The dynamics of two diffusively coupled predator-prey populations

I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator-prey metapopulation or as a spatially explicit predator-prey system. Asynchronous local dynamics are presumed by metapopulation theory. The main question I address is when synchronous and when asynchronous dynamics arise. Contrary to biological intuition, for very small migration rates the oscillations always synchronize. For intermediate migration rates the synchronous oscillations are unstable and I found periodic, quasi-periodic, and intermittently chaotic attractors with asynchronous dynamics. For large predator migration rates, attractors in the form of equilibria or limit cycles exist in which one of the patches contains no prey. The dynamical behavior of the system is described using bifurcation diagrams. The model shows that spatial predator-prey populations can be regulated through the interplay of local dynamics and migration.     

On the dynamics of a pair of coupled neurons subject to alternating input rates

We present a statistical analysis of the firing activity of two coupled neuronal units that interact according to a 'sending-receiving' model. The membrane potential's behavior of both units is described by the Stein equations under the additional assumption that the spikes released by the sending neuron constitute an extra excitation for the receiving one. We also assume the presence of an alternating behavior for the rates of inputs to the sending neuron. By means of ad hoc simulations, we obtain, and then discuss, some statistical results concerning the spike production times of the units within the subintervals of the alternating inputs, as well as the reaction times of the receiving neuron.     

Effect of control measures on pest populations subject to regulation by parasites and pathogens

The effects of control measures on a disease regulated pest population are analyzed using the May-Anderson model of infectious disease. Control measures that increase the pest death rate (e.g. pesticides) increase the threshold pest population required for spread of the pathogen and lengthen the time required for the pathogen to control the pest. In contrast, control measures that decrease the pest birth rate (e.g. sterile males) do not interfere with pest regulation by pathogens.     

The competitive dynamics of metapopulations subject to the Allee-like effect

It is well recognized that individuals of many species can benefit from the presence of conspecifics, a concept broadly referred to as the Allee effect. At the metapopulation level, there is an analogous but essentially different phenomenon called the Allee-like effect that leads to metapopulation extinction thresholds at low habitat occupancy. But so far not adequate attention has been paid to this phenomenon. In this paper, the Allee-like effect is introduced into a metapopulation model of one species and also that of a three-state two-species competitive system. Phase plane analysis is used to investigate the dynamics of these models. We demonstrate that the Allee-like effect alone could lead to multiple stable states in three-state two-species competitive systems at the metapopulation level, and the number of stable states decrease as the Allee-like effect becomes more severe. Severe Allee-like effects may make coexistence impossible and may even lead to the extinction of both species even if their initial habitat occupancies are high and suitable habitats are enough. It is especially noticeable that depending on their initial conditions one species may exclude the other one that subjects to a weaker Allee-like effect than the former, while the second species always excludes the first one when both species are assumed to be in the absence of the Allee-like effect. We also investigate the habitat destructive effect on the Allee-like system mentioned above. Research indicates that the existence of the Allee-like effect makes a metapopulation more susceptible to habitat destruction. All in all, the Allee-like effect is probably a destabilizing factor that, together with habitat destruction, would affect the continuous existence of species. These conclusions may have important implications for conservation and metacommunity organization.     

The dynamics of a discrete geotropic sensor subject to rotation-induced gravity compensation

A clinostat achieves gravity compensation by providing circular rotation with uniform speed, about a horizontal axis. The dynamics of an assumed, discrete and free-moving subcellular gravity receptor, subject to clinostat rotation, is analyzed. The results imply that there is an optimum rotation rate; higher speeds result in circular motions with diameters more comparable to thermal noise fluctuations, but with greater linear velocities due to increasing centrifugal forces. An optimizing function is proposed. The nucleolus and mitochondrion is chosen as a gravity receptor for illustrating the use of this theory. The characteristics of their clinostat-induced motions are incorporated with experimental results on Avena plant shoots in an illustrative example.     

Natural selection in populations subject to a migration load

Migration tends to oppose the effects of divergent natural selection among populations. Numerous theoretical and empirical studies have demonstrated that this migration-selection balance constrains genetic divergence among populations. In contrast, relatively few studies have examined immigration's effects on fitness and natural selection within recipient populations. By constraining local adaptation, migration can lead to reduced fitness, known as a "migration load," which in turn causes persistent natural selection. We develop a simple two-island model of migration-selection balance that, although very general, also reflects the natural history of Timema cristinae walking-stick insects that inhabit two host plant species that favor different cryptic color patterns. We derive theoretical predictions about how migration rates affect the level of maladaptation within populations (measured as the frequency of less-cryptic color-pattern morphs), which in turn determines the selection differential (the within-generation morph frequency change). Using data on color morph frequencies from 25 natural populations, we confirm previous results showing that maladaptation is higher in populations receiving more immigrants. We then present novel evidence that this increased maladaptation leads to larger selection differentials, consistent with our model. Our results provide comparative evidence that immigration elevates the variance in fitness, which in turn leads to larger selection differentials, consistent with Fisher's Theorem of Natural Selection. However, we also find evidence that recurrent adult migration between parapatric populations may tend to obscure the effects of selection.     

The dynamics of hierarchical age-structured populations

An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.     

Habitat selection reduces extinction of populations subject to Allee effects

Theoretical studies indicate that a single population under an Allee effect will decline to extinction if reduced below a particular threshold, but the existence of multiple local populations connected by random dispersal improves persistence of the global population. An additional process that can facilitate persistence is the existence of habitat selection by dispersers. Using analytic and simulation models of population change, I found that when habitat patches exhibiting Allee effects are connected by dispersing individuals, habitat selection by these dispersers increases the likelihood that patches persist at high densities, relative to results expected by random settlement. Populations exhibiting habitat selection also attain equilibrium more quickly than randomly dispersing populations. These effects are particularly important when Allee effects are large and more than two patches exist. Integrating habitat selection into population dynamics may help address why some studies have failed to find extinction thresholds in populations, despite well-known Allee effects in many species.     

似Allee效应对2-物种集合种群竞争动态的影响

集合种群具有与局域种群Allee效应相似的现象被称为似Allee效应.将似Allee效应引入2-竞争物种集合种群系统,建立了具有似Allee效应的2-物种集合种群演化动态模型.大量的数值模拟表明:(1)似Allee效应导致集合种群水平上两竞争物种构成的系统具有多个平衡态;(2)似Allee效应使竞争共存物种无法续存甚至全部灭绝,即使种群具有很高的初始斑块占有率,并且最终平衡态随初始斑块占有率变化而改变;(3)似Allee效应可能使竞争排斥物种共同灭绝,且效应越强,物种存活时间越短;但似Allee效应不会增强强物种对弱物种的排斥强度,反而可能使强物种变为弱物种,弱物种变为强物种,其具有与栖息地毁坏类似的影响种群竞争等级排序的作用;(4)似Allee效应对竞争集合种群续存是一个不稳定的干扰因素,微小的变化都将引起系统平衡态的剧变.但对于已经达到平衡态的集合种群系统,似Allee效应对强弱种群多度起到调节与制约的作用,有助于平衡态集合种群的稳定与共存,这一结论更完整的揭示了似Allee效应在竞争集合种群系统发展的不同阶段所起的不同作用.以上这些结论对物种保护及集合群落的管理具有重要的指导意义.     

The dynamics of spatially coupled food webs

The dynamics of ecological systems include a bewildering number of biotic interactions that unfold over a vast range of spatial scales. Here, employing simple and general empirical arguments concerning the nature of movement, trophic position and behaviour we outline a general theory concerning the role of space and food web structure on food web stability. We argue that consumers link food webs in space and that this spatial structure combined with relatively rapid behavioural responses by consumers can strongly influence the dynamics of food webs. Employing simple spatially implicit food web models, we show that large mobile consumers are inordinately important in determining the stability, or lack of it, in ecosystems. More specifically, this theory suggests that mobile higher order organisms are potent stabilizers when embedded in a variable, and expansive spatial structure. However, when space is compressed and higher order consumers strongly couple local habitats then mobile consumers can have an inordinate destabilizing effect. Preliminary empirical arguments show consistency with this general theory.     

Persistence of host and parasite populations subject to experimental size-selective removal

Predators have the potential to limit the spread of pathogens not only by selecting infected prey but also by shaping prey demographics. We tested this idea with an epidemiological experiment in which we simulated variable levels of size-selective predation on zooplankton hosts and monitored the persistence of host and parasite populations. In the absence of simulated predation, the virulent protozoan Caullerya mesnili frequently drove its host Daphnia galeata to extinction. Uninfected control populations showed lower extinction rates and higher average densities than infected populations in the absence of simulated predation (all of the latter went extinct or remained infected). With a weak removal rate of the largest hosts, the proportion of populations in which the parasite drove the host to extinction decreased, while the number of populations in which the host persisted and the parasite went extinct increased. Host-parasite coexistence was also observed in some cases. With intermediate levels of removal, most of the parasite populations went extinct, while the host populations persisted. With an even higher removal rate, Daphnia were driven to extinction as well. Thus, variation in one factor, size-selective mortality, resulted in four different patterns of population dynamics. Our results highlight the potential role of predation in shaping the epidemiology and community structure of host-parasite systems.     

A flexible forward simulator for populations subject to selection and demography

This article introduces a new forward population genetic simulation program that can efficiently generate samples from populations with complex demographic histories under various models of natural selection. The program (SFS_CODE) is highly flexible, allowing the user to simulate realistic genomic regions with several loci evolving according to a variety of mutation models (from simple to context-dependent), and allows for insertions and deletions. Each locus can be annotated as either coding or non-coding, sex-linked or autosomal, selected or neutral, and have an arbitrary linkage structure (from completely linked to independent). AVAILABILITY: The source code (written in the C programming language) is available at http://sfscode.sourceforge.net, and a web server (http://cbsuapps.tc.cornell.edu/sfscode.aspx) allows the user to perform simulations using the high-performance computing cluster hosted by the Cornell University Computational Biology Service Unit.     

The regulation of the dynamics of human populations

The important aspects of population dynamics are shown in a model along with the changes of population structure, the reasons for these changes and the conditions under which such changes take place. Subsequently, the reasons for these population dynamic processes which can be arranged in a three step scale are shown. Here, it must be differentiated between endogenous processes, due to factors inherent in the population, and exogenous ones caused by external forces effecting structural changes. The population political trends has to be incorporated as a part of the exogenous factors. The questions of regularities in the population dynamics are shown in the examples of important population theories in history. At the same time the theoretically possible borders are described, within which, due to purely physiological reasons, a population dynamic process has to occur. However, these borders will never be reached. Examination of the inertia of the population dynamic processes suggests an examination of the questions about the probability of the self-destructive processes in population dynamics. Considering the strong self-regulatory processes within a population the hypothesis of a population extinction is refuted.     

The dynamics of transposable elements in structured populations

We analyzed the dynamics of transposable elements (TEs) according to Wright's island and continent-island models, assuming that selection tends to counter the deleterious effects of TEs. We showed that migration between host populations has no impact on either the existence or the stability of the TE copy number equilibrium points obtained in the absence of migration. However, if the migration rate is slower than the transposition rate or if selection is weak, then the TE copy numbers in all the populations can be expected to slowly become homogeneous, whereas a heterogeneous TE copy number distribution between populations is maintained if TEs are mobilized in some populations. The mean TE copy number is highly sensitive to the population size, but as a result of migration between populations, it decreases as the sum of the population sizes increases and tends to reach the same value in these populations. We have demonstrated the existence of repulsion between TE insertion sites, which is established by selection and amplified by drift. This repulsion is reduced as much as the migration rate is higher than the recombination rate between the TE insertion sites. Migration and demographic history are therefore strong forces in determining the dynamics of TEs within the genomes and the populations of a species.     

The dynamics of diversification in evolving Pseudomonas populations

Determining the mechanisms that promote the evolution of diversity is a central problem in evolutionary biology. Previous studies have demonstrated that diversification occurs in complex environments and that genotypes specialized on alternative resources can be maintained over short time scales. Here, we describe a selection experiment that has tracked the dynamics of adaptive diversification within selection lines of the asexual bacteria Pseudomonas fluorescens over about 900 generations. We cultured experimental populations from the same two isogenic ancestral strains in simple, single-substrate environments or in complex, four-substrate environments. Following selection we assayed the growth of genotypes from each population on each substrate individually. We estimated mutational heritability, Vm/VE, as 1 x 10(-3) per generation in simple environments and 3 x 10(-3) per generation in complex environments. These values are roughly consistent with estimates reported in other systems. Populations selected in complex environments evolved into genetically diverse communities. Genotypes exhibited greater metabolic differentiation from other genotypes in their own population than to genotypes evolving in other populations, presumably as a result of resource competition. In populations selected in simple environments, little genetic diversity evolved, and genotypes shared very similar phenotypes. Our findings suggest that ecological opportunity provided by environmental complexity plays a major role in the evolution and maintenance of diversity.     

Dynamics of a sex-linked deleterious mutation in populations subject to sex reversal

The heterogametic sex chromosomes (i.e. mammalian Y and avian W) do not usually recombine with the homogametic sex chromosomes which is known to lead into rapid degeneration of Y and W due to accumulation of deleterious mutations. On the other hand, some 96% of amphibian species have homomorphic, i.e. non-degenerate Y chromosomes. Nicolas Perrin's fountain-of-youth hypothesis states that this is a result of recombination between X and Y chromosomes in sex-reversed individuals. In this study, I model the consequences of such recombination for the dynamics of a deleterious mutation occurring in Y chromosomes. As expected, even relatively low levels of sex reversal help to purge deleterious mutations. However, the population-dynamic consequences of this depend on the type of selection that operates on the population undergoing sex reversal. Under fecundity selection, sex reversal can be beneficial for some parameter values, whereas under survival selection, it seems to be always harmful.     

Decision science for effective management of populations subject to stochasticity and imperfect knowledge

Many species are threatened by human activity through processes such as habitat modification, water management, hunting, and introduction of invasive species. These anthropogenic threats must be mitigated as efficiently as possible because both time and money available for mitigation are limited. For example, it is essential to address the type and degree of uncertainties present to derive effective management strategies for managed populations. Decision science provides the tools required to produce effective management strategies that can maximize or minimize the desired objective(s) based on imperfect knowledge, taking into account stochasticity. Of particular importance are questions such as how much of available budgets should be invested in reducing uncertainty and which uncertainties should be reduced. In such instances, decision science can help select efficient environmental management actions that may be subject to stochasticity and imperfect knowledge. Here, we review the use of decision science in environmental management to demonstrate the utility of the decision science framework. Our points are illustrated using examples from the literature. We conclude that collaboration between theoreticians and practitioners is crucial to maximize the benefits of decision science’s rational approach to dealing with uncertainty.     

The adaptive dynamics of altruism in spatially heterogeneous populations

Abstract.— We study the spatial adaptive dynamics of a continuous trait that measures individual investment in altruism. Our study is based on an ecological model of a spatially heterogeneous population from which we derive an appropriate measure of fitness. The analysis of this fitness measure uncovers three different selective processes controlling the evolution of altruism: the direct physiological cost, the indirect genetic benefits of cooperative interactions, and the indirect genetic costs of competition for space. In our model, habitat structure and a continuous life cycle makes the cost of competing for space with relatives negligible. Our study yields a classification of adaptive patterns of altruism according to the shape of the costs of altruism (with decelerating, linear, or accelerating dependence on the investment in altruism). The invasion of altruism occurs readily in species with accelerating costs, but large mutations are critical for altruism to evolve in selfish species with decelerating costs. Strict selfishness is maintained by natural selection only under very restricted conditions. In species with rapidly accelerating costs, adaptation leads to an evolutionarily stable rate of investment in altruism that decreases smoothly with the level of mobility. A rather different adaptive pattern emerges in species with slowly accelerating costs: high altruism evolves at low mobility, whereas a quasi-selfish state is promoted in more mobile species. The high adaptive level of altruism can be predicted solely from habitat connectedness and physiological parameters that characterize the pattern of cost. We also show that environmental changes that cause increased mobility in those highly altruistic species can beget selection-driven self-extinction, which may contribute to the rarity of social species.