Movements and source–sink dynamics of a Masai giraffe metapopulation

Spatial variation in habitat quality and anthropogenic factors, as well as social structure, can lead to spatially structured populations of animals. Demographic approaches can be used to improve our understanding of the dynamics of spatially structured populations and help identify subpopulations critical for the long-term persistence of regional metapopulations. We provide a regional metapopulation analysis to inform conservation management for Masai giraffes (Giraffa camelopardalis tippelskirchi) in five subpopulations defined by land management designations. We used data from an individual-based mark–recapture study to estimate subpopulation sizes, subpopulation growth rates, and movement probabilities among subpopulations. We assessed the source–sink structure of the study population by calculating source–sink statistics, and we created a female-based matrix metapopulation model composed of all subpopulations to examine how variation in demographic components of survival, reproduction, and movement affected metapopulation growth rate. Movement data indicated no subpopulation was completely isolated, but movement probabilities varied among subpopulations. Source–sink statistics and net flow of individuals indicated three subpopulations were sources, while two subpopulations were sinks. We found areas with higher wildlife protection efforts and fewer anthropogenic impacts were sources, and less-protected areas were identified as sinks. Our results highlight the importance of identifying source–sink dynamics among subpopulations for effective conservation planning and emphasize how protected areas can play an important role in sustaining metapopulations.     

Population fluctuation and persistence of one-host–two-parasitoid systems depending on resource distribution: from parasitizing behavior to population dynamics

Population dynamics and variability were examined in one-host–two-parasitoid experimental systems with different resource distributions: resource-clumped and resource-sparse conditions. The system consists of a seed beetle host, Callosobruchus chinensis, and two parasitoid wasps, Anisopteromalus calandrae (Pteromalidae) and Heterospilus prosopidis (Braconidae). In the resource-clumped condition, suitable hosts for parasitism (the late fourth-instar larvae and pupae) were clumped in 1 large resource patch, but they were scattered evenly among 16 small patches in the resource-sparse condition. Population censuses were conducted at 10-day intervals in long-term cultures, renewing 10 g of azuki beans (Vigna angularis). In both resource conditions, the first period was a single-species system of C. chinensis only, and A. calandrae was added in the second period. The one-host–one-parasitoid system with C. chinensis and A. calandrae showed stable population dynamics with small fluctuations. After addition of H. prosopidis in the third period, two of three replicates persisted to day 800 in each resource condition, although one replicate in each went to extinction at an immediate outbreak of the H. prosopidis population after the introduction. Population variabilities of C. chinensis and H. prosopidis were significantly higher and the mean population size of A. calandrae was significantly smaller in the resource-sparse condition than that in the resource-clumped one. A short-term experiment on parasitism efficiencies revealed that H. prosopidis parasitized significantly more at a low host density in the resource-sparse condition than in the resource-clumped one. Mutual interference of H. prosopidis was weak enough at low parasitoid densities but became abruptly stronger with high densities. Providing fresh hosts in a mixture of already parasitized ones, host-searching behaviors of a parasitoid were recorded by video for 3 h and were compared between the two wasp species. H. prosopidis could parasitize fresh hosts more efficiently than A. calandrae through frequent long-distance walks (walking to distant beans at one bout or outside a clump of beans with hosts and back soon on a distant bean of the clump) after reencounters with parasitized hosts. Considering all the experimental results, populations were judged to be more fragile and more likely to go to extinction in the resource-sparse condition than in the resource-clumped one. A higher attacking efficiency of H. prosopidis destabilized population dynamics more in the resource-sparse condition. Received: December 23, 1998 / Accepted: January 20, 1999     

Why be amphidromous: expatrial dispersal and the place of source and sink population dynamics?

Amphidromous fishes are found predominantly on the tropical and subtropical islands of the globe and there are few amphidromous species on continents. I suggest that this idiosyncratic distribution relates in part to problems in self-recruitment on islands that are often young or volcanic, and which may have streams with ephemeral flows across relatively short times scales. Amphidromy provides the ability to invade new habitats as these become available either on newly emergent (often volcanic) islands, or following perturbation after stream dewatering or the impacts of volcanism on older islands as a consequence of expatrial dispersal. Source/sink population dynamics may also be involved with islands ‘downstream’ in oceanic current systems behaving as sinks, with little or no self-recruitment. Streams in steep topography seem to be favoured by amphidromous species, perhaps because they provide more rapid transport to sea of the tiny, newly hatched larvae.     

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

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

The dynamics of the lynx–hare system: an application of the Lotka–Volterra model

The Lotka–Volterra model of predator–prey dynamics was used for approximation of the wellknown empirical time series on the lynx–hare system in Canada that was collected by the Hudson Bay Company in 1845–1935. The model was assumed to demonstrate satisfactory data approximation if the sets of deviations of the model and empirical data for both time series satisfied a number of statistical criteria (for the selected significance level). The frequency distributions of deviations between the theoretical (model) trajectories and empirical datasets were tested for symmetry (with respect to the Y-axis; the Kolmogorov–Smirnov and Lehmann–Rosenblatt tests) and the presence or absence of serial correlation (the Swed–Eisenhart and “jumps up–jumps down” tests). The numerical calculations show that the set of points of the space of model parameters, when the deviations satisfy the statistical criteria, is not empty and, consequently, the model is suitable for describing empirical data.     

On the accuracy of a diffusion approximation to a discrete state–space Markovian model of a population

The traditional Kolmogorov equations treat the size of a population as a discrete random variable. A model is introduced that extends these equations to incorporate environmental variability. Difficulties with this discrete model motivate approximating the population size as a continuous random variable through the use of diffusion processes. The set of cumulants for both the population size and the environmental factors affecting the population size characterize the population–environmental system. The evolution of this set, as predicted by the diffusion approximation, closely matches the corresponding predictions for the discrete model. It is also noted that the simulation estimates of the cumulants against which the predictions of the diffusion model are checked can vary considerably between simulations — despite averaging over a large number of simulation runs. The precision of the simulation estimates–both over time and with differing cumulant order–is discussed.     

Analyzing the spatial dynamics of a prey–predator lattice model with social behavior

A lattice prey–predator model is studied. Transition rules applied sequentially describe processes such as reproduction, predation, and death of predators. The movement of predators is governed by a local particle swarm optimization algorithm, which causes the formation of swarms of predators that propagate through the lattice. Starting with a single predator in a lattice fully covered by preys, we observe a wavefront of predators invading the zones dominated by preys; subsequent fronts arise during the transient phase, where a monotonic approach to a fixed point is present. After the transient phase the system enters an oscillatory regime, where the amplitude of oscillations appears to be bounded but is difficult to predict. We observe qualitative similar behavior even for larger lattices. An empirical approach is used to determine the effects of the movement of predators on the temporal dynamics of the system. Our results show that the algorithm used to model the movement of predators increases the proficiency of predators.     

Global dynamics of a mutualism–competition model with one resource and multiple consumers

Journal of Mathematical Biology - Recent simulation modeling has shown that species can coevolve toward clusters of coexisting consumers exploiting the same limiting resource or resources, with...     

How population loss through habitat boundaries determines the dynamics of a predator–prey system

The increased persistence of predator–prey systems when interactions are distributed through the space has been acknowledged by both empirical and theoretical studies. One salient feature of predator–prey interactions in heterogeneous space, for example, is the existence of cycles with reduced amplitude when compared with a homogeneous landscape. Although the role of spatial interactions in shaping the dynamics of predator–prey systems has been extensively studied, still very few works have focused on the effects of habitat loss and fragmentation on these systems. In this work, we study the population dynamics of a predator–prey system in a single finite habitat with flux at the boundaries. Species movement and growth are described through a reaction–diffusion model with Rosenzweig–MacArthur type local interactions. Conforming with the existing literature, we find that the reduction of habitat size, or increasing of species movement rates equivalently, has the potential to decrease the amplitude of oscillations and even bring the system to a steady coexistence equilibrium above a threshold. We observe, however, situations in which this trend is reversed. This occurs when species movement rates and response at patch boundaries interact to induce non-trivial patterns of species distributions. These distributions are characterized by anti-correlation between predator and prey, creating then spatial refugia for prey. Our results highlight the role of population loss through habitat boundaries in determining the dynamics of predator–prey interactions.     

What drives the dynamics of a soil mite population under seasonal flooding? A null model analysis

Floods can inflict high mortality on terrestrial organisms, but may also promote adaptive evolution. In seasonal floodplains, several taxa show flood-related traits that may be important for their long-term persistence, but the available evidence is conflicting. Here, we used a simulation approach to investigate the interplay between seasonal floods and submersion resistance in driving the population dynamics of the parthenogenetic soil mite Rostrozetes ovulum in an Amazonian blackwater floodplain. First, we gathered data from two flood cycles to estimate field survival rate. Next, we used further data from a submersion survival laboratory experiment and a historical flood record to build a null model for R. ovulum’s survival rate under seasonal flooding, and then tested it against field survival estimates. Floods caused marked density declines, but the two estimates of field survival rate were statistically equivalent, suggesting relatively constant survival across years. Submersion survival time varied tenfold among individuals, but its variability was within the range known for life history traits of other asexual invertebrates. Both field survival rates were consistent with the null model, supporting seasonal flooding as the main mortality factor. Surprisingly, though, average flood duration was actually larger than the average mite could survive, suggesting that population persistence relies on relatively rare, super-resistant phenotypes. Overall, the studied R. ovulum population appears to have a mainly density-independent dynamics across years, with its viability depending on mechanisms that buffer flood survival rate against temporal oscillations.     

Intra- and interspecific density dependence mediates weather effects on the population dynamics of a plant–insect herbivore system

Temperature and precipitation are two major factors determining arthropod population densities, but the effects from these climate variables are seldom evaluated in the same study system and in combination with inter- and intraspecific density dependence. In this study, I used a 19 year time series on plant variables (shoot height and flowering incidence) and insect density in order to understand direct and indirect effects of climatic fluctuations on insect population densities. The study system includes two closely related leaf beetle species (Galerucella spp.) and a flower feeding weevil Nanophyes marmoratus attacking the plant purple loosestrife Lythrum salicaria. Results suggest that both intraspecific density dependence and weather variables affected Galerucella population densities, with interactive effects of rain and temperature on insect densities that depended on the timing relative to insect life cycles. In spring, high temperatures increased Galerucella densities only when combined with high rain, as low rain implies a high drought risk. Low temperatures are only beneficial if combined with little rain, as high rain cause chilly and wet conditions that are bad for insects. In summer, interactive effects of rain and temperature are different because high temperatures and little rain cause drought that induce wilting in plants, thus reducing food availability for the leaf feeding larvae. In contrast, the density of the flower feeding weevil was less affected by temperature and precipitation directly, and more indirectly interspecific density dependent effects through reduced resource availability caused by previous Galerucella damage.     

The complex dynamics of a diffusive prey–predator model with an Allee effect in prey

This paper investigates complex dynamics of a predator–prey interaction model that incorporates: (a) an Allee effect in prey; (b) the Michaelis–Menten type functional response between prey and predator; and (c) diffusion in both prey and predator. We provide rigorous mathematical results of the proposed model including: (1) the stability of non-negative constant steady states; (2) sufficient conditions that lead to Hopf/Turing bifurcations; (3) a prior estimates of positive steady states; (4) the non-existence and existence of non-constant positive steady states when the model is under zero-flux boundary condition. We also perform completed analysis of the corresponding ODE model to obtain a better understanding on effects of diffusion on the stability. Our analytical results show that the small values of the ratio of the prey's diffusion rate to the predator's diffusion rate are more likely to destabilize the system, thus generate Hopf-bifurcation and Turing instability that can lead to different spatial patterns. Through numerical simulations, we observe that our model, with or without Allee effect, can exhibit extremely rich pattern formations that include but not limit to strips, spotted patterns, symmetric patterns. In addition, the strength of Allee effects also plays an important role in generating distinct spatial patterns.     

Invasion waves and pinning in the Kirkpatrick–Barton model of evolutionary range dynamics

Journal of Mathematical Biology - The Kirkpatrick–Barton model, well known to invasion biologists, is a pair of reaction–diffusion equations for the joint evolution of population...     

A stochastic model for the spatial distribution of species based on an aggregation–repulsion rule

The heterogeneity associated with the spatial distribution of organisms is an awkward problem in ecology because this heterogeneity directly depends on the sampling scale. To specify the scope of the influence of sampling scale on the level of species aggregation, we need data sets that entail excessive sampling costs in situ. To find a solution for this problem, we can use models to simulate patterns of organisms. These models are often very complex models that take into account heterogeneity of habitats and displacement or longevity of studied species. In this article, we introduce a new stochastic model to simulate patterns for one taxon and we want this model to be parsimonious, i.e., with few parameters and able to simulate observed patterns. This model is based on an aggregation–repulsion rule. This aggregation–repulsion rule is defined by two parameters. On a large scale, the number of aggregates present on the pattern is the first parameter. On a smaller scale, the level of aggregation–repulsion among individuals is determined by a probability distribution. These two parameters are estimated from field data set in a robust way so that the simulated patterns reflect the observed heterogeneity. We apply this model to entomological data: four Diptera families, namely the Sciaridae, Phoridae, Cecidomyiidae, and Empididae. The field data for the Phoridae family are used to simulate sampling using different trap sizes. We record changes in the coefficient of variation (C) as a function of the sampling scale, and we can suggest to ecologists emergence traps of 0.6 m², in other words a square 77 × 77 cm trap, to obtain a C value under 20%. Received: February 28, 2000 / Accepted: October 14, 2000     

Time to the MRCA of a sample in a Wright–Fisher model with variable population size

Determining the expected distribution of the time to the most recent common ancestor of a sample of individuals may deliver important information about the genetic markers and evolution of the population. In this paper, we introduce a new recursive algorithm to calculate the distribution of the time to the most recent common ancestor of the sample from a population evolved by any conditional multinomial sampling model. The most important advantage of our method is that it can be applied to a sample of any size drawn from a population regardless of its size growth pattern. We also present a very efficient method to implement and store the genealogy tree of the population evolved by the Galton–Watson process. In the final section we present results applied to a simulated population with a single bottleneck event and to real populations of known size histories.     

Global dynamics and bifurcation analysis of a host–parasitoid model with strong Allee effect

In this paper, we study the global dynamics and bifurcations of a two-dimensional discrete time host–parasitoid model with strong Allee effect. The existence of fixed points and their stability are analysed in all allowed parametric region. The bifurcation analysis shows that the model can undergo fold bifurcation and Neimark–Sacker bifurcation. As the parameters vary in a small neighbourhood of the Neimark–Sacker bifurcation condition, the unique positive fixed point changes its stability and an invariant closed circle bifurcates from the positive fixed point. From the viewpoint of biology, the invariant closed curve corresponds to the periodic or quasi-periodic oscillations between host and parasitoid populations. Furthermore, it is proved that all solutions of this model are bounded, and there exist some values of the parameters such that the model has a global attractor. These theoretical results reveal the complex dynamics of the present model.     

Large-scale synchrony of gap dynamics and the distribution of understory tree species in maple–beech forests

Large-scale synchronous variations in community dynamics are well documented for a vast array of organisms, but are considerably less understood for forest trees. Because of temporal variations in canopy gap dynamics, forest communities—even old-growth ones—are never at equilibrium at the stand scale. This paucity of equilibrium may also be true at the regional scale. Our objectives were to determine (1) if nonequilibrium dynamics caused by temporal variations in the formation of canopy gaps are regionally synchronized, and (2) if spatiotemporal variations in canopy gap formation affect the relative abundance of tree species in the understory. We examined these questions by analyzing variations in the suppression and release history of Acer saccharum Marsh. and Fagus grandifolia Ehrh. from 481 growth series of understory saplings taken from 34 mature stands. We observed that (1) the proportion of stems in release as a function of time exhibited a U-shaped pattern over the last 35 years, with the lowest levels occurring during 1975–1985, and that (2) the response to this in terms of species composition was that A. saccharum became more abundant at sites that had the highest proportion of stems in release during 1975–1985. We concluded that the understory dynamics, typically thought of as a stand-scale process, may be regionally synchronized.