Population dynamics of prey exhibiting inducible defenses: the role of associated costs and density-dependence

The effect of antipredator behavior on the dynamics of a resource-consumer model was analyzed in relation to the magnitude of associated costs, and the strength of density-dependence. For this purpose, I present a deterministic continuous resource-consumer model that exhibits biomass conversion, structural homogeneity, and competition for renewable and fixed resources as separate processes. Antipredator behavior is incorporated as an inducible response to consumer density, and has metabolic and feeding costs. By means of numerical methods, I show: (1) that antipredator behavior is stabilizing for certain parameter ranges, where other stabilizing forces do not dominate the dynamics; (2) intraspecific competition for both fixed and renewable resources have a stabilizing role; (3) metabolic cost is always stabilizing, and feeding cost can be stabilizing or destabilizing, depending on the relative strength of the two competition forces.     

Crossing habitat boundaries: coupling dynamics of ecosystems through complex life cycles

Ecosystems are often indirectly connected through consumers with complex life cycles (CLC), in which different life stages inhabit different ecosystems. Using a structured consumer resource model that accounts for the independent effects of two resources on consumer growth and reproductive rates, we show that such indirect connections between ecosystems can result in alternative stable states characterized by adult-dominated and juvenile-dominated consumer populations. As a consequence, gradual changes in ecosystem productivity or mortality rates of the consumer can lead to dramatic and abrupt regime shifts across different ecosystems, hysteresis and counterintuitive changes in the consumer abundances. Whether these counter intuitive or abrupt responses occur depend on the relative productivity of both habitats and which consumer life-stage inhabits the manipulated ecosystem. These results demonstrate the strong yet complex interactions between ecosystems coupled through consumers with CLC and the need to think across ecosystems to reliably predict the consequences of natural or anthropogenic changes.     

Alternative attractors in an ecological-genetic model of populations with non-overlapping generations

This study classifies and analyzes various bifurcations of fixed points of the simple model of population dynamics with its number described by Ricker’s model and intrapopulation parameters determined by a single di-allelic locus. The model considered shows such nonlinear phenomena as multistability and coexistence of alternative attractors, which can violate the simple combination of the action of evolutionary-genetic and density-dependent ecological-dynamic processes, where gene elimination is determined by the genotypes’ resource parameters and the population number stability depends on their Malthusian parameters. The most interesting pattern in this regard is existence of polymorphic attractors, when the resource parameter of heterozygotes is not maximal. It presents a clear violation of the principle of natural selection optimality, which is caused precisely by the multistable phenomena of nonlinear dynamics. By which of the alternative attractors the dynamics is characterized by depends sensitively on the initial conditions, even small external influences can became significant, as they can shift the system from one attraction basin to another, and thus fundamentally change the dynamic mode and nature of the evolutionary process.     

THE ECO‐EVOLUTIONARY RESPONSES OF A GENERALIST CONSUMER TO RESOURCE COMPETITION

This article explores the combined evolutionary and ecological responses of resource uptake abilities in a generalist consumer to exploitative competition for one resource using a simple 2‐resource model. It compares the sizes of ecologically and evolutionarily caused changes in population densities in cases where the original consumer has a strong or a weak trade‐off in its abilities to consume the two resources. The analysis also compares the responses of the original species to competition when the competitor's population size is or is not limited by the shared resource. Although divergence in resource use traits in the resident generalist consumer is expected under all scenarios when resources are substitutable, the changes in population densities of the resources and resident consumer frequently differ between scenarios. The population of the original consumer often decreases as a result of its own adaptive divergence, and this decrease is often much greater than the initial ecological decrease. If the evolving consumer has a strong trade‐off, the overlapped resource increases in equilibrium population density in response to being consumed by a generalist competitor. Some of these predictions differ qualitatively in alternative scenarios involving sustained variation in population densities or nutritionally essential resources.     

High competition with low similarity and low competition with high similarity: exploitative and apparent competition in consumer-resource systems

This article investigates the relationship between the similarity of resource capture abilities and the amount of competition between two consumer species that exploit common resources. Most of the analysis is based on a consumer-resource model introduced by Robert MacArthur. Contrary to many statements in the literature and in textbooks, measures of competition may decrease as similarity increases and may be greatest when similarity of the two species' sets of resource capture rates is very low. High competition with low similarity may occur whether competition is measured by a competition coefficient near equilibrium or is measured by the proportional increase in a species' population density when its competitor is removed. However, these two measures may differ considerably and may change in opposite directions with a given change in similarity. The general conditions required for such counterintuitive relationships between similarity and competition are that the consumer species have relatively low resource requirements for successful reproduction and that the resources be self-reproducing. These same conditions also frequently lead to exclusion of one or more resources via apparent competition, and this is always true of MacArthur's model. A variety of other models of competition are analyzed, and circumstances most likely to produce large competitive effects with little overlap are identified.     

The interplay between behavior and morphology in the evolutionary dynamics of resource specialization

We analyze the consequences of diet choice behavior for the evolutionary dynamics of foraging traits by means of a mathematical model. The model is characterized by the following features. Consumers feed on two different substitutable resources that are distributed in a fine-grained manner. On encounter with a resource item, consumers decide whether to attack it so as to maximize their energy intake. Simultaneously, evolutionary change occurs in morphological traits involved in the foraging process. The assumption here is that evolution is constrained by a trade-off in the consumer's ability to forage on the alternative resources. The model predicts that flexible diet choice behavior can guide the direction of evolutionary change and mediate coexistence of different consumer types. Such polymorphisms can evolve from a monomorphic population at evolutionary branching points and also at points where a small genetic change in a trait can provoke a sharp instantaneous and nongenetic change in choice behavior. In the case of weak trade-offs, the evolutionary dynamics of a dimorphic consumer population can lead to alternative evolutionarily stable communities. The robustness of these predictions is checked with individual-based simulations and by relaxing the assumption of optimally foraging consumers.     

Adaptive feeding across environmental gradients and its effect on population dynamics

This paper analyzes a consumer's adaptive feeding response to environmental gradients. We consider a consumer-resource system where resources are distributed among many discrete resource patches. Each consumer exhibits a feeding morphology allowing it to remove resources from a patch down to some threshold density (or level) before having to seek resources elsewhere. Assuming consumers trade off resource extraction with patch access and predation, we show that for a given environment there often exists a single evolutionarily stable feeding threshold and it is an evolutionary attractor. We then investigate how the population dynamics of the resource and the consumer change as the environment changes. Two cases are considered: (i) all consumers exhibit a fixed feeding threshold that is adaptive for an intermediate environment; and (ii) the consumer population adapts and adopts the evolutionarily stable feeding threshold associated with the current environment. In less harsh environments (i.e., environments where consumers experience a lower risk of predation, or environments where resource patches are more abundant) the adaptive consumer population is predicted to evolve so that resources within a patch are depleted to lower densities. We show that the change in consumer density due to environmental change can be rather different depending on whether or not the population can adapt. In some situations we observe that when the consumer's environment becomes harsher, the consumer population may increase in density before a rapid crash to extinction. This result has implications for monitoring and managing a population.     

Ontogenetic antagonism–mutualism coupling: perspectives on resilience of stage‐structured communities

Organisms typically change their diets ontogenetically. Recent studies have shown that an ontogenetic diet shift undermines the resilience of stage‐structured food webs. Here, we study the integration of stage‐structured food‐web theory into theory of hybrid community (i.e. mixture of different interaction types), considering that not only diet but also interaction type often changes because of ontogenetic niche shift (e.g. the metamorphosis of pollinating insects, in which juveniles and adults are herbivores and pollinators, respectively). We developed and mathematically analysed a one‐consumer two‐resource model in which juvenile and adult consumers utilise different resources as antagonists and mutualists, respectively. Model analyses illustrated that the consumer either goes extinct or coexists with the resources depending on the initial condition when the resources have low carrying capacities while their community dynamics always converge to a single steady state when the resources have high carrying capacities. These dynamic features are different from those of the corresponding purely antagonistic module in previous studies, in which the consumer always goes extinct for low resource carrying capacities while the dynamics converge to either juvenile‐dominated or adult‐dominated state depending on the initial conditions for high resource carrying capacities. Taken together, we can suggest that ontogenetic antagonism–mutualism coupling is stabilising in that it increases the potential for species coexistence in unproductive environments while improving community resilience in productive environments. Further, these effects are generally robust to interaction nonlinearity. Beyond the previous concern of the instability in stage‐structured food‐webs, our results suggest that antagonism–mutualism coupling can play a crucial role in stabilising stage‐structured hybrid (e.g. plant–animal) communities under environmental changes. The present study represents an important first step in understanding how interaction type diversity can mediate the dynamics of stage‐structured communities.     

The effect of density-independent mortality on the coexistence of exploitative competitors for renewing resources

Many ecologists believe that higher mortality imposed on competing species increases the probability that they will coexist. This belief has persisted in spite of many theoretical counterarguments. However, few of those counterarguments have been based on models having explicit representation of the resources for which competition is occurring. This article analyzes a series of consumer-resource models of competition for nutritionally substitutable renewable resources and determines the range of relative resource requirements that allow coexistence. In most cases, if consumers are initially efficient at reducing resource densities, increasing density-independent mortality widens the range of resource requirements of the consumers that allow coexistence, provided the increase in mortality is not too great. The coexistence-promoting effects of mortality occur because a very efficient consumer species usually reduces the diversity of the set of resources it consumes. This lessens the extent to which resource utilization differences between consumer species can be expressed. Mortality, in this case, increases the diversity of resource types, widening the conditions for coexistence. However, sufficiently high mortality will usually reduce the range of parameters allowing coexistence, in agreement with much previous theory. The results presented here also predict maximal diversity at intermediate levels of productivity. Previous empirical studies and theory are reviewed in light of the theory developed here.     

Distribution-free simultaneous tests for location–scale and Lehmann alternative in two-sample problem

The paper deals with the classical two-sample testing problem for the equality of two populations, one of the most fundamental problems in biomedical experiments and case–control studies. The most familiar alternatives are the difference in location parameters or the difference in scale parameters or in both the parameters of the population density. All the tests designed for classical location or scale or location–scale alternatives assume that there is no change in the shape of the distribution. Some authors also consider the Lehmann-type alternative that addresses the change in shape. Two-sample tests under Lehmann alternative assume that the location and scale parameters are invariant. In real life, when a shift in the distribution occurs, one or more of the location, scale, and shape parameters may change simultaneously. We refer to change of one or more of the three parameters as a versatile alternative. Noting the dearth of literature for the equality two populations against such versatile alternative, we introduce two distribution-free tests based on the Euclidean and Mahalanobis distance. We obtain the asymptotic distributions of the two test statistics and study asymptotic power. We also discuss approximating p-values of the proposed tests in real applications with small samples. We compare the power performance of the two tests with several popular existing distribution-free tests against various fixed alternatives using Monte Carlo. We provide two illustrations based on biomedical experiments. Unlike existing tests which are suitable only in certain situations, proposed tests offer very good power in almost all types of shifts.     

The effect of the Holling type II functional response on apparent competition

This article analyzes the classical 2-resource-1-consumer apparent competition community module with the Holling type II functional response. Two types of resource regulation (top-down vs. combined top-down and bottom-up) and two types of consumer behaviors (inflexible consumers with fixed preferences for resources vs. adaptive consumers) are considered. When resources grow exponentially and consumers are inflexible foragers, one resource is always outcompeted due to strong apparent competition. Density dependent resource growth relaxes apparent competition so that resources can coexist. As multiple attractors (either equilibria or limit cycles) coexist, population dynamics and community composition depend on initial population densities. Population dynamics change dramatically when consumers forage adaptively. In this case, the results both for top-down, and combined top-down and bottom-up regulation are similar and they show that species persistence occurs for a much larger set of parameter values when compared with inflexible consumers. Moreover, population dynamics will be chaotic when resource carrying capacities are high enough. This shows that adaptive consumer switching can destabilize population dynamics.     

Alternative dynamical states in stage-structured consumer populations

The population dynamics of a consumer population with an internal structure is investigated. The population is divided into juvenile and adult individuals that consume different resources and do not interfere with each other. Over a broad range of external conditions (varying mortality and different resource levels), alternative stable states exist. These population states correspond to domination of juveniles and domination of adults, respectively. When mortality is varied, hysteresis between the alternative states only occurs if juveniles have more resources than adults. In the opposite case the juvenile-dominated state is stable for all values of mortality, but the adult-dominated state is not. When the population is modelled with more than one juvenile stage, the adult-dominated state becomes a periodic orbit due to a delay in the regulatory mechanism of the population dynamics. It is shown numerically that the stage-structured model converges to a model with continuous size structure for very large numbers of successive juvenile stages.     

Catastrophic shifts in vertical distributions of phytoplankton The existence of a bifurcation set

A model of phytoplankton dynamics within a water column was analyzed with special consideration on the existence of a bifurcation set in the parameter space. We considered two resources, light and a limiting nutrient, for phytoplankton growth and assumed that the water column is separated into two layers by thermal and/or density stratification. It was shown that there exists a bifurcation set in the parameter space when the growth function meets several conditions that are general for growth functions of two essential resources. Specifically, these conditions include that a less abundant of the two resources limits the growth while the effect of the other is sufficiently small. Folded structure with two stable states separated by one unstable state appears in the catastrophe manifold when parameters move to a certain direction with a certain curvature from a point in the bifurcation set. These results suggest that occurrence of discontinuous transition between two alternative vertical patterns is possible nature of phytoplankton dynamics within a stratified water column.     

Does competition between resources change the competition between their consumers to mutualism? Variations on two themes by Vandermeer

How does competition between resources affect the interaction between consumer species that share those resources? Existing theory suggests that high resource competition can lead to mutualism. However, this is based on an analysis that need only apply near equilibrium, and experimental demonstrations of such mutualism are rare. Two alternative approaches to measuring food web mutualism are examined here. These are based on the population-level effects of adding or removing a consumer species or on the amount of additional mortality that can be applied to one consumer without excluding it. Both measures suggest that mutualism is likely to be confined to two situations: when overlap in resource use by the consumers is very low and when the consumers are inefficient users of their resources. Competition between resources is also likely to increase the occurrence and magnitude of "hypercompetition" between consumers, where the reduction in population size caused by the introduced consumer is greater than that caused by a consumer that is identical to the resident species. Competition between resources can also increase the negative interaction between consumers by destabilizing the dynamics of the system. Such destabilization can cause negative indirect interactions between specialist consumers having no overlap in resource use.     

Changes and Relationships of Climatic and Hydrological Droughts in the Jialing River Basin,China

The comprehensive assessment of climatic and hydrological droughts in terms of their temporal and spatial evolutions is very important for water resources management and social development in the basin scale. To study the spatial and temporal changes of climatic and hydrological droughts and the relationships between them, the SPEI and SDI are adopted to assess the changes and the correlations of climatic and hydrological droughts by selecting the Jialing River basin, China as the research area. The SPEI and SDI at different time scales are assessed both at the entire Jialing River basin and at the regional levels of the three sub basins. The results show that the SPEI and SDI are very suitable for assessing the changes and relationships of climatic and hydrological droughts in large basins. Based on the assessment, for the Jialing River basin, climatic and hydrological droughts have the increasing tendency during recent several decades, and the increasing trend of climatic droughts is significant or extremely significant in the western and northern basin, while hydrological drought has a less significant increasing trend. Additionally, climatic and hydrological droughts tend to increase in the next few years. The results also show that on short time scales, climatic droughts have one or two months lag impact on hydrological droughts in the north-west area of the basin, and have one month lag impact in south-east area of the basin. The assessment of climatic and hydrological droughts based on the SPEI and SDI could be very useful for water resources management and climate change adaptation at large basin scale.     

Multiple stable recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models

A seasonally forced nonlinear SEIR epidemic model is used to simulate small and large amplitude periodic outbreaks. The model is shown to exhibit bistable behavior for a fixed set of parameters. Basins of attraction for each recurrent outbreak are computed, and it is shown that the basins of two coexisting stable outbreaks are intertwined in a complicated manner. The effect of such a basin structure is shown to result in an obstruction in predicting asymptotically the type of outbreak given an uncertainty in the initial population of susceptibles and infectives.     

Adaptive omnivory and species coexistence in tri-trophic food webs

The commonness of omnivory in natural communities is puzzling, because simple dynamic models of tri-trophic systems with omnivory are prone to species extinction. In particular, the intermediate consumer is frequently excluded by the omnivore at high levels of enrichment. It has been suggested that adaptive foraging by the omnivore may facilitate coexistence, because the intermediate consumer should persist more easily if it is occasionally dropped from the omnivore's diet. We explore theoretically how species permanence in tri-trophic systems is affected if the omnivore forages adaptively according to the "diet rule", i.e., feeds on the less profitable of its two prey species only if the more profitable one is sufficiently rare. We show that, compared to systems where omnivory is fixed, adaptive omnivory may indeed facilitate 3-species persistence. Counter to intuition, however, facilitation of 3-species coexistence requires that the intermediate consumer is a more profitable prey than the basal resource. Consequently, adaptive omnivory does not facilitate persistence of the intermediate consumer but enlarges the persistence region of the omnivore towards parameter space where a fixed omnivore would be excluded by the intermediate consumer. Overall, the positive effect of adaptive omnivory on 3-species persistence is, however, small. Generally, whether omnivory is fixed or adaptive, 3-species permanence is most likely when profitability (=conversion efficiency into omnivores) is low for basal resources and high for intermediate consumers.     

Psychological distance to reward in monkeys

A concurrent-chains schedule was employed to examine crab-eating macaques' choice between segmented and unsegmented fixed-interval 30-s schedules. A stimulus change occurred during one of the fixed-interval schedules (segmented schedule), while no stimulus change occurred during the other (unsegmented schedule). The subjects were exposed to three consecutive stimulus-change conditions, in an attempt to explore whether correlation of the stimulus changes with a fixed interval of nonreinforcement affects the preference between the alternatives. When the stimulus change always occurred at a half point of the segmented schedule (the first and third conditions), all subjects preferred the fixed-interval schedule without stimulus changes. This replicated previous findings with pigeons and humans. On the other hand, when the intervals before and after the stimulus change varied on every entry to the segmented schedule with the sum of them being constant (the second condition), the subjects were indifferent to the alternatives. These results are consistent with the view that the preference for unsegmented schedules over segmented ones might be due to aversiveness which the initial component in the segmented schedule possesses as a result of its correlation with a fixed interval of nonreinforcement.     

毛乌素沙地景观格局变化研究

通过对毛乌素沙地不同时期的景观分类和制图以及景观格局计算,分析了50年代到90年代毛乌素沙地景观动态与景观格局变化的特征和模式。研究表明,50年代以来,毛乌索沙地景观发生了巨大变化,流动沙地、半固定沙地面积大幅度增加,固定沙地面积迅速减少,农田面积明显增加,草原、柳湾和盐湿低地等面积显著减少。50年代时,整个景观以流动沙地和固定沙地占优势,而90年代,则以流动沙地占绝对优势。伴随着荒漠化的发展,各种景观要素类型之间相互转化,景观格局发生显著变化。固定沙地面积减少伴随着斑块的破碎化,大型斑块数量减少,小型斑块数量增加;流动沙地面积增加的同时,一方面,较小的斑块不断联合形成更多的大型斑块,另一方面,流动沙地不断向固定、半固定沙地内部渗透,形成更多的小型斑块,使整个景观更加破碎。不合理的人类活动是荒漠化扩展及景观格局发生显著变化的主要驱动因素。     

The prerequisites for and likelihood of generalist-specialist coexistence

Mathematical models of three-consumer-two-resource systems are used to explore the possibility of coexistence when one consumer is a generalist utilizing both resources, and the other two are specialists utilizing only one. Such coexistence requires strongly saturating functional or numerical responses in at least one consumer and the presence of sustained asynchronous variation in resource abundances. Given these conditions, the effects of three dichotomous factors on the range of parameters allowing coexistence are examined: flexible versus inflexible resource choice by the generalist, endogenous or exogenous cause of resource cycles, and location of the two resources in a single habitat versus two habitats. Coexistence of all three species is found to be possible for all combinations of these factors except for inflexible choice in a two-habitat environment. Generalists experience frequency-dependent fitness because, when they are abundant, they synchronize resource cycles and/or reduce their amplitude. When the generalist can adaptively adjust its relative foraging on the two resources, coexistence conditions are broadened considerably, and coexistence commonly occurs readily with exogenous variation in resource growth and with resources located in distinct habitats. Adaptive behavior increases the generalist's ability to both synchronize and dampen resource cycles.