Predator-prey coevolution driven by size selective predation can cause anti-synchronized and cryptic population dynamics

Population dynamics and evolutionary dynamics can occur on similar time scales, and a coupling of these two processes can lead to novel population dynamics. Recent theoretical studies of coevolving predator-prey systems have concentrated more on the stability of such systems than on the characteristics of cycles when they are unstable. Here I explore the characteristics of the cycles that arise due to coevolution in a system in which prey can increase their ability to escape from predators by becoming either significantly larger or significantly smaller in trait value (i.e., a bidirectional trait axis). This is a reasonable model of body size evolution in some systems. The results show that antiphase population cycles and cryptic cycles (large population fluctuation in one species but almost no change in another species) can occur in the coevolutionary system but not systems where only a single species evolves. Previously, those dynamical patterns have only been theoretically shown to occur in single species evolutionary models and the coevolutionary model which do not involve a bi-directional axis of adaptation. These unusual dynamics may be observed in predator-prey interactions when the density dependence in the prey species is strong.     

Consequences of behavioral dynamics for the population dynamics of predator-prey systems with switching

This article explores how different mechanisms governing the rate of change of the predators preference alter the dynamics of predator-prey systems in which the predator exhibits positive frequency-dependent predation. The models assume that individuals of the predator species adaptively adjust a trait that determines their relative capture rates of each of two prey species. The resulting switching behavior does not instantaneously attain the optimum for current prey densities, but instead lags behind it. Several mechanisms producing such lags are discussed and modeled. In all cases examined, our question is whether a realistic behavioral lag can significantly change the dynamics of the system relative to an analogous case in which the predators switching is effectively instantaneous. We also explore whether increasing the rate parameters of dynamic models of behavior results in convergence to the population dynamics of analogous models with instantaneous switching, and whether different behavioral models produce similar population dynamics. The analysis concentrates on systems that undergo endogenously generated predator-prey cycles in the absence of switching behavior. The average densities and the nature of indirect interactions are often sensitive to the rate of behavioral change, and are often qualitatively different for different classes of behavioral models. Dynamics and average densities can be very sensitive to small changes in parameters of either the prey growth or predator switching functions. These differences suggest that an understanding of switching in natural systems will require research into the behavioral mechanisms that govern lags in the response of predator preference to changes in prey density.     

Effects of behavioral adaptation on a predator-prey model

The Volterra-Lotka predator-prey equations are modified so that the predator's ability to utilize the prey varies in proportion to the average number of encounters between the two species in the past. The behavior of this adaptive system is then described in terms of three parameters — the carrying capacity of the prey, the relative death rate of the predator, and the predator's memoryspan. The most stable situation is shown to occur when the carrying capacity of the prey is large, the predator's death rate is close to zero, and the predator is able to adapt quickly to changing levels of prey density.     

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).     

Adaptive foraging by predators as a cause of predator-prey cycles

Summary When foraging has costs, it is generally adaptive for foragers to adjust their foraging effort in response to changes in the population density of their food. If effort decreases in response to increased food density, this can result in a type-2 functional response; intake rate increases in a negatively accelerated manner as prey density increases. Unlike other mechanisms for type-2 responses, adaptive foraging usually involves a timelag, because foraging behaviours do not often change instantaneously with changes in food density or risks. This paper investigates predator-prey models in which there are explicit dynamics for the rate of adaptive change. Models appropriate to both behavioural and evolutionary change are considered. Both types of change can produce cycles under similar circumstances, but under some evolutionary models there is not sufficient genetic variability for evolutionary change to produce cycles. If there is sufficient variability, the remaining conditions required for cycles are surprisingly insensitive to the nature of the adaptive process. A predator population that approaches the optimum foraging strategy very slowly usually produces cycles under similar conditions as does a very rapidly adapting population.     

Global dynamics of a ratio-dependent predator-prey system

Recently, ratio-dependent predator-prey systems have been regarded by some researchers to be more appropriate for predator-prey interactions where predation involves serious searching processes. However, such models have set up a challenging issue regarding their dynamics near the origin since these models are not well-defined there. In this paper, the qualitative behavior of a class of ratio-dependent predator-prey system at the origin in the interior of the first quadrant is studied. It is shown that the origin is indeed a critical point of higher order. There can exist numerous kinds of topological structures in a neighborhood of the origin including the parabolic orbits, the elliptic orbits, the hyperbolic orbits, and any combination of them. These structures have important implications for the global behavior of the model. Global qualitative analysis of the model depending on all parameters is carried out, and conditions of existence and non-existence of limit cycles for the model are given. Computer simulations are presented to illustrate the conclusions.     

Physiological flexibility in the Andean lizard <Emphasis Type="Italic">Liolaemus bellii</Emphasis>: seasonal changes in energy acquisition,storage and expenditure

According to the “barrel model”, an organism may be represented by a container, with input energy constraints (foraging, digestion, and absorption) symbolized by funnels connected in tandem, and energy outputs (maintenance, growth, and reproduction) symbolized by a series of spouts arranged in parallel. Animals can respond to changes in environmental conditions, through adjustments in the size of the funnels, the fluid stored inside the barrel, or the output flow through the spouts. In the present study, we investigate the interplay among these processes through the analysis of seasonal changes in organ size and metabolic rate in a lizard species (Liolaemus bellii) that inhabits extremely seasonal environments in the Andes range. We found that digestive organ size showed the greatest values during spring and summer, that is, during the foraging seasons. Energy reserves were larger during summer and autumn, and then decreased through winter and spring, which was correlated with overwintering maintenance and reproductive costs. Standard metabolic rate was greater during the high-activity seasons (spring and summer), but this increase was only noticeable at higher environmental temperatures. The ability of many lizard species to reduce their maintenance cost during the cold months of the year, beyond what is expected from temperature decrease, is probably related to their success in coping with highly fluctuating environments. Here, we demonstrate that this ability is correlated with high physiological flexibility, which allows animals to adjust energy acquisition, storing and expenditure processes according to current environmental conditions.     

Impact of spatial heterogeneity on a predator-prey system dynamics

This paper deals with the study of a predator-prey model in a patchy environment. Prey individuals moves on two patches, one is a refuge and the second one contains predator individuals. The movements are assumed to be faster than growth and predator-prey interaction processes. Each patch is assumed to be homogeneous. The spatial heterogeneity is obtained by assuming that the demographic parameters (growth rates, predation rates and mortality rates) depend on the patches. On the predation patch, we use a Lotka-Volterra model. Since the movements are faster that the other processes, we may assume that the frequency of prey and predators become constant and we would get a global predator-prey model, which is shown to be a Lotka-Volterra one. However, this simplified model at the population level does not match the dynamics obtained with the complete initial model. We explain this phenomenom and we continue the analysis in order to give a two-dimensional predator-prey model that gives the same dynamics as that provided by the complete initial one. We use this simplified model to study the impact of spatial heterogeneity and movements on the system stability. This analysis shows that there is a globally asymptotically stable equilibrium in the positive quadrant, i.e. the spatial heterogeneity stabilizes the equilibrium.     

Reproductive system and pattern of genetic variation in two Limnanthes species

Summary Several populations of two species of the genus Limnanthes, (L. alba, an outbreeder and L. floccosa, an inbreeder) were examined with respect to variability of fifteen quantitative characters, allozyme variation at 11 loci, and response to different pollination conditions and moisture stress. Nearly equal amounts of phenotypic variability were found in the two species. L. alba had higher within-family variability than L. floccosa, but this result was highly heterogeneous among characters. A study of between- and within-population variance estimates did not reject the null hypothesis that L. alba and L. floccosa are similar with regard to the partitioning and amount of variability for quantitative characters. However, allozyme variation at 11 loci in a large number of populations showed L. alba to be highly polymorphic in contrast to the virtual monomorphism within L. floccosa populations. The average number of alleles per locus in L. alba and L. floccosa was 1.97 and 1.02, respectively, and on an average, L. alba and L. floccosa populations had 63% and 3% loci with polymorphism, respectively. Three groups of allozyme allelic combinations emerged which correlated well with the taxonomic delineation of allogamous L. alba, three semi-autogamous L. floccosa forms and two autogamous L. floccosa forms.All taxa showed a significant reduction in the seed output per plant due to moisture stress. L. alba suffered a further loss of fecundity under the paucity of pollinators, L. floccosa ssp. floccosa showed no significant effect from this factor, whereas L. floccosa ssp. grandiflora exhibited a curvilinear response which peaked at partial pollination and decreased to a lower level at full pollination.The geographic distribution of the two species with regard to the temperature and rainfall distribution did not suggest L. floccosa to be living in drier marginal areas. Patterns of variation in flowering time showed L. alba to be less variable than L. floccosa. Overall, there seemed to be little direct support for the thesis that inbreeding species originated from outcrossing taxa in marginal environments as a direct adaptation to a shortened growing season of xeric environments and to the lack of pollinators. Alternative hypotheses suggest that autogamy in L. floccosa might have evolved as a reproductive isolating barrier acting through either cleistogamy or divergence in flowering times.     

Stabilizing effects in spatial parasitoid-host and predator-prey models: a review

We review the literature on spatial host-parasitoid and predator-prey models. Dispersal on its own is not stabilizing and can destabilize a stable local equilibrium. We identify three mechanisms whereby limited dispersal of hosts and parasitoids combined with other features, such as spatial and temporal heterogeneity, can promote increased persistence and stability. The first mechanisms, "statistical stabilization", is simply the statistical effect that summing a number of out-of-phase population trajectories results in a relatively constant total population density. The second mechanism involves decoupling of immigration from local density, such that limited dispersal between asynchronous patches results in an effect that mimics density-dependence at the local patch level. The third mechanism involves altering spatially averaged parameter values resulting from spatial heterogeneity in density combined with non-linear responses to density. Persistence in spatially explicit models with local dispersal frequently associated with self-organized spatial patterning.     

Effects of habitat drying on size at and time to metamorphosis in the tree hole mosquito Aedes triseriatus

Models of complex life cycles predict that greater mortality of immature stages should induce earlier metamorphosis at smaller sizes. We tested for effects of one source of mortality, habitat drying, on size at and time to metamorphosis of the tree hole mosquito Aedes triseriatus. In a laboratory experiment, we manipulated two variables associated with drying, volume of water and solute concentration, and recorded mean mass at and median days to eclosion for males and females in replicate cohorts. We also tested for treatment effects on the correlation of mass at and time to eclosion. For females, decreasing volume consistently induced metamorphosis at smaller sizes than did constant volume. Decreasing volume also led to earlier metamorphosis of females than did constant volume, but only in one of two experimental runs. For both sexes, increasing concentration led to greater size at metamorphosis and, for males, earlier metamorphosis than did constant volume, but again only in one of two experimental runs. Correlations of size at and time to metamorphosis tended to be positive for females and negative for males, and this difference was significant. For both sexes, decreasing volume led to larger (more positive) correlations than did constant volume, but only in one of two experimental runs. The effects of decreasing volume on females are consistent with the predictions of models of complex life cycles, and suggest that A. triseriatus can perceive volume changes and modify metamorphosis to escape a deteriorating habitat. The effects of increasing concentration are opposite to those predicted, and are consistent with enhanced growth rates, possibly due to enhanced microbial growth, as solutes become concentrated due to drying. The responses of these mosquitoes to habitat drying are complex, and we suggest that habitat drying increases both mortality and growth rates, yielding no simple predictions of how habitat drying will affect these mosquitoes in natural tree holes.     

The costs of phenotypic adaptation to repeatedly fluctuating temperatures in a soil arthropod

Costs of phenotypic adaptation to changing environments have often been studied in morphological structures. Such structures typically are irreversible for at least some stage in the organism's life. In this study we investigated whether recurrent and reversible adaptation to changes in the thermal environment incurs a cost in terms of some key life-history traits in the collembolan Orchesella cincta. We exposed juvenile O. cincta to two treatments differing in the frequency of temperature fluctuation but with equal total temperature sums. In the high frequency treatment temperature fluctuated daily between 10 and 20 °C, while in the low frequency treatment temperature fluctuated on a weekly schedule. During the treatments we measured juvenile growth rate and juvenile mortality, and after six weeks the animals were transferred to constant 15 °C and adult starvation resistance was assessed. We found no significant differences between the treatments in juvenile growth rate or juvenile survival. Also, adults that had grown up under high frequency temperature fluctuations did not suffer from reduced starvation resistance compared to animals growing under low frequency temperature fluctuations. This finding supports the hypothesis that selection minimizes the production costs of inducible phenotypes and suggests that the development of optimal phenotypes and evolution of temperature reaction norms are not constrained by such costs.     

Global analysis of the Michaelis-Menten-type ratio-dependent predator-prey system

The recent broad interest on ratio-dependent based predator functional response calls for detailed qualitative study on ratio-dependent predator-prey differential systems. A first such attempt is documented in the recent work of Kuang and Beretta(1998), where Michaelis-Menten-type ratio-dependent model is studied systematically. Their paper, while contains many new and significant results, is far from complete in answering the many subtle mathematical questions on the global qualitative behavior of solutions of the model. Indeed, many of such important open questions are mentioned in the discussion section of their paper. Through a simple change of variable, we transform the Michaelis-Menten-type ratio-dependent model to a better studied Gause-type predator-prey system. As a result, we can obtain a complete classification of the asymptotic behavior of the solutions of the Michaelis-Menten-type ratio-dependent model. In some cases we can determine how the outcomes depend on the initial conditions. In particular, open questions on the global stability of all equilibria in various cases and the uniqueness of limit cycles are resolved. Biological implications of our results are also presented.     

Functional response,numerical response,and stability in arthropod predator-prey ecosystems involving age structure

Summary A general model of arthropod predator-prey systems incorporating age structure in the predator is employed to study the role of functional and numerical responses on stability and the paradox of enrichment. The destabilizing effect of age structure leads to both qualitatively and quantitatively new results for an environment which has an infinite prey carrying capacity, including a lower bound to prey density for a stable equilibrium, a feature not present in models without age structure. When applied to an environment with finite prey carrying capacity, the effect of age structure is to reinforce the arguments implicit to the paradox of enrichment originally developed for traditional models lacking age structure.     

Genetic and environmental effects on growth of children from a subsistence agricultural community in southern Mexico

Sibling correlations for size attained in height, weight, sitting height, estimated leg length, the triceps skinfold, arm circumference, and estimated midarm muscle circumference were compared in 6- through 13-year-old schoolchildren grouped by household socioeconomic status. The children were residents of a Zapotec-speaking, subsistence agricultural community in the Valley of Oaxaca in southern Mexico. Sibling pairs were classified as being from high and low socioeconomic status (SES) households, and sibling correlations were computed within each SES group controlling for environmental effects derived from a factor analysis of information on household demography and land and livestock holdings. Like-sex siblings from lower SES households have significantly different correlations in four instances. Correlations are higher for leg length in lower SES brothers and higher for sitting height and weight in lower SES sisters, while the correlation for sitting height is higher in upper SES brothers. The sibling correlation results are not entirely consistent with observations on growth status by SES, particularly if the power and similarity of a common environment is the only cause of higher sibling correlations. Reduced body size under poorer socioeconomic and presumably nutritional circumstances is apparent, but it is not possible in this analysis to distinguish whether genotypic (developmental) plasticity or genetic adaptation, or both, are involved.     

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.     

Multiple dynamics in a single predator-prey system: experimental effects of food quality.

Recent work with the freshwater zooplankton Daphnia has suggested that the quality of its algal prey can have a significant effect on its demographic rates and life-history patterns. Predator-prey theory linking food quantity and food quality predicts that a single system should be able to display two distinct patterns of population dynamics. One pattern is predicted to have high herbivore and low algal biomass dynamics (high HBD), whereas the other is predicted to have low herbivore and high algal biomass dynamics (low HBD). Despite these predictions and the stoichiometric evidence that many phytoplankton communities may have poor access to food of quality, there have been few tests of whether a dynamic predator-prey system can display both of these distinct patterns. Here we report, to the authors' knowledge, the first evidence for two dynamical patterns, as predicted by theory, in a single predator-prey system. We show that the high HBD is a result of food quantity effects and that the low HBD is a result of food quality effects, which are maintained by phosphorus limitation in the predator. These results provide an important link between the known effects of nutrient limitation in herbivores and the significance of prey quality in predator-prey population dynamics in natural zooplankton communities.     

Inducible defenses,competition and shared predation in planktonic food chains

Ecologists have long debated the role of predation in mediating the coexistence of prey species. Theory has mainly taken a bitrophic perspective that excludes the effects of inducible defenses at different trophic levels. However, inducible defenses could either limit or enhance the effects of predation on coexistence, by means of effects on bottom-up control and population stability. Our aim was to investigate how inducible defenses at different trophic levels affect the possibilities for predator-mediated coexistence, as opposed to competitive exclusion, in replicated experimental plankton communities. In particular, we analyzed how the presence or absence of inducible defenses in algal basal prey affected the outcome of competition between an inducible defended and an undefended herbivore, in the presence or absence of a carnivore. We found the undefended herbivore to be a superior competitor in the absence of predation. This outcome was reversed in the presence of a shared carnivore: populations of the undefended herbivore then strongly declined. The extent of this population decline differed between food webs based on undefended as opposed to inducible defended algal prey. In the former the undefended herbivore became undetectable for most of the duration of the experiment. In the latter the undefended herbivore also crashed to low densities, but it could still be detected during most of the experiment. In food webs based on inducible defended algae, the carnivore failed to reach high densities and exerted weaker top-down control on the two competing herbivores. We conclude that the inducible defense in one of our two competing herbivores allowed the outcome of competition to be reversed when a shared carnivore was added. Inducible defenses in algae did not change this outcome, but they significantly delayed extinction of the undefended herbivore. Predation itself did not promote coexistence in these experimental plankton communities.     

Effect of photoperiod on the size–temperature relationship in a pentatomid bug, Dolycoris baccarum

(1) The effects of photoperiod and temperature on nymphal growth, development and adult size in a pentatomid bug, Dolycoris baccarum, were examined. (2) The temperature–size relationship was not stable but was highly affected by the photoperiod, and showed a geographical variation. (3) There were variations also in the developmental period and the growth rate. (4) The responses to temperature and photoperiod can explain the seasonal and geographical adaptations of the insect, and thus are considered to be important seasonal adaptations in D. baccarum.     

Phenotypic plasticity in numbers of antennal chemoreceptors in a grasshopper: effects of food

Grasshoppers, Schistocerca americana, reared from hatching on artificial diet had fewer sensilla on the antennae in the final larval stage than insects reared on lettuce. This was true of basiconic and coeloconic sensilla (presumed olfactory) and trichoid sensilla (presumed gustatory). The degree of difference varied along the antenna and with sensillum type. Adding salicin to the diet restored the numbers of all types of sensillum to levels equal to, or approaching, those in lettuce-fed insects. The addition of some volatile compounds – carvone (monoterpene), chalcone (flavonoid), citral (monoterpene) and guaiacol (phenolic) – resulted in slight increases in number, but coumarin (phenylpropanoid) had no effect. None of the compounds, either singly or in combination, produced more sensilla than were present in plant-fed insects. Accepted: 26 January 1998