Neutral and non-neutral macroecology

Because of the multiscalar nature of processes underlying biodiversity dynamics, macroecology has emerged as a discipline that seeks to build an understanding of this complexity by examining statistical patterns in large assemblages of species in geographic space and ecological time. Models that assume individual organisms within trophically defined assemblages are ecologically equivalent can produce many patterns identified by macroecology. Neutral models predict two important dynamical patterns that can be tested in real assemblages. First, they predict that species diversity will decline within an assemblage over time. The rate of this decay in species diversity can be predicted from estimates of migration rates from a “metacommunity” or species pool. Second, neutral models predict a divergence of species composition among local communities over time. The rate and degree of divergence among communities also depend on the migration rate. The few studies that have been done to date imply that the rate of migration in real species assemblages is much lower than that required to explain the degree of community similarity maintained in space and time. There are at least two alternative ways to extend neutral models to incorporate more biological realism. First, competitive asymmetries among species may be introduced to allow for the possibility that individuals of some species may have an advantage in replacing individuals that die. Second, environmental heterogeneity can be introduced by assuming sites available to individuals differ in quality to individuals of different species. The neutral model, because of its conceptual simplicity and rigor, should be considered as a null model for baseline comparison to actual patterns of distribution, abundance, species composition, and beta diversity.

Zusammenfassung

Wegen der multiskalaren Natur der Prozesse, die der Biodiversitätsdynamik zugrunde liegen, entstand die Makroökologie als eine Disziplin, die anstrebt ein Verständnis dieser Komplexität zu schaffen, indem sie statistische Muster in großen Vergesellschaftungen von Arten im geografischen Raum und ökologischer Zeit untersucht. Modelle, die davon ausgehen, dass individuelle Organismen innerhalb trophisch definierter Vergesellschaftungen ökologisch äquivalent sind, können viele Muster erzeugen, die durch die Makroökologie indentifiziert werden. Neutrale Modelle sagen zwei wichtige dynamische Muster vorher, die in realen Vergesellschaftungen getestet werden können. Als Erstes sagen sie vorher, dass die Artendiversität in einer Vergesellschaftung mit der Zeit abnehmen wird. Die Rate der Abnahme der Artendiversität kann über Schätzungen der Migrationsraten aus einer Metagemeinschaft bzw. einem Artenpool vorhergesagt werden. Als Zweites sagen neutrale Modelle eine Divergenz der Artenzusammensetzung zwischen den lokalen Gemeinschaften mit der Zeit vorher. Die Rate und der Grad der Divergenz zwischen den Gemeinschaften hängt ebenfalls von der Migrationsrate ab. Die wenigen Untersuchungen, die bis heute gemacht wurden, implizieren, dass die Rate der Migration in realen Artenvergesellschaftungen viel geringer als erforderlich sind, um den Grad der Gemeinschaftsähnlichkeit zu erklären, der in Raum und Zeit aufrecht erhalten wird. Es gibt mindestens zwei alternative Weisen neutrale Modelle zu erweitern, um mehr biologische Realität mit einzubeziehen. Als Erstes können Asymmetrien der Konkurrenz unter Arten einbezogen werden, um die Möglichkeit zu zulassen, dass Individuen einiger Arten einen Vorteil bei der Ersetzung von sterbenden Individuen haben. Als Zweites kann die Umweltheterogenität mit einbezogen werden, indem angenommen wird, dass sich die verfügbaren Standorte in ihrer Qualität für Individuen verschiedener Arten unterscheiden. Wegen seiner konzeptuellen Einfachheit und Starrheit sollte das neutrale Modell als Null-Modell für grundlegende Vergleiche von Verbreitung, Abundanz, Artenzusammensetzung und Betadiversität angesehen werden.     

Uniform persistence for sigmoidal diet selection with keystone prey species

In this paper we discuss uniform persistence (UP) criteria of two prey- one predator systems, where we consider that the predator's diet selection is a sigmoidal function of the most profitable prey type in place of a step function of conventional diet choice theory. We also derive UP results of the system with direct interspecific competition between the prey. The role of the most profitable prey item as a keystone species, the magnitude of its carrying capacity, the ability to withstand predation of both prey species, and the ratios of their profitability values (to predators) are important to whether or not adaptive foraging may promote UP. In general, foraging decision rules play no role in UP if the alternative prey item is the keystone species. The result is also not affected by the effect of direct competitive coexistence or dominance relationship of the prey. In some cases, dominance of one of the prey species provides the most advantageous situation for ensuring UP. Received: 1 February 1999 / Revised version: 20 September 1999 / Published online: 4 July 2000     

Unpredictability induced by unfocused games in evolutionary game dynamics

Evolutionary game theory is a basis of replicator systems and has applications ranging from animal behavior and human language to ecosystems and other hierarchical network systems. Most studies in evolutionary game dynamics have focused on a single game, but, in many situations, we see that many games are played simultaneously. We construct a replicator equation with plural games by assuming that a reward of a player is a simple summation of the reward of each game. Even if the numbers of the strategies of the games are different, its dynamics can be described in one replicator equation. We here show that when players play several games at the same time, the fate of a single game cannot be determined without knowing the structures of the whole other games. The most absorbing fact is that even if a single game has a ESS (evolutionary stable strategy), the relative frequencies of strategies in the game does not always converge to the ESS point when other games are played simultaneously.     

带有正负系数的一阶震荡中立型微分方程

本文建立了中立型微分方程d/dt[x（t）-R（t）x（t-r）]＋P（t）x（t-r）-Q（t）x（t-δ）=0震荡的一个充分条件．     

Adaptive foraging does not always lead to more complex food webs

Recent modeling studies exploring the effect of consumers’ adaptivity in diet composition on food web complexity invariably suggest that adaptivity in foraging decisions of consumers makes food webs more complex. That is, it allows for survival of a higher number of species when compared with non-adaptive food webs. Population-dynamical models in these studies share two features: parameters are chosen uniformly for all species, i.e. they are species-independent, and adaptive foraging is described by the search image model. In this article, we relax both these assumptions. Specifically, we allow parameters to vary among the species and consider the diet choice model as an alternative model of adaptive foraging. Our analysis leads to three important predictions. First, for species-independent parameter values for which the search image model demonstrates a significant effect of adaptive foraging on food web complexity, the diet choice model produces no such effect. Second, the effect of adaptive foraging through the search image model attenuates when parameter values cease to be species-independent. Finally, for the diet choice model we observe no (significant) effect of adaptive foraging on food web complexity. All these observations suggest that adaptive foraging does not always lead to more complex food webs. As a corollary, future studies of food web dynamics should pay careful attention to the choice of type of adaptive foraging model as well as of parameter values.     

Evolutionary graph theory: breaking the symmetry between interaction and replacement

We study evolutionary dynamics in a population whose structure is given by two graphs: the interaction graph determines who plays with whom in an evolutionary game; the replacement graph specifies the geometry of evolutionary competition and updating. First, we calculate the fixation probabilities of frequency dependent selection between two strategies or phenotypes. We consider three different update mechanisms: birth-death, death-birth and imitation. Then, as a particular example, we explore the evolution of cooperation. Suppose the interaction graph is a regular graph of degree h, the replacement graph is a regular graph of degree g and the overlap between the two graphs is a regular graph of degree l. We show that cooperation is favored by natural selection if b/c>hg/l. Here, b and c denote the benefit and cost of the altruistic act. This result holds for death-birth updating, weak-selection and large population size. Note that the optimum population structure for cooperators is given by maximum overlap between the interaction and the replacement graph (g=h=l), which means that the two graphs are identical. We also prove that a modified replicator equation can describe how the expected values of the frequencies of an arbitrary number of strategies change on replacement and interaction graphs: the two graphs induce a transformation of the payoff matrix.     

Genetic studies in Ecuador: Acetylator phenotypes,red cell enzyme and serum protein polymorphisms of Shuara Indians

Population genetic studies of Shuara Indians in Ecuador are performed for GPT, AP, PGM₁, Ak, EsD, 6-PGD, Hp, Gc, C3, Bg, ChE, Tf, Pi, Bf phenotypes, IgG, IgA, IgM, C3, C3-proactivator, C4 levels and acetylator phenotypes. Some systems having a polymorphism in many other populations showed a lack of some of those alleles in the population under study (C3, ChE, Tf, AK and almost absent 6-PGD, Bg, Bf).     

Population dynamics with a stable efficient equilibrium

We propose a game-theoretic dynamics of a population of replicating individuals. It consists of two parts: the standard replicator one and a migration between two different habitats. We consider symmetric two-player games with two evolutionarily stable strategies: the efficient one in which the population is in a state with a maximal payoff and the risk-dominant one where players are averse to risk. We show that for a large range of parameters of our dynamics, even if the initial conditions in both habitats are in the basin of attraction of the risk-dominant equilibrium (with respect to the standard replication dynamics without migration), in the long run most individuals play the efficient strategy.     

关于高阶多时滞中立型微分方程的周期解

本文研究高阶常系数线性多时滞中立型方程的周期解,得到了周期解存在的充分 必要条件,改进或推广了文［１－７］的主要结果。     

Stability of the replicator equation for a single species with a multi-dimensional continuous trait space

The replicator equation model for the evolution of individual behaviors in a single species with a multi-dimensional continuous trait space is developed as a dynamics on the set of probability measures. Stability of monomorphisms in this model using the weak topology is compared to more traditional methods of adaptive dynamics. For quadratic fitness functions and initial normal trait distributions, it is shown that the multi-dimensional continuously stable strategy (CSS) of adaptive dynamics is often relevant for predicting stability of the measure-theoretic model but may be too strong in general. For general fitness functions and trait distributions, the CSS is related to dominance solvability which can be used to characterize local stability for a large class of trait distributions that have no gaps in their supports whereas the stronger neighborhood invader strategy (NIS) concept is needed if the supports are arbitrary.     

Game Dynamics with Learning and Evolution of Universal Grammar

We investigate a model of language evolution, based on population game dynamics with learning. First, we examine the case of two genetic variants of universal grammar (UG), the heart of the human language faculty, assuming each admits two possible grammars. The dynamics are driven by a communication game. We prove using dynamical systems techniques that if the payoff matrix obeys certain constraints, then the two UGs are stable against invasion by each other, that is, they are evolutionarily stable. Then, we prove a similar theorem for an arbitrary number of disjoint UGs. In both theorems, the constraints are independent of the learning process. Intuitively, if a mutation in UG results in grammars that are incompatible with the established languages, then the mutation will die out because mutants will be unable to communicate and therefore unable to realize any potential benefit of the mutation. An example for which these theorems do not apply shows that compatible mutations may or may not be able to invade, depending on the population's history and the learning process. These results suggest that the genetic history of language is constrained by the need for compatibility and that mutations in the language faculty may have died out or taken over due more to historical accident than to any straightforward notion of relative fitness. MSC 1991: 37N25 · 92D15 · 91F20     

昆虫种群动态非线性建模理论与应用

本文以非线性动力学为基础,对自然界中昆虫种群动态的复杂性、不确定性进行了建模方法的探讨,在讨论了昆虫种群动态的混沌与非线性时间序列预测方法的前提下,以山东省玉米螟等种群动态资料进行了实例分析。     

From discrete to continuous evolution models: A unifying approach to drift-diffusion and replicator dynamics

We study the large population limit of the Moran process, under the assumption of weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral evolution) or natural selection; for one precise scaling, both effects are present. For the scalings that take the genetic-drift into account, the continuous model is given by a singular diffusion equation, together with two conservation laws that are already present at the discrete level. For scalings that take into account only natural selection, we obtain a hyperbolic singular equation that embeds the Replicator Dynamics and satisfies only one conservation law. The derivation is made in two steps: a formal one, where the candidate limit model is obtained, and a rigorous one, where convergence of the probability density is proved. Additional results on the fixation probabilities are also presented.     

The effect of recombination on the neutral evolution of genetic robustness

Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable, however, it has become apparent that the context dependent effect of mutations and the many-to-one nature inherent in these genotype-phenotype maps can have fundamental evolutionary consequences. It has previously been demonstrated that populations of genotypes evolving on the neutral networks corresponding to all genotypes with the same secondary structure only through neutral mutations can evolve mutational robustness [E. van Nimwegen, J.P. Crutchfield, M. Huynen, Neutral evolution of mutational robustness, Proc. Natl. Acad. Sci. USA 96(17), 9716-9720 (1999)], by concentrating the population on regions of high neutrality. Introducing recombination we demonstrate, through numerically calculating the stationary distribution of an infinite population on ensembles of random neutral networks that mutational robustness is significantly enhanced and further that the magnitude of this enhancement is sensitive to details of the neutral network topology. Through the simulation of finite populations of genotypes evolving on random neutral networks and a scaled down microRNA neutral network, we show that even in finite populations recombination will still act to focus the population on regions of locally high neutrality.     

Neutral space analysis for a Boolean network model of the fission yeast cell cycle network

Background

Interactions between genes and their products give rise to complex circuits known as gene regulatory networks (GRN) that enable cells to process information and respond to external stimuli. Several important processes for life, depend of an accurate and context-specific regulation of gene expression, such as the cell cycle, which can be analyzed through its GRN, where deregulation can lead to cancer in animals or a directed regulation could be applied for biotechnological processes using yeast. An approach to study the robustness of GRN is through the neutral space. In this paper, we explore the neutral space of a Schizosaccharomyces pombe (fission yeast) cell cycle network through an evolution strategy to generate a neutral graph, composed of Boolean regulatory networks that share the same state sequences of the fission yeast cell cycle.

Results

Through simulations it was found that in the generated neutral graph, the functional networks that are not in the wildtype connected component have in general a Hamming distance more than 3 with the wildtype, and more than 10 between the other disconnected functional networks. Significant differences were found between the functional networks in the connected component of the wildtype network and the rest of the network, not only at a topological level, but also at the state space level, where significant differences in the distribution of the basin of attraction for the G₁ fixed point was found for deterministic updating schemes.

Conclusions

In general, functional networks in the wildtype network connected component, can mutate up to no more than 3 times, then they reach a point of no return where the networks leave the connected component of the wildtype. The proposed method to construct a neutral graph is general and can be used to explore the neutral space of other biologically interesting networks, and also formulate new biological hypotheses studying the functional networks in the wildtype network connected component.     

非线性年龄结构种群发展方程解的存在唯一性

本文讨论非线性年龄结构种群动力系统,证明了方程的解的存在唯一性．     

Use of isoenzyme and protein phenotypes to discriminate between six Pratylenchus species from Great Britain

Six species of Pratylenchus indigenous to Great Britain, P. crenatus, P. fallax, P. neglectus, P. penetrans, P. pinguicaudatus and P. thornei were analysed by slab gel electrophoresis to compare protein patterns and isoenzyme phenotypes of esterase, glucose-6-phosphate dehydrogenase, isocitrate dehydrogenase, phosphoglucose isomerase and phosphoglucomutase. Multiple electromorphs were obtained from all enzymes examined. The results demonstrated that isoenzyme phenotypes are useful to supplement the morphological characterisation of these nematode species. Pair-wise comparisons of the six species were performed giving coefficients of similarity in the range 11–41%. A dendrogram of the six species, generated from the five enzyme banding patterns, gave two groups: group 1 contained P. pinguicaudatus, P. fallax and P. thornei and group 2 contained P. penetrans, P. neglectus and P. crenatus.     

Research of population with impulsive perturbations based on dynamics of a neutral delay equation and ecological quality system

This paper studies the global behaviors of a nonlinear autonomous neutral delay differential population model with impulsive perturbation. This model may be suitable for describing the dynamics of population with long larval and short adult phases. It is shown that the system may have global stability of the extinction and positive equilibria, or grow without being bounded under some conditions.     

Statistical mechanics of relative species abundance

Statistical mechanics of relative species abundance (RSA) patterns in biological networks is presented. The theory is based on multispecies replicator dynamics equivalent to the Lotka–Volterra equation, with diverse interspecies interactions. Various RSA patterns observed in nature are derived from a single parameter related to productivity or maturity of a community. The abundance distribution is formed like a widely observed left-skewed lognormal distribution. It is also found that the “canonical hypothesis” is supported in some parameter region where the typical RSA patterns are observed. As the model has a general form, the result can be applied to similar patterns in other complex biological networks, e.g. gene expression.     

CSS, NIS and dynamic stability for two-species behavioral models with continuous trait spaces

Static continuously stable strategy (CSS) and neighborhood invader strategy (NIS) conditions are developed for two-species models of frequency-dependent behavioral evolution when individuals have traits in continuous strategy spaces. These are intuitive stability conditions that predict the eventual outcome of evolution from a dynamic perspective. It is shown how the CSS is related to convergence stability for the canonical equation of adaptive dynamics and the NIS to convergence to a monomorphism for the replicator equation of evolutionary game theory. The CSS and NIS are also shown to be special cases of neighborhood p^*- superiority for p^* equal to one half and zero, respectively. The theory is illustrated when each species has a one-dimensional trait space.