Spatial selection and inheritance: applying evolutionary concepts to population dynamics in heterogeneous space

Organisms in highly suitable sites generally produce more offspring, and offspring can inherit this suitability by not dispersing far. This combination of spatial selection and spatial inheritance acts to bias the distribution of organisms toward suitable sites and thereby increase mean fitness (i.e., per capita population increase). Thus, population growth rates in heterogeneous space change over time by a process conceptually analogous to evolution by natural selection, opening avenues for theoretical cross-pollination between evolutionary biology and ecology. We operationally define spatial inheritance and spatial selective differential and then combine these two factors in a modification of the breeder's equation, derived from simple models of population growth in heterogeneous space. The modified breeder's equation yields a conservative criterion for persistence in hostile environments estimable from field measurements. We apply this framework for understanding gypsy moth population persistence amidst abundant predators and find that the predictions of the modified breeder's equation match initial changes in population growth rate in independent simulation output. The analogy between spatial dynamics and natural selection conceptually links ecology and evolution, provides a spatially implicit framework for modeling spatial population dynamics, and represents an important null model for studying habitat selection.     

Ultimate causes and the evolution of altruism

Reconciling the evolution of altruism with Darwinian natural selection is frequently presented as a fundamental problem in biology. In addition to an exponentially increasing literature on specific mechanisms that can permit altruism to evolve, there has been a recent trend to establish general principles to explain altruism in populations undergoing natural selection. This paper reviews and extends one approach to understanding the ultimate causes underlying the evolution of altruism and mechanisms that can realise them, based on the Price equation. From the Price equation, we can see that such ultimate causes equate to the different ways in which the frequency of an altruistic allele in a population can increase. Under this approach, the ultimate causes underlying the evolution of altruism, given some positive fitness costs and benefits, are positive assortment of altruistic alleles with the altruistic behaviour of others, positive deviations from additive fitness effects when multiple altruists interact or bias in the inheritance of altruistic traits. In some cases, one cause can be interpreted in terms of another. The ultimate causes thus identified can be realised by a number of different mechanisms, and to demonstrate its general applicability, I use the Price equation approach to analyse a number of classical mechanisms known to support the evolution of altruism (or cooperation): repeated interaction, ‘greenbeard’ traits, games played on graphs and payoff synergism. I also briefly comment on other important points for the evolution of altruism, such as the ongoing debate over the predominant status of inclusive fitness as the best way to understand its evolution. I conclude by arguing that analysing the evolution of altruism in terms of its ultimate causes is the logical way to approach the problem and that, despite some of its technical limitations, the Price equation approach is a particularly powerful way of doing so.     

A new model for the CBL growth based on the turbulent kinetic energy equation

Starting from the evolution equation for the turbulent energy density spectrum (EDS), we develop a new model for the growth of the Convective boundary layer (CBL). We apply dimensional analysis to parameterize the unknown inertial transport and convective source term in the dynamic equation for the three-dimensional (3-D) spectrum and solve the 3-D EDS equation. The one-dimensional vertical spectrum is derived from the 3-D spectrum, employing a weight function. This allows us to select the magnitude of the vertical spectral component for the construction of the growing 3-D EDS. Furthermore, we employ the vertical component of the energy spectrum to calculate the eddy diffusivity (required in dispersion models). Currently there are no available experimental data to directly verify our EDS model.     

Models predicting the fate of pollutants in rivers

The spill of 2,4,‐D in the Rhine river was used to show the evolution from simple to sophisticated models. The first simulation was done with an analytical solution of the dispersion‐advection equation without elimination. Elimination was introduced in a second simulation. The third simulation was carried out with a numerical model. This included elimination and variable dispersion. The lack of data limited the use of very detailed models.     

Population growth in snow geese: a modeling approach integrating demographic and survey information

There are few analytic tools available to formally integrate information coming from population surveys and demographic studies. The Kalman filter is a procedure that facilitates such integration. Based on a state-space model, we can obtain a likelihood function for the survey data using a Kalman filter, which we may then combine with a likelihood for the demographic data. In this paper, we used this combined approach to analyze the population dynamics of a hunted species, the Greater Snow Goose (Chen caerulescens atlantica), and to examine the extent to which it can improve previous demographic population models. The state equation of the state-space model was a matrix population model with fecundity and regression parameters relating adult survival and harvest rate estimated in a previous capture-recapture study. The observation equation combined the output from this model with estimates from an annual spring photographic survey of the population. The maximum likelihood estimates of the regression parameters from the combined analysis differed little from the values of the original capture-recapture analysis, though their precision improved. The model output was found to be insensitive to a wide range of coefficient of variation (CV) in fecundity parameters. We found a close match between the surveyed and smoothed population size estimates generated by the Kalman filter over an 18-year period, and the estimated CV of the survey (0.078-0.150) was quite compatible with its assumed value (approximately 0.10). When we used the updated parameter values to predict future population size, the model underestimated the surveyed population size by 18% over a three-year period. However, this could be explained by a concurrent change in the survey method. We conclude that the Kalman filter is a promising approach to forecast population change because it incorporates survey information in a formal way compared with ad hoc approaches that either neglect this information or require some parameter or model tuning.     

Predicting reproduction rate of varroa

A single equation is derived to predict population-density effects on the reproduction rate of the honey bee parasite Varroa destructor Anderson and Trueman. This equation provides a simpler alternative to the approach currently used in the literature, and additionally corrects an anomaly in that approach. The method is then extended to the case of co-existing haplotypes of Varroa. It thus derives an equation used without proof for modelling biocontrol of Varroa, and examines the error caused by an approximation necessary for a closed form solution. Additionally a varroa population model incorporating the derived equation is described.     

A model of ecological and evolutionary consequences of color polymorphism

We summarize direct and indirect effects on fitness components of animal color pattern and present a synthesis of theories concerning the ecological and evolutionary dynamics of chromatic multiple niche polymorphisms. Previous endeavors have aimed primarily at identifying conditions that promote the evolution and maintenance of polymorphisms. We consider in a conceptual model also the reciprocal influence of color polymorphism on population processes and propose that polymorphism entails selective advantages that may promote the ecological success of polymorphic species. The model begins with an evolutionary branching event from mono- to polymorphic condition that, under the influence of correlational selection, is predicted to promote the evolution of physical integration of coloration and other traits (cf. multi-trait coevolution and complex phenotypes). We propose that the coexistence within a population of alternative ecomorphs with coadapted gene complexes promotes utilization of diverse environmental resources, population stability and persistence, colonization success, and range expansions, and enhances the evolutionary potential and speciation. Conversely, we predict polymorphic populations to be less vulnerable to environmental change and at lower risk of range contractions and extinctions compared with monomorphic populations. We offer brief suggestions as to how these falsifiable predictions may be tested.     

The role of migration and founder effect for the evolution of cooperation in a multilevel selection context

The idea that natural selection can be meaningfully applied at the group level may be more important than previously thought. This perspective, a modern version of group selection, is called multilevel selection. Multilevel selection theory could incorporate previous explanations for the evolution of cooperation including kin selection. There is general agreement that natural selection favors noncooperators over cooperators in the case of an unstructured population. Therefore, the evolution of cooperation by multilevel selection often requires positive assortment between cooperators and noncooperators. The question is how this positive assortment can arise in the ecological meaning. We constructed an individual-based model of multilevel selection and introduced migration and evolution. The results showed that positive assortment was generated especially when a migration strategy was adopted in which individuals respond specifically to bad environmental conditions. It was also shown that the founder effect in the evolutionary process could further facilitate positive assortment by working with migration. We analyzed assortment by using relatedness defined in group-structured populations. The fact that cooperation was achieved by such migration and by the founder effect highlights the importance of sensitiveness to the ecological environment and of fluctuations in group size, respectively.     

Evolutionary diversity and spatiotemporal dynamics of a spatial game

In this paper, the evolution of cooperation is studied by a spatially structured evolutionary game model in which the players are located on a two-dimensional square lattice. Each player can choose one of the following strategies: “always defect” (ALLD), “tit-for-tat” (TFT), and “always cooperate” (ALLC). Players merely interact with four immediate neighbors at first and adjust strategies according to their rewards. First, the evolutionary dynamics of the three strategies in non-spatial population is investigated, and the results indicate that cooperation is not favored in most settings without spatial structure. Next, an analytical method, which is based on comparing the local payoff structures, is introduced for the spatial game model. Using the conditions derived from the method as criteria, the parameter plane for two major parameters of the spatial game model is divided and nine representative regions are identified. In each parameter region, a distinct spatiotemporal dynamics is characterized. The spatiotemporal dynamics not only verify that the spatial structure promote the evolution of cooperation but also reveal how cooperation is favored. Our results show that spatial structure is the keystone of the evolution of intraspecific diversity.     

Population as an oscillating system

In this paper we present a new approach describing population dynamics based on the view of a population as an oscillating system. To develop a mathematical model of an oscillating population, we applied a third-order differential equation. Our model describes population dynamics within a parametric-temporal continuum, formed by the relative values of population growth and decrease over time. In this paper we also illustrate how our oscillative model effectively compliments the existing suite of models in population dynamics.     

A stage-structured, Aedes albopictus population model

Aedes albopictus has been the fastest spreading invasive animal species in the world from the mid-1980s until the mid-2000s. In areas it infests, it disrupts native mosquito ecology and can potentially vector up to 21 viruses. To better understand the population dynamics of this species, we created a temperature dependent population model. A stage-structured model was chosen to allow each life-stage to have different temperature dependent mortality and development rates, and each stage was modeled with an ordinary differential equation. Model parameters and distributions were based upon literature values. Initially, a basic model was constructed. This model then had parameters that were forced based upon daily average temperatures. Several criteria were used to evaluate the model, including a comparison to field data from Lubbock, TX. In a stochastic version of the model, a 95% confidence limit contained 70.7% of the field data points. Based upon these results, we feel reasonably confident that we have captured the role of temperature in driving the population dynamics of Ae. albopictus.     

人口经济与环境整体优化模型初步研究

一个城市在发展中做到人口经济与环境的整体优化，传统的思路是控制人口经济发展。８０年代以来持续发展理论的提出，以产业技术结构的演进，二、三产业的融合来促使人口经济环境由低级向高级发展，取得人口经济与环境的整体优化，这就要求提供实用的研究方法。本文提出人口经济与环境整体优化模型的思路，给出了具体模型的建立方法，讨论各项参数的获取，从而可为城市人口经济与环境整体优化研究奠定基础。     

Modeling leaf dispersal in mixed hardwood forests using a ballistic approach

In mixed-species stands, modeling leaf litter dispersal is important to predict the physical and chemical characteristics of the forest floor, which plays a major role in nutrient cycling and in plant population dynamics. In this study, a spatially explicit model of leaf litterfall was developed and compared with two other models. These three models were calibrated for a mixed forest of oak and beech using litterfall data from mapped forest plots. All models assumed that an allometric equation described individual leaf litter production, but they strongly differed in the modeling of the probability density of leaf shedding with distance from source trees. Two models used a negative exponential function to account for leaf dispersal with distance, and this function was allowed to vary according to wind direction in one of them. In contrast, our approach was based on a simple ballistic equation considering release height, wind speed, wind direction, and leaf fall velocity; the distributions of wind speeds and wind directions were modeled according to a Weibull and a Von Mises distribution, respectively. Using an independent validation data set, all three models provided predictions well correlated to measurements (r > 0.83); however, the two models with a direction-dependent component were slightly more accurate. In addition, parameter estimates of the ballistic model were in close agreement with a foliar litter production equation derived from the literature for beech and with wind characteristics measured during leaf litterfall for both species. Because of its mechanistic background, such a spatially explicit model might be incorporated as a litterfall module in larger models (nutrient cycling, plant population dynamics) or used to determine the manner in which patch size in mixed-species stands influences litter mixture.     

Variation in adult annual survival probability and remigration intervals of sea turtles

We analyzed a large dataset to quantify adult annual survival probability and remigration intervals for the Tortuguero, Costa Rica green turtle population. Annual survival probability was estimated at 0.85 (95% CI 0.75–0.92) using a recovery model and at 0.85 (95% CI 0.83–0.87) using an open robust design model. The two most common modes of remigration are 2 and 3 years. Annual survival probability is lower and remigration intervals are shorter than for other green turtle populations. Explanations for short remigration intervals include reproductive compensation due to historic population declines, availability of better quality food items, favorable environmental conditions, and short distance to the main foraging grounds. Variation in survival and remigration intervals have profound consequences for management and life history evolution. The short remigration intervals of Tortuguero green turtles partly offset mortality caused by turtle fishing in Nicaragua and mean that low juvenile survival represents a more urgent threat to the population than low adult survival. Low adult survival probability could result in selective pressure for earlier age at maturity.     

Information processing in models for density-dependent emigration: A comparison

Density-dependent emigration has been recognized as a fitness enhancing strategy. Yet, especially in the modelling literature there is no consensus about how density-dependent emigration should quantitatively be incorporated into metapopulation models. In this paper we compare the performance of five different dispersal strategies (defined by the functional link between density and emigration probability). Four of these strategies are based on published functional relationships between local population density and emigration probability, one assumes density-independent dispersal. We use individual-based simulations of time-discrete metapopulation dynamics and conduct evolution experiments for a broad range of values for dispersal mortality and environmental stochasticity. For each set of these conditions we analyze the evolution of emigration rates in ‘monoculture experiments’ (with only one type of dispersal strategy used by all individuals in the metapopulation) as well as in selection experiments that allow a pair-wise comparison of the performance of each functional type. We find that a single-parameter ‘asymptotic threshold’ strategy - derived from the marginal value theorem - with a decelerating increase of emigration rate with increasing population density, out-competes any other strategy, i.e. density-independent emigration, a ‘linear threshold’ strategy and a flexible three-parameter strategy. Only when environmental conditions select for extremely high emigration probabilities (close to one), strategies may perform approximately equally. A simple threshold strategy derived for the case of continuous population growth performs even worse than the density-independent strategy. As the functional type of the dispersal function implemented in metapopulation models may severely affect predictions concerning the survival of populations, range expansion, or community changes we clearly recommend to carefully select adequate functions to model density-dependent dispersal.     

Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data

Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize “boom and bust” population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl–Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.     

Survival analysis of stochastic single-species population models in polluted environments

This paper reports on the behaviors of single species models with and without pollution. We consider three basic models, one is deterministic, and others are stochastic. We first obtained the acute thresholds between local extinction and (stochastic) weakly persistent in the mean for population respectively. Then we study the attainability of population size 0 for the stochastic cases and show that a randomized non-autonomous logistic equation will be stochastic permanent under some conditions. Finally, we introduce some numerical simulink graphics to illustrate our main results.     

Use of individual-based models for population parameters estimation

A method for parameters estimation of stage-specific mortality and fecundity rate functions in poikilotherm organisms, and in particular for arthropod structured population, is proposed. The application of this method requires three types of information: stage-frequency data of a sampled population, development rate function and time evolution of forcing variables affecting the rate functions. By means of an individual-based model (a microscopic model) the number of eggs produced by the adults is generated starting from the number of individuals collected at each sampling time. Using a compartmental model (a macroscopic model) a stage-structured population dynamics is described and compared with observations. Non-linear regression methods based on least square principle are used to estimate the optimal parameters of the mortality and fecundity rate functions combining microscopic and macroscopic models. As a case study, the parameter estimation of the temperature-dependent mortality function of olives fruit fly Bactrocera oleae is presented.     

Reproductive plasticity,oviposition site selection,and maternal effects in fragmented landscapes

Traditionally, evolutionary ecology and conservation biology have primarily been concerned with how environmental changes affect population size and genetic diversity. Recently, however, there has been a growing realization that phenotypic plasticity can have important consequences for the probability of population persistence, population growth, and evolution during rapid environmental change. Habitat fragmentation due to human activities is dramatically changing the ecological conditions of life for many organisms. In this review, we use examples from the literature to demonstrate that habitat fragmentation has important consequences on oviposition site selection in insects, with carryover effects on offspring survival and, therefore, population dynamics. We argue that plasticity in oviposition site selection and maternal effects on offspring phenotypes may be an important, yet underexplored, mechanism by which environmental conditions have consequences across generations. Without considering the impact of habitat fragmentation on oviposition site selection, it will be difficult to assess the effect of fragmentation on offspring fitness, and ultimately to understand the impact of anthropogenic-induced environmental change on population viability.     

Performance of Greater Sage-Grouse Models for Conservation Assessment in the Interior Columbia Basin, U.S.A.

Abstract: Valid modeling of habitats and populations of Greater Sage-Grouse ( Centrocercus urophasianus) is a critical management need because of increasing concern about population viability. Consequently, we evaluated the performance of two models designed to assess landscape conditions for Greater Sage-Grouse across 13.6 million ha of sagebrush steppe in the interior Columbia Basin and adjacent portions of the Great Basin of the western United States (referred to as the basin). The first model, the environmental index model, predicted conditions at the scale of the subwatershed (mean size of approximately 7800 ha) based on inputs of habitat density, habitat quality, and effects of human disturbance. Predictions ranged on a continuous scale from 0 for lowest environmental index to 2 for optimal environmental index. The second model, the population outcome model, predicted the composite, range-wide conditions for sage grouse based on the contribution of environmental index values from all subwatersheds and measures of range extent and connectivity. Population outcomes were expressed as five classes (A through E) that represented a gradient from continuous, well-distributed populations (outcome A) to sparse, highly isolated populations with a high likelihood of extirpation (outcome E). To evaluate performance, we predicted environmental index values and population outcome classes in areas currently occupied by sage grouse versus areas where extirpation has occurred. Our a priori expectations were that models should predict substantially worse environmental conditions ( lower environmental index) and a substantially higher probability of extirpation ( lower population outcome class) in extirpated areas. Results for both models met these expectations. For example, a population outcome of class E was predicted for extirpated areas, as opposed to class C for occupied areas. These results suggest that our models provided reliable landscape predictions for the conditions tested. This finding is important for conservation planning in the basin, where the models were used to evaluate management of federal lands for sage grouse.