Neighborhood models of plant population dynamics. 2. Multi-species models of annuals

Models are developed for the dynamics of multi-species communities of annual plants that lack seed dormancy. These models explicitly include plastic plant growth, the spatial distribution of individuals, and the fact that individuals interact primarily with nearby individuals. Because the models are based on submodels of individual plants (fecundity, survivorship and dispersal, and how these are affected by inter-individual interactions), they provide explanations of community-level phenomena in terms of the biology of individuals. All model parameters and functional forms may be estimated from data obtained in simple experiments of a single years's duration. The models are used to examine the community-level consequences of some types of inter-individual interactions that have been reported in the ecological literature. In addition, the models are used to demonstrate that dispersal may markedly influence the outcome of competition among plant species, even in a physically homogeneous environment, due to an effect of dispersal on the spatial distribution of individuals.     

The effects of spatial heterogeneity in population dynamics

The dynamics of a population inhabiting a heterogeneous environment are modelled by a diffusive logistic equation with spatially varying growth rate. The overall suitability of an environment is characterized by the principal eigenvalue of the corresponding linearized equation. The dependence of the eigenvalue on the spatial arrangement of regions of favorable and unfavorable habitat and on boundary conditions is analyzed in a number of cases.Research supported by National Science Foundation grant #DMS 88-02346     

Density-structured models for plant population dynamics

Density-structured models are structured population models in which the state variable is the proportion of populations or sites in a small number of discrete density states. Although such models have rarely been used, they have the advantage that they are straightforward to parameterize, make few assumptions about population dynamics, and permit rapid data collection using coarse density assessment. In this article, we highlight their use in relating population dynamics to environmental variation and their robustness to measurement error. We show that density-structured models are able to accurately represent population dynamics under a wide range of conditions. We look at the effects of including a persistent seedbank and describe numerical approximations for the mean and variance of population size. For simulated data, we determine the extent to which the underlying continuous process may be inferred from density-structured data. Finally, we discuss issues of parameter estimation and applications for which these types of models may be useful.     

Incorporating spatial variation in density enhances the stability of simple population dynamics models

Simple discrete time models of population growth admit a wide variety of dynamic behaviors, including population cycles and chaos. Yet studies of natural and laboratory populations typically reveal their dynamics to be relatively stable. Many explanations for the apparent rarity of unstable or chaotic behavior in real populations have been developed, including the possible stabilizing roles of migration, refugia, abrupt density-dependence, and genetic variation in sensitivity to density. We develop a theoretical framework for incorporating random spatial variation in density into simple models of population growth, and apply this approach to two commonly used models in ecology: the Ricker and Hassell maps. We show that the incorporation of spatial density variation into both these models has a strong stabilizing influence on their dynamic behavior, and leads to their exhibiting stable point equilibria or stable limit cycles over a relatively much larger range of parameter values. We suggest that one reason why chaotic population dynamics are less common than the simple models indicate is, these models typically neglect the potentially stabilizing role of spatial variation in density.     

The spatial structure of the physical environment

There is substantial environmental variance at small spatial scales (1 m or less) in both natural and disturbed environments. We have investigated the spatial structure of physical variables at larger scales (up to 10⁶ m). We analysed surveys of edaphic properties of Wisconsin forest soils, of the water chemistry of lakes in Ontario and Labrador, and of temperature and precipitation in northeastern North America. We found no clear indication that the variance among sites approaches some maximal value as the distance between them increases. We suggest instead that the variance of the physical environment tends to increase continually with distance. The slope of the log-log regression of variance on distance provides a means of comparing the heterogeneity of different environments with respect to a given factor, or of comparing different factors within a given environment. This slope provides a useful measure of environmental structure that can be related to the biodiversity or plasticity of native organisms.     

森林土壤物理性质的空间异质性研究

土壤空间质性是土壤的重要属性之一。采用地统计的理论和方法,研究了阔叶红松林上层土壤物理因子的空间异质性。变异函数分析结果表明,土壤水分、容重、毛管持水量和孔隙讴具有明显的空间异质性。在０～１０ｃｍ土层深,空间异质性尺度为１１～１３ｍ,１１～２０ｃｍ土层深为６～８ｍ,空间异质性程度随尺度变化。自相关部分的空间异质性在０～１０ｃｍ和１１～２０ｃｍ土层深为５２．９％～７３．７％和６９．３％～９３．６％,     

Site-dependent population dynamics: the influence of spatial habitat heterogeneity on individual fitness in the sedge warbler Acrocephalus schoenobaenus

During nine years of study, we detected a mechanism corresponding to site dependence operating in a population of the sedge warbler Acrocephalus schoenobaenus inhabiting a natural wetland of high within-habitat heterogeneity. Sites with a larger share of cover by tall wetland vegetation were preempted during spring settlement; they were occupied in more breeding seasons and by more experienced males. The fitness of males occupying these sites was higher in terms of local recruit production. The total area occupied by the population expanded or contracted depending on its population size. This mechanism increased or decreased the mean site quality, influencing local recruitment of young, although mainly by changing the share of unproductive sites in the total pool of occupied sites. The results indicate that population demographic rates may depend on the spatial heterogeneity of resources at the level of individuals.     

集合种群动态对生境毁坏空间异质性的响应

首次将分形几何(Fractal geometry)与元胞自动机(Cellular automata)相结合,研究了破碎化生境中集合种群的空间分布格局动态,以及集合种群动态对生境毁坏空间异质性的响应。研究发现:(1)各个物种种群在生境中的分布具有很好的分形特征,物种的计盒维数(Box dimension)不仅可以很好地反映种群的空间分布结构,也能很好地反映种群动态。(2)如果将空间因素考虑进来的话,生境毁坏的灭绝债务(Time debt)将大于空间隐含模式所模拟的结果。(3)物种灭绝同时存在强物种灭绝和弱物种灭绝。并且只有在生境随机毁坏下,才与空间隐含的模拟结果比较接近,即强物种中将是最强物种率先灭绝。而在边缘毁坏这种比较集中成块的开发方式下,将是较强的物种灭绝。(4)边缘毁坏相对随机毁坏有利于物种,尤其是弱物种的长期续存。     

Models of an annual plant population with a seedbank

Two models are set up, in terms of difference equations, for a population of a species of annual plant, of which a proportion of the seeds remain dormant for at least one year. Analytical and numerical results are presented demonstrating the effect of the seedbank on the return to equilibrium of the plant population following an initial disturbance. The seedbank can exert both a damping (stabilising) effect, speeding up oscillatory return, and an inertial (destabilising) effect, slowing down exponential return to the equilibrium population.     

Separable models in age-dependent population dynamics

A class of population models is considered in which the parameters such as fecundity, mortality and interaction coefficients are assumed to be age-dependent. Conditions for the existence, stability and global attractivity of steady-state and periodic solutions are derived. The dependence of these solutions on the maturation periods is analyzed. These results are applied to specific single and multiple population models. It is shown that periodic solutions cannot occur in a general class of single population age-dependent models. Conditions are derived that determine whether increasing the maturation period has a stabilizing effect. In specific cases, it is shown that any number of switches in stability can occur as the maturation period is increased. An example is given of predator-prey model where each one of these stability switches corresponds to a stable steady state losing its stability via a Hopf bifurcation to a periodic solution and regaining its stability upon further increase of the maturation period.     

Dispersal and spatial scale affect synchrony in spatial population dynamics

A large body of theoretical studies has shown that synchrony among populations is critical for the long-term persistence of species in fragmented habitats. Although the effects of dispersal and environmental factors on synchrony have been investigated theoretically, empirical studies of these relationships have been lacking. We explored the interplay between environmental and demographic factors (fecundity, survival, dispersal) on population synchrony for 53 species of birds. We show that the interspecific differences in mean synchrony were determined by global environmental factors whose action was probably mediated by the abundance of each species. After removing the effect of these global factors on synchrony, the residual synchrony was strongly correlated with dispersal distance. The relationship between dispersal and synchrony was stronger for the species nesting in wet habitats than for those nesting in dry habitats. Our results indicate that different factors synchronize bird populations at different spatial scales, thus highlighting the role of scale in understanding spatial population dynamics and extinction risks.     

Impact of spatial heterogeneity on a predator-prey system dynamics

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

Periodic solutions of population models in a periodically fluctuating environment.

A periodically fluctuating environment is assumed in a population-modeling process that generates nonautonomous difference equations. The existence and uniqueness of periodic solutions are studied. A sufficient condition for existence and a necessary condition for uniqueness are obtained. Stability of the periodic solutions is investigated. Several numerical examples are given to illustrate the basic results, and a brief discussion is presented.     

Epidemic models with spatial spread due to population migration

A spatial diffusion operator that governs the migration of polymorphic populations is derived and some specific epidemic models are analyzed in the presence of this type of diffusion. Threshold criteria and asymptotic behavior of solutions are derived, and it is shown that spatially heterogeneous steady states can occur in these models.The work of this author was partially supported by the National Science Foundation's Ecosystem Studies Program under Interagency Agreement No. DED80-21024 with the U.S. Department of Energy under contract W-7405-eng-26 with Union Carbide Corporation     

The dynamics of population models with distributed maturation periods

An integro-differential equation for the dynamics of a subpopulation of adults in a closed system where only the adults compete and where there is a distribution of maturation periods is described. We show how the careful choice of a general weighting function based on the gamma distribution with a shift in origin enables us to characterize adequately some observed maturation-period distributions, and also makes local stability and numerical analyses straightforward. Using these results we examine the progression in the behavior of the distributed-delay model as the distribution is narrowed toward the limit of a discrete delay. We conclude that while local stability properties approach those of the limiting equation very rapidly, the persistent fluctuation behavior converges more slowly, with the dominant period and maximum amplitude being least affected by the details of the distribution, and the fine structure of solutions being most sensitive. Finally, we examine the consequences for population modeling, and using several examples of insect populations, conclude that although quite often a full maturation-period distribution should be incorporated in a given model, in many cases a discrete-delay approximation will suffice.     

Models for spatial polymerization dynamics of rod-like polymers

 We investigate the polymerization kinetics of rod-like polymer filaments interacting with a distribution of monomer in one spatial dimension (e.g. along a narrow tube). We consider a variety of possible cases, including competition by the filament tips for the available monomer, and behaviour analogous to “treadmilling” in which the polymer adds subunits to one end and loses them at the other end so as to maintain a constant length. Applications to biological polymers such as actin filaments and microtubules are discussed. Received: 16 March 1999