Adaptive dynamics for physiologically structured population models

We develop a systematic toolbox for analyzing the adaptive dynamics of multidimensional traits in physiologically structured population models with point equilibria (sensu Dieckmann et al. in Theor. Popul. Biol. 63:309–338, 2003). Firstly, we show how the canonical equation of adaptive dynamics (Dieckmann and Law in J. Math. Biol. 34:579–612, 1996), an approximation for the rate of evolutionary change in characters under directional selection, can be extended so as to apply to general physiologically structured population models with multiple birth states. Secondly, we show that the invasion fitness function (up to and including second order terms, in the distances of the trait vectors to the singularity) for a community of N coexisting types near an evolutionarily singular point has a rational form, which is model-independent in the following sense: the form depends on the strategies of the residents and the invader, and on the second order partial derivatives of the one-resident fitness function at the singular point. This normal form holds for Lotka–Volterra models as well as for physiologically structured population models with multiple birth states, in discrete as well as continuous time and can thus be considered universal for the evolutionary dynamics in the neighbourhood of singular points. Only in the case of one-dimensional trait spaces or when N = 1 can the normal form be reduced to a Taylor polynomial. Lastly we show, in the form of a stylized recipe, how these results can be combined into a systematic approach for the analysis of the (large) class of evolutionary models that satisfy the above restrictions.      

A model of physiologically structured population dynamics with a nonlinear individual growth rate

In this article we consider a size structured population model with a nonlinear growth rate depending on the individual's size and on the total population. Our purpose is to take into account the competition for a resource (as it can be light or nutrients in a forest) in the growth of the individuals and study the influence of this nonlinear growth in the population dynamics. We study the existence and uniqueness of solutions for the model equations, and also prove the existence of a (compact) global attractor for the trajectories of the dynamical system defined by the solutions of the model. Finally, we obtain sufficient conditions for the convergence to a stationary size distribution when the total population tends to a constant value, and consider some simple examples that allow us to know something about their global dynamics.This work was partially supported by DGICYT PB90-0730-C02-01 and PB91-0497.     

Scale-dependent spatial population dynamics of gall-makers on oak

The patterns of synchrony in the population fluctuations of six species of gall‐makers on oak (Hymenoptera, Cynipidae and Diptera, Cecidomyiidae) were analyzed over a small‐scale transect (8 km) and a large‐scale transect (500 km). Gall‐maker species differed in their degree of synchrony. At the small scale some species showed synchrony among local sites, whereas at the large scale, with one exception, population fluctuations of all species were largely independent. The patterns of synchrony differed between the two spatial scales. At the small scale a considerable degree of synchrony was found among sites for two species, Cynips divisa and Neuroterus quercusbaccarum, whereas at the large scale no synchrony was seen for these species. For one species, Macrodiplosis volvens, the fluctuations were asynchronous at both the small and large scales. At the large scale, synchrony among sites was found for one species: the fluctuations of Neuroterus anthracinus were largely synchronous at both scales (i.e. over several hundred kilometers). Distance‐dependent synchronies (i.e. decreasing synchrony with increasing distance) were found for only one species, Neuroterus anthracinus. In summary, the levels of synchrony in the population fluctuations of these insects differed among species and were scale‐dependent. Scaling up from the small scale to the large scale does not seem appropriate.     

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.     

Northern Atlantic Oscillation effects on the temporal and spatial dynamics of green spruce aphid populations in the UK

1. The role of climate variability in determining the spatial and temporal patterns of numerical fluctuations is a central problem in ecology. The influence of the North Atlantic Oscillation (NAO) index on the population dynamics and spatial synchrony of the green spruce aphid Elatobium abietinum across the UK was shown. 2. Fifteen overlapping time series within the UK were analysed; we used nonparametric models for determining the feedback nonlinear structure and the climatic effects. The spatial synchrony of these populations and the relationship between synchrony and NAO was estimated. 3. From the 15 time series across the UK, 11 showed positive and significant NAO effects. In most of the cases the NAO effects were nonlinear showing strong negative effects of low values. The NAO variation improve the explained variance of the first-order feedback models in 14.5%; ranging from 0% to 48%. All data showed strong-nonlinear (concave) feedback structure. In most of the localities the explained variance by the first-order feedback was about 50-60%. 4. The spatial synchrony of the per capita growth rates and residuals is high across long distances for those populations affected by NAO. The correlation function predicts a spatial scale of synchrony of about 350-400 km for NAO influenced populations. 5. We think that simple population theoretical models describing the link between NAO fluctuations and green spruce aphid dynamics may be fundamental for predicting and simulating the consequences of different climatic scenarios of the future.     

Asymptotic behaviour of a model of hierarchically structured population dynamics

 A hierarchically structured population model with a dependence of the vital rates on a function of the population density (environment) is considered. The existence, uniqueness and the asymptotic behaviour of the solutions is obtained transforming the original non-local PDE of the model into a local one. Under natural conditions, the global asymptotical stability of a nontrivial equilibrium is proved. Finally, if the environment is a function of the biomass distribution, the existence of a positive total biomass equilibrium without a nontrivial population equilibrium is shown. Received 16 February 1996; received in revised form 16 September 1996     

Climate and spatio-temporal variation in the population dynamics of a long distance migrant, the white stork

1. A central question in ecology is to separate the relative contribution of density dependence and stochastic influences to annual fluctuations in population size. Here we estimate the deterministic and stochastic components of the dynamics of different European populations of white stork Ciconia ciconia. We then examined whether annual changes in population size was related to the climate during the breeding period (the 'tap hypothesis' sensu Saether, Sutherland & Engen (2004, Advances in Ecological Research, 35, 185 209) or during the nonbreeding period, especially in the winter areas in Africa (the 'tube hypothesis'). 2. A general characteristic of the population dynamics of this long-distance migrant is small environmental stochasticity and strong density regulation around the carrying capacity with short return times to equilibrium. 3. Annual changes in the size of the eastern European populations were correlated by rainfall in the wintering areas in Africa as well as local weather in the breeding areas just before arrival and in the later part of the breeding season and regional climate variation (North Atlantic Oscillation). This indicates that weather influences the population fluctuations of white storks through losses of sexually mature individuals as well as through an effect on the number of individuals that manages to establish themselves in the breeding population. Thus, both the tap and tube hypothesis explains climate influences on white stork population dynamics. 4. The spatial scale of environmental noise after accounting for the local dynamics was 67 km, suggesting that the strong density dependence reduces the synchronizing effects of climate variation on the population dynamics of white stork. 5. Several climate variables reduced the synchrony of the residual variation in population size after accounting for density dependence and demographic stochasticity, indicating that these climate variables had a synchronizing effect on the population fluctuations. In contrast, other climatic variables acted as desynchronizing agents. 6. Our results illustrate that evaluating the effects of common environmental variables on the spatio-temporal variation in population dynamics require estimates and modelling of their influence on the local dynamics.     

Harvesting in a resource dependent age structured Leslie type population model

We analyse the effect of harvesting in a resource dependent age structured population model, deriving the conditions for the existence of a stable steady state as a function of fertility coefficients, harvesting mortality and carrying capacity of the resources. Under the effect of proportional harvest, we give a sufficient condition for a population to extinguish, and we show that the magnitude of proportional harvest depends on the resources available to the population. We show that the harvesting yield can be periodic, quasi-periodic or chaotic, depending on the dynamics of the harvested population. For populations with large fertility numbers, small harvesting mortality leads to abrupt extinction, but larger harvesting mortality leads to controlled population numbers by avoiding over consumption of resources. Harvesting can be a strategy in order to stabilise periodic or quasi-periodic oscillations in the number of individuals of a population.     

桃一点斑叶蝉种群消长动态和空间分布型研究

研究探明了桃一点斑叶蝉Erythroneurasudra种群消长动态和空间分布型 ,结果表明 :该虫在桃园全年共出现 3个为害高峰 ,分别发生于 4月下旬、5月下旬和 8月上旬 ;该害虫在桃园中呈聚集型的负二项分布。讨论了适宜取样调查方法。     

INSTAR,a discrete event model for simulating zooplankton population dynamics

In this paper we discuss the basic principles of discrete event, individual oriented, data based modelling in ecology, and we present an application of this modelling strategy. The strategy is contrasted with some more conventional modelling strategies with respect to its purpose, its basic units and its heuristic properties.INSTAR applies this modelling strategy to the simulation of the fluctuations of the population structure and density of microcrustaceans through the year. The model encompasses one microcrustacean species at a time, and its interface with the rest of the ecosystem; it has been applied to several Cladocera and Copepoda species in a shallow eutrophic lake in the Netherlands (Vijverberg & Richter 1982a, b). Possibilities for extending the model are discussed.     

荔枝蝽田间种群消长动态及空间分布型研究

对海南省儋州地区荔枝园中荔枝蝽Tessaratoma papillosa(Drury)种群动态及空间分布进行了系统调查与分析。结果表明,在2005—2006与2008—2009年期间,荔枝蝽的产卵高峰期分别为4月与2月,若虫高峰期为3月,成虫高峰期分别为4月及7月;分析表明荔枝蝽各虫态在荔枝园中均为聚集分布,且成虫个体间相互排斥。     

Population dynamics of a phytophagous lady-beetle,Epilachna vigintioctopunctata (Fabricius), living in spatio-temporally heterogeneous habitats. III. Effects of habitat structure on population dynamics

Temporal changes in the population size of a phytophagous lady-beetle were analyzed to identify mechanisms affecting lady-beetle population dynamics at different spatial scales. The study area (15 ha) included 18 habitat patches. The major host plants were potato for first generation larvae and eggplant for second generation larvae. The habitat patches were classified into three groups according to the major host plants in each patch: P-E patches (both host plants available), P patches (potato only), and E patches (eggplant only). The winter disappearance of adults in the whole study area, and larval mortality in E patches were apparently the most important factors disturbing the overall population density. Density-dependent movement of females appeared to have the greatest stabilizing effect on the yearly fluctuation of population density. Rate of increase of female adults from the first to the second generation,R, was generally higher on eggplants in E patches than in P-E patches because the adult density of the first generation was much higher in P-E patches. The yearly fluctuation of adult density in each generation tended to be less in patches with all habitat components necessary for the full life cycle (P-E patches). However, such patches were not favorable for first generation females, as indicated by the lower rate of increase from the first to the second generation. The density and stability of lady-beetle populations is discussed in relation to habitat structure.     

Host-feeding and oviposition by parasitoids in relation to host stage: Consequences for parasitoid-host population dynamics

Among parasitoids which host-feed destructively, there is a tendency for females to partition their feeding and oviposition behaviour in relation to different host stages, feeding preferentially or exclusively on earlier host stages and ovipositing preferentially or exclusively in (or on) later ones. We explored the dynamic implications of this behaviour for parasitoid-host population dynamics, using modifications of the age-structured simulation models of Kidd and Jervis (1989, 1991). Using the new versions of the models, we compared the situation where parasitoids practice host stage discrimination with respect to feeding and oviposition, with the situation where they do not. Additionally, we examined the effects of host stage discrimination on populations by (a) having generations either discrete or overlapping, (b) varying initial age structure, (c) having varying degrees of density dependence acting on host adult mortality, and (d) varying parasitoid develoment times in relation to the length of host development. With either discrete or overlapping generations of the host population, a reduction in the parasitoid development time had a destabilizing influence on the parasitoid-host population interaction. With discrete generations stage discrimination had no effect on the risk of extinction, irrespective of either the degree of density dependence acting on the host population, or the initial age structure of the host population. When parasitoid search was uncoupled from the insect's adult energy requirements, the interaction was always unstable. With continuous generations, stage discrimination affected stability at certain parasitoid development times, but not at others. The relative lengths of parasitoid and host development times also influenced the tendency of the host population to show discrete or overlapping generations.     

Chaos and population control of insect outbreaks

We used small perturbations in adult numbers to control large fluctuations in the chaotic demographic dynamics of laboratory populations of the flour beetle Tribolium castaneum . A nonlinear mathematical model was used to identify a sensitive region of phase space where the addition of a few adult insects would result in a dampening of the life stage fluctuations. Three experimental treatments were applied: one in which perturbations were made whenever the populations were inside the sensitive region ("in-box treatment"), another where perturbations were made whenever the populations were outside the sensitive region ("out-box treatment"), and an unperturbed control. The in-box treatment caused a stabilization of insect densities at numbers well below the peak values exhibited by the out-box and control populations. This study demonstrates how small perturbations can be used to influence the chaotic dynamics of an ecological system.     

Assessing spatial coupling in complex population dynamics using mutual prediction and continuity statistics

A number of important questions in ecology involve the possibility of interactions or "coupling" among potential components of ecological systems. The basic question of whether two components are coupled (exhibit dynamical interdependence) is relevant to investigations of movement of animals over space, population regulation, food webs and trophic interactions, and is also useful in the design of monitoring programs. For example, in spatially extended systems, coupling among populations in different locations implies the existence of redundant information in the system and the possibility of exploiting this redundancy in the development of spatial sampling designs. One approach to the identification of coupling involves study of the purported mechanisms linking system components. Another approach is based on time series of two potential components of the same system and, in previous ecological work, has relied on linear cross-correlation analysis. Here we present two different attractor-based approaches, continuity and mutual prediction, for determining the degree to which two population time series (e.g., at different spatial locations) are coupled. Both approaches are demonstrated on a one-dimensional predator-prey model system exhibiting complex dynamics. Of particular interest is the spatial asymmetry introduced into the model as linearly declining resource for the prey over the domain of the spatial coordinate. Results from these approaches are then compared to the more standard cross-correlation analysis. In contrast to cross-correlation, both continuity and mutual prediction are clearly able to discern the asymmetry in the flow of information through this system.     

Unpredictable selection in a structured population leads to local genetic differentiation in evolved reaction norms

Unpredictability during development of the optimum phenotype under future selection leads to a compromise reaction norm with a slope that is shallower than the slope of the optimum reaction norm. Unpredictability of selection can lead to an evolved curved reaction norm when genetic variation for curvature is available even if the optimum reaction norm is linear. This requires asymmetry in the frequency distribution of the habitats of selection; at small population size, stochasticity in the number of individuals per selection habitat is sufficient to generate such asymmetry. Unpredictability of selection in structured populations leads to local genetic differentiation of reaction norms. The mean habitat of a subpopulation is defined as the subpopulation's focal habitat. The evolved mean reaction norm of each subpopulation is anchored at the optimum genotypic value in its focal habitat. Linear reaction norms are parallel if the conditional distribution of adults around the focal habitats is the same for each subpopulation. Adult migration and absence of zygote dispersal represents the ultimate structured population, each habitat playing the role of focal habitat. Absence of zygote dispersal requires that the flow of individuals through the habitats is used instead of the habitats’ frequencies in the prediction of the evolved reaction norm. Adult migration in absence of zygote dispersal leads to an evolved pattern of locally differentiated reaction norms with optimum genotypic value anchored in the focal habitat and, for linear reaction norms, parallel slopes.     

The demographic impact of extreme events: stochastic weather drives survival and population dynamics in a long-lived seabird

1. Most scenarios for future climate change predict increased variability and thus increased frequency of extreme weather events. To predict impacts of climate change on wild populations, we need to understand whether this translates into increased variability in demographic parameters, which would lead to reduced population growth rates even without a change in mean parameter values. This requires robust estimates of temporal process variance, for example in survival, and identification of weather covariates linked to interannual variability. 2. The European shag Phalacrocorax aristotelis (L.) shows unusually large variability in population size, and large-scale mortality events have been linked to winter gales. We estimated first-year, second-year and adult survival based on 43 years of ringing and dead recovery data from the Isle of May, Scotland, using recent methods to quantify temporal process variance and identify aspects of winter weather linked to survival. 3. Survival was highly variable for all age groups, and for second-year and adult birds process variance declined strongly when the most extreme year was excluded. Survival in these age groups was low in winters with strong onshore winds and high rainfall. Variation in first-year survival was not related to winter weather, and process variance, although high, was less affected by extreme years. A stochastic population model showed that increasing process variance in survival would lead to reduced population growth rate and increasing probability of extinction. 4. As in other cormorants, shag plumage is only partially waterproof, presumably an adaptation to highly efficient underwater foraging. We speculate that this adaptation may make individuals vulnerable to rough winter weather, leading to boom-and-bust dynamics, where rapid population growth under favourable conditions allows recovery from periodic large-scale weather-related mortality. 5. Given that extreme weather events are predicted to become more frequent, species such as shags that are vulnerable to such events are likely to exhibit stronger reductions in population growth than would be expected from changes in mean climate. Vulnerability to extreme events thus needs to be accounted for when predicting the ecological impacts of climate change.     

松突圆蚧及友恩蚜小蜂空间分布型和种群消长动态研究

通过对广东省试验林区内松突圆蚧Hemiberlesia pitysophila Takagi及其本地种寄生蜂友恩蚜小蜂Encarsia amicula Viggiani et Ren林间空间分布型和种群消长动态的调查研究发现:两者空间分布型相吻合,都为均匀分布;两者在林间全年种群消长曲线均呈"S"型变化。松突圆蚧种群密度高峰期出现在3月下旬至4月下旬,友恩蚜小蜂种群密度高峰期则分别出现在2月下旬和4月下旬至5月中旬。另外友恩蚜小蜂对松突圆蚧的寄生率全年共出现2个高峰期,分别是2月下旬和4月下旬至6月上旬。结果表明,友恩蚜小蜂和寄主松突圆蚧在林间时空发生规律具有高度一致性。