This article presents a statistic for testing the sphericity in a GMANOVA- MANOVA model with normal error. It is shown that the null distribution of this statistic is beta and its nonnull distribution is given in series form of beta distributions.
Research on species interactions has generally assumed that species have a fixed interaction and therefore linear or non-linear parametric regression models (e.g. exponential, logistic) have been widely used to describe the species interaction. However, these models that describe the relationship between interacting species as a specific functional response might not be appropriate for real biological communities, for instance, in a chaotic system, when the species relationship varies among different situations. To allow a more accurate description of the relationship, we developed a species correlation model with varying coefficient analysis, in which a non-parametric estimation is applied to identify, as a function of related factors, variation in the correlation coefficient. This was applied to a fig-fig wasp model system. When the effect of the factors on the relationship can be described with parameters, the new method reduces to traditional parametric correlation analysis. In this way, the new method is more general and flexible for empirical data analyses, but different by allowing investigation of whether a species interaction varies with respect to factors, and of the factors that maintain or change the species interaction. This method will have important applications in both theoretical and applied research (e.g. epidemiology, community management).
SHI LeiWANG RuiWuZHU LiXingZEN WeiMingXU WangLiZHENG Qi
Classical theories explaining the evolution of cooperation often rely on the assumption that the involved players are symmetrically interacted.However,in reality almost all well-documented cooperation systems show that cooperative players are in fact asymmetrically interacted and that this dynamic may greatly affect the cooperative behavior of the involved players.Here,we developed several models based on the most well known spatial game of the Hawk-Dove game,while also considering the effects of asymmetric interaction.Such asymmetric games possess four kinds of strategies:cooperation or defection of strong player and cooperation or defection of weak player.Computer simulations showed that the probability of defection of the strong player decreases with decreasing the benefit to cost ratio,and that all kinds of strategy will be substituted by cooperation on behalf of the strong player if the benefit to cost ratio is sufficiently small.Moreover,weak players find it difficult to survive and the surviving weak players are mostly defectors,similar to the Boxed Pigs game.Interestingly,the patterns of kinds of strategies are chaotic or oscillate in some conditions with the related factors.
Explaining the "Tragedy of the Commons" of the evolution of cooperation remains one of the greatest problems for both biology and social science.Asymmetrical interaction,which is one of the most important characteristics of cooperative systems,has not been sufficiently considered in the existing models of the evolution of cooperation.Considering the inequality in the number and payoff between the cooperative actors and recipients in cooperation systems,discriminative density-dependent interference competition will occur in limited dispersal systems.Our model and simulation show that the local but not the global stability of a cooperative interaction can be maintained if the utilization of common resource remains unsaturated,which can be achieved by density-dependent restraint or competition among the cooperative actors.More intense density dependent interference competition among the cooperative actors and the ready availability of the common resource,with a higher intrinsic contribution ratio of a cooperative actor to the recipient,will increase the probability of cooperation.The cooperation between the recipient and the cooperative actors can be transformed into conflict and,it oscillates chaotically with variations of the affecting factors under different environmental or ecological conditions.The higher initial relatedness(i.e.similar to kin or reciprocity relatedness),which is equivalent to intrinsic contribution ratio of a cooperative actor to the recipient,can be selected for by penalizing less cooperative or cheating actors but rewarding cooperative individuals in asymmetric systems.The initial relatedness is a pivot but not the aim of evolution of cooperation.This explains well the direct conflict observed in almost all cooperative systems.
WANG RuiWu1 & SHI Lei2 1 State Key Laboratory of Genetic Resources and Evolution,Kunming Institute of Zoology,Chinese Academy of Science,Kunming 650223,China
