Seasonal cycles and persistence in an acarine predator-prey system on cassava in Africa

We applied time series analysis and a mechanistic predator-prey model to long-term data of monthly population counts of the herbivorous pest mite Mononychellus tanajoa and its introduced phytoseiid predator Typhlodromalus aripo from a cassava field in Benin, West Africa. In this approach, we determined the extent to which the main features of the observed predator-prey fluctuations in cassava fields can be explained from biotic traits inherent to the biology of predator and prey, and the extent of the significance of abiotic factors in determining population levels. The time series analyses with cross-correlation showed that the period of predator-prey fluctuations coincided with the annual pattern of intense rainfall and onset of dry season. A pronounced M. tanajoa peak followed after a short lag (2 weeks) by a T. aripo peak coincided with a trough in rainfall intensity. Both the prey and predator had local and lower peaks that coincided with high rainfall intensity, but with a considerably longer lag (ca. 3 months) compared with the high peaks occurring at the onset of the dry season. Regression of log-transformed data series (over a 7-year period) showed that—except for the first year after predator release—M. tanajoa fluctuated around an almost time-invariant mean population density, while T. aripo densities showed a consistent decline over the full observation period. To explain observed trends and periodic components in the data-series of predator and prey densities, we review hypotheses that are based on (1) the annual patterns and trends in abiotic factors, (2) mechanisms endogenous to the predator-prey system and (3) a combination of exogenous and endogenous factors.     

Effect of resource subsidies on predator-prey population dynamics: a mathematical model

The influence of a resource subsidy on predator-prey interactions is examined using a mathematical model. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). In one version of the model, the predator, prey and subsidy all occur in the same location; in a second version, the predator moves between two patches, one containing only the prey and the other containing only the subsidy. Criteria for feasibility and stability of the different equilibrium states are studied both analytically and numerically. At small subsidy input rates, there is a minimum prey carrying capacity needed to support both predator and prey. At intermediate subsidy input rates, the predator and prey can always coexist. At high subsidy input rates, the prey cannot persist even at high carrying capacities. As predator movement increases, the dynamic stability of the predator-prey-subsidy interactions also increases.     

Long-term microtine dynamics in north Fennoscandian tundra: the vole cycle and the lemming chaos

Densities of microtine rodents in two habitat complexes in the tundra of Finnmarks-vidda, Norwegian Lapland, were studied during 1977-89 by means of snap trapping (Small Quadrat Method) Predator populations were studied by mapping breeding raptors and by snow-tracking small mustelids During 1977-85, snow-trackmg was conducted only during peak and decline years, whereas during 1986-89, snow-tracking was conducted every winter (November-December) and live-trapping (in August) was used as an additional method
Lowland vole populations had regular density fluctuations with peaks in 1978-79. 1982-84 and 1987-88 Highland vole populations fluctuated less regularly and at lower over-all densities Highland lemming populations had two outbreaks, in 1978 and 1988, ending in abrupt winter crashes In the lowland, outbreak levels were reached only in 1978 All microtine declines in relatively productive lowland habitats were accompanied by intense activity of small mustelids. whereas avian predators were common only in 1983 Lowland declines also showed clear between-habitat asynchrony they started in areas with an exceptional abundance of productive habitats and then spread to more barren areas These lowland data are consistent with the hypothesis of a mustelid-microtine limit cycle, although also several other hypotheses remain unrefuted The highland lemming data suggest a simple exploiter-victim interaction between lemmings and the vegetation     

Predation across spatial scales in heterogeneous environments

A hierarchy of scales is introduced to the spatially heterogeneous Lotka-Volterra predator-prey diffusion model, and its effects on the model's spatial and temporal behavior are studied. When predators move on a large scale relative to prey, local coupling of the predator-prey interaction is replaced by global coupling. Prey with low dispersal ability become narrowly confined to the most productive habitats, strongly amplifying the underlying spatial pattern of the environment. As prey diffusion rate increases, the prey distribution spreads out and predator abundance declines. The model retains neutrally stable Lotka-Volterra temporal dynamics: different scales of predator and prey dispersal do not stabilize the interaction. The model predicts that, for prey populations that are limited by widely ranging predators, species with low dispersal ability should be restricted to discrete high density patches, and those with greater mobility should be more uniformly distributed at lower density.     

Dynamics of voles and small mustelids in the taiga landscape of northern Fennoscandia in relation to habitat quality

In the forests of northern Fennoscandia during the I980's, the dynamics of microtine rodents changed from multiannual high amplitude fluctuations (cycles) to, depending on species, fluctuations with a strong seasonal component or fluctuations with smaller amplitude and lower frequency. Microtine and predator data from the Pallasjarvi area, Finnish Lapland, suggest that this transition took place at different rates in different parts of the taiga landscape. Generally, densities in forest habitats have been primarily seasonal since 198S-86. In mesic spruce taiga and in drier forest habitats microtines had a prolonged peak in 1981-83 and a crash in 1984-83. At the timberline, however, microtine populations dropped from peak to low densities already in 1982-83 but the final crash did not occur until spring 1985. The synchronous decrease in microtines densities in all habitat types in 1984-85 coincided with increase in weasel activity. Activity of other carnivores was consistently high in mesic lowland habitats. The data support following three conjectures. 1) Periodic abundance of least weasels is crucial for sustained vole cycles. 2) Predominance of stoats and other generalist predators lead to less regular fluctuations with a strong seasonal component where density declines occur in autumn and early winter. 3) In barren tundra areas, the vegetation cannot sustain high densities of microtines and. consequently, predation is not a necessary condition for population crashes.     

Effect of predator density dependent dispersal of prey on stability of a predator-prey system

This work presents a predator-prey Lotka-Volterra model in a two patch environment. The model is a set of four ordinary differential equations that govern the prey and predator population densities on each patch. Predators disperse with constant migration rates, while prey dispersal is predator density-dependent. When the predator density is large, the dispersal of prey is more likely to occur. We assume that prey and predator dispersal is faster than the local predator-prey interaction on each patch. Thus, we take advantage of two time scales in order to reduce the complete model to a system of two equations governing the total prey and predator densities. The stability analysis of the aggregated model shows that a unique strictly positive equilibrium exists. This equilibrium may be stable or unstable. A Hopf bifurcation may occur, leading the equilibrium to be a centre. If the two patches are similar, the predator density dependent dispersal of prey has a stabilizing effect on the predator-prey system.     

Effects of density-dependent migrations on stability of a two-patch predator-prey model

We consider a predator-prey model in a two-patch environment and assume that migration between patches is faster than prey growth, predator mortality and predator-prey interactions. Prey (resp. predator) migration rates are considered to be predator (resp. prey) density-dependent. Prey leave a patch at a migration rate proportional to the local predator density. Predators leave a patch at a migration rate inversely proportional to local prey population density. Taking advantage of the two different time scales, we use aggregation methods to obtain a reduced (aggregated) model governing the total prey and predator densities. First, we show that for a large class of density-dependent migration rules for predators and prey there exists a unique and stable equilibrium for migration. Second, a numerical bifurcation analysis is presented. We show that bifurcation diagrams obtained from the complete and aggregated models are consistent with each other for reasonable values of the ratio between the two time scales, fast for migration and slow for local demography. Our results show that, under some particular conditions, the density dependence of migrations can generate a limit cycle. Also a co-dim two Bautin bifurcation point is observed in some range of migration parameters and this implies that bistability of an equilibrium and limit cycle is possible.     

A resolution of the paradox of enrichment

Theoretical studies have shown a paradoxical destabilizing response of predator-prey ecosystems to enrichment, but there is the gap between the intuitive view of nature and this theoretical prediction. We studied a minimal predator-prey system (a two predator-two prey system) in which the paradox of enrichment pattern can vanish; the destabilization with enrichment is reversed, leading to stabilization (a decrease in the amplitude of oscillation of population densities). For resolution of the paradox, two conditions must be met: (1) the same prey species must be preferred as a dietary item by both predator species, creating the potential for high exploitative competition between the predator species, and (2), while both predators are assumed to select their diet in accordance with optimal diet utilization theory, one predator must be a specialist and the other a generalist. In this system, the presence of a less profitable prey species can cause the increase in population oscillation amplitudes associated with increasing enrichment to be suppressed via the optimal diet utilization of the generalist predator. The resulting stabilization is explained by the mitigating effect of the less profitable prey showing better population growth with increasing enrichment on the destabilization underlying the specialist predator and prey relation, thus resolving the paradox of enrichment.     

Implications of shared predation for space use in two sympatric leporids

Spatial variation in habitat riskiness has a major influence on the predator–prey space race. However, the outcome of this race can be modulated if prey shares enemies with fellow prey (i.e., another prey species). Sharing of natural enemies may result in apparent competition, and its implications for prey space use remain poorly studied. Our objective was to test how prey species spend time among habitats that differ in riskiness, and how shared predation modulates the space use by prey species. We studied a one‐predator, two‐prey system in a coastal dune landscape in the Netherlands with the European hare (Lepus europaeus) and European rabbit (Oryctolagus cuniculus) as sympatric prey species and red fox (Vulpes vulpes) as their main predator. The fine‐scale space use by each species was quantified using camera traps. We quantified residence time as an index of space use. Hares and rabbits spent time differently among habitats that differ in riskiness. Space use by predators and habitat riskiness affected space use by hares more strongly than space use by rabbits. Residence time of hare was shorter in habitats in which the predator was efficient in searching or capturing prey species. However, hares spent more time in edge habitat when foxes were present, even though foxes are considered ambush predators. Shared predation affected the predator–prey space race for hares positively, and more strongly than the predator–prey space race for rabbits, which were not affected. Shared predation reversed the predator–prey space race between foxes and hares, whereas shared predation possibly also released a negative association and promoted a positive association between our two sympatric prey species. Habitat riskiness, species presence, and prey species’ escape mode and foraging mode (i.e., central‐place vs. noncentral‐place forager) affected the prey space race under shared predation.     

Predator behaviour and predation risk in the heterogeneous Arctic environment

1. Habitat heterogeneity and predator behaviour can strongly affect predator-prey interactions but these factors are rarely considered simultaneously, especially when systems encompass multiple predators and prey. 2. In the Arctic, greater snow geese Anser caerulescens atlanticus L. nest in two structurally different habitats: wetlands that form intricate networks of water channels, and mesic tundra where such obstacles are absent. In this heterogeneous environment, goose eggs are exposed to two types of predators: the arctic fox Vulpes lagopus L. and a diversity of avian predators. We hypothesized that, contrary to birds, the hunting ability of foxes would be impaired by the structurally complex wetland habitat, resulting in a lower predation risk for goose eggs. 3. In addition, lemmings, the main prey of foxes, show strong population cycles. We thus further examined how their fluctuations influenced the interaction between habitat heterogeneity and fox predation on goose eggs. 4. An experimental approach with artificial nests suggested that foxes were faster than avian predators to find unattended goose nests in mesic tundra whereas the reverse was true in wetlands. Foxes spent 3.5 times more time between consecutive attacks on real goose nests in wetlands than in mesic tundra. Their attacks on goose nests were also half as successful in wetlands than in mesic tundra whereas no difference was found for avian predators. 5. Nesting success in wetlands (65%) was higher than in mesic tundra (56%) but the difference between habitats increased during lemming crashes (15%) compared to other phases of the cycle (5%). Nests located at the edge of wetland patches were also less successful than central ones, suggesting a gradient in accessibility of goose nests in wetlands for foxes. 6. Our study shows that the structural complexity of wetlands decreases predation risk from foxes but not avian predators in arctic-nesting birds. Our results also demonstrate that cyclic lemming populations indirectly alter the spatial distribution of productive nests due to a complex interaction between habitat structure, prey-switching and foraging success of foxes.     

Habitat choice in predator-prey systems: spatial instability due to interacting adaptive movements

The role of habitat choice behavior in the dynamics of predator-prey systems is explored using simple mathematical models. The models assume a three-species food chain in which each population is distributed across two or more habitats. The predator and prey adjust their locations dynamically to maximize individual per capita growth, while the prey's resource has a low rate of random movement. The two consumer species have Type II functional responses. For many parameter sets, the populations cycle, with predator and prey "chasing" each other back and forth between habitats. The cycles are driven by the aggregation of prey, which is advantageous because the predator's saturating functional response induces a short-term positive density dependence in prey fitness. The advantage of aggregation in a patch is only temporary because resources are depleted and predators move to or reproduce faster in the habitat with the largest number of prey, perpetuating the cycle. Such spatial cycling can stabilize population densities and qualitatively change the responses of population densities to environmental perturbations. These models show that the coupled processes of moving to habitats with higher fitness in predator and prey may often fail to produce ideal free distributions across habitats.     

不同栖息地破坏格局下具捕食偏爱似然竞争结局的模拟分析

使用元胞自动机模型,对具有捕食偏爱、不同栖息地破坏比例和不同空间破坏格局条件下的捕食-食饵系统中各物种的变化动态进行了模拟分析。在捕食者和两猎物物种共存时:栖息地破坏比例、栖息地破坏的聚集度对猎物物种间强弱关系产生相反的作用,若增加栖息地破坏比例不利于某一猎物生存,则提高聚集度对其有利;适当提高适宜栖息地的聚集度,对所有物种都有利,若聚集度过高,效果相当于减少了栖息地的破坏比例,可能对某些猎物物种不利,但对整体系统有利;被破坏栖息地的聚集度发生变化时,捕食者的反应更敏感;在一定条件下,增强弱势种群的捕食偏爱会有助于其生存。     

The stability of predator-prey systems subject to the Allee effects

In recent years, many theoreticians and experimentalists have concentrated on the processes that affect the stability of predator-prey systems. But few papers have addressed the Allee effect with focus on the their stability. In this paper, we select two classical models describing predator-prey systems and introduce the Allee effects into the dynamics of both the predator and prey populations in these models, respectively. By combining mathematical analysis with numerical simulation, we have shown that the Allee effect may be a destabilizing force in predator-prey systems: the equilibrium point of the system could be changed from stable to unstable or otherwise, the system, even when it is stable, will take much longer time to reach the stable state. We also conclude that the equilibrium of the prey population will be enlarged due to the Allee effect of the predator, but the Allee effects of the prey may decrease the equilibrium value of the predator, or that of both the predator and prey. It should also be pointed out that the impact of the Allee effects of predator and prey due to different mechanisms on different predator-prey systems could also vary.     

Effects of Density Dependent Migrations on the Dynamics of a Predator Prey Model

We study the effects of density dependent migrations on the stability of a predator-prey model in a patchy environment which is composed with two sites connected by migration. The two patches are different. On the first patch, preys can find resource but can be captured by predators. The second patch is a refuge for the prey and thus predators do not have access to this patch. We assume a repulsive effect of predator on prey on the resource patch. Therefore, when the predator density is large on that patch, preys are more likely to leave it to return to the refuge. We consider two models. In the first model, preys leave the refuge to go to the resource patch at constant migration rates. In the second model, preys are assumed to be in competition for the resource and leave the refuge to the resource patch according to the prey density. We assume two different time scales, a fast time scale for migration and a slow time scale for population growth, mortality and predation. We take advantage of the two time scales to apply aggregation of variables methods and to obtain a reduced model governing the total prey and predator densities. In the case of the first model, we show that the repulsive effect of predator on prey has a stabilizing effect on the predator-prey community. In the case of the second model, we show that there exists a window for the prey proportion on the resource patch to ensure stability.     

Comparing the genetic population structure of two species of arctic lemmings: more local differentiation in Lemmus trimucronatus than in Dicrostonyx groenlandicus

Collared and brown lemmings ( Dicrostonyx groenlandicus and Lemmus trimucronatus ) are two largely sympatric and ecologically comparable species of arctic microtine rodents, differing however in some respects which allow us to hypothesise differences in the genetic structure of their populations. Collared lemmings are particularly well adapted to life at high latitude, they occasionally emerge to the surface of the snow and may disperse over larger distances than brown lemmings – possibly even over snow and ice. This should result in more local differentiation among populations of brown lemmings than among populations of collared lemmings. We compared the genetic population structure between the two lemming species in a fragmented landscape with small islands in the central Canadian Arctic using four microsatellite loci and partial mitochondrial control region sequences. Both types of genetic markers showed higher differentiation ( F _ST values) among local populations for brown lemmings than for collared lemmings. We discuss to what extent the observed genetic differences may be explained by differences in dispersal rates in addition to differences in average effective population size.     

Dynamics of a stochastic predator-prey model with habitat complexity and prey aggregation

Interplay between predator and prey is a complex process in ecosystems due to its nature. The population dynamics can be affected by many extrinsic and intrinsic factors. In this paper, we make an attempt to uncover the effects from environmental disturbances when populations are subject to habitat complexity and aggregation effect. We firstly propose a stochastic predator-prey model with habitat complexity and aggregation efficiency for prey. We then mathematically analyze the model, to demonstrate the existence, uniqueness and the stochastically ultimately boundedness of the global positive solution, and to establish sufficient conditions for the existence of ergodic stationary distribution of the solution. We also establish sufficient conditions under which either only predator population dies out or the entire predator-prey model becomes extinct. Our theoretical and numerical results indicate that: (1) the environmental noises are disadvantage for the survival of biological populations; (2) when the density of prey is greater than one, prey aggregation can heighten the capability of predator species to capture prey and reduce the effect of environmental fluctuations, while when the density of prey is less than one, the results are opposite; (3) habitat complexity is propitious to the survival of prey population and may seriously threaten the persistence of the predator population.     

Predator–prey coupling: interaction between mink Mustela vison and muskrat Ondatra zibethicus across Canada

In this paper we explore variation in the predator-prey interaction between mink Mustela vison and muskrat Ondatra zibethicus across Canada based on 25 years of mink (predator) and muskrat (prey) data from the Hudson's Bay Company. We show that predator–prey interactions have stronger signatures in the west of Canada than in the east. In particular, we show that the observed phase plot trajectories of mink and muskrat rotate significantly clock-wise, consistent with predator–prey theory. We also investigate four phases of the mink muskrat interaction sequence (predator crash phase, prey recovery phase, etc.) and show that they are all consistent with a strong coupling in the west, whereas the presence of generalist predators and alternative preys can explain deviations from this pattern in the east.     

Influence of cruising and ambush predators on 3-dimensional habitat use in age 0 juvenile Atlantic cod Gadus morhua

Predators and prey often co-exist at high densities within the same habitat, yet the behavioural and spatial dynamics underlying this co-existence are not well known. To better understand small-scale, predator-prey co-occurrence, the spatial patterns and behaviour of age 0 juvenile cod Gadus morhua 75-88 mm SL and two of their known predators, age 2+ cod and short-horn sculpin Myoxocephalus scorpinus, were examined in two habitats (i.e., sand and eelgrass) using three-dimensional video analysis. Both habitat and predator type interacted to result in unique spatial patterns of prey. Spatial overlap between predators and prey was highest in open habitat in the presence of the cruising predator but lowest in the presence of sculpin in the same habitat. In eelgrass, age 0 cod avoided predators primarily along the vertical axis (i.e., distance off bottom). Age 0 cod stayed above eelgrass in the presence of sculpin but lowered themselves into the eelgrass while in the presence of predator cod. Anti-predator behaviour (i.e., predator-prey distance, prey cohesion and freezing) was significantly reduced over eelgrass compared to sand, suggesting eelgrass has lower ‘inherent risk’ than open habitats. However, predator consumption was similar across all treatments, suggesting that, 1) complex habitat also impairs the visual cues needed for anti-predator behaviour (e.g., schooling) and assessing the location of predators, and 2) predators change their behaviour with habitat to enhance their opportunities for finding and capturing prey.     

Habitat-dependent foraging in a classic predator–prey system: a fable from snowshoe hares

Current research contrasting prey habitat use has documented, with virtual unanimity, habitat differences in predation risk. Relatively few studies have considered, either in theory or in practice, simultaneous patterns in prey density. Linear predator–prey models predict that prey habitat preferences should switch toward the safer habitat with increasing prey and predator densities. The density‐dependent preference can be revealed by regression of prey density in safe habitat versus that in the riskier one (the isodar). But at this scale, the predation risk can be revealed only with simultaneous estimates of the number of predators, or with their experimental removal. Theories of optimal foraging demonstrate that we can measure predation risk by giving‐up densities of resource in foraging patches. The foraging theory cannot yet predict the expected pattern as predator and prey populations covary. Both problems are solved by measuring isodars and giving‐up densities in the same predator–prey system. I applied the two approaches to the classic predator–prey dynamics of snowshoe hares in northwestern Ontario, Canada. Hares occupied regenerating cutovers and adjacent mature‐forest habitat equally, and in a manner consistent with density‐dependent habitat selection. Independent measures of predation risk based on experimental, as well as natural, giving‐up densities agreed generally with the equal preference between habitats revealed by the isodar. There was no apparent difference in predation risk between habitats despite obvious differences in physical structure. Complementary studies contrasting a pair of habitats with more extreme differences confirmed that hares do alter their giving‐up densities when one habitat is clearly superior to another. The results are thereby consistent with theories of adaptive behaviour. But the results also demonstrate, when evaluating differences in habitat, that it is crucial to let the organisms we study define their own habitat preference.     

Effects of a disease affecting a predator on the dynamics of a predator-prey system

We study the effects of a disease affecting a predator on the dynamics of a predator-prey system. We couple an SIRS model applied to the predator population, to a Lotka-Volterra model. The SIRS model describes the spread of the disease in a predator population subdivided into susceptible, infected and removed individuals. The Lotka-Volterra model describes the predator-prey interactions. We consider two time scales, a fast one for the disease and a comparatively slow one for predator-prey interactions and for predator mortality. We use the classical “aggregation method” in order to obtain a reduced equivalent model. We show that there are two possible asymptotic behaviors: either the predator population dies out and the prey tends to its carrying capacity, or the predator and prey coexist. In this latter case, the predator population tends either to a “disease-free” or to a “disease-endemic” state. Moreover, the total predator density in the disease-endemic state is greater than the predator density in the “disease-free” equilibrium (DFE).