Variables aggregation in a time discrete linear model

In this work we extend approximate aggregation methods to deal with a very general linear time discrete model. Approximate aggregation consists in describing some features of the dynamics of a general system in terms of the dynamics of a reduced system governed by a few global variables. We present a time discrete model for a structured population (i.e., the population is subdivided in subpopulations) in which we can distinguish two processes of a general nature and whose corresponding time scales are very different from each other. We transform the general system to make the global variables appear and obtain the reduced system. These global variables are, for each subpopulation, a certain linear combination of the corresponding state variables. We show that, under quite general conditions, the asymptotic behavior of the reduced system can be known in terms of the corresponding behavior for the reduced system. The general method is applied to aggregate a multiregional Leslie model in which the demographic process is supposed to be fast with respect to migration.     

非自治阶段结构合作系统的持久性与周期解

本文研究一类非自治阶段结构的合作系统,得到系统的最终有界性,对应周期系统正周期解的存在性,唯一性以及全局渐近稳定性的充分条件。     

Impact of demography on extinction/fixation events

In this article we consider diffusion processes modeling the dynamics of multiple allelic proportions (with fixed and varying population size). We are interested in the way alleles extinctions and fixations occur. We first prove that for the Wright–Fisher diffusion process with selection, alleles get extinct successively (and not simultaneously), until the fixation of one last allele. Then we introduce a very general model with selection, competition and Mendelian reproduction, derived from the rescaling of a discrete individual-based dynamics. This multi-dimensional diffusion process describes the dynamics of the population size as well as the proportion of each type in the population. We prove first that alleles extinctions occur successively and second that depending on population size dynamics near extinction, fixation can occur either before extinction almost surely, or not. The proofs of these different results rely on stochastic time changes, integrability of one-dimensional diffusion processes paths and multi-dimensional Girsanov’s tranform.

     

Cooperative hunting in a discrete predator–prey system II

ABSTRACT

We investigate a discrete-time predator–prey system with cooperative hunting in the predators proposed by Chow et al. by determining local stability of the interior steady states analytically in certain parameter regimes. The system can have either zero, one or two interior steady states. We provide criteria for the stability of interior steady states when the system has either one or two interior steady states. Numerical examples are presented to confirm our analytical findings. It is concluded that cooperative hunting of the predators can promote predator persistence but may also drive the predator to a sudden extinction.     

On the further integration of cooperative breeding and cooperation theory

We present a synopsis about the commentaries to the target article "Integrating cooperative breeding into theoretical concepts of cooperation", in which we attempted to integrate general mechanisms to explain cooperative behaviour among unrelated individuals with classic concepts to explain helping behaviour in cooperative breeders that do not invoke kin-based benefits. Here we (1) summarize the positions of the commentators concerning the main issues we raised in the target article and discuss important criticisms and extensions. (2) We relate our target article to some recent reviews on the evolution of cooperation and, (3) clarify how we use terminology with regard to cooperation and cooperative behaviour. (4) We discuss several aspects that were raised with respect to cooperative interactions including by-product mutualism, generalised reciprocity and multi-level selection and, (5) examine the alternatives to our classification scheme as proposed by some commentaries. (6) Finally, we highlight several aspects that might hinder the application of game theoretical mechanisms of cooperation in cooperatively breeding systems. Although there is broad agreement that cooperative breeding theory should be integrated within the more general concepts of cooperation, there is some debate about how this may be achieved. We conclude that the contributions in this special issue provide a fruitful first step and ample suggestions for future directions with regard to a more unified framework of cooperation in cooperative breeders.     

Stochastic treatment of cooperative specific adsorption

A stochastic treatment of cooperative specific adsorption of ions at a linear chain of discrete sites leads to a set of differential equations for the various probabilities involved in which the coefficients are determined by nearest neighbor interactions and relative adsorption specificities of the ions for the sites. It is shown that the cooperative specific adsorption isotherm derived earlier on the basis of statistical mechanics for essentially a very large number of sites can be obtained with maximum deviations of only three per cent with this approach by considering only five sites.     

HORIZONTAL GENE TRANSFER AND THE EVOLUTION OF BACTERIAL COOPERATION

Bacteria frequently exhibit cooperative behaviors but cooperative strains are vulnerable to invasion by cheater strains that reap the benefits of cooperation but do not perform the cooperative behavior themselves. Bacterial genomes often contain mobile genetic elements such as plasmids. When a gene for cooperative behavior exists on a plasmid, cheaters can be forced to cooperate by infection with this plasmid, rescuing cooperation in a population in which mutation or migration has allowed cheaters to arise. Here we introduce a second plasmid that does not code for cooperation and show that the social dilemma repeats itself at the plasmid level in both within‐patch and metapopulation scenarios, and under various scenarios of plasmid incompatibility. Our results suggest that although plasmid carriage of cooperative genes can provide a transient defense against defection in structured environments, plasmid and chromosomal defection remain the only stable strategies in an unstructured environment. We discuss our results in the light of recent bioinformatic evidence that cooperative genes are overrepresented on mobile elements.     

Morphometric variation in the hominoid orbital aperture: a case study with implications for the use of variable characters in Miocene catarrhine systematics

Variable characters are ubiquitous in hominoid systematics and present a number of unique problems for phylogenetic analyses that include extinct taxa. As yet, however, few studies have quantified ranges of variation in complex morphometric characters within extant taxa and then used those data to assess the consistency with which discrete character states can be applied to poorly represented fossil species. In this study, ranges of intrageneric morphometric variation in the shape of the hominoid orbital aperture are estimated using exact randomization of average pairwise taxonomic distances (ATDs) derived from size-adjusted centroid, height-width, and elliptic Fourier (EF) variables. Using both centroid and height-width variables, 19 of the 21 possible ATDs between individuals representing seven extinct catarrhine taxa (Aegyptopithecus, Afropithecus, Ankarapithecus, Ouranopithecus, Paranthropus, Sivapithecus and Turkanapithecus) can be observed within a single extant hominoid subspecies, although generally with low probabilities. A resampling study is employed as a means for gauging the effect that this intrataxonomic variation may have on the consistency with which discrete orbital shape character states can be delimited given the small sample sizes available for most Miocene catarrhine taxa preserving this feature (i.e., n=1). For each type of morphometric variable, 100 cluster (UPGMA) analyses of pairwise ATDs are performed in which a single individual is randomly selected from each hominoid genus and analyzed alongside known extinct taxa; consensus trees are computed in order to obtain the frequencies with which different shape clusters appeared in each of the three analyses. The two major clusters appearing most frequently in all three consensus trees are found in only 57% (centroid variables), 49% (height-width variables), and 36% (EF variables) of these trees. If ranges of variation within represented extinct taxa could also be estimated, these frequencies would certainly be far lower. Hominoids clearly exhibit considerable intrageneric, intraspecific, and even intrasubspecific variation in orbit shape, and substantial morphometric overlap exists between taxa; consequently, discrete character states delimiting these patterns of continuous variation are likely to be highly unreliable in phylogenetic analyses of living and extinct species, particularly as the number of terminal taxa increases. Morphological phylogenetic studies of extant catarrhines that assess the effect of different methods (e.g., use of objective a priori weighting or frequency coding of variable characters, inclusion vs. exclusion of variable characters, use of specific vs. supraspecific terminal taxa) on phylogenetic accuracy may help to improve the techniques that systematists employ to make phylogenetic inferences about extinct taxa.     

一类扩散循环系统正解的存在性与稳定性

利用上下解方法及全藕合线性互惠系统的最大值原理,研究了一类非线性椭圆系统,给出了其正解存在的充分必要条件,同时也得到了其正解局部稳定的某些结果．     

Breeding system evolution influenced the geographic expansion and diversification of the core Corvoidea (Aves: Passeriformes)

Birds vary greatly in their life‐history strategies, including their breeding systems, which range from brood parasitism to a system with multiple nonbreeding helpers at the nest. By far the most common arrangement, however, is where both parents participate in raising the young. The traits associated with parental care have been suggested to affect dispersal propensity and lineage diversification, but to date tests of this potential relationship at broad temporal and spatial scales have been limited. Here, using data from a globally distributed group of corvoid birds in concordance with state‐dependent speciation and extinction models, we suggest that pair breeding is associated with elevated speciation rates. Estimates of transition between breeding systems imply that cooperative lineages frequently evolve biparental care, whereas pair breeders rarely become cooperative. We further highlight that these groups have differences in their spatial distributions, with pair breeders overrepresented on islands, and cooperative breeders mainly found on continents. Finally, we find that speciation rates appear to be significantly higher on islands compared to continents. These results imply that the transition from cooperative breeding to pair breeding was likely a significant contributing factor facilitating dispersal across tropical archipelagos, and subsequent world‐wide phylogenetic expansion among the core Corvoidea.     

多假设成立的多agent合作决策

对复杂环境对象进行决策时,多agent合作可以融合各agent的知识经验,提高决策结果的可靠性,针对环境对象的辩识空间中多假设同时成立的决策问题,本文提出了一种基于证据理论的多agent合作决策算法,详细描述与分析了多agent合作决策的原理。为提高系统决策的可靠性,降低了合成计算的复杂度,在多agent合作决策系统中引入正确的训练案例进行学习。本文提出的算法应用于蔬菜的病害判别,实验结果验证了本文提出的多agent合作决策算法的有效性。     

Life-history characters and phylogeny are correlated with extinction risk in the Australian angiosperms

Aim To determine whether life‐history characters that affect population persistence (e.g. habit and life span) and those that influence reproductive success (e.g. sexual system and fruit type) are non‐randomly correlated with extinction risk (i.e. threat category) in the Australian flora (c. 19,000 species, of which c. 14% is threatened). To identify patterns that present useful conservation directions. To understand patterns of extinction risk in the Australian flora at a broad scale. Location Continental Australia. Methods A country‐wide exploration of four life‐history characters in the Australian flora (n = 18,822 species) was undertaken using reference texts, expert opinion, herbarium records and field work. For each character and threat‐category combination, a G‐test (using a log‐linear model) was performed to test the null hypothesis that the two factors were independent in their effects on count. A generalized linear model (GLM) with a logit link and binomial error distribution was constructed with the proportion of taxa in each extinction risk category as the response variable and the habit, sex and fruit‐type characters as explanatory terms. In a separate approach, we investigated patterns across the threat categories of non‐endangered extant, endangered, and extinct using a multinomial model. We examined whether or not species‐poor genera were more likely to contain threatened or extinct species than species‐rich genera. A GLM with a binomial error distribution and logit link function was constructed to obtain a weighted regression on the proportion of species listed as extinct or endangered within a genus versus the log of the size of the genus. We also used a supertree analysis and character tracing to investigate the role of phylogeny on extinction risk. Results We found that the Australian flora is primarily composed of bisexual shrubs with dry‐dehiscent fruits. Dioecious breeding systems (separate female and male flowers on separate plants) in many floras are the predominant unisexual system, but in Australia there are unexpectedly high levels of monoecy (separate female and male flowers on the same plant). Within the extinct data set of 31 species we detected a significant departure from that expected for habit but not for life span, sexual system or fruit type. There are significantly fewer trees on the extinct list than expected. This may reflect the greater resilience of trees than of other growth habits to extinction processes as well as the observation time‐frame. Within the endangered data set of 450 species we found significant differences in the representation of the observed characters from that expected within sex systems and fruit types. We show that, depending on the life form, unisexual breeding systems can be significantly and positively associated with endangered species compared with non‐threatened species. For example, there are more monoecious species than expected by chance among the tree species listed as endangered but fewer among the herbaceous life forms. Threat category was found to be non‐randomly clustered in some clades. Main conclusions Life‐history characters in certain combinations are predictive of extinction risk. Phylogeny is also an important component of extinction risk. We suggest that specific life‐history characters could be used for conservation planning and as an early warning sign for detecting vulnerability in lists of species.     

Persistence and patchiness of predator-prey systems induced by discrete event population exchange mechanisms

We consider a spatially distributed predator-prey system in which population exchange between cells can occur at only certain points in the predation cycle. Studying the characteristics of this discrete event model, by both analytic and simulation methods, we show that indefinite persistence of populations is possible over a wide range of parameter settings, even though the cells all tend to rapid extinction in isolation. The persistence is shown to take two forms: one in which a constant distribution of cells both in phase and space is maintained, and one in which this homogeneity of distribution is replaced by dynamically stable patterns of patches and waves. The former is shown to be neatly describable by the classical Lotka-Volterra equation. In contrast, persistence of locally unstable Lotka-Volterra predator-prey systems in both forms is shown to be impossible when the discrete population exchange mechanism is replaced by one of the continuous linear diffusion type.     

Cooperative charge fluctuations by migrating protons in globular proteins

A review of the hydrogen bonded network on the protein surface shows the presence of a charged complex system with parallel and competitive interactions, including ionizable side-chains, migrating protons, bound water and nearby backbone peptides. This system displays cooperative effects of dynamical nature, reviewed for lysozyme as a case. By increasing the water coverage of the protein powder, the bound water cluster exhibits a percolative transition, detectable by the onset of large water-assisted displacements of migrating protons, with a parallel emergence of protein mobility and biological function. By lowering the temperature, migrating protons exhibit a glassy dielectric relaxation in the low frequency range, pointing to a frustration by competing interactions similar to that observed in spin glasses and fragile glass forming liquids. The observation of these dissipative processes implies the occurrence of spontaneous charge fluctuations. A simplified model of the protein surface, where conformational and ionizable side-chain fluctuations are averaged out, is used to discuss the statistical physics of these cooperative effects. Some biological implications of this dynamical cooperativity for enzymatic activity are briefly suggested at the end.     

Multiscale analysis of pattern formation via intercellular signalling

Lateral inhibition, a juxtacrine signalling mechanism by which a cell adopting a particular fate inhibits neighbouring cells from doing likewise, has been shown to be a robust mechanism for the formation of fine-grained spatial patterns (in which adjacent cells in developing tissues diverge to achieve contrasting states of differentiation), provided that there is sufficiently strong feedback. The fine-grained nature of these patterns poses problems for analysis via traditional continuum methods since these require that significant variation takes place only over lengthscales much larger than an individual cell and such systems have therefore been investigated primarily using discrete methods. Here, however, we apply a multiscale method to derive systematically a continuum model from the discrete Delta-Notch signalling model of Collier et al. (J.R. Collier, N.A.M. Monk, P.K. Maini, J.H. Lewis, Pattern formation by lateral inhibition with feedback: a mathematical model of Delta-Notch intercellular signalling, J. Theor. Biol., 183, 1996, 429-446) under particular assumptions on the parameters, which we use to analyse the generation of fine-grained patterns. We show that, on the macroscale, the contact-dependent juxtacrine signalling interaction manifests itself as linear diffusion, motivating the use of reaction-diffusion-based models for such cell-signalling systems. We also analyse the travelling-wave behaviour of our system, obtaining good quantitative agreement with the discrete system.     

Cooperativity in nucleosomes assembly on supercoiled pBR322 DNA.

Many studies have shown that in reconstituted chromatin model systems, containing only purified DNA and histone octamer, nucleosomes can adopt well defined locations with respect to DNA nucleotide sequence. Recently, nucleosome-nucleosome interactions were suggested as one of the factors underlying preferential nucleosomes positioning. In the present paper this aspect has been studied by topological analysis and electron microscopy visualization of minichromosomes reconstituted at different histone/DNA ratios. Both methods suggest that cooperativity plays a role in nucleosomes formation. A linear cooperative model in which nucleosomes are formed on discrete sites with cooperative interactions occurring only between nearest neighbours allows to calculate the cooperative constant. The reported results show that basic interactions, which are of relevance in the process of chromatin folding, are present also in very simple model system.     

An unusual case of cooperative hunting in a solitary carnivore

Cooperative hunting has been documented for several group-living carnivores and had been invoked as either the cause or the consequence of sociality. We report the first detailed observation of cooperative hunting for a solitary species, the Malagasy fossa (Cryptoprocta ferox). We observed a 45 min hunt of a 3 kg arboreal primate by three male fossas. The hunters changed roles during the hunt and subsequently shared the prey. We hypothesize that social hunting in fossas could have either evolved to take down recently extinct larger lemur prey, or that it could be a by-product of male sociality that is beneficial for other reasons.