one-prey multi-predators of Holling type II function response system with impulsive biological control

In this paper, one investigates the dynamic behaviors of one-prey multi-predator model with Holling type II functional response by introducing impulsive biological control strategy (periodic releasing natural enemies at different fixed time). By using Floquet theorem and small amplitude perturbation method, it is proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value and permanence condition is established via the method of comparison involving multiple Liapunov functions. It is shown that multi-predator impulsive control strategy is more effective than the classical and single one.     

Seasonal variation in the functional response of a coral-reef piscivore alters the inverse density-dependent mortality of its prey

Density-dependent processes are critical for regulating species’ populations, and piscivory of coral-reef fishes is frequently density dependent. However, the mechanism driving this density-dependent mortality is poorly understood, but may be caused by changes in a predator’s feeding rate at different prey densities (its functional response). An aquarium experiment replicated in winter and summer examined the functional response after 22 and 47 h of Cephalopholis cruentata feeding on Halichoeres pictus. With the exception of summer data after 47 h (density-independent mortality), mortality was inversely density dependent across all prey densities and increased with higher summer temperatures. The absence of an asymptotic pattern of inverse density-dependent mortality was caused by type II (summer) or dome-shaped type IV (winter) functional responses, with the benefits of schooling likely to cause the low mortality rates at higher prey densities. Predators’ functional responses may underlie the inverse density-dependent mortality reported in field studies of aggregating fishes.     

Competition as a demolition derby: why tolerating competitors is more important than suppressing them

Tolerance and suppression are distinct components of competition among plants, and recognizing how they affect competitive outcomes is important for understanding the mechanisms and consequences of competition. We used simulations informed by experimental trials to ask whether tolerance or suppression of competitors was more important for the survival of native plants experiencing competition with an exotic invasive species. When competition was pairwise, tolerance and suppression contributed equally to competitive rank in simulations. However, when multiple native genotypes competed together against an invader, the ability to tolerate competition was up to 50 times more important than the ability to suppress the invader. In two-competitor communities the chief advantage of suppressing competitors was a global decrease in their abundance, but this advantage did not exist in communities of multiple competitors – which is more representative of natural conditions – because decreased competitor abundance benefited all plants regardless of their competitive ability. We suggest that this concept is analogous to a ‘demolition derby,' an automotive contest where participants attempt to have the last functional vehicle on the playing field. Because strong suppressors share the benefits of eliminating competitors with other remaining competitors, we propose that tolerance of competitors is more beneficial than suppression when competition occurs in a multiplayer scenario – in a demolition derby and in nature. This finding has implications for our understanding of how competition influences plant species coexistence, plant community structure and invasion outcomes.     

Modelling the population consequences of age- and sex-related differences in winter mortality in the oystercatcher, Haematopus ostralegus

A modelling approach is used to explore the effect of age and sex differences in oystercatcher ( Haematopus ostralegus ) winter mortality on population size, population structure and the population response to habitat loss or change. Increasing the mortality of first and second year birds reduced population size, but had very little effect on the proportion of the population that were adults. Increasing female mortality reduced population size and resulted in a male-biased population. A sex bias amongst birds of breeding age meant that there were fewer potential breeding pairs for a given population size, reducing the size of the breeding population and the breeding output. Increasing the mortality of one sex relative to the other reduced population size, even when mean adult mortality rates remained unchanged. Increasing the strength of density-dependent mortality in young birds caused a greater reduction in population size as habitat was lost. Increasing the strength of female density-dependent mortality had the same effect, even though male density-dependent mortality had been correspondingly reduced. Increasing density-independent or density-dependent winter mortality in one sex relative to another also exaggerated the disproportional effect of winter habitat loss on separate breeding subpopulations using the same overwintering area. These results suggest that any study of population dynamics should be aware of both age and sex differences in mortality. Conservationists should be particularly aware of any age or sex differences in diet or habitat use that may result in a differential response to environmental change.     

Dynamical behaviour of a two-predator model with prey refuge

A three-component model consisting on one-prey and two-predator populations is considered with a Holling type II response function incorporating a constant proportion of prey refuge. We also consider the competition among predators for their food (prey) and shelter. The essential mathematical features of the model have been analyzed thoroughly in terms of stability and bifurcations arising in some selected situations. Threshold values for some parameters indicating the feasibility and stability conditions of some equilibria are determined. The range of significant parameters under which the system admits different types of bifurcations is investigated. Numerical illustrations are performed in order to validate the applicability of the model under consideration.     

Effects of native predators and eelgrass habitat structure on the introduced Asian mussel Musculista senhousia (Benson in Cantor) in southern California

The ability of predators to control the abundance of non-native species has been little explored in marine systems. Native predators may be used to control non-native species or may confer invasion resistance to communities if predation rates on invaders are density-dependent. We studied the response of southern California native predators to the density of Musculista senhousia (Benson in Cantor, 1842), a small, fast growing mussel that has been introduced from Japan to several coastlines worldwide. We performed field experiments to determine if M. senhousia proportional mortality is density-dependent and if eelgrass Zostera marina L. habitat structure influenced mussel density-dependent mortality. We also evaluated the effect of seagrass habitat structure on the aggregative and functional responses of the predatory gastropod Pteropurpura festiva (Hinds, 1844) to Asian mussel density. In the summer of 2002, P. festiva aggregated in plots with high mussel density and was responsible for nearly all predation on M. senhousia. However, M. senhousia proportional mortality was inversely density-dependent at all levels of eelgrass above-ground and below-ground habitat structure. Asian mussel proportional mortality also was inversely density-dependent and was not influenced by eelgrass habitat structure in the spring of 2004 when wading birds were the chief predator of mussels. In contrast to results for mussel proportional mortality, the aggregative and functional responses of P. festiva varied with seagrass habitat structure. P. festiva density increased with Asian mussel density in plots with low simulated habitat structure, but the relationship between P. festiva density and Asian mussel density was parabolic at zero, intermediate and high levels of habitat structure. In field enclosures, P. festiva exhibited a Type I (linear) functional response to Asian mussel density at low levels of eelgrass structure, and a Type II (hyperbolic) functional response to mussel density at high levels of eelgrass structure. Our results and those of others suggest that the degree to which local benthic communities in southern California are resistant to Asian mussel invasion depends on habitat structure, mussel settlement rates, and the density and diversity of predators.     

The effects of density-dependent offspring mortality on the synchrony of reproduction

Mortality rates often depend on the size of a population. Using ideal free theory to model the optimal timing of reproduction in model populations, I considered how the specific relationship between density-dependent offspring mortality and population size affects the optimal temporal distribution of reproduction. The results suggest that the specific form of the relationship between density-dependent mortality and the number of offspring produced determines the degree to which reproduction within a population is synchronous. Specifically, reproductive synchrony decreases as density-dependent mortality becomes increasingly inversely related to the number of offspring produced and is highest when density-dependent mortality is directly density-dependent. These findings support the suggestion that predation pressure selects for greater reproductive synchrony in species where mortality is directly density-dependent, but does not affect the timing of reproduction in species with density-independent rates of mortality. This revised version was published online in July 2006 with corrections to the Cover Date.     

Vulnerability of newly settled plaice (Pleuronectes platessa L.) to predation: effects of habitat structure and predator functional response

Plaice (Pleuronectes platessa) nursery grounds on the Swedish west coast have been subject to increasing cover of annual green macroalgae during recent years, with growth of algae starting at the time of plaice settlement in April to May. A laboratory experiment was performed to investigate how the vulnerability to predation of metamorphosing plaice was affected by the presence of filamentous algae. Predation by shrimps (Crangon crangon) on settling plaice larvae was higher on sand than among algae, whereas predation by crabs (Carcinus maenas) was unaffected by habitat type, suggesting a lower overall mortality of plaice in the vegetated habitat. When predators and prey were presented with a combination of the two habitats, predation by shrimps was as high as that in the sand treatment alone, whereas predation by crabs was lower than that in the two treatments with one habitat. Based on these results, an additional experiment was performed, investigating the functional response of shrimps to six densities of juvenile plaice in a sand habitat with alternative prey present. The proportional mortality of juvenile plaice (12-16 mm total length (TL)) was density-dependent and was best described by a type III (sigmoid) functional response of the predatory shrimps. The results suggested that the combined predation pressure from shrimps and crabs was lower among algae than on sand, but settling plaice and predatory shrimps chose the sand habitat. Plaice densities in the sigmoid part of the obtained functional response curve represented normal to high field densities of plaice on the Swedish west coast, suggesting that shrimp predation could have a stabilising effect on plaice recruitment. The formation of macroalgae mats could therefore lead to a concentration of plaice juveniles in the remaining sand habitat and increased mortality through density-dependent predation by shrimps.     

The impact of consumer-resource cycles on the coexistence of competing consumers

This article seeks to determine the extent to which endogenous consumer-resource cycles can contribute to the coexistence of competing consumer species. It begins with a numerical analysis of a simple model proposed by Armstrong and McGehee. This model has a single resource and two consumers, one with a linear functional response and one with a saturating response. Coexistence of the two consumer species can occur when the species with a saturating response generates population cycles of the resource, and also has a lower resource requirement for zero population growth. Coexistence can be achieved over a wide range of relative efficiencies of the two consumers provided that the functional response of the saturating consumer reaches its half-saturation value when the resource population is a small fraction of its carrying capacity. In this case, the range of efficiencies allowing coexistence is comparable to that when two competitors have stable dynamics and a high degree of resource partitioning. A variety of modifications of this basic model are analyzed to investigate the consequences for coexistence of different resource growth equations, different functional and numerical response shapes, and other factors. Large differences in functional response shape appear to be the most important factor in producing robust coexistence via resource cycles. If the unstable species has a concave numerical response, this greatly expands the conditions allowing coexistence. If the stable consumer species has a convex (accelerating) functional and/or numerical response, the range of conditions allowing coexistence is also expanded. We argue that large between-species differences in functional response form can often be produced by between-consumer differences in the adaptive adjustments of foraging effort to food density. Consumer-resource cycles can also expand the conditions allowing coexistence when there is resource partitioning, but do so primarily when resource partitioning is relatively slight; this makes the ease of coexistence relatively independent of consumer similarity.     

Does structural sensitivity alter complexity–stability relationships?

Structural sensitivity, namely the sensitivity of a model dynamics to slight changes in its mathematical formulation, has already been studied in some models with a small number of state variables. The aim of this study is to investigate the impact of structural sensitivity in a food web model. Especially, the importance of structural sensitivity is compared to that of trophic complexity (number of species, connectance), which is known to strongly influence food web dynamics. Food web structures are built using the niche model. Then food web dynamics are modeled using several type II functional responses parameterized to fit the same predation fluxes. Food web persistence was found to be mostly determined by trophic complexity. At the opposite, even if food web connectance promotes equilibrium dynamics, their occurrence is mainly driven by the choice of the functional response. These conclusions are robust to changes in some parameter values, the fitting method and some model assumptions. In a one-prey/one-predator system, it was shown that the possibility that multiple stable states coexist can be highly structural sensitive. Quantifying this type of uncertainty at the scale of ecosystem models will be both a natural extension to this work and a challenging issue.     

Density-dependent dispersal in integrodifference equations

Many species exhibit dispersal processes with positive density- dependence. We model this behavior using an integrodifference equation where the individual dispersal probability is a monotone increasing function of local density. We investigate how this dispersal probability affects the spreading speed of a single population and its ability to persist in fragmented habitats. We demonstrate that density-dependent dispersal probability can act as a mechanism for coexistence of otherwise non-coexisting competitors. We show that in time-varying habitats, an intermediate dispersal probability will evolve. Analytically, we find that the spreading speed for the integrodifference equation with density-dependent dispersal probability is not linearly determined. Furthermore, the next-generation operator is not compact and, in general, neither order-preserving nor monotonicity-preserving. We give two explicit examples of non-monotone, discontinuous traveling-wave profiles.      

A spatial theory for characterizing predator–multiprey interactions in heterogeneous landscapes

Trophic interactions in multiprey systems can be largely determined by prey distributions. Yet, classic predator–prey models assume spatially homogeneous interactions between predators and prey. We developed a spatially informed theory that predicts how habitat heterogeneity alters the landscape-scale distribution of mortality risk of prey from predation, and hence the nature of predator interactions in multiprey systems. The theoretical model is a spatially explicit, multiprey functional response in which species-specific advection–diffusion models account for the response of individual prey to habitat edges. The model demonstrates that distinct responses of alternative prey species can alter the consequences of conspecific aggregation, from increasing safety to increasing predation risk. Observations of threatened boreal caribou, moose and grey wolf interacting over 378 181 km² of human-managed boreal forest support this principle. This empirically supported theory demonstrates how distinct responses of apparent competitors to landscape heterogeneity, including to human disturbances, can reverse density dependence in fitness correlates.     

Larva-to-adult and pupa-to-adult mortality dynamics in crowded cultures ofDrosophila melanogaster

Pupal mortality is shown here to bear the main responsibility for total mortality duringDrosophila melanogaster development in crowded conditions. The dynamics of the pupa-to-adult and larva-to-adult processes of mortality follows a S-shaped logistic model, like survival in density-dependent processes. Data given here confirm to some extent Wallace's suggestion that pupal mortality is a density-dependent process.     

Consequences of habitat loss and change to populations of wintering migratory birds: predicting the local and global effects from studies of individuals

Population models show that the response of migratory bird populations to a reduction in the area, or change in the quality, of their winter feeding areas depends critically on the shape (linear or non-linear) and strength (slope) of the relationship describing how the proportion dying from starvation changes with population density. Yet the parameters that define such density-dependent functions are extremely difficult to estimate from direct measurements of mortality at different population sizes. Even if they could be estimated, there would be uncertainty as to whether or not the relationship would remain the same, and thus provide reliable predictions, in the new circumstances for which forecasts are required. This paper summarizes studies of the Oystercatcher Haematopus ostralegus which aim to derive the shape and strength of the winter density-dependent mortality and emigration function for one estuary, under existing and new circumstances, from the responses of individual birds to each other and to their spatially and seasonally varying food supply. Based on these studies, an individuals-based, physiologically structured game theoretic distribution model has been built which predicts the carrying capacity and numbers of birds dying at different population sizes. The model also can be applied to Oyster-catchers occupying several estuaries distributed throughout their wintering range and can thus be extended to the entire biogeographical or global population. In addition, it can be used to identify some easily measured behavioural and ecological parameters that identify those species, from a wide range of taxa, that are most likely to be affected by habitat loss and change.     

The invisible niche: Weakly density-dependent mortality and the coexistence of species

Weakly density-dependent effects, characterized by fractional scaling exponents close to one, are rarely studied in the ecological literature. Here, we consider the effect of an additional weakly density-dependent term on a simple competition model. Our investigation reveals that weak density-dependence opens up an “invisible niche”. This niche does not constitute a new mechanism for coexistence, but is a previously unexplored consequence of known mechanisms. In the invisible niche a weaker competitor can survive at very low density. Coexistence thus requires large habitat size. Such niches, if found in nature, would have a direct impact on species-area laws and species-abundance curves and should therefore receive more attention.