A coalescent model for the effect of advantageous mutations on the genealogy of a population

When an advantageous mutation occurs in a population, the favorable allele may spread to the entire population in a short time, an event known as a selective sweep. As a result, when we sample n individuals from a population and trace their ancestral lines backwards in time, many lineages may coalesce almost instantaneously at the time of a selective sweep. We show that as the population size goes to infinity, this process converges to a coalescent process called a coalescent with multiple collisions. A better approximation for finite populations can be obtained using a coalescent with simultaneous multiple collisions. We also show how these coalescent approximations can be used to get insight into how beneficial mutations affect the behavior of statistics that have been used to detect departures from the usual Kingman's coalescent.     

Is the dying individual the oldest?

Consider a population in which the birth times are a Poisson process with rate γ lifetimes are independent and identically distributed and lifetimes are independent of the birth process. In the paper we provide methods for calculation of several quantities involving the oldest member (senior) of the population. In particular we study the senior's age process and the point process of seniors' deaths obtained by dependent thinning of a Poisson process.     

Stochastic evolution of a nonlinear model of diffusion of information*

A theoretical method based on the concept of “system‐sized expansion” is applied to a generalization of Bartholomew's model of diffusion of information in a population of size N. The model considers a combination of mass‐mediated and interactively mediated messages, with the provision that the spreaders of information may not remain active for an indefinite period of time; it also takes into account the possibility that the parameters governing the process be time‐dependent. Explicit expressions for the time evolution of the diffusion process (including the probability distribution of the relevant variable, its mean value and variance) are derived in the asymptotic regime N ? 1. The nonlinear character of the model enables us to exploit our asymptotic expressions for studying finite‐size effects as well; the resulting expressions turn out to be reliable for N as low as 10.     

Non‐homogeneous infinitely many sites discrete‐time model with exact coalescent

Kingman's coalescent is among the most fertile concepts in mathematical population genetics. However, it only approximates the exact coalescent process associated with the Wright–Fisher model, in which the ancestry of a sample does not have to be a binary tree. The distinction between the approximate and exact coalescent becomes important when population size is small and time has to be measured in discrete units (generations). In the present paper, we explore the exact coalescent, with mutations following the infinitely many sites model. The methods used involve random point processes and generating functionals. This allows obtaining joint distributions of segregating sites in arbitrary intervals or collections of intervals, and generally in arbitrary Borel subsets of two or more chromosomes. Using this framework it is possible to find the moments of the numbers of segregating sites on pairs of chromosomes, as well as the moments of the average of the number of pairwise differences, in the form that is more general than usually. In addition, we demonstrate limit properties of the first two moments under a range of demographic scenarios, including different patterns of population growth. This latter part complements results obtained earlier for Kingman's coalescent. Finally, we discuss various applications, including the analysis of fluctuation experiments, from which mutation rates of biological cells can be inferred. Copyright © 2009 John Wiley & Sons, Ltd.     

The tree length of an evolving coalescent

A well-established model for the genealogy of a large population in equilibrium is Kingman??s coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study the sum of the branch lengths, briefly denoted as tree length, and prove that the (suitably compensated) sequence of tree length processes converges, as the population size tends to infinity, to a limit process with càdlàg paths, infinite infinitesimal variance, and a Gumbel distribution as its equilibrium.     

Time development of a Markov process in a finite population: Application to diffusion of information

A systematic procedure of truncating the hierarchy of moment equations describing the stochastic evolution of a Markov process in a finite population is developed. The procedure makes use of the asymptotic expression for a certain higher‐order moment of the relevant probability distribution and yields finite‐size corrections to all lower‐order moments. The usefulness of the method is illustrated by applying it to study the mean and the variance of the stochastic variable n(t), the number of active spreaders at time t, in Bartholomew's model of diffusion of information. The results thus obtained are compared with the ones following from the exact probability distribution for the model (wherever known) and the agreement between the two sets of results is found to be remarkably good.     

Colony and evolutionary dynamics of a two‐stage model with brood cannibalism and division of labor in social insects

Division of labor (DOL) is a major factor for the great success of social insects because it increases the efficiency of a social group where different individuals perform different tasks repeatedly and presumably with increased performance. Cannibalism plays an important role in regulating colony growth and development by regulating the number of individuals in a colony and increasing survival by providing access to essential nutrients and minimizing competition among colony mates. To understand the synergy effects of DOL and cannibalistic behavior on colony dynamic outcomes, we propose and study a compartmental two‐stage model using ecological and evolutionary game theory settings. Our analytical results of the ecological and evolutionary models suggest that: (1) A noncannibalistic colony can survive if the efficiency of energy investment reflecting the DOL is greater than the relative death rate of the older population. (2) A cannibalistic colony can die out if both the efficiency of energy investment and the relative cannibalism rate (where each is also reflecting the DOL) are too large; or if the relative cannibalism rate alone is too small. (3) From our numerical analysis, cannibalism can increase or reduce the colony's total population size, which greatly depends on the benefit of egg cannibalism increasing or decreasing of adult's lifespan. (4) A cannibalistic and noncannibalistic colony can experience bistability due to cooperative behavior. (5) In the evolutionary settings, DOL can prevent colony death and natural selection can preserve strong Allee effects by selecting the traits with the largest investment on brood care and the lowest cannibalism rate. (6) Evolutionary dynamics may increase the fitness of the colony, i.e., the successful production of workforce which results in the increase of total worker population size, colony survival, and reproduction. Our results suggest both cannibalism and DOLs are adaptive strategies that increase the size of the worker population, and therefore, persistence of the colony.     

Knight's paths towards Catalan numbers

We provide enumerating results for partial knight's paths of a given size. We prove algebraically that zigzag knight's paths of a given size ending on the x-axis are enumerated by the generalized Catalan numbers, and we give a constructive bijection with peakless Motzkin paths of a given length. After enumerating partial knight's paths of a given length, we prove that zigzag knight's paths of a given length ending on the x-axis are counted by the Catalan numbers. Finally, we give a constructive bijection with Dyck paths of a given length.     

Kendall's τ is equal to the correlation coefficient for the BVE distribution

For the BVE (BiVariate Exponential) distribution, defined and explained by Marshall and Olkin (1967), the population Kendall's τ (1948), which is the probability of concordance minus the probability of discordance for a bivariate distribution, is shown to be equal to the population correlation coefficient. Moreover, Kendall's t statistic is superior to Pearson's r for estimating the BVE correlation. Some other bivariate distributions, due to Gumbel, Morgenstern and Freund, are also considered.     

一种新的死亡率模型及基于中国人口数据的比较分析

基于中国人口死亡率数据, 对APC模型进行扩展, 并将扩展的死亡率模型(EAPC模型)与APC模型和LC模型进行对比. 通过比较模型的拟合效果和预测效果, 并对其稳定性进行检验, 发现由APC模型扩展而来的EAPC模型更适合于拟合和预测中国的人口死亡率, 这为我国死亡率模型的使用提供了更多可行的方案.     

A Case Study of Three Childrens' Original Interpretations of the Moon's Changing Appearance

A case study of three children was conducted to shed light on the process that children undergo in developing their understanding of physical phenomena. Using the notion of spontaneous construction and its relationship with school learning of scientific concepts, children's early thoughts of the moon's appearance were explored. Research questions were primarily concerned with how children view the moon's appearance, explain how and/or why its appearance changes, quantify the moon's size and its distance to Earth, and explain the moon's illumination. A Piagetian interview was conducted with each child and then each was asked to tell a story about the moon. The external interest of this research study involves when and why do children develop the commonly held Earth's shadow alternative conception as the cause of the moon's phases. The findings show that children have stories and experiences that give meaning to the existence of such things as the moon, stars, sun, and clouds. Similarities were found in the children's interpretations with regard to their natural tendencies to animate celestial objects. Clues were discovered of cultural influence such as family, personal observations and experiences, books, pictures, car travel, and even a strategically placed Palladian window.     

Improved biogeography-based optimization with random ring topology and Powell's method

Biogeography-based optimization (BBO) is a competitive population optimization algorithm based on biogeography theory with inherently insufficient exploration capability and slow convergence speed. To overcome limitations, we propose an improved variant of BBO, named PRBBO, for solving global optimization problems. In PRBBO, a hybrid migration operator with random ring topology, a modified mutation operator, and a self-adaptive Powell's method are rational integrated together. The hybrid migration operator with random ring topology, denoted as RMO, is created by using local ring topology to replace global topology, which can avoid the asymmetrical migration operation and enhance potential population diversity. The self-adaptive Powell's method is amended by using self-adaptive parameters for suiting evolution process to enhance solution precision quickly. Extensive experimental tests are carried out on 24 benchmark functions to show effectiveness of the proposed algorithm. Simulation results were compared with original BBO, ABC, DE, other variants of the BBO, and other state-of-the-art evolutionary algorithms. Finally, the effectiveness of operators on the performance of PRBBO is also discussed.     

EDGE PERMEABILITY AND POPULATION PERSISTENCE IN ISOLATED HABITAT PATCHES

ABSTRACT. Population persistence in isolated habitat fragments is investigated using integrodifference equations. The propensity of individual dispersers encountering the boundary of the patch to emigrate is defined by edge permeability. A dispersal model incorporating movement, settlement and edge permeability defines dispersal success as a function of a disperser's starting location. This dispersal model is used to generate dispersal kernels for integrodifference equation models, analysis of which gives a condition for population persistence in terms of edge permeability, patch size and average dispersal distance. An approximation reduces the spatial problem to a simple nonspatial model that can be easily analyzed.     

Solution of Volterra's population model via block‐pulse functions and Lagrange‐interpolating polynomials

A numerical method for solving Volterra's population model for population growth of a species in a closed system is proposed. Volterra's model is a nonlinear integro‐differential equation where the integral term represents the effects of toxin. The approach is based on hybrid function approximations. The properties of hybrid functions that consist of block‐pulse and Lagrange‐interpolating polynomials are presented. The associated operational matrices of integration and product are then utilized to reduce the solution of Volterra's model to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. Applications are demonstrated through an illustrative example. Copyright © 2008 John Wiley & Sons, Ltd.     

How neutral networks influence evolvability

Evolutionary algorithms apply the process of variation, reproduction, and selection to look for an individual capable of solving the task at hand. In order to improve the evolvability of a population we propose to copy important characteristics of nature's search space. Desired characteristics for a genotype–phenotype mapping are described and several highly redundant genotype–phenotype mappings are analyzed in the context of a population‐based search. We show that evolvability, defined as the ability of random variations to sometimes produce improvement, is influenced by the existence of neutral networks in genotype space. Redundant mappings allow the population to spread along the network of neutral mutations and the population is quickly able to recover after a change has occurred. The extent of the neutral networks affects the interconnectivity of the search space and thereby affects evolvability. © 2002 Wiley Periodicals, Inc.     

AN INDIVIDUAL-BASED FISHERY MODEL AND ASSESSING FISHERY STABILITY

ABSTRACT. The stability of a fishery system was investigated using two forms of a stochastic computer simulation model that was individually based in terms of the fishing boats. Fish catch was partitioned among boats according to two catch processes: an unranked process in which all boats had equal ability to catch fish and a ranked catch model in which a boat's ability to catch fish depended on its wealth. Stock size, total catch, fleet size and individual boat wealth were modeled over a series of years. In the unranked catch model the fish stock size and fleet size were significantly more variable than in the ranked catch model.     

Wallace's unfinished business: The “Other Man” in evolutionary theory

After a century in the shadows, Alfred Russel Wallace (1823–1913) has recently become the subject of increasing attention. It is suggested here, expanding on observations made by anthropologist Gregory Bateson some years ago, that Wallace's cybernetics‐like view of the operation of natural selection—as a governor‐like principle tending to keep species unvarying—can be expanded to a more complete evolutionary understanding by exploring in modern context Wallace's idea that “more recondite forces” are driving the process. Specifically, when the environment is regarded as a final cause (but not a deterministic force), individual adaptations may be viewed as entropy‐relaying structures (acting in response to, and as a part of, larger scale biogeochemical agenda), whereas negentropy is accumulated by nonrandomly directed organism‐ and population‐level forms of ecological engagement. Thus, range change in particular is viewed as a process that is both driven and nonrandom, and ultimately connected to the derivation of more and more organized individual, population, and community structures. © 2004 Wiley Periodicals, Inc. Complexity 10:25–32, 2004     

Some new limit theorems for the critical branching process allowing immigration

Some limit theorems are obtained for the population size of a critical Bienaymé-Galton-Watson process allowing immigration and where the variance of the offspring distribution is infinite. An application is given to a limit theorem for the situation where the immigration does not occur but the population size is conditioned on non-extinction until the remote future. This complements a well-known result of Slack.     

基于支持向量机的辽宁省粮食产量预测

随着中国经济的不断发展,城市化进程不断推进,总人口逐年增加;农村人口逐年减少,粮食的需求量逐年增加,某些贫困地区已经出现粮食短缺的状况.本文选取了1986年-2016年辽宁省年粮食总产量、有效灌溉面积、农业化肥施用量、农业机械总动力、播种面积以及受灾面积等相关数据.利用支持向量机回归、线性回归,随机森林三种方法,对辽宁省粮食产量进行了预测,并比较了三种方法预测的精准度.     

Hilbert-valued self-intersection local times for planar Brownian motion

Dynkin's construction for self-intersection local time of a planar Wiener process is extended to Hilbert-valued weights. In Dynkin's construction, the weight is bounded and measurable. Since the weight function describes the properties of the medium in which the Brownian motion moves, relative to the external medium's properties, the weight function can be random and unbounded. In this article, we discuss the possibility to consider Hilbert-space-valued weights. It appears that the existence of Hilbert-valued Dynkin-renormalized self-intersection local time is equivalent to the embedding of the values of Hilbert-valued weight into a Hilbert–Schmidt brick. Using Dorogovtsev's sufficient condition for the embedding of compact sets into a Hilbert–Schmidt brick in terms of an isonormal process, we prove the existence of Hilbert-valued Dynkin-renormalized self-intersection local time. Also using Dynkin's construction we construct the self-intersection local time for the deterministic image of the planar Wiener process.