Can spatial variation alone lead to selection for dispersal?

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

A reconciliation of simple and complex models of age-dependent predation

Predation intensity often varies with prey age or development stage. Several theoretical studies have considered what effect such age-dependent predation has on the stability of predator-prey interactions. The simple models suggest its effect is typically stabilizing; more complex models suggest otherwise. Current theory is therefore divided on this issue. Here I show that the conclusion of previous studies of simple models is due to biologically extreme restrictions on certain parameter values. When these are relaxed, age-dependent predation becomes equally capable of a stabilizing or destabilizing effect, just as in more complex models. Specific conditions favoring each effect are identified and discussed.     

Predator and Prey Models with Flexible Individual Behavior and Imperfect Information

To begin identifying what behavioral details might be needed to characterize community dynamics and stability, we examined the effect of prey behavioral responses to predation risk on community dynamics and stability. We considered the case of prey altering their foraging effort to trade off energy gain and predation risk. We used state-dependent dynamic optimization to calculate the optimal trade-off for four models of prey behaviorally responding to predation risk. We consider a fixed behavior model in which prey use constant levels of foraging effort and three flexible behavior models in which prey change their foraging effort according to their physiological state and their perceived level of predation risk. Flexible behavior was destabilizing at the community level as evidenced by higher predator-prey oscillations and lower community persistence times. The mechanisms by which prey estimated predation risk also affected community stability. We found that community dynamics resulting from prey with flexible behavior and fixed perception of risk approximated community dynamics resulting from prey with flexible behavior and perfect information about predation risk, however neither approximated the community dynamics resulting from prey with flexible behavior and flexible perception of risk. Thus, whether it might be possible to abstract complex behavior with simpler rules when modeling community dynamics depends on the prey's behavioral mechanisms, which are empirically poorly known.     

The impact of mortality on predator population size and stability in systems with stage-structured prey

The relationships between a predator population's mortality rate and its population size and stability are investigated for several simple predator-prey models with stage-structured prey populations. Several alternative models are considered; these differ in their assumptions about the nature of density dependence in the prey's population growth; the nature of stage-transitions; and the stage-selectivity of the predator. Instability occurs at high, rather than low predator mortality rates in most models with highly stage-selective predation; this is the opposite of the effect of mortality on stability in models with homogeneous prey populations. Stage-selective predation also increases the range of parameters that lead to a stable equilibrium. The results suggest that it may be common for a stable predator population to increase in abundance as its own mortality rate increases in stable systems, provided that the predator has a saturating functional response. Sufficiently strong density dependence in the prey generally reverses this outcome, and results in a decrease in predator population size with increasing predator mortality rate. Stability is decreased when the juvenile stage has a fixed duration, but population increases with increasing mortality are still observed in large areas of stable parameter space. This raises two coupled questions which are as yet unanswered; (1) do such increases in population size with higher mortality actually occur in nature; and (2) if not, what prevents them from occurring? Stage-structured prey and stage-related predation can also reverse the 'paradox of enrichment', leading to stability rather than instability when prey growth is increased.     

Perch or plankton: top‐down control of Daphnia by yellow perch (Perca flavescens) or Bythotrephes cederstroemi in an inland lake?

1. Seasonal termination of the vernal clear-water phase in Long Lake, Grand Traverse Co., Michigan coincided with severe size-selective predation on juvenile Daphnia pulicaria from 0.8 to 1.8 mm in length. This could be caused by predation by age-0 yellow perch ( Perca flavescens ) or by the exotic predatory zooplankter Bythotrephes cederstroemi .
2. During the initial decline of Daphnia , Ivlev's electivity coefficient for yellow perch from 15.0 to 20.0 mm in length was 0.50 for copepods and −0.75 for D. pulicaria .
3. Bioenergetics modelling of both yellow perch and Bythotrephes demonstrates that, during the initial Daphnia decline, Bythotrephes consumed 1.5–5 times greater total mass than yellow perch. Furthermore, models in which Bythotrephes consumed juvenile Daphnia were more consistent with the timing of the Daphnia decline than those in which yellow perch consumed juvenile Daphnia .
4. The invasion of Bythotrephes into Long Lake seems to be a significant perturbation, introducing effects that propagate throughout the food chain. Bythotrephes created a possible bottleneck for age-0 yellow perch in late June by suppressing Daphnia .     

Stabilizing and destabilizing clusters in the hydrophobic core of long two-stranded alpha-helical coiled-coils

Detailed sequence analyses of the hydrophobic core residues of two long two-stranded alpha-helical coiled-coils that differ dramatically in sequence, function, and length were performed (tropomyosin of 284 residues and the coiled-coil domain of the myosin rod of 1086 residues). Three types of regions were present in the hydrophobic core of both proteins: stabilizing clusters and destabilizing clusters, defined as three or more consecutive core residues of either stabilizing (Leu, Ile, Val, Met, Phe, and Tyr) or destabilizing (Gly, Ala, Cys, Ser, Thr, Asn, Gln, Asp, Glu, His, Arg, Lys, and Trp) residues, and intervening regions that consist of both stabilizing and destabilizing residues in the hydrophobic core but no clusters. Subsequently, we designed a series of two-stranded coiled-coils to determine what defines a destabilizing cluster and varied the length of the destabilizing cluster from 3 to 7 residues to determine the length effect of the destabilizing cluster on protein stability. The results showed a dramatic destabilization, caused by a single Leu to Ala substitution, on formation of a 3-residue destabilizing cluster (DeltaT(m) of 17-21 degrees C) regardless of the stability of the coiled-coil. Any further substitution of Leu to Ala that increased the size of the destabilizing cluster to 5 or 7 hydrophobic core residues in length had little effect on stability (DeltaT(m) of 1.4-2.8 degrees C). These results suggested that the contribution of Leu to protein stability is context-dependent on whether the hydrophobe is in a stabilizing cluster or its proximity to neighboring destabilizing and stabilizing clusters.     

Experimental assessment of predation risk for juvenile green sturgeon,Acipenser medirostris,by two predatory fishes

Predation is a common cause of early life stage mortality in fishes, with reduced risk as individuals grow and become too large to be consumed by gape-limited predatory fishes. Large-bodied species, such as sturgeon, may reach this size-refuge within the first year. However, there is limited understanding of what this size threshold is despite the value of this information for conservation management. We conducted laboratory-based predation experiments on juvenile green sturgeon, Acipenser medirostris, to estimate vulnerability to predation during outmigration from their natal reaches in California to the Pacific Ocean. Two highly abundant and non-native predatory fish species (largemouth bass, Micropterus salmoides, and striped bass, Morone saxatilis) were captured in the wild to be tested with developing juvenile green sturgeon from the UC Davis Green Sturgeon Broodstock Program. Experimental tanks, each containing five predators, received thirty prey for 24-hr exposures. Between sturgeon prey trials, predators were exposed to alternative prey species to confirm predators were exhibiting normal feeding behaviors. In addition to green sturgeon mortality data, trials were video recorded and predatory behaviors were quantified. Overall, these predator species displayed much lower rates of predation on juvenile green sturgeon than alternate prey. Predation decreased with green sturgeon size, and predation risk diminished to zero once sturgeon reached a length threshold of roughly 20–22 cm total length, or between 38% and 58% of predator total length. Behavioral analyses showed low motivation to feed on green sturgeon, with both predators attempting predation less frequently as sturgeon grew. Results of this study imply that optimizing growth rates for larval and juvenile sturgeon would shorten the time in which they are vulnerable to predation. Future experiments should assess predation risk of juvenile green sturgeon by additional predator species common to the Sacramento-San Joaquin watershed.     

Juvenile versus adult competition

A general class of age-structured models based upon the McKendrick/von Foerster equations are used to study intraspecific competition between juveniles and adults. Criteria for the existence and stability of equilibria are obtained and the dependence of equilibrium stability (i.e. equilibrium resilience) on competition coefficients is analyzed for low inherent net reproductive numbers. The results are applied to the question of whether juvenile vs. adult intraspecific competition is stabilizing or destabilizing. Two types of competition are studied. The first, involving suppressed adult fertility due to competition from juveniles, was found to be destabilizing in that equilibrium levels are lowered and equilibrium resilience weakened by increased competition. The second, involving increased juvenile mortality due to competition from adults, was found to be considerably more complicated. While equilibrium levels were again reduced by increased competition, equilibrium resilience can either be weakened or strengthened. A criterion for determining the effects on resilience is derived and several examples are given to illustrate various possibilities in this case.The author gratefully acknowledges the support of the Applied Mathematics Division and the Population Biology/Ecology Division of the National Science Foundation under NSF grant No. DMS-8902508Research supported by the Department of Energy under contracts W-7405-ENG-36 and KC-07-01-01     

Fewer newborn result in superior juveniles in the paternally brooding pipefish Syngnathus typhle L.

In the pipefish Syngnathus typhle L. parental care is exclusively paternal. Males brood embryos in a brood pouch for about a month, providing nutrients and oxygen. The newborn juveniles are free-swimming and no further care is provided. The influence of paternal length and number of newborn on juvenile weight and growth rate, and how in turn the latter relates to juvenile survival, were investigated. It was found, using partial correlations, that paternal length is significantly and positively correlated to weight of newborn, weight of a two-week-old juvenile and juvenile growth rate (weight increment day^-1). Furthermore, number of newborn is correlated negatively to weight of newborn, weight after two weeks and juvenile growth rate. In an experiment in which juvenile pipefish of different sizes were exposed to predation it was shown that larger juveniles survived better. It is concluded that, in S. typhle , large juvenile size and rapid juvenile growth positively influence offspring performance. Offspring performance is positively influenced by paternal length which, however, may be a consequence of larger males receiving larger eggs. The number of newborn, i.e. the number of siblings in the male's pouch, has a negative effect on offspring performance, independently of other factors. Thus, the results show that for males the benefits of having superior juveniles will be at the cost of having fewer offspring.     

THE EFFECTS OF PREDATION ON THE AGE AND SIZE OF MATURITY OF PREY

The effects of nonselective predation on the optimal age and size of maturity of their prey are investigated using mathematical models of a simple life history with juvenile and adult stages. Fitness is measured by the product of survival to the adult stage and expected adult reproduction, which is usually an increasing function of size at maturity. Size is determined by both age at maturity and the value of costly traits that increase mean growth rate (growth effort). The analysis includes cases with fixed size but flexible time to maturity, fixed time but flexible size, and adaptively flexible values of both variables. In these analyses, growth effort is flexible. For comparison with previous theory, models with a fixed growth effort are analyzed. In each case, there may be indirect effects of predation on the prey's food supply. The effect of increased predation depends on (1) which variables are flexible; (2) whether increased growth effort requires increased exposure to predators; and (3) how increased predator density affects the abundance of food for juvenile prey. If there is no indirect effect of predators on prey food supply, size at maturity will generally decrease in response to increased predation. However, the indirect effect from increased food has the opposite effect, and the net result of predation is often increased size. Age at maturity may either increase or decrease, depending on functional forms and parameter values; this is true regardless of the presence of indirect effects. The results are compared with those of previous theoretical analyses. Observed shifts in life history in response to predation are reviewed, and the role of size-selective predation is reassessed.     

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

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

The effect of predator avoidance and travel time delay on the stability of predator-prey metacommunities

The stability conditions for an isolated specialist predator-prey community are fairly well understood. The spatial coupling of several such systems through dispersal of individuals can generate new dynamic behavior that is not yet completely understood. Many factors are known to be stabilizing or neutral, e.g., random dispersal or time delays, while others may induce instabilities in some cases but not others, e.g., density-dependent movement. We study the combination of two stabilizing mechanisms in a two-patch Rosenzweig-MacArthur model with a novel density-dependent movement term. Specifically, we assume that prey move between patches according to their perceived predation risk, and we include travel time between patches as a time delay. We show that the combination of mechanisms may be destabilizing even though each mechanism by itself is stabilizing. Our results show that a detailed knowledge of mechanisms and their temporal scales is necessary to correctly predict the stability of a metacommunity.     

Stability properties of 2-species models of mutualism: Simulation studies

Summary Most previous analyses of the stability properties of models of mutualism have emphasized the destabilizing effects of mutualism. However, these analyses can be shown to be based upon inappropriate assumptions, or to be applicable only for special cases of mutualism. In this paper three basic 2-species models of mutualism are presented and their six combinations are analyzed by computer simulation for their return time stability and persistence stability. Four out of six models show greater return time stability than an appropriate model without mutualism, and all models show higher persistence stability than the model without mutualism. It is argued that real biological systems can be related to the qualitative structure of each of the basic models of mutualism, and that therefore none of the basic models or their stability properties can be eliminated a priori as being inappropriate. The conclusion follows that while some kinds of mutualistic interactions may be relatively unstable, other mutualisms, probably representing the majority of cases, can be considered to be relatively stable. The limitations of these models and analyses are considered.     

Co-evolution of seed size and seed predation

Using the evolutionarily stable strategy (ESS) approach in a model for the co-evolution of seed size and seed predation, I show that seed size variation within individual plants is favoured if there is a trade-off in the predator's attack rate for different seed sizes. A single seed size is not evolutionarily stable because a predator that is optimally adapted to one particular seed size cannot prevent invasion by plants with a different seed size. The model generates the following predictions. The ESS consists of a continuous range of seed sizes. Small seeds tend to be attacked more frequently than big seeds. Plants with many resources and plants with low (frequency-independent) juvenile mortality have more variable seeds than plants with few resources and a high juvenile mortality. Seed size variation is higher in fluctuating populations regulated by seed predation alone than in stable populations (partially) regulated by seedling competition. Predator searching behaviour does not directly affect the ESS seed size range, but may have an indirect effect by affecting population stability or the significance of seedling competition as a population regulating mechanism. Moreover, seed size distributions are found to be more skewed in favour of small seeds if predation is spatially non-uniform than if predation is more even. Application of the model to systems of several co-evolving plant and predator species is discussed.     

Stability effects of a juvenile period in age-structured populations

Prior theoretical studies have shown that the juvenile period's length is an important determinant of local stability in age-structured population dynamics. For example, both short and long periods produce stability, but intermediate lengths can cause instability. Short juvenile periods significantly increase stability (compared to no juvenile period) if fecundity is independent of adult age. Here I re-examine these and other patterns, using a model which includes a variable juvenile period, juvenile mortality, density-dependent fecundity and adult mortality, and age-dependence is adult fecundity. Among other things, the results confirm the stable-unstable-stable pattern with increasing juvenile period length, but show that the stabilizing effect of short periods disappears when fecundity varies with adult age. Broadly speaking, the results suggest that age-dependence in adult fecundity has important dynamical consequences, and that models assuming that fecundity is independent of adult age may be unreliable guides to the dynamics of populations for which this assumption is not reasonably accurate.     

Why don't small snakes bask? Juvenile broad‐headed snakes trade thermal benefits for safety

Previous studies have suggested that most small Australian elapid snakes are nocturnal and rarely bask in the open because of the risk of predation by diurnal predatory birds. Because the physiology and behaviour of reptiles is temperature dependent, staying in refuges by day can entail high thermoregulatory costs, particularly for juveniles that must grow rapidly to maximise their chances of survival. We investigated whether the risk of predation deters juveniles of the endangered broad-headed snake ( Hoplocephalus bungaroides ) from basking, and if so, whether there are thermal costs associated with refuge use. To estimate avian attack rates on snakes, we placed 900 plasticine snake replicas in sunny locations and underneath small stones on three sandstone plateaus for 72 h. At the same time we quantified the thermal benefits of basking vs refuge use. On sunny days, juveniles could maintain preferred body temperatures for 4.7 h by basking but only for 2.0 h if they remained inside refuges. Our predation experiment showed that basking has high costs for juvenile snakes. Predators attacked a significantly higher proportion of exposed models (13.3%) than models under rocks (1.6%). Birds were the major predators of exposed models (75% of attacks), and avian predation did not vary across the landscape. By trading heat for safety, juvenile H. bungaroides decreased the potential time period that they could maintain preferred body temperatures by 57%. Thermal costs of refuge use may therefore contribute to the slow growth and late maturation of this endangered species. Our results support the hypothesis that nocturnal activity in elapid snakes has evolved to minimise the risk of avian predation.     

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

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

Dynamic state-dependent modelling predicts optimal usage patterns of responsive defences

Chemical defences against predation often involve responses to specific predation events where the prey expels fluids, such as haemolymph or gut contents, which are aversive to the predator. The common link is that each predation attempt that is averted results in an energetic cost and a reduction in the chemical defences of the prey, which might leave the prey vulnerable if the next predation attempt occurs soon afterwards. Since prey appear to be able to control the magnitude of their responses, we should expect them to trade-off the need to repel the current threat against the need to preserve defences against future threats and conserve energy for other essential activities. Here we use dynamic state-dependent models to predict optimal strategies of defence deployment in the juvenile stage of an animal that has to survive to maturation. We explore the importance of resource level, predator density, and the costs of making defences on the magnitude of the responses and optimal age and size at maturation. We predict the patterns of investment and the magnitude of the deployment of defences to potentially multiple attacks over the juvenile period, and show that responses should be smaller when the costs of defences and/or predation risk are higher. The model enables us to predict that animals in which defences benefit the adult stage will employ different strategies than those that do not use the same defences as adults, and thereby experience a smaller reduction in body size as a result of repeated attacks. We also explore the effect of the importance of adult size, and find that the sex and mating system of the prey should also affect defensive strategies. Our work provides the first predictive theory of the adaptive use of responsive defences across taxa.     

Delays in recruitment at different trophic levels: Effects on stability

Predator prey models in which there is a delay in recruitment in both species and only adults interact are formulated and studied. Stability results show that the length of delays in recruitment in the prey are more critical than the length of recruitment delays in the predator. Thus the destabilizing effect of recruitment delays may be less important in higher trophic levels than some single species models indicate. Variance in the recruitment delay is shown to be an important stabilizing influence.     

Destabilizing effect of cannibalism on a structured predator-prey system

The dynamics of a predator-prey system, where the predator has two stages, a juvenile stage and a mature stage, are modelled by a system of three ordinary differential equations. The mature predators prey on the juvenile predators in addition to the prey. If the mortality rate of juveniles is low and/or the recruitment rate to the mature population is high, then there is a stable equilibrium with all three population sizes positive. On the other hand, if the mortality rate of juveniles is high and/or the recruitment rate to the mature population is low, then the equilibrium will be stable for low levels of cannibalism, but a loss of stability by a Hopf bifurcation will take place as the level of cannibalism increases. Numerical studies indicate that a stable limit cycle appears. Cannibalism can therefore be a destabilizing force in a predator-prey system.