A density dependent model describing Salmo trutta population dynamics in an arborescent river network. Effects of dams and channelling

Our aim is to model the Salmo trutta population dynamics (three age-classes) in an arborescent river network (four levels, 15 patches), by considering both migrations (fast time scale) and demography (slow time scale). We study how the environmental management can influence the global population dynamics. We present a general model coupling both a linear discrete model for constant migrations and a non-linear density-dependent Leslie model for the demography, with (15 × 3) difference equations (15 patches, three age-classes). The variable aggregation method applied to discrete time models allows us to aggregate the previous model into a new one with only three equations. We assume fecundity and survival gradients with respect to the river network levels. The Salmo trutta whole population tends towards an equilibrium state depending on the environmental structure, and we show that dams have a stronger influence than channelling on this equilibrium.     

Reduction of Supercritical Multiregional Stochastic Models with Fast Migration

In this work we study the behavior of a time discrete multiregional stochastic model for a population structured in age classes and spread out in different spatial patches between which individuals can migrate. The dynamics of the population is controlled both by reproduction-survival and by migration. These processes take place at different time scales in the sense of the latter being much faster than the former. We incorporate the effect of demographic stochasticity into the population, which results in both dynamics being modelled by multitype Bienaymé–Galton–Watson branching processes. We present a multitype global model that incorporates the effect of both processes and, making use of the existence of different time scales for demography and migration, build a reduced model in which the variables correspond to the total population in each age class. We extend previous results that relate the behavior of the original and the reduced model showing that, given a large enough separation of time scales between demography and migration, we can obtain information about the behavior of the multitype global model through the study of the simpler reduced model. We concentrate on the case where the two systems are supercritical and therefore the expected number of individuals grows to infinity, and show that we can approximate the asymptotic structure of the population vector and the asymptotic population size of the original system through the study of the reduced model.     

Variables aggregation in a time discrete linear model

In this work we extend approximate aggregation methods to deal with a very general linear time discrete model. Approximate aggregation consists in describing some features of the dynamics of a general system in terms of the dynamics of a reduced system governed by a few global variables. We present a time discrete model for a structured population (i.e., the population is subdivided in subpopulations) in which we can distinguish two processes of a general nature and whose corresponding time scales are very different from each other. We transform the general system to make the global variables appear and obtain the reduced system. These global variables are, for each subpopulation, a certain linear combination of the corresponding state variables. We show that, under quite general conditions, the asymptotic behavior of the reduced system can be known in terms of the corresponding behavior for the reduced system. The general method is applied to aggregate a multiregional Leslie model in which the demographic process is supposed to be fast with respect to migration.     

Effects of altered river network connectivity on the distribution of Salmo trutta: Insights from a metapopulation model

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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。     

Behavioral choices based on patch selection: a model using aggregation methods

The aim of this work is to study the influence of patch selection on the dynamics of a system describing the interactions between two populations, generically called 'population N' and 'population P'. Our model may be applied to prey-predator systems as well as to certain host-parasite or parasitoid systems. A situation in which population P affects the spatial distribution of population N is considered. We deal with a heterogeneous environment composed of two spatial patches: population P lives only in patch 1, while individuals belonging to population N migrate between patch 1 and patch 2, which may be a refuge. Therefore they are divided into two patch sub-populations and can migrate according to different migration laws. We make the assumption that the patch change is fast, whereas the growth and interaction processes are slower. We take advantage of the two time scales to perform aggregation methods in order to obtain a global model describing the time evolution of the total populations, at a slow time scale. At first, a migration law which is independent on population P density is considered. In this case the global model is equivalent to the local one, and under certain conditions, population P always gets extinct. Then, the same model, but in which individuals belonging to population N leave patch 1 proportionally to population P density, is studied. This particular behavioral choice leads to a dynamically richer global system, which favors stability and population coexistence. Finally, we study a third example corresponding to the addition of an aggregative behavior of population N on patch 1. This leads to a more complicated situation in which, according to initial conditions, the global system is described by two different aggregated models. Under certain conditions on parameters a stable limit cycle occurs, leading to periodic variations of the total population densities, as well as of the local densities on the spatial patches.     

The importance of sampling scale in the assessment of intraspecific life-history differences in plains killifish,Fundulus zebrinus,populations (Pisces: Cyprinodontidae)

Synopsis The purpose of this study was to determine the effects of unpredictable environmental fluctuations on the demographic and genetic structure of Fundulus zebrinus populations. Collections of F. zebrinus were taken from three rivers in the Arkansas River basin: the Arkansas, Chikaskia, and Ninnescah. Fish were sampled from three sites on each river on nine collection dates throughout 1984 and 1985. Totals of 2100 fish and 6000 fish were included in electrophoretic and demographic analyses, respectively. The results of the study indicate that within a limited geographic region (i.e. within rivers) spatial differences and temporal changes in both demographic and genetic population characteristics occur frequently and are primarily stochastic. However, on a larger spatial scale (i.e. across rivers), general trends emerge for demographic and especially for genetic population characteristics. These results illustrate the importance of sampling scale for conclusions of life-history evolution in fluctuating environments. In addition, it was found that regulation of Fundulus zebrinus populations includes an important density-independent component. Stochastic demographic differences across space and changes through time and spatially and temporally heterogeneous allele frequencies, are both indicative of density-independent regulation. Variation in population parameters, both demographic and genetic, was observed between populations sampled from each river. These population differences were attributed to differences between the rivers themselves.     

Population dynamics of Salmincola salmoneus on Atlantic salmon in a northern Norwegian river

Atlantic salmon Salmo salar are often heavily infected by the gill maggot Salmincola salmoneus, but little information exists on the population dynamics of this parasite. Through a combination of in vivo field examination and laboratory analysis of gills from the Alta River S. salar population in northern Norway, we describe the population dynamics of the parasite and suggest a model for the host-parasite interactions. S. salar did not become infected with S. salmoneus until they returned to the river as first-time spawners. The infection increased rapidly until autumn, and just after spawning 96% of the spent fish (kelts) were infected with a mean intensity of 53 parasites per fish. In May, the prevalence of S. salmoneus on the descending kelts had increased to 100%, but the intensity exhibited little change. A small proportion of the adult S. salar population returned as immature to the river during autumn and had lower parasite intensities than the kelts the following spring. When the fish that had spawned previously (repeat spawners) returned from their second (or more) sea migration, they had an average infection rate of 36 S. salmoneus individuals per fish. The kelts seemed to be the main habitat for the parasite during winter and spring, and they stay long enough in the river to pass the infection to maiden S. salar that enter the river early in summer. These fish then became a source of infection for the maiden fish entering the river later. However, in years that have a possible mismatch between the opposite migration of kelts and maiden S. salar, the immature fall-running and returning repeat spawners will be crucial for maintaining the parasite population. We hypothesize that heavily infected S. salar may suffer reduced growth and survival at sea, potentially reducing the abundance of repeat spawners.     

Effects of branching spatial structure and life history on the asymptotic growth rate of a population

The dendritic structure of a river network creates directional dispersal and a hierarchical arrangement of habitats. These two features have important consequences for the ecological dynamics of species living within the network. We apply matrix population models to a stage-structured population in a network of habitat patches connected in a dendritic arrangement. By considering a range of life histories and dispersal patterns, both constant in time and seasonal, we illustrate how spatial structure, directional dispersal, survival, and reproduction interact to determine population growth rate and distribution. We investigate the sensitivity of the asymptotic growth rate to the demographic parameters of the model, the system size, and the connections between the patches. Although some general patterns emerge, we find that a species’ modes of reproduction and dispersal are quite important in its response to changes in its life history parameters or in the spatial structure. The framework we use here can be customized to incorporate a wide range of demographic and dispersal scenarios.     

Approximate reduction of multiregional models with environmental stochasticity

In this work we extend previous results regarding the use of approximate aggregation techniques to simplify the study of discrete time models for populations that live in an environment that changes randomly with time. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter. We present the reduction of a stochastic multiregional model in which the population, structured by age and spatial location, lives in a random environment and in which migration is fast with respect to demography. However, the technique works in much more general settings as, for example, those of stage-structured populations living in a multipatch environment. By manipulating the original system and appropriately defining the global variables we obtain a simpler system. The paper concentrates on establishing relationships between the original and the reduced systems for a given separation of time scales between the two processes. In particular, we relate the original state variables and the global variables and, in the case the pattern of temporal variation is Markovian, we relate the presence of strong stochastic ergodicity for the original and reduced systems. Moreover, we relate different measures of asymptotic population growth for these systems.     

Spatial synchrony in population fluctuations: extending the Moran theorem to cope with spatially heterogeneous dynamics

The recent interest in the spatial structure and dynamics of populations motivated numerous theoretical and empirical studies of spatial synchrony, the tendency of populations to fluctuate in unison over regional areas. The first comprehensive framework applied to spatial synchrony was probably the one elaborated by P. A. P. Moran back in 1953. He suggested that if two populations have the same linear density-dependent structure, the correlation between them will be equal to that between the local density-independent conditions. Surprisingly, the consequences of violating the assumption that the dynamics of the populations are identical has received little attention. In this paper, making the assumption that population dynamics can be described by linear and stationary autoregressive processes, I show that the observed spatial synchrony between two populations can be decomposed into two multiplicative components: the demographic component depending on the values of the autoregressive coefficients, and the correlation of the environmental noise. The Moran theorem corresponds to the special case where the demographic component equals unity. Using published data, I show that the spatial variability in population dynamics may substantially contribute to the spatial variability of population synchrony, and thus should not be neglected in future studies.     

Common bottlenose dolphin (Tursiops truncatus) social structure and distribution changes following the 2008 Unusual Mortality Event in the Indian River Lagoon,Florida

In animal societies with fission-fusion dynamics, demographic disturbances can influence the social and spatial structure of the population. Within the Indian River Lagoon (IRL), Florida, common bottlenose dolphins (Tursiops truncatus) have experienced recurrent unusual mortality events (UMEs) providing an opportunity to examine postdisturbance population and social cluster restructuring. This study investigates the impact of the potentially nonepizootic 2008 UME on the IRL dolphin population. Photo-identification surveys conducted from August 2006 to May 2010 were stratified into pre- (August 2006–April 2008) and post-UME (September 2008–May 2010) time periods. Social network and spatial (univariate kernel density) analyses were limited to individuals sighted 5+ times per period (pre-UME = 183, post-UME = 134), and indicated a change from 11 to ten social clusters, although individuals did not always reassociate with pre-UME cluster associates. Despite the social and spatial disconnect between IRL proper and Mosquito Lagoon clusters, both network density and core area spatial overlap increased post-UME allowing for increased intercluster interactions. However, intracluster associations increased as well, allowing the population to maintain multiple social clusters within a loosely connected network. This study shows the important role sociality may play in the adaptability of cetaceans to environmental and demographic changes.     

Local population dynamics and the impact of scale and isolation: a study on different little owl populations

The understanding of how variation of demographic rates translates into variation of population growth is a central aim in population ecology. Besides stochastic and deterministic factors, the spatial extent and the isolation of a local population may have an impact on the contribution of the different demographic components. Using long-term demographic data we performed retrospective population analyses of four little owl ( Athene noctua ) populations with differential spatial extent and degree of isolation to assess the contribution of demographic rates to the variation of the growth rate (λ) of each local population and to the difference of λ among populations. In all populations variation of fecundity contributed least to variation of λ, and variation of adult survival contributed most to variation of λ in three of four populations. Between population comparisons revealed that differences mainly stem from differences of immigration and juvenile local survival. The relative importance of immigration to λ tended to decrease with increasing spatial extent and isolation of the local populations. None of the four local populations was self-sustainable. Because the local populations export and import individuals, they can be considered as open recruitment systems in which part of the recruited breeding birds are not produced locally. The spatial extent and the degree of isolation of a local population have an impact on local population dynamics; hence these factors need to be considered in studies about local population dynamics and for deriving conservation measures.     

Estimating demographic models for the range dynamics of plant species

Aims To better understand how demographic processes shape the range dynamics of woody plants (in this case, Proteaceae), we introduce a likelihood framework for fitting process‐based models of range dynamics to spatial abundance data. Location The fire‐prone Fynbos biome (Cape Floristic Region, South Africa). Methods Our process‐based models have a spatially explicit demographic submodel (describing dispersal, reproduction, mortality and local extinction) as well as an observation submodel (describing imperfect detection of individuals), and are constrained by species‐specific predictions of habitat distribution models and process‐based models for seed dispersal by wind. Free model parameters were varied to find parameter sets with the highest likelihood. After testing this approach with simulated data, we applied it to eight Proteaceae species that differ in breeding system (monoecy versus dioecy) and adult fire survival. We assess the importance of Allee effects and negative density dependence for range dynamics, by using the Akaike information criterion to select between alternative models fitted for the same species. Results The best model for all dioecious study species included Allee effects, whereas this was true for only one of four monoecious species. As expected, sprouters (in which adults survive fire) were estimated to have lower rates of reproduction and catastrophic population extinction than related non‐sprouters. Overcompensatory population dynamics seem important for three of four non‐sprouters. We also found good quantitative agreement between independent data and most estimates of reproduction, carrying capacity and extinction probability. Main conclusions This study shows that process‐based models can quantitatively describe how large‐scale abundance distributions arise from the movement and interaction of individuals. It stresses links between the life history, demography and range dynamics of Proteaceae: dioecious species seem more susceptible to Allee effects which reduce migration ability and increase local extinction risk, and sprouters seem to have high persistence of established populations, but their low reproduction limits habitat colonization and migration.     

Interplay between ecological, behavioural and historical factors in shaping the genetic structure of sympatric walleye populations (Sander vitreus)

Disentangling ecological, behavioural and evolutionary factors responsible for the presence of stable population structure within wild populations has long been challenging to population geneticists. This study primarily aimed at decoding population structure of wild walleye (Sander vitreus) populations of Mistassini Lake (Québec, Canada) in order to define source populations to be used for the study of spatial partitioning using individual-based multilocus assignment methods, and decipher the dynamics of individual dispersal and resulting patterns of spatial resource partitioning and connectivity among populations. A second objective was to elucidate the relationships between biological characteristics (sex, size, age and population of origin) and an individual's probability to migrate and/or disperse. To do so, a total of 780 spawning individuals caught on five distinct spawning sites, and 1165 postspawning individuals, captured over two sampling seasons (2002-2003) were analysed by means of eight microsatellite loci. Four temporally stable walleye populations associated with distinct reproductive grounds were detected. These populations were differentially distributed among lake sectors during their feeding migration and their spatial distribution was stable over the two sampling seasons. Dispersing individuals were identified (n=61); these revealed asymmetrical patterns of dispersal between populations, which was also confirmed by divergent admixture proportions. Regression models underlined population of origin as the only factor explaining differential dispersal of individuals among populations. An analysis of covariance (ancova) indicated that larger individuals tended to migrate from their river of origin further away in the lake relative to smaller fish. In summary, this study underlined the relevance of using individual-based assignment methods for deciphering dynamics of connectivity among wild populations, especially regarding behavioural mechanisms such as differential spatial partitioning and dispersal responsible for the maintenance of genetic population structure.     

The extended Moran effect and large-scale synchronous fluctuations in the size of great tit and blue tit populations

1. Synchronous fluctuations of geographically separated populations are in general explained by the Moran effect, i.e. a common influence on the local population dynamics of environmental variables that are correlated in space. Empirical support for such a Moran effect has been difficult to provide, mainly due to problems separating out effects of local population dynamics, demographic stochasticity and dispersal that also influence the spatial scaling of population processes. Here we generalize the Moran effect by decomposing the spatial autocorrelation function for fluctuations in the size of great tit Parus major and blue tit Cyanistes caeruleus populations into components due to spatial correlations in the environmental noise, local differences in the strength of density regulation and the effects of demographic stochasticity. 2. Differences between localities in the strength of density dependence and nonlinearity in the density regulation had a small effect on population synchrony, whereas demographic stochasticity reduced the effects of the spatial correlation in environmental noise on the spatial correlations in population size by 21.7% and 23.3% in the great tit and blue tit, respectively. 3. Different environmental variables, such as beech mast and climate, induce a common environmental forcing on the dynamics of central European great and blue tit populations. This generates synchronous fluctuations in the size of populations located several hundred kilometres apart. 4. Although these environmental variables were autocorrelated over large areas, their contribution to the spatial synchrony in the population fluctuations differed, dependent on the spatial scaling of their effects on the local population dynamics. We also demonstrate that this effect can lead to the paradoxical result that a common environmental variable can induce spatial desynchronization of the population fluctuations. 5. This demonstrates that a proper understanding of the ecological consequences of environmental changes, especially those that occur simultaneously over large areas, will require information about the spatial scaling of their effects on local population dynamics.     

珠江水系鱼类群落多样性空间分布格局

珠江是我国南方第一大河,是我国重要淡水渔业生产基地和水生生物资源基因库。珠江鱼类在维持生物多样性、提供鱼类种质资源方面举足轻重。但是到目前为止,关于其鱼类空间分布格局的研究甚少。特别是近几十年来各种水工建设和过度捕捞使得渔业资源急剧衰退,鱼类空间分布的研究显得尤为重要。2015年对珠江全流域13个站位进行了全面调查,共采集渔获物10119尾,隶属于94种72属17科。鲤科鱼类占显著优势,其次种类较多的依次为鲿科、鳅科。采用非度量多维标度排序(NMDS)方法对鱼类群落空间分布特征进行了分析,结果表明珠江鱼类被划分为3个类群,即以餐、南方拟餐、黄颡鱼等小型鱼类为主的中上游类群、以赤眼鳟、鲮鱼、广东鲂等中型鱼类为主的中下游类群和以罗非鱼为主的重要支流类群。同时发现中下游物种多样性高,上游及河口江段多样性低的格局。采用冗余分析方法(RDA)分析了鱼类多样性与环境因子的关系,发现年均气温、降雨量、年均径流量、河流宽度与透明度是珠江水系河流鱼类群落结构差异的主要影响因子,其中年均气温是影响鱼类群落分布的最关键因子之一。与历史资料对比后发现,珠江鱼类种类明显减少、空间分布也发生了巨大改变。研究是珠江水系野生渔业资源长期调查的一部分,研究结果将对渔业资源的多样性保护和可持续利用具有指导意义。     

Individual variation in migration speed of upriver-migrating sockeye salmon in the Fraser River in relation to their physiological and energetic status at marine approach

Little research has examined individual variation in migration speeds of Pacific salmon (Oncorhynchus spp.) in natural river systems or attempted to link migratory behavior with physiological and energetic status on a large spatial scale in the wild. As a model, we used three stocks of summer-run sockeye salmon (Oncorhynchus nerka) from the Fraser River watershed, British Columbia, to test the hypothesis that individual variation in migration speed is determined by a combination of environmental factors (i.e., water temperature), intrinsic biological differences (sex and population), and physiological and energetic condition. Before the freshwater portion of the migration, sockeye salmon (Quesnel, Chilcotin, and Nechako stock complexes) were captured in Johnstone Strait ( approximately 215 km from river entry), gastrically implanted with radio transmitters, and sampled for blood, gill tissue, and energetic status before release. Analyses focused solely on individuals that successfully reached natal subwatersheds. Migration speeds were assessed by an extensive radiotelemetry array. Individuals from the stock complex that migrated the longest distance (Nechako) traveled at speeds slower than those of other stock complexes. Females traveled slower than males. An elevated energetic status of fish in the ocean was negatively correlated with migration speed in most river segments. During the transition from the ocean to the river, migration speed was negatively correlated with mean maximum water temperature; however, for the majority of river segments, it was positively correlated with migration speed. Physiological status measured in the ocean did not explain among-individual variability in river migration speeds. Collectively, these findings suggest that there could be extensive variation in migration behavior among individuals, sexes, and populations and that physiological condition in the ocean explained little of this variation relative to in-river environmental conditions and energetic status. Interestingly, individual fish generally retained their rank in swimming speed across different segments, except when transiting a challenging canyon midway during the migration.     

Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models

In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of ‘global’ variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.     

The reliability of approximate reduction techniques in population models with two time scales

As a result of the complexity inherent in some natural systems, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often find multiregional models for structured populations in which individuals are classified regarding their age and their spatial location. Dealing with such structured populations leads to high dimensional models. Moreover, in many instances the dynamics of the system is controlled by processes whose time scales are very different from each other. For example, in multiregional models migration is often a fast process in comparison to the growth of the population.Approximate reduction techniques take advantage of the presence of different time scales in a system to introduce approximations that allow one to transform the original system into a simpler low dimensional system. In this way, the dynamics of the original system can be approximated in terms of that of the reduced system. This work deals with the study of that approximation. In particular, we work with a non-autonomous discrete time model previously presented in the literature and obtain different bounds for the error we incur when we describe the dynamics of the original system in terms of the reduced one.The results are illustrated by some numerical simulations corresponding to the reduction of a Leslie type model for a population structured in two age classes and living in a two patch system.