Steady states in population models with monotone,stochastic dynamics

Existence, uniqueness and asymptotic stability of stochastic equilibrium are established in multi-dimensional population models with monotone dynamics.     

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.     

Population models with environmental stochasticity

Two discrete population models, one with stochasticity in the carrying capacity and one with stochasticity in the per capita growth rate, are investigated. Conditions under which the corresponding Markov processes are null recurrent and positively recurrent are derived.     

Population models for diseases with no recovery

An S I epidemic model with a general shape of density-dependent mortality and incidence rate is studied. The asymptotic behaviour is global convergence to an endemic equilibrium, above a threshold, and to a disease-free equilibrium, below the threshold. The effect of vaccination is then examined.     

On simulating strongly interacting, stochastic population models. II. Multiple compartments

In Wick and Stelf [Math. Biosci. 187 (2004) 1], we showed how to simulate a pair of strongly interacting biological populations evolving stochastically over many orders-of-magnitude. Here we generalize the method to any (finite) number of compartments; transitions including births, deaths, progression through life-stages, and mitoses; and arbitrary rate functions. We illustrate the technique for a seven-compartment model of the cellular immune response to a viral infection.     

Population growth with randomly distributed jumps

 The growth of populations with continuous deterministic and random jump components is treated. Three special models in which random jumps occur at the time of events of a Poisson process and admit formal explicit solutions are considered: A) Logistic growth with random disasters having exponentially distributed amplitudes; B) Logistic growth with random disasters causing the removal of a uniformly distributed fraction of the population size; and C) Exponential decay with sudden increases (bonanzas) in the population and with each increase being an exponentially distributed fraction of the current population. Asymptotic and numerical methods are employed to determine the mean extinction time for the population, qualitatively and quantitatively. For Model A, this time becomes exponentially large as the carrying capacity becomes much larger than the mean disaster size. Implications for colonizing species for Model A are discussed. For Models B and C, the practical notion of a small, but positive, effective extinction level is chosen, and in these cases the expected extinction time rises rapidly with population size, yet at less than an e xponentially large order. Received 21 June 1996; received in revised form 17 February 1997     

Population dynamics of shrews on small islands accord with the equilibrium model

Three of the six species of shrew in Finland, Sorex araneus, S. caecutiens, and S. minutus , are common on the mainland and widespread on islands in lakes. The islands range from 0.01 to 500 ha in area, and from 10 to 3000 m in isolation (distance from the mainland). The species-area relationship, the lack of importance of habitat diversity, the increasing frequency of unoccupied small islands with isolation, and direct observations of small populations, all suggest that populations on small islands have a high extinction rate. Demographic stochasticity is the main cause of extinctions in the superior competitor, S. araneus , which occurs consistently on islands greater than 2 ha. The small species, S. caecutiens and S. minutus , are more sensitive to environmental stochasticity than is S. araneus , and are inferior to it in interspecific competition; these factors probably contribute to the absence of the small species from many islands tens of hectares in area. Frequent colonization of islands less than 500 m from the mainland is indicated by large numbers of shrews trapped from tiny islets where breeding is not possible, by increasing epigenetic divergence of island populations with isolation, and by observations of dispersal to and colonization of islands. Dispersal ability decreases with decreasing individual size, which may partly explain the absence of the small shrews from many relatively large islands. The shrew populations persist in a dynamic equilibrium on the islands. Epigenetic morphological variation is a useful tool in ecological studies of island populations.     

Effects of predation on host-pathogen dynamics in SIR models

The integration of infectious disease epidemiology with community ecology is an active area of research. Recent studies using SI models without acquired immunity have demonstrated that predation can suppress infectious disease levels. The authors recently showed that incorporating immunity (SIR models) can produce a “hump”-shaped relationship between disease prevalence and predation pressure; thus, low to moderate levels of predation can boost prevalence in hosts with acquired immunity. Here we examine the robustness of this pattern to realistic extensions of a basic SIR model, including density-dependent host regulation, predator saturation, interference, frequency-dependent transmission, predator numerical responses, and explicit resource dynamics. A non-monotonic relationship between disease prevalence and predation pressure holds across all these scenarios. With saturation, there can also be complex responses of mean host abundance to increasing predation, as well as bifurcations leading to unstable cycles (epidemics) and pathogen extinction at larger predator numbers. Firm predictions about the relationship between prevalence and predation thus require one to consider the complex interplay of acquired immunity, host regulation, and foraging behavior of the predator.     

黄瓜根际重要病原与其拮抗菌消长规律的研究

研究了4个不同黄瓜品种根际两类重要土传植物病原菌(Pythiumspp.和Fusariumoxysporum f.sp.cucumerinum)的种群动态变化.结果表明,同一品种不同生长期间种群数有差异,与通常的发病规律相吻合.统计分析可见,腐霉种群和尖孢镰刀菌黄瓜专化型种群品种间差异极显著(F=495.54>F_0.01=7.59;F=2355.57>F_0.01=7.59).整个生育期,所有黄瓜品种种群数极显著地高于其它时期的腐霉种群数,结主蔓瓜期镰刀菌种群数极显著地高于其它时期的镰刀菌种群数.同时,2种病原菌与其拮抗菌均呈较密切的正相关关系,相关系数分别为0.95和0.81.     

Population genetic models of duplicated genes

Various population genetic models of duplicated genes are introduced. The problems covered in this review include the fixation process of a duplicated copy, copy number polymorphism, the fates of duplicated genes and single nucleotide polymorphism in duplicated genes. Because of increasing evidence for concerted evolution by gene conversion, this review introduces recently developed gene conversion models. In the first half, models assuming independent evolution of duplicated genes are introduced, and then the effect of gene conversion is considered in the second half.     

Do “infectious” prey select for high levels of natural antibodies in tropical pythons?

Natural antibodies (NAbs) constitute an important component in vertebrate immune system, but, in spite of this, have often been dismissed as “non-specific background” signals. We observed a significant positive relationship between water python (Liasis fuscus) body length/age and levels of antibodies reactive with two administered antigens (tetanus and diphtheria). However, no humoral immune response to the antigens was observed. The lack of elevated immune response, and the age-associated increase in antibody titres, strongly suggest that the antibodies consisted of polyreactive NAbs, and that absence of an elevated immune response was caused by such high levels of NAbs that they were able to mask the epitopes of the antigens. In our study area pythons feed mainly on rodents that frequently, before being killed, are able to inflict numerous bites to the snakes. The bites most likely transmit pathogens such as bacteria. As NAbs have been shown to act as a first line defence against bacterial infections, the high levels of NAbs in the pythons may be an adaptation to reduce pathogenic effects of bacteria transmitted by the prey when the snakes are feeding. Thus, the results from present study suggest that NAbs may have an important immunological function by reducing deleterious effects of pathogens in wild populations.     

生长季节和非生长季节交替出现的种群动态模型及环境变化的影响

有些生物的生长季节和非生长季节交替出现,本文建立了描述这种生物种群动态的方程,并研究了在环境稳定、随机波动、定向变化的情况下种群的变化方式,还讨论了种群的危害及濒危情况．生长季节延长时种群增大,有害生物的危害加重,濒危生物濒危程度减轻;生长季节缩短时种群减小,有害生物的危害减轻,濒危生物更加濒危或灭绝．     

一类基于比率且具双线性密度制约的捕食-食饵系统的全局稳定性分析

研究一类基于比率和具双线性密度制约的捕食-食饵系统．由Bendixson环域定理及比较定理给出了奇点（0,0）和（1,0）全局渐近稳定的条件．通过对等倾线的研究给出了正平衡点存在的条件,并构造了Dulac函数讨论其全局渐近稳定性．     

Sensitivity analysis of equilibrium in density-dependent matrix population models

We consider the effects of parameter perturbations on a density‐dependent population at equilibrium. Such perturbations change the dominant eigenvalue λ of the projection matrix evaluated at the equilibrium as well as the equilibrium itself. We show that, regardless of the functional form of density dependence, the sensitivity of λ is equal to the sensitivity of an effective equilibrium density , which is a weighted combination of the equilibrium stage densities. The weights measure the contributions of each stage to density dependence and their effects on demography. Thus, is in general more relevant than total density, which simply adds all stages regardless of their ecological properties. As log λ is the invasion exponent, our results show that successful invasion will increase , and that an evolutionary stable strategy will maximize . Our results imply that eigenvalue sensitivity analysis of a population projection matrix that is evaluated near equilibrium can give useful information about the sensitivity of the equilibrium population, even if no data on density dependence are available.     

基于CGE碳税政策对北京社会经济系统的影响分析

根据研究需要与北京市2010年投入产出表部门划分情况,尽可能地对能源部门进行细分,并编制社会核算矩阵。构建可计算一般均衡(CGE)模型模拟碳税政策对北京市社会经济的影响。实证结果显示:碳税政策具有显著的节能减排效果,对于化石能源密集型产业产出具有明显的抑制作用,但对于清洁能源、服务业等行业产出具有促进作用。因此严格限制煤炭、石油等高碳化石能源的使用、开发高碳能源低碳化利用技术是减排的重要措施。由于碳税会使产品价格上升,从而导致消费需求减少,碳税对国内生产总值和社会福利具有一定的负面影响,虽然影响程度的相对量有限,但影响的绝对效果较大,应该避免较高的碳税税率。     

Dynamic disequilibrium: a long-term, large-scale perspective on the equilibrium model of island biogeography

• 1 The equilibrium model of island biogeography developed in the 1960s by MacArthur and Wilson has provided an excellent framework in which to investigate the dynamics of species richness in island and island‐like systems. It is comparable in many respects to the Hardy–Weinberg equilibrium model used in genetics as the basis for defining a point of reference, thus allowing one to discover the factors that prevent equilibrium from being achieved. Hundreds of studies have used the model effectively, especially those dealing with brief spans of time and limited geographical areas. In spite of this utility, however, there are important limitations to the MacArthur–Wilson model, especially when we consider long‐term and large‐scale circumstances.
• 2 Although their general theory is more complex, the MacArthur–Wilson equilibrium model treats colonization and extinction as the only two processes that are relevant to determining species richness. However, it is likely that phylogenetic diversification (phylogenesis) often takes place on the same time‐scale as colonization and extinction; for example, colonization, extinction, and phylogenesis among mammals on oceanic and/or old land‐bridge islands in South‐east Asia are all measured in units of time in the range of 10 000–1 million years, most often in units of 100 000 years.
• 3 Phylogenesis is not a process that can be treated simply as ‘another form of colonization’, as it behaves differently than colonization. It interacts in a complex manner with both colonization and extinction, and can generate patterns of species richness almost independently of the other two processes. In addition, contrary to the implication of the MacArthur–Wilson model, extinction does not drive species richness in highly isolated archipelagoes (those that receive very few colonists) to progressively lower values; rather, phylogenesis is a common outcome in such archipelagoes, and species richness rises over time. In some specific instances, phylogenesis may have produced an average of 14 times as many species as direct colonization, and perhaps 36 species from one such colonization event. Old, stable, large archipelagoes should typically support not just endemic species but endemic clades, and the total number of species and the size of the endemic clades should increase with age of the archipelago.
• 4 The existence of long‐term equilibrium in actual island archipelagoes is unlikely. The land masses that make up island archipelagoes are intrinsically unstable because the geological processes that cause their formation are dynamic, and substantial changes can occur (under some circumstances) on a time‐scale comparable to the processes of colonization, phylogenesis, and extinction. Large‐scale island‐like archipelagoes on continents also are unstable, in the medium term because of global climatic fluctuations, and in the long term because of the geologically ephemeral existence of, for example, individual mountain ranges.
• 5 Examples of these phenomena using the mammals of South‐east Asia, especially the Philippines, make it clear that the best conceptual model of the long‐term dynamics of species richness in island archipelagoes would be one in which colonization, extinction, and phylogenesis are recognized to be of equivalent conceptual importance. Furthermore, we should expect species richness to be always in a dynamic state of disequilibrium due to the constantly changing geological/geographical circumstances in which that diversity exists, always a step or two out of phase with the constantly changing equilibrium point for species richness.

     

关于一类时滞人口模型的全局吸引性

给出了保证时滞人口模型N'(t)=r(t)N(t) t≤0的每一正解N(t)趋于正平衡点 N*=1(t→∞)的一族充分条件．改进了Joseph和Yu的相关结果．     

Lichenicolous fungi show population subdivision by host species but do not share population history with their hosts

Lichenicolous fungi are a species-rich biological group growing on lichen thalli. Here, we analyze the genetic structure of the lichenicolous basidiomycete Tremella lobariacearum and three host species (Lobaria pulmonaria, Lobaria macaronesica, and Lobaria immixta) in Macaronesia. We used ordination and analysis of molecular variance to investigate the structuring of genetic variation, and a simulation test to investigate whether rDNA haplotypes of T. lobariacearum were significantly associated with host species. To investigate the evolutionary and demographic history of the lichenicolous fungus and its hosts, we used coalescent samplers to generate trees, and Bayesian skyline plots. We found that the hosts were most important in structuring populations of the lichenicolous species. Despite their wide geographic distribution, the same haplotypes of T. lobariacearum consistently associated with a given host species. Our results suggest that the Lobaria hosts create a selective environment for the lichenicolous fungus. Both the pathogen and the host populations exhibited substantial genetic structure. However, evolutionary and demographic histories differed between the parasite and its hosts, as evidenced by different divergence times and tree topologies.