Interfering waves of adaptation promote spatial mixing

A fundamental problem of asexual adaptation is that beneficial substitutions are not efficiently accumulated in large populations: Beneficial mutations often go extinct because they compete with one another in going to fixation. It has been argued that such clonal interference may have led to the evolution of sex and recombination in well-mixed populations. Here, we study clonal interference, and mechanisms of its mitigation, in an evolutionary model of spatially structured populations with uniform selection pressure. Clonal interference is much more prevalent with spatial structure than without, due to the slow wave-like spread of beneficial mutations through space. We find that the adaptation speed of asexuals saturates when the linear habitat size exceeds a characteristic interference length, which becomes shorter with smaller migration and larger mutation rate. The limiting speed is proportional to μ(1/2) and μ(1/3) in linear and planar habitats, respectively, where the mutational supply μ is the product of mutation rate and local population density. This scaling and the existence of a speed limit should be amenable to experimental tests as they fall far below predicted adaptation speeds for well-mixed populations (that scale as the logarithm of population size). Finally, we show that not only recombination, but also long-range migration is a highly efficient mechanism of relaxing clonal competition in structured populations. Our conservative estimates of the interference length predict prevalent clonal interference in microbial colonies and biofilms, so clonal competition should be a strong driver of both genetic and spatial mixing in those contexts.     

A shift from exploitation to interference competition with increasing density affects population and community dynamics

Intraspecific competition influences population and community dynamics and occurs via two mechanisms. Exploitative competition is an indirect effect that occurs through use of a shared resource and depends on resource availability. Interference competition occurs by obstructing access to a resource and may not depend on resource availability. Our study tested whether the strength of interference competition changes with protozoa population density. We grew experimental microcosms of protozoa and bacteria under different combinations of protozoan density and basal resource availability. We then solved a dynamic predator–prey model for parameters of the functional response using population growth rates measured in our experiment. As population density increased, competition shifted from exploitation to interference, and competition was less dependent on resource levels. Surprisingly, the effect of resources was weakest when competition was the most intense. We found that at low population densities, competition was largely exploitative and resource availability had a large effect on population growth rates, but the effect of resources was much weaker at high densities. This shift in competitive mechanism could have implications for interspecific competition, trophic interactions, community diversity, and natural selection. We also tested whether this shift in the mechanism of competition with protozoa density affected the structure of the bacterial prey community. We found that both resources and protozoa density affected the structure of the bacterial prey community, suggesting that competitive mechanism may also affect trophic interactions.     

Density dependence in a recovering osprey population: demographic and behavioural processes

1. Understanding how density-dependent and independent processes influence demographic parameters, and hence regulate population size, is fundamental within population ecology. We investigated density dependence in growth rate and fecundity in a recovering population of a semicolonial raptor, the osprey Pandion haliaetus [Linnaeus, 1758], using 31 years of count and demographic data in Corsica. 2. The study population increased from three pairs in 1974 to an average of 22 pairs in the late 1990s, with two distinct phases during the recovery (increase followed by stability) and contrasted trends in breeding parameters in each phase. 3. We show density dependence in population growth rate in the second phase, indicating that the stabilized population was regulated. We also show density dependence in productivity (fledging success between years and hatching success within years). 4. Using long-term data on behavioural interactions at nest sites, and on diet and fish provisioning rate, we evaluated two possible mechanisms of density dependence in productivity, food depletion and behavioural interference. 5. As density increased, both provisioning rate and the size of prey increased, contrary to predictions of a food-depletion mechanism. In the time series, a reduction in fledging success coincided with an increase in the number of non-breeders. Hatching success decreased with increasing local density and frequency of interactions with conspecifics, suggesting that behavioural interference was influencing hatching success. 6. Our study shows that, taking into account the role of non-breeders, in particular in species or populations where there are many floaters and where competition for nest sites is intense, can improve our understanding of density-dependent processes and help conservation actions.     

Population growth rate and its determinants: an overview

We argue that population growth rate is the key unifying variable linking the various facets of population ecology. The importance of population growth rate lies partly in its central role in forecasting future population trends; indeed if the form of density dependence were constant and known, then the future population dynamics could to some degree be predicted. We argue that population growth rate is also central to our understanding of environmental stress: environmental stressors should be defined as factors which when first applied to a population reduce population growth rate. The joint action of such stressors determines an organism's ecological niche, which should be defined as the set of environmental conditions where population growth rate is greater than zero (where population growth rate = r = log(e)(N(t+1)/N(t))). While environmental stressors have negative effects on population growth rate, the same is true of population density, the case of negative linear effects corresponding to the well-known logistic equation. Following Sinclair, we recognize population regulation as occurring when population growth rate is negatively density dependent. Surprisingly, given its fundamental importance in population ecology, only 25 studies were discovered in the literature in which population growth rate has been plotted against population density. In 12 of these the effects of density were linear; in all but two of the remainder the relationship was concave viewed from above. Alternative approaches to establishing the determinants of population growth rate are reviewed, paying special attention to the demographic and mechanistic approaches. The effects of population density on population growth rate may act through their effects on food availability and associated effects on somatic growth, fecundity and survival, according to a 'numerical response', the evidence for which is briefly reviewed. Alternatively, there may be effects on population growth rate of population density in addition to those that arise through the partitioning of food between competitors; this is 'interference competition'. The distinction is illustrated using a replicated laboratory experiment on a marine copepod, Tisbe battagliae. Application of these approaches in conservation biology, ecotoxicology and human demography is briefly considered. We conclude that population regulation, density dependence, resource and interference competition, the effects of environmental stress and the form of the ecological niche, are all best defined and analysed in terms of population growth rate.     

The effect of predator limitation on the dynamics of simple food chains

We investigate the influence of competition between predators on the dynamics of bitrophic predator–prey systems and of tritrophic food chains. Competition between predators is implemented either as interference competition, or as a density-dependent mortality rate. With interference competition, the paradox of enrichment is reduced or completely suppressed, but otherwise, the dynamical behavior of the systems is not fundamentally different from that of the Rosenzweig–MacArthur model, which contains no predator competition and shows only continuous transitions between fixed points or periodic oscillations. In contrast, with density-dependent predator mortality, the system shows a surprisingly rich dynamical behavior. In particular, decreasing the density regulation of the predator can induce catastrophic shifts from a stable fixed point to a large oscillation where the predator chases the prey through a cycle that brings both species close to the threshold of extinction. Other catastrophic bifurcations, such as subcritical Hopf bifurcations and saddle-node bifurcations of limit cycles, do also occur. In tritrophic food chains, we find again that fixed points in the model with predator interference become unstable only through Hopf bifurcations, which can also be subcritical, in contrast to the bitrophic situation. The model with a density limitation shows again catastrophic destabilization of fixed points and various nonlocal bifurcations. In addition, chaos occurs for both models in appropriate parameter ranges.     

Prey abundance and the strength of interference in a foraging shorebird

Interference is an important component of food competition but is often difficult to detect and measure in natural animal populations. Although interference has been shown to occur between oystercatchers Haematopus ostralegus L. feeding on mussels Mytilus edulis L., four previous studies have not detected interference between oystercatchers feeding on cockles Cerastoderma edule L. In contrast, this study detected interference between cockle-feeding oystercatchers in the Baie de Somme, France. Prey stealing (kleptoparasitism), one of the main causes of interference between mussel-feeders, also occurred between oystercatchers in the Baie de Somme. The kleptoparasitism rate was related to the natural variation in the food supply, tending to be higher when cockles were rare. Feeding rate was negatively related to competitor density, so providing evidence for interference, but, as in mussel-feeders, only above a threshold density of about 50–100 birds ha⁻¹. The strength of interference at a fixed competitor density was related to the cockle food supply, usually being greater when cockles were rare. Previous studies probably failed to detect interference between cockle-feeders because competitor densities were too low, or cockles were too abundant, or because they were not conducted during late winter when interference is most intense. The study shows that natural variation in the food supply can influence the strength of interference within an animal population and provides support for those behaviour-based interference models which predict that the strength of interference will be greatest when competitor densities are high and prey scarce.     

From local interactions to population dynamics in site-based models of ecology

A central problem in ecology is relating the interactions of individuals-described in terms of competition, predation, interference, etc.-to the dynamics of the populations of these individuals-in terms of change in numbers of individuals over time. Here, we address this problem for a class of site-based ecological models, where local interactions between individuals take place at a finite number of discrete resource sites over non-overlapping generations and, between generations, individuals move randomly between sites over the entire system. Such site-based models have previously been applied to a wide range of ecological systems: from those involving contest or scramble competition for resources to host-parasite interactions and meta-populations. We show how the population dynamics of site-based models can be accurately approximated by and understood through deterministic and stochastic difference equations. Conversely, we use the inverse of this approximation to show what implicit assumptions are made about individual interactions by modelling of population dynamics in terms of difference equations. To this end, we prove a useful and general theorem: that any model in our class of site-based models has a corresponding stochastic difference equation population model, by which it can be approximated. This theorem allows us to calculate long-term population dynamics, evolutionary stable strategies and, by extending our theory to account for large deviations, extinction probabilities for a wide range of site-based systems. Our methodology is then illustrated to various examples of between species competition, predator-prey interactions and co-operation.     

Density‐dependent effects on reproductive performance in a recovering population of White‐tailed Eagles Haliaeetus albicilla

Understanding the mechanisms that shape density‐dependent processes and population dynamics is often essential for species conservation. Two key mechanisms of density‐dependent reductions in reproductive performance are a limited access to foraging habitats (the habitat heterogeneity hypothesis) and territorial aggression towards conspecifics (the interference competition hypothesis) at high population densities. Disentangling the relative importance of these mechanisms within populations below their carrying capacity is important for the evaluation of the success of conservation measures. However, relatively few studies have attempted to quantify the relative importance of both mechanisms for the reproductive performance of a population. Many raptor populations are ideal model systems to investigate density‐dependent effects because they are currently recovering from human‐induced reductions during the last decades. Using a 14‐year dataset, we combined analyses of individual reproductive performance with a mechanistic population model to investigate early signs of density‐dependent regulation in a population of White‐tailed Eagles Haliaeetus albicilla in north‐east Germany. We found a negative effect of the number of neighbouring breeding pairs and a positive effect of water surface area (as a proxy for the availability of favourable foraging habitat) on breeding success and on the average number of nestlings. The mean nearest neighbour distance between breeding pairs has decreased, and the mean distance of nests to the nearest water body has increased over the last 14 years. Moreover, the population model indicates that even though the population is still growing, carrying capacity could be reached at about 500–950 territorial pairs. These results suggest that the selection of nesting sites is determined by a trade‐off between the distance to favourable foraging habitat and the distance to neighbouring breeding pairs. To avoid increasing competition with conspecifics, due to continued population growth, breeding pairs seem to select increasingly suboptimal habitats. Therefore, our results suggest that the habitat heterogeneity and interference competition hypotheses are not necessarily mutually exclusive as mechanisms of density‐dependent population regulation, but can determine the reproductive performance of a raptor population simultaneously. Thus, a future decline in breeding success does not necessarily reflect a decrease in habitat quality but may rather be a consequence of density‐dependent mechanisms. This information may be useful for the interpretation of population trends and for the development of appropriate management strategies for recovering raptor populations.     

THE FUNDAMENTAL THEOREM OF NATURAL SELECTION

The fundamental theorem of natural selection was a valiant attempt by R. A. Fisher to fit a quart into a pint pot
The present author reviewing Population Genetics by Ewens, 1969 a (Edwards, 1969).
Many authors have maintained that the theorem holds only under very special conditions, while only a few (e.g. Edwards, 1967) have thought that Fisher may have been correct – if only we could understand what he meant! It will be shown here that this latter view is correct
Price, 1972.
My own reason for not including a planned chapter on the fundamental theorem is… [ that ] in spite of many efforts I am still not satisfied that I am able to provide an account that does the theorem justice
The present author in the Epilogue to Foundations of Mathematical Genetics (Edwards, 1977).     

Bayesian Inference on the Effect of Density Dependence and Weather on a Guanaco Population from Chile

Understanding the mechanisms that drive population dynamics is fundamental for management of wild populations. The guanaco (Lama guanicoe) is one of two wild camelid species in South America. We evaluated the effects of density dependence and weather variables on population regulation based on a time series of 36 years of population sampling of guanacos in Tierra del Fuego, Chile. The population density varied between 2.7 and 30.7 guanaco/km², with an apparent monotonic growth during the first 25 years; however, in the last 10 years the population has shown large fluctuations, suggesting that it might have reached its carrying capacity. We used a Bayesian state-space framework and model selection to determine the effect of density and environmental variables on guanaco population dynamics. Our results show that the population is under density dependent regulation and that it is currently fluctuating around an average carrying capacity of 45,000 guanacos. We also found a significant positive effect of previous winter temperature while sheep density has a strong negative effect on the guanaco population growth. We conclude that there are significant density dependent processes and that climate as well as competition with domestic species have important effects determining the population size of guanacos, with important implications for management and conservation.     

A simple completion of Fisher’s fundamental theorem of natural selection

Fisher''s fundamental theorem of natural selection shows that the part of the rate of change of mean fitness that is due to natural selection equals the additive genetic variance in fitness. Fisher embedded this result in a model of total fitness, adding terms for deterioration of the environment and density dependence. Here, a quantitative genetic version of this neglected model is derived that relaxes its assumptions that the additive genetic variance in fitness and the rate of deterioration of the environment do not change over time, allows population size to vary, and includes an input of mutational variance. The resulting formula for total rate of change in mean fitness contains two terms more than Fisher''s original, representing the effects of stabilizing selection, on the one hand, and of mutational variance, on the other, making clear for the first time that the fundamental theorem deals only with natural selection that is directional (as opposed to stabilizing) on the underlying traits. In this model, the total (rather than just the additive) genetic variance increases mean fitness. The unstructured population allows an explanation of Fisher''s concept of fitness as simply birth rate minus mortality rate, and building up to the definition in structured populations.     

Larval competition in serially transferred populations of Drosophila melanogaster

Summary Experiments showed that larval competition for food is not always the result of decreases in the amount of food available per larva as population density increases. The feeding period during which the larvae try to attain the minimum survival weight may be restricted when food quantity is not limiting. The scramble type competition involves both exploitation and interference components, in degrees which vary with population density.     

Farming with native bees (<Emphasis Type="Italic">Apis mellifera</Emphasis> subsp. <Emphasis Type="Italic">capensis</Emphasis> Esch.) has varied effects on nectar-feeding bird communities in South African fynbos vegetation

Outside their natural range, honeybees (Apis mellifera) are known to have detrimental effects on indigenous pollinators through exploitative or interference competition, but little is known about the effect of honeybee farming in areas where honeybees occur naturally. In the Cape Floristic Region of South Africa, where honeybees are indigenous, managed hives potentially elevate the abundance of honeybees far above natural levels, but impacts on other floral resource-dependent species have not been studied. Here we use experimental manipulation of honeybee density to test whether honeybee farming affects nectar-feeding birds. We selected the common sugarbush (Protea repens), utilized by both birds and bees, and analysed the time (before/after) by treatment (control/experiment) interaction to explore changes in bee abundance, nectar availability and bird abundance at three sites. Hive addition increased honeybee abundance in inflorescences of P. repens above expected levels. Despite experimental increase in honeybee numbers, there is no reduction in nectar sugar availability relative to the control areas. Where honeybee density was highest, sugarbird (Promerops cafer) numbers declined relative to expected, but sunbirds (Nectarinidae) were not affected at any of the sites. We conclude that stocking rates of more than one honey bee per P. repens inflorescence have detrimental effects on bird abundance due to interference, rather than resource competition.     

Roe and fallow deer: are they compatible neighbours?

The analysis of the relationships between population density and habitat features is important to evaluate the ecological needs of a species, its potential impact on ecosystems and its interspecific interactions. We analysed the spatial variation of roe deer Capreolus capreolus and fallow deer Dama dama densities in a Mediterranean area in summer 2007 and winter 2007/2008. Previous research has shown that fallow deer can actively displace and exclude roe deer from natural feeding sites. Here we show that both species have the greatest densities in ecotone habitats between wood and open fields (abandoned olive groves and pastures), but with contrasting geographic patterns. The fallow deer showed the greatest densities in the central northern part of the study area near to local historical release sites. The densities of roe deer were great where fallow deer were rare and low where fallow deer were abundant. Spatial overlap was great at the habitat scale, indicating a high potential for competition, but was low at the plot scale, suggesting that partitioning of space occurred at a fine scale. Supporting great numbers of deer, the ecotone areas are crucial for the management of ecosystems. We suggest that roe deer avoid areas with great densities of fallow deer and that interspecific interference from the latter affects the density and distribution of the former both at a fine and at a large scale.     

Costs of aggregation: shadow competition in a sit-and-wait predator

The role of top-down (e.g. parasitism) and bottom-up (e.g. resource competition) processes is of fundamental importance for the stability and persistence of insect herbivore populations. Although emphasis has often focused on single regulatory agents, the processes underpinning tri-trophic interactions may actually be more pluralistic. Recently, further complexities involved in the regulation of tri-trophic systems have been highlighted. In particular, life history characteristics may have a concomitant role when coupled with the regulatory effects of resource competition and/or parasitism. Here we present an age-structured model to investigate the effects of larval development period, parasitism and resource competition on the stability and persistence of herbivore–parasitoid interactions. We show that the influence of weak density dependent parasitism is sufficient to stabilise the interaction when the period of host susceptibility to parasitism is short. For longer periods of host susceptibility, parasitism needs to be highly non-linear to overcome the destabilising effects of the time delays. In systems where host development is protracted through the season we predict that resource competition is likely to be the dominant process for herbivore regulation. We use this age-structured approach to explore the population dynamics of two field studies from temperate ecosystems. Predictions from these case studies show 1) that both the strength and type of competition and parasitism are important for the stability and persistence of the particular system, and 2) that the length of the developmental period of the vulnerable host is critical to understand the influence of different regulatory processes. Host demography is of overriding importance in determining whether herbivores show outbreaks, and which particular ecological processes and mechanisms are responsible for generating such overcompensatory dynamics.     

沙地樟子松天然林南缘分布区林木竞争、空间格局及其更新特征

以呼伦贝尔沙地樟子松地理分布南缘天然林为研究对象,采用Hegyi竞争指数与点格局等分析方法,研究了沙地樟子松天然林的种群结构、种内竞争、空间格局及幼树更新等特征。结果表明:1)所调查区域天然沙地樟子松纯林处于中幼龄阶段,属增长型种群;2)其竞争指数与对象木胸径服从幂函数关系CI=242.24D~(-1.12)(R~2=0.91);3)幼树在小尺度上呈聚集分布,中树与大树在中大尺度上呈随机分布;幼树与中树在小尺度上呈正相关性,中树与大树在小尺度呈负相关性;4)竞争指数与更新幼树和存活更新幼树的密度均呈显著正相关性。在林分管理中需要充分考虑林木竞争、空间格局以及种群更新的关系,本研究可为沙地樟子松天然林的经营管理与保护提供重要的科学依据。     

Population dynamics ofTelenomus fariai (Hymenoptera: Scelionidae), a parasite of Chagas' disease vectors IX. Larval competition and population size regulation under laboratory conditions

A series of experiments were carried out with the endophagous egg parasite Telenomus fariai on its host Triatoma phyllosoma pallidipennis to determine the possible role of intraspecific competition by the parasite progeny in population regulation of the parasite. Eight parasite densities (1, 3, 5, 10, 20, 30, 40, and 50 individuals per vial) were used, and the design of sequentially sacrificed replicates applied. Survivorship curves for each density indicated smaller number of progeny per host at higher densities, and the shapes of the curves suggested a relatively early mortality process.Morris' linear regression technique for determining within-generation density-dependence was used, and the results showed that only larval mortality could be identified as density dependent. The same technique applied within the larval stage proved that only mortality of larvae in their second, third, and fourth day of development were responsible for population regulation. The applicability of the technique, as well as the relevance of the results for natural population, is discussed.