Stochastic model of population growth and spread

A stochastic model for the population regulated by logistic growth and spreading in a given region of two-or three-dimensional space has been introduced. For many-species population the interactions among the species have also been icorporated in this model. From the random variables that describe stochastic processes of a Wiener type the space-dependent random population densities have been formed and shown to satisfy the Langevin equations. The Fokker-Planck equation corresponding to these Langevin equations has been approximately solved for the transition probability of the population spreading and it has been found that such approximate expressions of the transition probability depend on the solutions of the deterministic equations of the diffusion model with logistic growth and interactions. Also, the stationary or equilibrium solutions of the Fokker-Planck equation together with the special discussion on the pattern of single-species population spreading have been made.     

Some simple models of cannibalism

A sequence of mathematical models for a species which engages in cannibalism are investigated. The models treat the species as age-structured, and assume that adults consume the unhatched eggs of their own kind. The McKendrick or von Foerster partial differential equation model is first converted into a set of three coupled, nonlinear ordinary differential equations, and then adjusted to describe cannibalism. Some rather unusual dynamical effects are discovered. These include both a Hopf bifurcation and a catastrophic transition from an asymptotically stable equilibrium point to a stable limit cycle.     

Dispersal and competition models for plants

New models for seed dispersal and competition between plant species are formulated and analyzed. The models are integrodifference equations, discrete in time and continuous in space, and have applications to annual and perennial species. The spread or invasion of a single plant species into a geographic region is investigated by studying the travelling wave solutions of these equations. Travelling wave solutions are shown to exist in the single-species models and are compared numerically. The asymptotic wave speed is calculated for various parameter values. The single-species integrodifference equations are extended to a model for two competing annual plants. Competition in the two-species model is based on a difference equation model developed by Pakes and Maller [26]. The two-species model with competition and dispersal yields a system of integrodifference equations. The effects of competition on the travelling wave solutions of invading plant species is investigated numerically.     

Species colonisation,not competitive exclusion,drives community overdispersion over long‐term succession

Ecological communities often transition from phylogenetic and functional clustering to overdispersion over succession as judged by space‐for‐time substitution studies. Such a pattern has been generally attributed to the increase in competitive exclusion of closely related species with similar traits through time, although colonisation and extinction have rarely been examined. Using 44 years of uninterrupted old‐field succession in New Jersey, USA, we confirmed that phylogenetic and functional clustering decreased as succession unfolded, but the transition was largely driven by colonisation. Early colonists were closely related and functionally similar to residents, while later colonists became less similar to the species present. Extirpated species were generally more distantly related to residents than by chance, or exhibited random phylogenetic/functional patterns, and their relatedness to residents was not associated with time. These results provide direct evidence that the colonisation of distant relatives, rather than extinction of close relatives, drives phylogenetic and functional overdispersion over succession.     

The probability distribution of ranked gene trees on a species tree

The properties of random gene tree topologies have recently been studied under a coalescent model that treats a species tree as a fixed parameter. Here we develop the analogous theory for random ranked gene tree topologies, in which both the topology and the sequence of coalescences for a random gene tree are considered. We derive the probability distribution of ranked gene tree topologies conditional on a fixed species tree. We then show that similar to the unranked case, ranked gene trees that do not match either the ranking or the topology of the species tree can have greater probability than the matching ranked gene tree.     

Emergence of non-random structure in local food webs generated from randomly structured regional webs

Previous studies have shown that high-resolution, empirical food webs possess a non-random network structure, typically characterized by uniform or exponential degree distributions. However, the empirical food webs that have been investigated for their structural properties represent local communities that are only a subset of a larger pool of regionally coexisting species. Here, we use a simple model to investigate the effects of regional food web structure on local food webs that are assembled by two simple processes: random immigration of species from a source web (regional food web), and random extinction of species within the local web. The model shows that local webs with non-random degree distributions can arise from randomly structured source webs. A comparison of local webs assembled from randomly structured source webs with local webs assembled from source webs generated by the niche model shows that the former have higher species richness at equilibrium, but have a nonlinear response to changing extinction rates. These results imply that the network structure of regional food webs can play a significant role in the assembly and dynamics of local webs in natural ecosystems. With natural landscapes becoming increasingly fragmented, understanding such structure may be a necessary key to understanding the maintenance and stability of local species diversity.     

Probability distribution of haplotype frequencies under the two-locus Wright-Fisher model by diffusion approximation

The probability distribution of haplotype frequencies in a population, and the way it is influenced by genetical forces such as recombination, selection, random drift ...is a question of fundamental interest in population genetics. For large populations, the distribution of haplotype frequencies for two linked loci under the classical Wright-Fisher model is almost impossible to compute because of numerical reasons. However the Wright-Fisher process can in such cases be approximated by a diffusion process and the transition density can then be deduced from the Kolmogorov equations. As no exact solution has been found for these equations, we developed a numerical method based on finite differences to solve them. It applies to transient states and models including selection or mutations. We show by several tests that this method is accurate for computing the conditional joint density of haplotype frequencies given that no haplotype has been lost. We also prove that it is far less time consuming than other methods such as Monte Carlo simulations.     

Weakly nonlinear stability analyses of one-dimensional Turing pattern formation in activator-inhibitor/immobilizer model systems

The development of one-dimensional Turing patterns characteristic of the chlorite-iodide-malonic acid/starch reaction as well as analogous Brussellator/immobilizer and Schnackenberg/immobilizer model systems is investigated by means of a weakly nonlinear stability analysis applied to the appropriately scaled governing equations. Then the theoretical predictions deduced from these pattern formation studies are compared with experimental evidence relevant to the Turing diffusive instabilities under examination in order to explain more fully the transition to such stationary symmetry-breaking spatial structures when the temperature or pool species concentrations vary.     

Dynamics of Random Boolean Networks under Fully Asynchronous Stochastic Update Based on Linear Representation

A novel algebraic approach is proposed to study dynamics of asynchronous random Boolean networks where a random number of nodes can be updated at each time step (ARBNs). In this article, the logical equations of ARBNs are converted into the discrete-time linear representation and dynamical behaviors of systems are investigated. We provide a general formula of network transition matrices of ARBNs as well as a necessary and sufficient algebraic criterion to determine whether a group of given states compose an attractor of length in ARBNs. Consequently, algorithms are achieved to find all of the attractors and basins in ARBNs. Examples are showed to demonstrate the feasibility of the proposed scheme.     

II. Transient phase of two-substrate enzyme systems

The time dependence in the transient phase of the two-substrate enzyme systems which evolve according to the random ternary-complex, ordered ternary-complex, ping-pong bi-bi and Theorell-Chance mechanisms has been studied. With this purpose, the equations derived in paper I have been applied. This has allowed to propose a method in order to obtain the rate constant values of these enzyme reactions. In addition, we show that, from experimental knowledge of the induction periods of the ligand species, it is possible to give a method which allows to discriminate between these mechanisms.     

Conformational transition state is responsible for assembly of microtubule-binding domain of tau protein

In the brains of Alzheimer's disease patients, the tau protein dissociates from the axonal microtubule and abnormally aggregates to form a paired helical filament (PHF). One of the priorities in Alzheimer research is to clarify the mechanism of PHF formation. Although several reports on the regulation of tau assembly have been published, it is not yet clear whether in vivo PHFs are composed of beta-structures or alpha-helices. Since the four-repeat microtubule-binding domain (4RMBD) of the tau protein has been considered to play an essential role in PHF formation, its heparin-induced assembly propensity was investigated by the thioflavin fluorescence method to clarify what conformation is most preferred for the assembly. We analyzed the assembly propensity of 4RMBD in Tris-HCl buffer with different trifluoroethanol (TFE) contents, because TFE reversibly induces the transition of the random structure to the alpha-helical structure in an aqueous solution. Consequently, it was observed that the 4RMBD assembly is most significantly favored to proceed in the 10-30% TFE solution, the concentration of which corresponds to the activated transition state of 4RMBD from a random structure to an alpha-helical structure, as determined from the circular dichroism (CD) spectral changes. Since such an assembly does not occur in a buffer containing TFE of < 10% or > 40%, the intermediate conformation between the random and alpha-helical structures could be most responsible for the PHF formation of 4RMBD. This is the first report to clarify that the non-native alpha-helical intermediate in transition from random coil is directly associated with filament formation at the start of PHF formation.     

Niche overlap and invasion of competitors in random environments I. Models without demographic stochasticity

The relationship between persistent, small to moderate levels of random environmental fluctuations and limits to the similarity of competing species is studied. The analytical theory hinges on deriving conditions under which a rare invading species will tend to increase when faced with an array of resident competitors in a fluctuating environment. A general approximation scheme predicts that the effects of low levels of stochasticity will typically be small. The technique is applied explicitly to a class of symmetric, discrete-time stochastic analogs of the Lotka-Volterra equations that incorporate cross-correlation but no autocorrelation. The random environment limits to similarity are always very close to the corresponding constant environment limits. However, stochasticity can either facilitate or hinder invasion. The exact limits to similarity are extremely model-dependent. In addition to the symmetric models, an analytically tractable class of models is presented that incorporates both auto- and cross-correlation and no symmetry assumptions. For all of the models investigated, the analytical theory predicts that small-scale stochasticity does little, if anything, to limit similarity. Extensive Monte Carlo results are presented that confirm the analytical results whenever the dynamics of the discretetime models are biologically reasonable in the sense that trajectories do not exhibit unrealistic crashes. Interestingly, the class of stochastic models that is well behaved in this sense includes models whose deterministic analogs are chaotic. The qualitative conclusion, supported by both the analytical and simulation results, is that for competitive guilds adequately modeled by Lotka-Volterra equations including small to moderate levels of random fluctuations, practical limits to similarity can be obtained by ignoring the stochastic terms and performing a deterministic analysis. The mathematical and biological robustness of this conclusion is discussed.     

Structures of steady states of an enzyme reaction in a CSTR

Structures at steady states have been investigated for an enzyme reaction in a continuous stirred tank reactor that has a random bi-uni reaction mechanism, using the imperfect bifurcation theory via singularities. The analysis has shown that two types of singular points exist. One of these points has the two types of transition states characterized by the hysteresis and double-limit points. It is obtained when the derivative of the steady-state equation with respect to the bifurcation parameter does not vanish. When the derivative vanishes, the other type of singular point is obtained. This point has the two transition states of hysteresis and bifurcation points.     

In vitro control of floral transition in tomato (Lycopersicon esculentum Mill.), the model for autonomously flowering plants, using the late flowering uniflora mutant.

In vitro control of floral transition in tomato (Lycopersicon esculentum Mill.), the model plant for autonomously flowering species has been investigated using the late flowering mutant uniflora (uf). Apices collected from truly vegetative plants were cultivated on solid media supplemented with different combinations of growth regulators and chemicals. Several chemical factors implicated in the promotion of floral transition of the uf mutant have been identified: sucrose, cytokinins and nitrogenous nutrients have all to be supplied at optimal concentrations. In contrast, gibberellic acid was found to be inhibitory. These results are discussed in relation to knowledge accumulated on the nature of the flowering signals circulating, at floral transition, in other plants, especially in photoperiodic species. This study suggests that tomato could constitute an adequate model to investigate the genetic and physiological control of floral transition and contribute in unravelling pathways which are constitutively regulating this important step of plant life cycle.     

Asymptotic states and topological structure of an activation-deactivation chemical network

The influence of the topology on the asymptotic states of a network of interacting chemical species has been studied by simulating its time evolution. Random and scale-free networks have been designed to support relevant features of activation-deactivation reactions networks (mapping signal transduction networks) and the system of ordinary differential equations associated to the dynamics has been numerically solved. We analysed stationary states of the dynamics as a function of the network's connectivity and of the distribution of the chemical species on the network; we found important differences between the two topologies in the regime of low connectivity. In particular, only for low connected scale-free networks it is possible to find zero activity patterns as stationary states of the dynamics which work as signal off-states. Asymptotic features of random and scale-free networks become similar as the connectivity increases.     

Wide-band tracheids are present in almost all species of Cactaceae

Wide-band tracheids (WBTs) have been found in seedlings of most species of cacti that have fibrous wood in their adult bodies. Consequently, this cell type is now known to be present in almost all cacti. Earlier studies of adult plants revealed WBTs to be present only in cacti with globose or short, broad bodies, whereas all species with large columnar or long slender bodies had fibrous wood without WBTs. However, even these species produce WBTs during the first several months after germination. In species with fibrous wood in their adult bodies (species with large or slender bodies), seedlings undergo a phase transition in wood morphogenesis after a few months and stop producing the juvenile (WBT) wood and begin producing adult (fibrous) wood. If adult plants have an intermediate size, the phase transition is delayed and the plant produces WBT wood for several years. Species with globose bodies repress the phase transition completely and never switch to producing adult (fibrous) wood. Because WBTs are so widespread, they probably originated only once in Cactaceae, not multiple times as suggested earlier, or there may have been just a single origin in the Cactaceae/Portulacaceae clade.     

Expression of the lactate dehydrogenase genes in Xenopus species hybrids

The lactate dehydrogenase isozyme patterns of six Xenopus species-hybrid combinations have been investigated. The genes from both parental species were equally expressed in all of them. “Hybrid” isozymes originating from aggregation of subunits from both parents could be visualized and demonstrated random aggregation of enzyme subunits. Reciprocal crosses displayed the same pattern demonstrating also random aggregation of subunits.     

HAS THE AGE AT TRANSITION OF SOUTHERN HEMISPHERE MINKE WHALES DECLINED OVER RECENT DECADES?

The earplugs of several baleen whale stocks exhibit seasonal growth layers which have been shown for some species to indicate the total age of the animals. A transition from early, irregular layers, to later, more regular layers can be seen in these earplugs, and this is thought to indicate the age at maturity of the whale. The earplugs of Southern Hemisphere minke whales are relatively difficult to read, particularly for the age at transition, and it has been suggested that these readings reflect no more than random allocations by the reader, rather than any real effect. Plots of average transition phase against year of birth (cohort) show a decline in the average age at transition. However, certain factors can result in a downward bias in this trend, particularly when only a short time-series is available for analysis, as was the case when this trend was first estimated some 15 yr ago. Data collected over 25 yr are now available and are reanalyzed here. A plot of mean age at transition against year of sampling for animals of similar age shows a decline, as does the conventional plot against cohort, suggesting that the decline is real. A model that simulates random allocation of the transition phase by earplug readers yields predictions that show systematic deviations from the data. In contrast, a second model that allows for a real trend in the average age at transition and that takes account of two potentially biasing effects (termed truncation and the fringe effect) fits the data well. A tendency is evident for readers to recognize a transition phase in a greater proportion of the earplugs that they read as they gain experience over time. This is taken into account in the model. This model shows a decline in the average age at transition from roughly 11 for the cohorts of the 1950s to roughly 7 for those of the 1970s. These results suggest that minke whale transition-phase readings are related to a real signal in the data and are not simply an artefact, and further that there has been a real decline in the age to which this signal corresponds.     

Cryptic freshwater ciliates in a hypersaline lagoon

Ubiquitous dispersal of free-living microbial species implies that each and every ecosystem supports a ‘seedbank’ of microbial species that are imported by random dispersal. However, many of the microbial species present in any particular ecosystem will probably never thrive there because the local environment is unsuitable for their population growth. To test this, we investigated the ciliated protozoa in a hypersaline lagoon in Almería, Spain, using selective enrichment to reveal typical freshwater species, as the ‘signature’ of random dispersal. Twenty-four ciliate species, 14 of them not previously recorded from hypersaline waters, were identified in the undiluted waters of the lagoon. But when the salinity was gradually diluted, further species typical of fresh- and brackish waters emerged, indicating that they had persisted in a viable state at the previously high salinity. These additional species increased the recorded ciliate species total for the lagoon to 36. The species found in the lagoon appeared to be adapted to either high, or variable, or low salinity, implying that they may have originated in a variety of habitats that differed greatly with respect to salinity regime.     

广西木论保护区喀斯特常绿落叶阔叶混交林优势种空间格局及其相关性

基于广西木论国家级自然保护区喀斯特常绿落叶阔叶混交林1 hm²样地调查数据,采用点格局方法分析了混交林4个优势种群空间格局,及种内和种间的相关关系.结果表明：木论常绿落叶阔叶混交林乔木层Ⅰ亚层以小栾树为主,Ⅱ亚层和Ⅲ亚层均以东女贞、铁榄和广西密花树为主;4个优势种群不同林层的空间分布格局在<10 m尺度上呈显著的聚集分布,>25 m尺度呈随机分布,有些尺度呈均匀分布,10～25 m尺度内则为聚集分布向随机分布过渡,且不同树种聚集分布向随机分布转化的临界尺度不同.Ⅰ亚层小栾树与Ⅱ亚层4个优势种的相关性较弱;Ⅲ亚层各优势种与Ⅱ亚层4个优势种中,小栾树与4个优势种相关关系波动较大,东女贞<50 m尺度内呈显著正相关,铁榄与4个优势种没有明显的相关性,广西密花树在<20 m尺度没有相关性,而在20～50 m尺度上呈显著负相关.