The influence of host demography, pathogen virulence, and relationships with pathogen virulence on the evolution of pathogen transmission in a spatial context

A major challenge in evolutionary ecology is to explain extensive natural variation in transmission rates and virulence across pathogens. Host and pathogen ecology is a potentially important source of that variation. Theory of its effects has been developed through the study of non-spatial models, but host population spatial structure has been shown to influence evolutionary outcomes. To date, the effects of basic host and pathogen demography on pathogen evolution have not been thoroughly explored in a spatial context. Here we use simulations to show that space produces novel predictions of the influence of the shape of the pathogen’s transmission–virulence tradeoff, as well as host reproduction and mortality, on the pathogen’s evolutionary stable transmission rate. Importantly, non-spatial models predict that neither the slope of linear transmission–virulence relationships, nor the host reproduction rate will influence pathogen evolution, and that host mortality will only influence it when there is a transmission–virulence tradeoff. We show that this is not the case in a spatial context, and identify the ecological conditions under which spatial effects are most influential. Thus, these results may help explain observed natural variation among pathogens unexplainable by non-spatial models, and provide guidance about when space should be considered. We additionally evaluate the ability of existing analytical approaches to predict the influence of ecology, namely spatial moment equations closed with an improved pair approximation (IPA). The IPA is known to have limited accuracy, but here we show that in the context of pathogens the limitations are substantial: in many cases, IPA incorrectly predicts evolution to pathogen-driven extinction. Despite these limitations, we suggest that the impact of ecology can still be understood within the conceptual framework arising from spatial moment equations, that of “self-shading’’, whereby the spread of highly transmissible pathogens is impeded by local depletion of susceptible hosts.     

Mechanistic Approaches to Community Ecology: A New Reductionism

Mechanistic approaches to community ecology are those whichemploy individual— ecological concepts—those ofbehavioral ecology, physiological ecology, and ecomorphology—as theoretical bases for understanding community patterns. Suchapproaches, which began explicitly about a decade ago, are justnow coming into prominence. They stand in contrast to more traditionalapproaches, such as MacArthur and Levins (1967),which interpretcommunity ecology almost strictly in terms of "megaparameters.". Mechanistic approaches can be divided into those which use populationdynamics as a major component of the theory and those whichdo not; examples of the two are about equally common. The firstapproach sacrifices a highly detailed representation of individual—ecological processes; the second sacrifices an explicit representationof the abundance and persistence of populations. Three subdisciplines of ecology—individual, populationand community ecology—form a "perfect" hierarchy in Beckner's(1974) sense. Two other subdisciplines—ecosystem ecologyand evolutionary ecology—lie somewhat laterally to thishierarchy. The modelling of community phenomena using sets ofpopulation-dynamical equations is argued as an attempt at explanationvia the reduction of community to population ecology. Much ofthe debate involving Florida State ecologists is over whetheror not such a relationship is additive (or conjunctive), a verystrong form of reduction. I argue that reduction of communityto individual ecology is plausible via a reduction of populationecology to individual ecology. Approaches that derive the population-dynamicalequations used in population and community ecology from individual-ecologicalconsiderations, and which provide a decomposition of megaparametersinto behavioral and physiological parameters, are cited as illustratinghow the reduction might be done. I argue that "sufficient parameters"generally will not enhance theoretical understanding in communityecology. A major advantage of the mechanistic approach is that variationin population and community patterns can be understood as variationin individual-ecological conditions. In addition to enrichingthe theory, this allows the best functional form to be chosenfor modeling higher-level phenomena, where "best" is definedas biologically most appropriate rather than mathematicallymost convenient. Disadvantages of the mechanistic approach arethat it may portend an overly complex, massive and special theory,and that it naturally tends to avoid many-species phenomenasuch as indirect effects. The paper ends with a scenario fora mechanistic-ecological utopia.     

A suggestion for another statistical interpretation of the fundamental equations of the mathematical biophysics of the central nervous system

In a preceding paper an interpretation of the ε andj factors has been given in terms of an average effect of a large number of interneurons. In the present paper, a different interpretation is given in terms of the probability of a sufficient number of afferents to fire within the period of latent addition of the efferent. From this interpretation it follows that the old equations for ε andj are only first linear approximations to more complicated equations, the nature of which is suggested by this interpretation.     

运用改进单纯形法拟合Logistic曲线的研究

Ｌｏｇｉｓｔｉｃ方程是研究有限空间内种群增长规律的重要工具之一本文运用改进单纯形法最优拟合Ｌｏｇｉｓｔｉｃ曲线,结果表明改进单纯形法具有较强的拟合非线性方程的能力,对生物实验及生态、生理学中诸多非线性曲线的参数估计具有普遍意义．     

Eco-evolution from deep time to contemporary dynamics: The role of timescales and rate modulators

Eco-evolutionary dynamics, or eco-evolution for short, are often thought to involve rapid demography (ecology) and equally rapid heritable phenotypic changes (evolution) leading to novel, emergent system behaviours. We argue that this focus on contemporary dynamics is too narrow: Eco-evolution should be extended, first, beyond pure demography to include all environmental dimensions and, second, to include slow eco-evolution which unfolds over thousands or millions of years. This extension allows us to conceptualise biological systems as occupying a two-dimensional time space along axes that capture the speed of ecology and evolution. Using Hutchinson's analogy: Time is the ‘theatre’ in which ecology and evolution are two interacting ‘players’. Eco-evolutionary systems are therefore dynamic: We identify modulators of ecological and evolutionary rates, like temperature or sensitivity to mutation, which can change the speed of ecology and evolution, and hence impact eco-evolution. Environmental change may synchronise the speed of ecology and evolution via these rate modulators, increasing the occurrence of eco-evolution and emergent system behaviours. This represents substantial challenges for prediction, especially in the context of global change. Our perspective attempts to integrate ecology and evolution across disciplines, from gene-regulatory networks to geomorphology and across timescales, from today to deep time.     

Population and community consequences of spatial subsidies derived from central-place foraging

Central-place foragers, such as ants, beavers, and colonial seabirds, can act as biological conduits, subsidizing local communities with allochthonous resources. To explore the consequences of such biologically vectored resource redistribution, we draw on an example from cave ecology and develop a population-level model of central-place foraging based on the dispersal kernel framework. We explore how the size of the patch in which central-place foraging occurs and the spatial distribution of foragers within that patch feed back to influence the population dynamics of the central-place forager and the species richness of the associated recipient community. We demonstrate that the particular way in which a population of central-place foragers uses space has two important effects. First, space use determines the stability of the forager population and establishes patch size thresholds for persistence, stable equilibria, and limit cycles. Second, alternative foraging kernels lead to qualitatively different scaling relationships between the size of the foraging patch and species richness back at the central place. These analyses provide a new link among elements of ecology related to animal behavior, population dynamics, and species diversity while also providing a novel perspective on the utility of integrodifference equations for problems in spatial ecology.     

Pollen and seed dispersal inferred from seedling genotypes: the Bayesian revolution has passed here too

Understanding precisely how plants disperse their seeds and pollen in their neighbourhood is a central question for both ecologists and evolutionary biologists because seed and pollen dispersal governs both the rate of spread of an expanding population and gene flow within and among populations. The concept of a 'dispersal kernel' has become extremely popular in dispersal ecology as a tool that summarizes how dispersal distributes individuals and genes in space and at a given scale. In this issue of Molecular Ecology, the study by Moran & Clark (2011) (M&C in the following) shows how genotypic and spatial data of established seedlings can be analysed in a Bayesian framework to estimate jointly the pollen and seed dispersal kernels and finally derive a parentage analysis from a full-probability approach. This approach applied to red oak shows important dispersal of seeds (138 m on average) and pollen (178 m on average). For seeds, this estimate contrasts with previous results from inverse modelling on seed trap data (9.3 m). This research gathers several methodological advances made in recent years in two research communities and could become a cornerstone for dispersal ecology.     

The Galilean turn in population ecology

The standard mathematical models in population ecology assume that a population's growth rate is a function of its environment. In this paper we investigate an alternative proposal according to which the rate of change of the growth rate is a function of the environment and of environmental change. We focus on the philosophical issues involved in such a fundamental shift in theoretical assumptions, as well as on the explanations the two theories offer for some of the key data such as cyclic populations. We also discuss the relationship between this move in population ecology and a similar move from first-order to second-order differential equations championed by Galileo and Newton in celestial mechanics.     

Evidence of hyperplanes in the genetic learning of neural networks

Genetic Algorithms have been successfully applied to the learning process of neural networks simulating artificial life. In previous research we compared mutation and crossover as genetic operators on neural networks directly encoded as real vectors (Manczer and Parisi 1990). With reference to crossover we were actually testing the building blocks hypothesis, as the effectiveness of recombination relies on the validity of such hypothesis. Even with the real genotype used, it was found that the average fitness of the population of neural networks is optimized much more quickly by crossover than it is by mutation. This indicated that the intrinsic parallelism of crossover is not reduced by the high cardinality, as seems reasonable and has indeed been suggested in GA theory (Antonisse 1989). In this paper we first summarize such findings and then propose an interpretation in terms of the spatial correlation of the fitness function with respect to the metric defined by the average steps of the genetic operators. Some numerical evidence of such interpretation is given, showing that the fitness surface appears smoother to crossover than it does to mutation. This confirms indirectly that crossover moves along privileged directions, and at the same time provides a geometric rationale for hyperplanes.     

Linkage and inbreeding coefficients in a finite random mating population

The notion of inbreeding coefficient associated with one single locus introduced by G. Malecot can be extended to two loci. For a panmictic model with separate generation the recurrence equations are given therein allowing to calculate the coefficients in the event of migration and mutation, or loss of kinship.Hence it is derived particularly that the limit genetic distance of two groups associated with two loci is, under specific hypotheses, little different from the sum of marginal genetic distances.For an isolat this paper studies, in terms of crossing over, mutations, and population size, the evolution of the inbreading coefficients of order 2 and especially the difference of this evolution from the evolution to independence of the two loci.     

Parameter redundancy in discrete state‐space and integrated models

Discrete state‐space models are used in ecology to describe the dynamics of wild animal populations, with parameters, such as the probability of survival, being of ecological interest. For a particular parametrization of a model it is not always clear which parameters can be estimated. This inability to estimate all parameters is known as parameter redundancy or a model is described as nonidentifiable. In this paper we develop methods that can be used to detect parameter redundancy in discrete state‐space models. An exhaustive summary is a combination of parameters that fully specify a model. To use general methods for detecting parameter redundancy a suitable exhaustive summary is required. This paper proposes two methods for the derivation of an exhaustive summary for discrete state‐space models using discrete analogues of methods for continuous state‐space models. We also demonstrate that combining multiple data sets, through the use of an integrated population model, may result in a model in which all parameters are estimable, even though models fitted to the separate data sets may be parameter redundant.     

Avoiding Dangerous Missense: Thermophiles Display Especially Low Mutation Rates

Rates of spontaneous mutation have been estimated under optimal growth conditions for a variety of DNA-based microbes, including viruses, bacteria, and eukaryotes. When expressed as genomic mutation rates, most of the values were in the vicinity of 0.003–0.004 with a range of less than two-fold. Because the genome sizes varied by roughly 10⁴-fold, the mutation rates per average base pair varied inversely by a similar factor. Even though the commonality of the observed genomic rates remains unexplained, it implies that mutation rates in unstressed microbes reach values that can be finely tuned by evolution. An insight originating in the 1920s and maturing in the 1960s proposed that the genomic mutation rate would reflect a balance between the deleterious effect of the average mutation and the cost of further reducing the mutation rate. If this view is correct, then increasing the deleterious impact of the average mutation should be countered by reducing the genomic mutation rate. It is a common observation that many neutral or nearly neutral mutations become strongly deleterious at higher temperatures, in which case they are called temperature-sensitive mutations. Recently, the kinds and rates of spontaneous mutations were described for two microbial thermophiles, a bacterium and an archaeon. Using an updated method to extrapolate from mutation-reporter genes to whole genomes reveals that the rate of base substitutions is substantially lower in these two thermophiles than in mesophiles. This result provides the first experimental support for the concept of an evolved balance between the total genomic impact of mutations and the cost of further reducing the basal mutation rate.     

Mutation rate dynamics reflect ecological change in an emerging zoonotic pathogen

Mutation rates vary both within and between bacterial species, and understanding what drives this variation is essential for understanding the evolutionary dynamics of bacterial populations. In this study, we investigate two factors that are predicted to influence the mutation rate: ecology and genome size. We conducted mutation accumulation experiments on eight strains of the emerging zoonotic pathogen Streptococcus suis. Natural variation within this species allows us to compare tonsil carriage and invasive disease isolates, from both more and less pathogenic populations, with a wide range of genome sizes. We find that invasive disease isolates have repeatedly evolved mutation rates that are higher than those of closely related carriage isolates, regardless of variation in genome size. Independent of this variation in overall rate, we also observe a stronger bias towards G/C to A/T mutations in isolates from more pathogenic populations, whose genomes tend to be smaller and more AT-rich. Our results suggest that ecology is a stronger correlate of mutation rate than genome size over these timescales, and that transitions to invasive disease are consistently accompanied by rapid increases in mutation rate. These results shed light on the impact that ecology can have on the adaptive potential of bacterial pathogens.     

Neural rate equations for bursting dynamics derived from conductance-based equations

A method of obtaining rate equations from conductance-based equations is developed and applied to fast-spiking and bursting neocortical neurons. It involves splitting systems of conductance-based equations into fast and slow subsystems, and averaging the effects of fast terms that drive the slowly varying quantities by showing that their average is closely proportional to the firing rate. The dependence of the firing rate on the injected current is then approximated in the analysis. The resulting behavior of the slow variables is then substituted back into the fast equations, with the further approximation of replacing the fast voltages in these terms by effective values. For bursting neurons the method yields two coupled limit-cycle oscillators: a self-exciting oscillator for the slow variables that commences limit-cycle oscillations at a critical current and modulates a fast spike-generating oscillator, thereby leading to slowly modulated bursts with a group of spikes in each burst. The dynamics of these coupled oscillators are then verified against those of the conductance-based equations. Finally, it is shown how to place the results in a form suitable for use in mean-field equations for neural population dynamics.     

Environmental forcing, invasion and control of ecological and epidemiological systems

Destabilising a biological system through periodic or stochastic forcing can lead to significant changes in system behaviour. Forcing can bring about coexistence when previously there was exclusion; it can excite massive system response through resonance, it can offset the negative effect of apparent competition and it can change the conditions under which the system can be invaded. Our main focus is on the invasion properties of continuous time models under periodic forcing. We show that invasion is highly sensitive to the strength, period, phase, shape and configuration of the forcing components. This complexity can be of great advantage if some of the forcing components are anthropogenic in origin. They can be turned into instruments of control to achieve specific objectives in ecology and disease management, for example. Culling, vaccination and resource regulation are considered. A general analysis is presented, based on the leading Lyapunov exponent criterion for invasion. For unstructured invaders, a formula for this exponent can typically be written down from the model equations. Whether forcing hinders or encourages invasion depends on two factors: the covariances between invader parameters and resident populations and the shifts in average resident population levels brought about by the forcing. The invasion dynamics of a structured invader are much more complicated but an analytic solution can be obtained in quadratic approximation for moderate forcing strength. The general theory is illustrated by a range of models drawn from ecology and epidemiology. The relationship between periodic and stochastic forcing is also considered.     

空间搭载诱导水稻种子突变的分子标记多态性分析

以卫星空间搭载广东水稻品种特籼占13干种子,返地种植后经5代选择、培育,获得一批形态及育性变异的突变体及品系（种）,如株高变矮,稻穗变大,雄性不育等。为了探索空间诱变的本质,对选出的6个突变体及2个优良品系,选用了130个10－mer随机扩增多态性DNA（RAPD经物和17对扩增片段长度多态性（AFLP）引物组合,分别对其基因组DNA进行多态性位点扫描分析,两种方法的结果均显示：不同的突变体与原种DNA之间存在不同程度的多态性差异,且由两法得到的结果较接近,为6％－12％。此结果从分子水平上进一步证明了空间环境确实对植物种子存在诱变作用。     

Causes and consequences of pattern diversification in a spatially self-organizing microbial community

Surface-attached microbial communities constitute a vast amount of life on our planet. They contribute to all major biogeochemical cycles, provide essential services to our society and environment, and have important effects on human health and disease. They typically consist of different interacting genotypes that arrange themselves non-randomly across space (referred to hereafter as spatial self-organization). While spatial self-organization is important for the functioning, ecology, and evolution of these communities, the underlying determinants of spatial self-organization remain unclear. Here, we performed a combination of experiments, statistical modeling, and mathematical simulations with a synthetic cross-feeding microbial community consisting of two isogenic strains. We found that two different patterns of spatial self-organization emerged at the same length and time scales, thus demonstrating pattern diversification. This pattern diversification was not caused by initial environmental heterogeneity or by genetic heterogeneity within populations. Instead, it was caused by nongenetic heterogeneity within populations, and we provide evidence that the source of this nongenetic heterogeneity is local differences in the initial spatial positionings of individuals. We further demonstrate that the different patterns exhibit different community-level properties; namely, they have different expansion speeds. Together, our results demonstrate that pattern diversification can emerge in the absence of initial environmental heterogeneity or genetic heterogeneity within populations and can affect community-level properties, thus providing novel insights into the causes and consequences of microbial spatial self-organization.Subject terms: Microbial ecology, Microbial ecology, Biofilms     

Chemoreception by a cell with age-dependent receptor binding sites

The authors determine the time-dependent ligand current into a spherical cell that is covered with a large number of age-dependent receptors. These receptors can be in either of two states: active (i.e., available for ligand binding) or inactive. An active receptor turns inactive upon binding a ligand, and it can reappear as active at some later time. The transition inactive----active is treated as a probabilistic process. The ligand distribution around the cell is determined analytically in terms of this distribution at the cell surface. A set of nonlinear integral equations is derived for the distribution at the cell surface, which is solved numerically. In this way the time-dependent ligand current into the cell as well as the average active receptor population at the cell surface are determined.     

A mathematical theory of capillary exchange as a function of tissue structure

A mathematical theory of the process of the exchange of substances between the blood in the capillaries of a homogeneous tissue and the extracellular space, and between the extracellular space and the cells is developed. An ideal geometry of the tissue is assumed, based to some extent on recent anatomical work concerning the functional distinction between two types of capillaries, the arteriolo-venular and the true capillaries. Equations are developed relating the concentration in the arterial blood to the mean capillary concentration, the concentration at the wall of the capillary in the extracellular space, and the average concentration in the extracellular space, and also relating the cellular concentration to the average extracellular concentration. The solutions of the equations are given for certain special cases and numerical results obtained. It is shown that the average extracellular concentration is a sensitive function of the permeability of the capillary wall and also is strongly influenced by the diffusion coefficient of the extracellular space. Furthermore, it is shown that the speed with which the average extracellular concentration approaches the steady state is largely a function of the permeability of the capillary wall.