On an extension of R.A. Fisher's result on the dynamics of the reproductive value

A classical result by Fisher concerning reproductive value dynamics is extended to the case of varying vital rates with a constant cohort Lotka's r. Based on the demographic potential approach, a generalization of the concept of reproductive value is introduced, which exhibits exponential dynamics both in the classical case of constant vital rates and in a wider class of populations. The generalized reproductive value introduced in this paper fits the classical interpretation by Fisher as a discounted sum of future births in the general class of models addressed here. Our results show when Fisher's classical results may be used as good approximations. They could also be of importance for estimating the fitness of biological populations, aggregate population modeling, and studying the long-term consequences of varying vital rates.     

The reproductive value in distributed optimal control models

We show that in a large class of distributed optimal control models (DOCM), where population is described by a McKendrick type equation with an endogenous number of newborns, the reproductive value of Fisher shows up as part of the shadow price of the population. Depending on the objective function, the reproductive value may be negative. Moreover, we show results of the reproductive value for changing vital rates. To motivate and demonstrate the general framework, we provide examples in health economics, epidemiology, and population biology.     

The relative importance of reproduction and survival for the conservation of two dolphin populations

It has been proposed that in slow‐growing vertebrate populations survival generally has a greater influence on population growth than reproduction. Despite many studies cautioning against such generalizations for conservation, wildlife management for slow‐growing populations still often focuses on perturbing survival without careful evaluation as to whether those changes are likely or feasible. Here, we evaluate the relative importance of reproduction and survival for the conservation of two bottlenose dolphin (Tursiops cf aduncus) populations: a large, apparently stable population and a smaller one that is forecast to decline. We also assessed the feasibility and effectiveness of wildlife management objectives aimed at boosting either reproduction or survival. Consistent with other analytically based elasticity studies, survival had the greatest effect on population trajectories when altering vital rates by equal proportions. However, the findings of our alternative analytical approaches are in stark contrast to commonly used proportional sensitivity analyses and suggest that reproduction is considerably more important. We show that

相似文献   

Bayesian Estimates of Transition Probabilities in Seven Small Lithophytic Orchid Populations: Maximizing Data Availability from Many Small Samples

Predicting population dynamics for rare species is of paramount importance in order to evaluate the likelihood of extinction and planning conservation strategies. However, evaluating and predicting population viability can be hindered from a lack of data. Rare species frequently have small populations, so estimates of vital rates are often very uncertain due to lack of data. We evaluated the vital rates of seven small populations from two watersheds with varying light environment of a common epiphytic orchid using Bayesian methods of parameter estimation. From the Lefkovitch matrices we predicted the deterministic population growth rates, elasticities, stable stage distributions and the credible intervals of the statistics. Populations were surveyed on a monthly basis between 18–34 months. In some of the populations few or no transitions in some of the vital rates were observed throughout the sampling period, however, we were able to predict the most likely vital rates using a Bayesian model that incorporated the transitions rates from the other populations. Asymptotic population growth rate varied among the seven orchid populations. There was little difference in population growth rate among watersheds even though it was expected because of physical differences as a result of differing canopy cover and watershed width. Elasticity analyses of Lepanthes rupestris suggest that growth rate is more sensitive to survival followed by growth, shrinking and the reproductive rates. The Bayesian approach helped to estimate transition probabilities that were uncommon or variable in some populations. Moreover, it increased the precision of the parameter estimates as compared to traditional approaches.     

Spatial covariation of fish population vital rates in a stream network

Animal populations are spatially structured in heterogeneous landscapes, in which local patches with differing vital rates are connected by dispersal of individuals to varying degrees. Although there is evidence that vital rates differ among local populations, much less is understood about how vital rates covary among local patches in spatially heterogeneous landscapes. In this study, we conducted a nine-year annual mark–recapture survey to characterize spatial covariation of survival and growth for two Japanese native salmonids, white-spotted charr Salvelinus leucomaenis japonicus and red-spotted masu salmon Oncorhynchus masou ishikawae, in a headwater stream network composed of distinctly different tributary and mainstem habitats. Spatial structure of survival and growth differed by species and age class, but results provided support for negative covariation between vital rates, where survival was higher in the tributary habitat but growth was higher in the mainstem habitat. Thus, neither habitat was apparently more important than the other, and local habitats with complementary vital rates may make this spatially structured population less vulnerable to environmental change (i.e. portfolio effect). Despite the spatial structure of vital rates and possibilities that fish can exploit spatially distributed resources, movement of fish was limited due partly to a series of low-head dams that prevented upstream movement of fish in the study area. This study shows that spatial structure of vital rates can be complex and depend on species and age class, and this knowledge is likely paramount to elucidating dynamics of spatially structured populations.     

Multiple attractors,catastrophes and chaos in seasonally perturbed predator-prey communities

A classical predator-prey model is considered in this paper with reference to the case of periodically varying parameters. Six elementary seasonality mechanisms are identified and analysed in detail by means of a continuation technique producing complete bifurcation diagrams. The results show that each elementary mechanism can give rise to multiple attractors and that catastrophic transitions can occur when suitable parameters are slightly changed. Moreover, the two classical routes to chaos, namely, torus destruction and cascade of period doublings, are numerically detected. Since in the case of constant parameters the model cannot have multiple attractors, catastrophes and chaos, the results support the conjecture that seasons can very easily give rise to complex populations dynamics.     

Estimating fluctuating selection in age-structured populations

In age-structured populations, viability and fecundity selection of varying strength may occur in different age classes. On the basis of an original idea by Fisher of weighting individuals by their reproductive value, we show that the combined effect of selection on traits at different ages acts through the individual reproductive value defined as the stochastic contribution of an individual to the total reproductive value of the population the following year. The selection differential is a weighted sum of age-specific differentials that are the covariances between the phenotype and the age-specific relative fitness defined by the individual reproductive value. This enables estimation of weak selection on a multivariate quantitative character in populations with no density regulation by combinations of age-specific linear regressions of individual reproductive values on the traits. Demographic stochasticity produces random variation in fitness components in finite samples of individuals and affects the statistical inference of the temporal average directional selection as well as the magnitude of fluctuating selection. Uncertainties in parameter estimates and test power depend strongly on the demographic stochasticity. Large demographic variance results in large uncertainties in yearly estimates of selection that complicates detection of significant fluctuating selection. The method is illustrated by an analysis of age-specific selection in house sparrows on a fitness-related two-dimensional morphological trait, tarsus length and body mass of fledglings.     

Effect of reproductive modes and environmental heterogeneity in the population dynamics of a geographically widespread clonal desert cactus

The dynamics of plant populations in arid environments are largely affected by the unpredictable environmental conditions and are fine-tuned by biotic factors, such as modes of recruitment. A single species must cope with both spatial and temporal heterogeneity that trigger pulses of sexual and clonal establishment throughout its distributional range. We studied two populations of the clonal, purple prickly pear cactus, Opuntia macrocentra, in order to contrast the factors responsible for the population dynamics of a common, widely distributed species. The study sites were located in protected areas that correspond to extreme latitudinal locations for this species within the Chihuahuan Desert. We studied both populations for four consecutive years and determined the demographic consequences of environmental variability and the mode of reproduction using matrix population models, life table response experiments (LTREs), and loop and perturbation analyses. Although both populations seemed fairly stable (population growth rate, λ∼1), different demographic parameters and different life cycle routes were responsible for this stability in each population. In the southernmost population (MBR) LTRE and loop and elasticity analyses showed that stasis is the demographic process with the highest contributions to λ, followed by sexual reproduction, and clonal propagation contributed the least. The northern population (CR) had both higher elasticities and larger contributions of stasis, followed by clonal propagation and sexual recruitment. Loop analysis also showed that individuals in CR have more paths to complete a life cycle than those in MBR. As a consequence, each population differed in life history traits (e.g., size class structure, size at sexual maturity, and reproductive value). Numerical perturbation analyses showed a small effect of the seed bank on the λ of both populations, while the transition from seeds to seedlings had an important effect mainly in the northern population. Clonal propagation (higher survival and higher contributions to vital rates) seems to be more important for maintaining populations over long time periods than sexual reproduction.     

Iteroparous reproduction strategies and population dynamics

Asymptotic relationships between a class of continuous partial differential equation population models and a class of discrete matrix equations are derived for iteroparous populations. First, the governing equations are presented for the dynamics of an individual with juvenile and adult life stages. The organisms reproduce after maturation, as determined by the juvenile period, and at specific equidistant ages, which are determined by the iteroparous reproductive period. A discrete population matrix model is constructed that utilizes the reproductive information and a density-dependent mortality function. Mortality in the period between two reproductive events is assumed to be a continuous process where the death rate for the adults is a function of the number of adults and environmental conditions. The asymptotic dynamic behaviour of the discrete population model is related to the steady-state solution of the continuous-time formulation. Conclusions include that there can be a lack of convergence to the steady-state age distribution in discrete event reproduction models. The iteroparous vital ratio (the ratio between the maximal age and the reproductive period) is fundamental to determining this convergence. When the vital ratio is rational, an equivalent discrete-time model for the population can be derived whose asymptotic dynamics are periodic and when there are a finite number of founder cohorts, the number of cohorts remains finite. When the ratio is an irrational number, effectively there is convergence to the steady-state age distribution. With a finite number of founder cohorts, the number of cohorts becomes countably infinite. The matrix model is useful to clarify numerical results for population models with continuous densities as well as delta measure age distribution. The applicability in ecotoxicology of the population matrix model formulation for iteroparous populations is discussed.     

Eco-evolutionary vs. habitat contributions to invasion in salmon: experimental evaluation in the wild

Although trait evolution over contemporary timescales is well documented, its influence on ecological dynamics in the wild has received much less attention particularly compared to traditional ecological and environmental factors. For example, evolution over ecologically relevant timescales is expected in populations that colonize new habitats, where it should theoretically enhance fitness, associated vital rates of survival and reproduction, and population growth potential. Nonetheless, success of exotic species is much more commonly attributed to ecological aspects of habitat quality and 'escape from enemies' in the invaded range. Here, we consider contemporary evolution of vital rates in introduced Chinook salmon (Oncorhynchus tshawytscha) that quickly colonized New Zealand and diverged over c. 26 generations. By using experimental translocations, we partitioned the roles of evolution and habitat quality in modifying geographical patterns of vital rates. Variation in habitat quality within the new range had the greatest influence on broad geographical patterns of vital rates, but locally adapted salmon still exhibited more than double the vital rate performance, and hence fitness, of nonlocal counterparts. The scope of this fitness evolution far exceeds the scale of divergence in trait values for these populations, or even the expected fitness effects of particular traits. These results suggest that contemporary evolution can be an important part of the eco-evolutionary dynamics of invasions and highlight the need for studies of the emergent fitness and ecological consequences of such evolution, rather than just changes in trait values.     

Demography of greater prairie-chickens: Regional variation in vital rates,sensitivity values,and population dynamics

Intensification of rangeland management has coincided with population declines among obligate grassland species in the largest remaining tallgrass prairie in North America, although causes of declines remain unknown. We modeled population dynamics and conducted sensitivity analyses from demographic data collected for an obligate grassland bird that is an indicator species for tallgrass prairie, the greater prairie-chicken (Tympanuchus cupido), during a 4-year study in east-central Kansas, USA. We examined components of reproductive effort and success, juvenile survival, and annual adult female survival for 3 populations of prairie-chickens across an ecological gradient of human landscape alteration and land use. We observed regional differences in reproductive performance, survivorship, and population dynamics. All 3 populations of prairie-chickens were projected to decline steeply given observed vital rates, but rates of decline differed across a gradient of landscape alteration, with the greatest declines in fragmented landscapes. Elasticity values, variance-scaled sensitivities, and contribution values from a random-effects life-table response experiment all showed that the finite rate of population change was more sensitive to changes in adult survival than other demographic parameters in our declining populations. The rate of population change was also sensitive to nest survival at the most fragmented and least intensively grazed study site; suggesting that patterns of landscape fragmentation and land use may be affecting the relative influences of underlying vital rates on rates of population growth. Our model results indicate that 1) populations of prairie-chickens in eastern Kansas are unlikely to be viable without gains from immigration, 2) rates of population decline vary among areas under different land management practices, 3) human land-use patterns may affect the relative influences of vital rates on population trajectories, and 4) anthropogenic effects on population demography may influence the regional life-history strategies of a short-lived game bird. © 2012 The Wildlife Society.     

Accounting for stochasticity in demographic compensation along the elevational range of an alpine plant

Demographic compensation arises when vital rates change in opposite directions across populations, buffering the variation in population growth rates, and is a mechanism often invoked to explain the stability of species geographic ranges. However, studies on demographic compensation have disregarded the effects of temporal variation in vital rates and their temporal correlations, despite theoretical evidence that stochastic dynamics can affect population persistence in temporally varying environments. We carried out a seven‐year‐long demographic study on the perennial plant Arabis alpina (L.) across six populations encompassing most of its elevational range. We discovered demographic compensation in the form of negative correlations between the means of plant vital rates, but also between their temporal coefficients of variation, correlations and elasticities. Even if their contribution to demographic compensation was small, this highlights a previously overlooked, but potentially important, role of stochastic processes in stabilising population dynamics at range margins.     

Generalized population models and the nature of genetic drift

The Wright–Fisher model of allele dynamics forms the basis for most theoretical and applied research in population genetics. Our understanding of genetic drift, and its role in suppressing the deterministic forces of Darwinian selection has relied on the specific form of sampling inherent to the Wright–Fisher model and its diffusion limit. Here we introduce and analyze a broad class of forward-time population models that share the same mean and variance as the Wright–Fisher model, but may otherwise differ. The proposed class unifies and further generalizes a number of population-genetic processes of recent interest, including the Λ and Cannings processes. Even though these models all have the same variance effective population size, they encode a rich diversity of alternative forms of genetic drift, with significant consequences for allele dynamics. We characterize in detail the behavior of standard population-genetic quantities across this family of generalized models. Some quantities, such as heterozygosity, remain unchanged; but others, such as neutral absorption times and fixation probabilities under selection, deviate by orders of magnitude from the Wright–Fisher model. We show that generalized population models can produce startling phenomena that differ qualitatively from classical behavior — such as assured fixation of a new mutant despite the presence of genetic drift. We derive the forward-time continuum limits of the generalized processes, analogous to Kimura’s diffusion limit of the Wright–Fisher process, and we discuss their relationships to the Kingman and non-Kingman coalescents. Finally, we demonstrate that some non-diffusive, generalized models are more likely, in certain respects, than the Wright–Fisher model itself, given empirical data from Drosophila populations.     

The structure and dynamics of woodreed Calamagrostis canescens population: a modelling approach

A scale of ontogenetic states has been developed for woodreed Calamagrostis canescens, a perennial species dominating the grass layer of fell forest areas. The population structure is considered as a set of age-stage groups of individuals differing both in the ontogenetic stage and the chronological age measured in years. to describe the dynamics through years a special kind of matrix formalism has been proposed which is reducible neither to the classic Leslie matrix for an age-structured population, nor to the well-known Lefkovitch matrix for a stage-structured one, and which does not suffer from excessiveness of the "two-dimensional" representation for the structure implying the projection matrix of a block pattern. It has been shown however that the protection matrix corresponding to C. canescens life-history graph embodies the canonical features of matrix formalism for structured population dynamics, such as the exponential population growth or decline, the convergence to a stable equilibrium structure, the calculable indicator of growth/decline/equilibrium (i.e., a measure of the population reproductive potential) as well as possibility to determine the relative reproductive value of each group. On the other hand, "left-sidedness of the age spectrum", a property that is often observed in real populations and is inherent in Leslie models of growing populations, may fail in the age-stage-structured model. The aggregation of age-stage groups into the age classes is possible only under special strict relationship among the age-stage-specific vital rates of the population. The both circumstances serve a methodical indication that an additional dimension such as the stages, for example, ought to be introduced into the age structure of the model population.     

Plant performance in central and northern peripheral populations of the widespread Plantago coronopus

Peripheral populations have long been predicted to show lower vital rates, higher demographic fluctuations, and lower densities than central populations. However, recent research has questioned the existence of clear patterns across species’ ranges. To test these hypotheses, we monitored five central and six northern peripheral populations of the widespread herb Plantago coronopus along the European Atlantic coast during 5 yr. We estimated population density, and calculated mean values and temporal variability of four vital rates (survival, individual growth, fecundity and recruitment) in hundreds of plants in permanent plots. Central populations showed higher fecundity, whereas peripheral populations had higher recruitment per reproductive plant, indicating a higher overall reproductive success in the periphery. Central populations showed a marginally significant tendency for higher growth, and there were no differences between range positions in survival. Fecundity and growth were affected by intraspecific competition, and recruitment was affected by precipitation, highlighting the importance of local environmental conditions for population performance. Central and peripheral populations showed no significant differences in temporal variability of vital rates. Finally, density was significantly higher in peripheral than in central populations, in discrepancy with the abundant‐centre model. Density was correlated to seedling recruitment, which would counterbalance in peripheral populations the lower fecundity and the tendency for lower growth of established plants. Such compensations among vital rates might be particularly common in widespread plants, and advise against simplistic assumptions of population performance across ranges. The whole species’ life cycle should be considered, since different arrangements of vital rates are expected to maximize fitness in local environments. Our results show also the importance of discerning between geographical periphery and ecological marginality. In a context of climate‐induced range shifts, these considerations are crucial for the reliability of niche‐models and the management of plant peripheral populations.     

On the stability of separable solutions of a sexual age-structured population dynamics model

The Sharpe-Lotka-McKendrick-von Foerster equations for non-dispersing age-sex-structured populations with a harmonic mean type mating law are considered and their separable solutions are analysed. For certain forms of the demographic rates the underlying evolution equations are reduced to systems of ODEs, the long time behavior of their solutions is studied, and the stability of separable solutions is discussed. It is found that for the constant death rates and constant sex ratio of newborns with stationary birth rates this model admits one one-parameter class of separable solutions, two such classes (repeated or different) or no such ones. In the case of special forms of age-dependent birth rates, solutions of one of these two different classes corresponding to the greater root of the characteristic equation are locally stable, solutions of the other one corresponding to the smaller root are unstable, and the population dies out if the model does not admit separable solutions or if initial densities of newborns are small enough in the case of the existence of separable solutions. In the case of constant vital rates, the model has no separable solutions or admits only one class of such ones that are globally stable.     

Demography in relation to population density in two herbivorous marsupials: testing for source–sink dynamics versus independent regulation of population size

We compared demography of populations along gradients of population density in two medium-sized herbivorous marsupials, the common brushtail possum Trichosurus vulpecula and the rufous bettong Aepyprymnus rufescens, to test for net dispersal from high density populations (acting as sources) to low density populations (sinks). In both species, population density was positively related to soil fertility, and variation in soil fertility produced large differences in population density of contiguous populations. We predicted that if source–sink dynamics were operating over this density gradient, we should find higher immigration rates in low-density populations, and positive relationships of measures of individual fitness—body condition, reproductive output, juvenile growth rates and survivorship—to population density. This was predicted because under source–sink dynamics, immigration from high-density sites would hold population density above carrying capacity in low-density sites. The study included 13 populations of these two species, representing a more than 50-fold range of density for each species, but we found that individual fitness, immigration rates and population turnover were similar in all populations. We conclude that net dispersal from high to low density populations had little influence on population dynamics in these species; rather, all populations appeared to be independently regulated at carrying capacity, with a balanced exchange of dispersers among populations. These two species have suffered recent reductions in range, and they are ecologically similar to other species that have declined to extinction in inland Australia. It has been argued that part of the cause of the vulnerability of species like these is that they exhibit source–sink dynamics, and disturbance to source habitats can therefore cause large-scale population collapses. The results of our study argue against this interpretation.     

The generality of management recommendations across populations of an invasive perennial herb

Demographic models are widely used to produce management recommendations for different species. For invasive plants, current management recommendations to control local population growth are often based on data from a limited number of populations per species, and the assumption of stable population structure (asymptotic dynamics). However, spatial variation in population dynamics and deviation from a stable structure may affect these recommendations, calling into question their generality across populations of an invasive species. Here, I focused on intraspecific variation in population dynamics and investigated management recommendations generated by demographic models across 37 populations of a short-lived, invasive perennial herb (Lupinus polyphyllus). Models that relied on the proportional perturbations of vital rates (asymptotic elasticities) indicated an essential role for plant survival in long-term population dynamics. The rank order of elasticities for different vital rates (survival, growth, retrogression, fecundity) varied little among the 37 study populations regardless of population status (increasing or declining asymptotically). Summed elasticities for fecundity increased, while summed elasticities for survival decreased with increasing long-term population growth rate. Transient dynamics differed from asymptotic dynamics, but were qualitatively similar among populations, that is, depending on the initial size structure, populations tended to either increase or decline in density more rapidly than predicted by asymptotic growth rate. These findings indicate that although populations are likely to exhibit transient dynamics, management recommendations based on asymptotic elasticities for vital rates might be to some extent generalised across established populations of a given short-lived invasive plant species.     

Existence of Traveling Waves for the Generalized F–KPP Equation

Variation in genotypes may be responsible for differences in dispersal rates, directional biases, and growth rates of individuals. These traits may favor certain genotypes and enhance their spatiotemporal spreading into areas occupied by the less advantageous genotypes. We study how these factors influence the speed of spreading in the case of two competing genotypes under the assumption that spatial variation of the total population is small compared to the spatial variation of the frequencies of the genotypes in the population. In that case, the dynamics of the frequency of one of the genotypes is approximately described by a generalized Fisher–Kolmogorov–Petrovskii–Piskunov (F–KPP) equation. This generalized F–KPP equation with (nonlinear) frequency-dependent diffusion and advection terms admits traveling wave solutions that characterize the invasion of the dominant genotype. Our existence results generalize the classical theory for traveling waves for the F–KPP with constant coefficients. Moreover, in the particular case of the quadratic (monostable) nonlinear growth–decay rate in the generalized F–KPP we study in detail the influence of the variance in diffusion and mean displacement rates of the two genotypes on the minimal wave propagation speed.     

Dynamics of isolated <Emphasis Type="Italic">Saponaria bellidifolia</Emphasis> Sm. populations at northern range periphery

Four populations of Saponaria bellidifolia situated at the species’ northern range periphery (Apuseni Mountains, southeastern Carpathians) were monitored over a period of 5 years. They were chosen to represent different habitat types (rocky, fixed screes, open screes and grassy), disturbance regime (fire), and population sizes (categorized as large and small). The reproductive effort was quantified, and matrix models were used to describe the population dynamics and to assess population viability. Saponaria bellidifolia had very stable population dynamics in the harsh and stable abiotic conditions of the outcrops where populations occur. Habitat conditions exerted a notable influence on the species’ population reproductive performance, growth rate, and vital rates, whereas population size and climate did not have a clear-cut effect on the dynamics of the species. Saponaria bellidifolia maintains viable populations in the southeastern Carpathians, at its northern range periphery.