Diffusive instabilities in a one-dimensional temperature-dependent model system for a mite predator-prey interaction on fruit trees: dispersal motility and aggregative preytaxis effects

A weakly nonlinear analysis relevant to the formation of one-dimensional spatial patterns generated by diffusive instabilities is performed on a particular interaction-diffusion model for a temperature-dependent predator-prey mite system on fruit trees. The bifurcation from a uniform steady state is of a subcritical nature in a low temperature-low population interval while in a high temperature-high population one there exist temperatures for which it can be supercritical resulting in a family of parallel stripes. The occurrence of such population clumping, caused both by the predator's having a sufficient dispersal advantage and by its strongly stabilizing tendency toward preytactic aggregation lying in some critical range, may help explain the inhomogeneous ecological patterns exhibited by phytophagous arthropods found on uniformly distributed vegetation or on plants grown in monocultures.     

Spatial dispersal of species

With few exceptions, spatial heterogeneity in ecological models has been largely ignored until relatively recently. The current upsurge in interest is partly due to cross-fertilization with other disciplines, particularly mathematics. Models of species interaction in which the species disperse by diffusion are mathematically similar to those that arise in chemical reaction-diffusion systems which have been proposed as a basis for morphogenesis. Reaction/species interaction-diffusion systems have been increasingly studied mathematically in the last 15 years; this work has unearthed interesting new phenomena which have been proposed as explanations for many long-standing ecological problems involving spatial movement and heterogeneity of species. This is a very brief introduction to some of the basic results and how they impinge on ecology.     

有色环境噪音对空间异质种群动态同步性的影响

随着种群动态和空间结构研究兴趣的增加,激发了大量的有关空间同步性的理论和实验的研究工作。空间种群的同步波动现象在自然界广泛存在,它的影响和原因引起了很多生态学家的兴趣。Moran定理是一个非常重要的解释。但以往的研究大多假设环境变化为空间相关的白噪音。越来越多的研究表明很多环境变化的时间序列具有正的时间自相关性,也就是说用红噪音来描述更加合理。因此,推广经典的Moran效应来处理空间相关红噪音的情形很有必要。利用线性的二阶自回归过程的种群模型,推导了两种群空间同步性与种群动态异质性和环境变化的时间相关性(即环境噪音的颜色)之间的关系。深入分析了种群异质性和噪音颜色对空间同步性的影响。结果表明种群动态异质性不利于空间同步性,但详细的关系比较复杂。而红色噪音的同步能力体现在两方面:一方面,本身的相关性对同步性有贡献;另一方面,环境变化时间相关性可以通过改变种群密度依赖来影响同步性,但对同步性的影响并无一致性的结论,依赖于种群的平均动态等因素。这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义。     

Population structure and spatial influence of agricultural variables on Hessian fly populations in the southeastern United States

Population structure dictates the evolution of each population, and thus, the species as a whole. Incorporating spatial variables with population genetic statistics allows for greater discovery beyond traditional population genetics alone and can inform management decisions. The understanding of population structure in Hessian fly, Mayetiola destructor (Say), a pest of wheat, has been limited in the past. We scored 14 microsatellite loci from 12 collections of Hessian fly in the southeastern United States. Through Bayesian clustering analysis, we found two major populations of Hessian fly covering the entire southeastern United States. We evaluated correlations between agriculturally significant spatial variables and population genetic differentiation to test if genetic structure has an ecological component in a wheat agro-ecosystem. Our results suggest the total amount of alternative host plants in the county may be driving some genetic differentiation. Although planting date may also be influential, geographic distance, mean annual temperature, and harvested wheat for grain do not seem to be contributing factors. The ecological or spatial component to population structure, however, may be minimal compared to factors such as genetic drift.     

Instability of non-constant equilibrium solutions of a system of competition-diffusion equations

The system of interaction-diffusion equations describing competition between two species is investigated. By using a version of the Perron-Frobenius theorem of positive matrices generalized to function spaces, it is proved that any non-constant equilibrium solution of the system is unstable both under Neumann boundary conditions (for the rectangular parallelepiped domain) and under periodic conditions. It is conjectured that this result extends to convex domains, and that the simple interaction-diffusion model cannot explain spatially segregated distributions of two competing species in such domains.     

Competition for space in a heterogeneous environment

We consider effects of competition for space in a heterogeneous environment, making use of nonlinear interaction-diffusion equations. Competition for space is assumed to mean mutual repulsive interactions that force other individuals to disperse from a crowded region. In other words, we are concerned with density-dependent dispersal forced by population pressures. Spatial heterogeneity is incorporated in the growth rates, and the environment is assumed to have a favorable habitat for two populations surrounded by largely hostile regions. Space-independent migration rates are assumed. We ignore the usual density-dependence in the growth rates to focus our attention on density-dependence in the migration rates. Our main conclusion is that two populations can coexist if the interspecific repulsive forces are weaker than the intraspecific ones. It is also emphasized that density-dependent dispersal in a heterogeneous environment is not always a stabilizing agent, and that either of two populations may become extinct by competition for space. Finally, the resemblance of our results to those from Lotka-Volterra competition equations is suggested.     

Detecting clinal and balanced selection using spatial autocorrelation analysis under kin-structured migration

Recently spatial autocorrelation has been employed to infer microevolutionary processes from patterns of genetic variation. In theory, different processes should show characteristic signature correlograms; e. g., clinal selection should produce correlograms decreasing from positive to negative autocorrelation, whereas uniform balanced selection should lead to no spatial autocorrelation. The ability of a statistical method such as spatial autocorrelation analysis to distinguish between these selective regimes or even to detect departures from neutrality is dependent on the strength of the evolutionary force and the population structure. Weak selection or migration will not be apparent against the expected background of stochastic noise. Moreover, the population structure may generate sufficient stochastic variation such that even strong evolutionary forces may fail to be detected. This study uses computer simulation to examine the effects of kin-structured migration and three different selective regimes on the shape of spatial correlograms to assess the ability of this technique to detect different microevolutionary processes. Genetic variation among 8 loci is simulated in a linear set of 25 artificial populations. Kin-structured stepping-stone migration among adjacent populations is modeled; directional, balanced, and clinal selection, as well as neutral loci are considered. These experiments show that strong selection produces correlograms of the predicted shape. However, with an anthropologically reasonable population structure, considerable stochastic variation among correlograms for different alleles may still exist. This suggests the need for caution in inferring genetic process from spatial patterns. © 1994 Wiley-Liss, Inc.     

Estimating population size by spatially explicit capture–recapture

The number of animals in a population is conventionally estimated by capture–recapture without modelling the spatial relationships between animals and detectors. Problems arise with non‐spatial estimators when individuals differ in their exposure to traps or the target population is poorly defined. Spatially explicit capture–recapture (SECR) methods devised recently to estimate population density largely avoid these problems. Some applications require estimates of population size rather than density, and population size in a defined area may be obtained as a derived parameter from SECR models. While this use of SECR has potential benefits over conventional capture–recapture, including reduced bias, it is unfamiliar to field biologists and no study has examined the precision and robustness of the estimates. We used simulation to compare the performance of SECR and conventional estimators of population size with respect to bias and confidence interval coverage for several spatial scenarios. Three possible estimators for the sampling variance of realised population size all performed well. The precision of SECR estimates was nearly the same as that of the null‐model conventional population estimator. SECR estimates of population size were nearly unbiased (relative bias 0–10%) in all scenarios, including surveys in randomly generated patchy landscapes. Confidence interval coverage was near the nominal level. We used SECR to estimate the population of a species of skink Oligosoma infrapunctatum from pitfall trapping. The estimated number in the area bounded by the outermost traps differed little between a homogeneous density model and models with a quadratic trend in density or a habitat effect on density, despite evidence that the latter models fitted better. Extrapolation of trend models to a larger plot may be misleading. To avoid extrapolation, a large region of interest should be sampled throughout, either with one continuous trapping grid or with clusters of traps dispersed widely according to a probability‐based and spatially representative sampling design.     

Anisotropic patterned population synchrony in climatic gradients indicates nonlinear climatic forcing

Although climatic forcing has been suspected to be the most common cause of spatial population synchrony owing to the Moran effect, it has proved difficult to disentangle the impact of climate from other possible causes of synchrony based on population survey data. Nonlinear population responses to climatic variation may be a part of this difficulty, but they can also provide an opportunity to highlight the climate impacts through targeted survey designs. In particular, when species distribution ranges encompass consistent spatial gradients in climate (e.g. according to latitude or altitude), such gradients can be strategically included in the spatial design of population surveys as to facilitate comparisons of spatial synchrony patterns across and along the gradient. In that case, we predict that nonlinear impacts of climatic variation on population growth rates will result in anisotropic (direction specific) synchrony patterns in the sense that synchrony will drop faster with distance along the climatic gradient than across it. We provide an empirical case study to exemplify survey design and analyses. Of two sympatric species of geometrids, inhabiting an altitudinal gradient in subarctic birch forest, one (Operophtera brumata L.) showed anisotropic synchrony consistent with a strongly nonlinear sensitivity to climatic variation, whereas the other (Epirrita autumnata Bkh.) did not. These results are interpreted in light of the biological characteristics of the species.     

Scaling population responses to spatial environmental variability in advection-dominated systems

We model the spatial dynamics of an open population of organisms that disperse solely through advection in order to understand responses to multiscale environmental variability. We show that the distance over which a population responds to a localized perturbation, called the response length, can be characterized as an organisms average lifetime dispersal distance, unless there is strong density‐dependence in demographic or dispersal rates. Continuous spatial fluctuations in demographic rates at scales smaller than the response length will be largely averaged in the population distribution, whereas those in per capita emigration rates will be strongly tracked. We illustrate these results using a parameterized example to show how responses to environmental variability may differ in streams with different average current velocities. Our model suggests an approach to linking local dynamics dominated by dispersal processes to larger‐scale dynamics dominated by births and deaths.     

Slaves of the environment: the movement of herbivorous insects in relation to their ecology and genotype

The majority of insect species do not show an innate behavioural migration, but rather populations expand into favourable new habitats or contract away from unfavourable ones by random changes of spatial scale. Over the past 50 years, the scientific fascination with dramatic long-distance and directed mass migratory events has overshadowed the more universal mode of population movement, involving much smaller stochastic displacement during the lifetime of the insects concerned. This may be limiting our understanding of insect population dynamics. In the following synthesis, we provide an overview of how herbivorous insect movement is governed by both abiotic and biotic factors, making these animals essentially ''slaves of their environment''. No displaced insect or insect population can leave a resource patch, migrate and flourish, leaving descendants, unless suitable habitat and/or resources are reached during movement. This must have constrained insects over geological time, bringing about species-specific adaptation in behaviour and movements in relation to their environment at a micro- and macrogeographical scale. With insects that undergo long-range spatial displacements, e.g. aphids and locusts, there is presumably a selection against movement unless overruled by factors, such as density-dependent triggering, which cause certain genotypes within the population to migrate. However, for most insect species, spatial changes of scale and range expansion are much slower and may occur over a much longer time-scale, and are not innate (nor directed). Ecologists may say that all animals and plants are figuratively speaking ''slaves of their environments'', in the sense that their distribution is defined by their ecology and genotype. But in the case of insects, a vast number must perish daily, either out at sea or over other hostile habitats, having failed to find suitable resources and/or a habitat on which to feed and reproduce. Since many are blown by the vagaries of the wind, their chances of success are serendipitous in the extreme, especially over large distances. Hence, the strategies adopted by mass migratory species (innate pre-programmed flight behaviour, large population sizes and/or fast reproduction), which improve the chances that some of these individuals will succeed. We also emphasize the dearth of knowledge in the various interactions of insect movement and their environment, and describe how molecular markers (protein and DNA) may be used to examine the details of spatial scale over which movement occurs in relation to insect ecology and genotype.     

Understanding the interplay between density dependent birth function and maturation time delay using a reaction-diffusion population model

The present work employs a nonlocal delay reaction-diffusion model to study the impacts of the density dependent birth function, maturation time delay and population dispersal on single species dynamics (i.e., extinction, survival, extinction-survival). It is shown that the maturation time and the birth function are two major factors determining the fate of single species. Whereas the dispersal acts as a subsidiary factor that only affects the spatial patterns of population densities. When the birth function has a compensating density dependence, maturation time delay cannot destabilize the population survival at the positive equilibrium. Nevertheless, when the birth function has an over-compensating density dependence, the population densities of single species fluctuate in the spatial domain due to the increased maturation time delay. With the Allee effect and over-compensating density dependence, the increases in the maturation time may cause extinction of the single species in the entire spatial domain. The numerical simulations suggest that the solutions of the general model may temporarily remain nearby a stationary wave pulse or a stationary wavefront of the reduced model. The former indicates the survival of single species in a narrow region of the spatial domain. Whereas the latter represents the survival in the entire left-half or right-half of the spatial domain.     

Spatial distribution of limited resources and local density regulation in juvenile Atlantic salmon

1. Spatial heterogeneity of resources may influence competition among individuals and thus have a fundamental role in shaping population dynamics and carrying capacity. In the present study, we identify shelter opportunities as a limiting resource for juvenile Atlantic salmon (Salmo salar L.). Experimental and field studies are combined in order to demonstrate how the spatial distribution of shelters may influence population dynamics on both within and among population scales. 2. In closed experimental streams, fish performance scaled negatively with decreasing shelter availability and increasing densities. In contrast, the fish in open stream channels dispersed according to shelter availability and performance of fish remaining in the streams did not depend on initial density or shelters. 3. The field study confirmed that spatial variation in densities of 1-year-old juveniles was governed both by initial recruit density and shelter availability. Strength of density-dependent population regulation, measured as carrying capacity, increased with decreasing number of shelters. 4. Nine rivers were surveyed for spatial variation in shelter availability and increased shelter heterogeneity tended to decrease maximum observed population size (measured using catch statistics of adult salmon as a proxy). 5. Our studies highlight the importance of small-scale within-population spatial structure in population dynamics and demonstrate that not only the absolute amount of limiting resources but also their spatial arrangement can be an important factor influencing population carrying capacity.     

Isolation-by-time population structure in potamodromous Dourado <Emphasis Type="Italic">Salminus brasiliensis</Emphasis> in southern Brazil

Isolation-by-distance is recognized as a useful model for describing the spatial distribution of gene frequencies depending on dispersal characteristics of the species under study. However, some species may have populations that occupy the same geographic distribution during the breeding season yet reproduce at different time periods resulting in isolation-by-time (IBT). IBT may complicate investigations of spatial population structure if samples are obtained from multiple discrete time periods or may remain undiscovered if surveys are conducted with limited temporal scope. IBT has been observed in several studies of anadromous fishes (primarily salmon) as well as a few examples in taxa such as frogs, plants, birds and insects, but has not been rigorously tested in freshwater fishes. In this study, we assessed spatial and temporal genetic variation and tested for IBT in Dourado (Salminus brasiliensis), a large and commercially-important potamodromous fish species found in multiple river basins of South America. Using 11 polymorphic microsatellite loci, we estimated genetic differentiation of 317 adult Dourado collected monthly during the breeding season at three locations along the Uruguay River in southern Brazil. Analyses identified three populations that were clustered in time (i.e. early, middle and late), suggesting an IBT pattern of population structure with no significant spatial structure. Our results contribute to the mounting evidence across a wide range of taxa that suggests IBT may be more common that currently considered, even for species with very high dispersal capabilities such as potamodromous fishes.     

Invasion Waves in Populations with Excitable Dynamics

Whilst the most obvious mechanism for a biological invasion is the occupation of a new territory as a result of direct ingress by individuals of the invading population, a more subtle “invasion” may occur without significant motion of invading individuals if the population dynamics in a predator prey scenario has an “excitable” character. Here, “excitable” means that a local equilibrium state, either of coexistence of predator and prey, or of prey only, may, when disturbed by a small perturbation, switch to a new, essentially invaded state. In an invasion of this type little spatial movement of individuals occurs, but a wave of rapid change of population level nevertheless travels through the invaded territory. In this article we summarise and review recent modelling research which shows that the macroscopic features of these invasion waves depend strongly on the detailed spatial dynamics of the predator–prey relationship; the models assume simple (linear) diffusion and pursuit-evasion, represented by (non-linear) cross-diffusion, as examples. In the context of plankton population dynamics, such waves may be produced by sudden injections of nutrient and consequent rapid increase in plankton populations, brought about, for example, by the upwelling caused by a passing atmospheric low pressure system.     

Dispersal of introduced house sparrows Passer domesticus: an experiment

An important issue concerning the introduction of non-indigenous organisms into local populations is the potential of the introduced individuals to spread and interfere both demographically and genetically with the local population. Accordingly, the potential of spatial dispersal among introduced individuals compared with local individuals is a key parameter to understand the spatial and temporal dynamics of populations after an introduction event. In addition, if the variance in dispersal rate and distance is linked to individual characteristics, this may further affect the population dynamics. We conducted a large-scale experiment where we introduced 123 house sparrows from a distant population into 18 local populations without changing population density or sex ratio. Introduced individuals dispersed more frequently and over longer distances than residents. Furthermore, females had higher probability of dispersal than males. In females, there was also a positive relationship between the wing length and the probability of dispersal and dispersal distance. These results suggest that the distribution and frequency of introduced individuals may be predicted by their sex ratio as well as their phenotypic characteristics.     

Inter-specific competition from fallow deer Dama dama reduces habitat quality for the Italian roe deer Capreolus capreolus italicus

The roe deer of Mediterranean habitats in the central and southern parts of Italy has recently been recognised as a distinct subspecies, Capreolus capreolus italicus . A population of this endangered subspecies has been monitored in the Preserve of Castelporziano, near Rome, since 1988. We observed an abrupt population decline in 2000, which may severely threaten the sustainability of this population. We evaluated the hypothesis that competition by fallow deer may be a principal cause of this decline. By a new and innovative methodology, we modelled the spatial distribution of fallow deer density (FDD) in the study area to show that 1) habitat quality for roe deer was an inverse function of FDD, 2) habitat apportionment between fallow and roe deer increased as a function of FDD and – by applying structural equation modelling – 3) FDD was superior to habitat composition in explaining observed variations in home range size and probably in habitat quality for roe deer. This analysis is the first to document that inter-specific competition may influence the spatial behaviour of a deer species leading to poor phenotypic performance in the inferior competitor. We conclude that the conservation of this relict population would benefit by reducing fallow deer numbers at Castelporziano and from other measures aimed to decrease the level of inter-specific competition.     

Accounting for spatial autocorrelation from model selection to statistical inference: Application to a national survey of a diurnal raptor

Planning actions for species conservation involves working at both an ecologically meaningful spatial scale and a scale suitable for implementing management or conservation plans. Animal populations and conservation policies often operate across wide areas. Large-extent spatial datasets are thus often used, but their analyses rarely deal with problems inherent to spatial datasets such as residual spatial autocorrelation, which can bias or even reverse results. Here we propose a procedure for analysing a large-scale count dataset integrating residual spatial autocorrelation in a Generalized Linear Model framework by combining and extending previously published methods. The first step concerns the selection of the environmental variables by a modified cross-validation procedure allowing for residual spatial autocorrelation. Then the second step consists in evaluating the spatial effect of the model using a spatial filtering approach based on the variogram parameters. We apply this method to the Black kite (Milvus migrans) to estimate the distribution and population size of this species in France. We found some divergence in estimated population size between spatial and non spatial models, as well as in the distribution map. We also found that the uncertainty of the model was underestimated by the residual spatial autocorrelation. Our analysis confirms previous results, that residual spatial autocorrelation should be always accounted for, especially in conservation where false results may lead to poor management decisions.     

The effect of spatial variation for predicting aphid outbreaks

In order to improve forecasting of pest epidemics, it is important to know the spatial scale at which specific forecasts are reliable. To investigate the spatial scale of aphid outbreaks, we have developed a spatio-temporal stochastic aphid population growth model and fitted the model to empirical spatial time series of aphid population data using a Bayesian hierarchical fitting procedure. Furthermore, detailed spatial data of the initial phases of population growth were investigated in semivariograms. Our results suggest that spatial variation is low in the initial occurrence probability at a spatial scale of 10 km. Consequently, the results support the hypothesis that initial aphid population sizes and outbreaks may be predicted in fields within a 10 km radius. For farmers, this may imply that they can rely their decision of whether to spray against aphids on observations made by other nearby farmers or by the consultancy service.     

Genetic spatial structure in a butterfly metapopulation correlates better with past than present demographic structure

The Glanville fritillary butterfly ( Melitaea cinxia ) has been studied in the Åland Islands in Finland since 1991, where it occurs as a classic metapopulation in a large network of 4000 dry meadows. Much ecological work has been conducted on this species, but population genetic studies have been hampered by paucity of suitable genetic markers. Here, using single nucleotide polymorphisms and microsatellites developed for the Glanville fritillary, we examine the correspondence between the demographic and genetic spatial structures. Given the dynamic nature of the metapopulation, the current genetic spatial structure may bear a signal of past changes in population sizes and past patterns of gene flow rather than reflect the current demographic structure or landscape structure. We analyse this question with demographic data for 10 years, using the Rand index to assess the similarity between the genetic, demographic, and landscape spatial structures. Our results show that the current genetic spatial structure is better explained by the past rather than by the current demographic spatial structure or by the spatial configuration of the habitat in the landscape. Furthermore, current genetic diversity is significantly explained by past metapopulation sizes. The time lag between major demographic events and change in the genetic spatial structure and diversity has implications for the study of spatial dynamics.