Parameter estimation for the distribution of single cell lag times

In Quantitative Microbial Risk Assessment, it is vital to understand how lag times of individual cells are distributed over a bacterial population. Such identified distributions can be used to predict the time by which, in a growth-supporting environment, a few pathogenic cells can multiply to a poisoning concentration level.We model the lag time of a single cell, inoculated into a new environment, by the delay of the growth function characterizing the generated subpopulation. We introduce an easy-to-implement procedure, based on the method of moments, to estimate the parameters of the distribution of single cell lag times. The advantage of the method is especially apparent for cases where the initial number of cells is small and random, and the culture is detectable only in the exponential growth phase.     

Comparing Stochastically Restricted Linear Estimators in a Regression Model

Conditions for superiority of the minimum dispersion estimator over another with respect to the covariance matrix are derived when the vector parameter of a regression model is subject to competing stochastic restrictions. The restrictions may also consist both of a deterministic part and a stochastic part.     

Population dynamics of two small pelagic fish in the central-south area off Chile: delayed density-dependence and biological interaction

It is widely believed that environmental variability is the main cause for fluctuations in commercially exploited small pelagic fish populations around the world. Nevertheless, density-dependent factors also can drive population dynamics. In this paper, we analyzed thirteen years of a relative abundance index of two clupeoids fish populations coexisting in the central-south area off Chile, namely the common sardine, Strangomera bentincki, and anchovy, Engraulis ringens. We applied the classical diagnostic tools of time series analysis to the observed time-series. Also, the realized per capita population growth rate was studied with the aim of detecting the feedback structure that is characterizing the population dynamics of the two species. The analysis suggests that population fluctuations of the two species have an important density-dependent component, displaying first-order (direct density-dependent) and second-order (delayed density-dependent) simultaneously. The density-dependent component explained 70.5 and 55.6 % of the realized per capita population growth rate of common sardine and anchovy, respectively. The deterministic skeleton model showed an asymptotic convergence to equilibrium density. In presence of a stochastic environment, fluctuations were reproduced for the species showing a component of fluctuation with a period of 4 year. The intrinsic dynamics of each species is typical of interacting species resulting from trophic interactions. It is postulated that the second-order dynamics of S. bentincki and E. ringens in central-south Chile, may be the result from interactions with a specialist predator (the fishing fleet), interacting with exogenous environmental factors.     

A stochastic model for the membrane potential of a stimulated neuron

We present a simple model describing the transition between the prefiring, firing and postfiring phases of a single neuron in a large neural net. Using typical values for the physiological parameters that enter the model, we find average interspike times that are close to those reported in experimental measurements.     

Convergence to stationary distributions in two-species stochastic competition models

Two sets of sufficient conditions are given for convergence to stationary distributions, for some general models of two species competing in a randomly varying environment. The models are nonlinear stochastic difference equations which define Markov chains. One set of sufficient conditions involves strong continuity and -irreducibility of the transition probability for the chain. The second set has a much weaker irreducibility condition, but is only applicable to monotonic models. The results are applied to a stochastic two-species Ricker model, and to Chesson's lottery model with vacant space, to illustrate how the assumptions can be checked in specific models.     

Stochastic simulation of clonal growth in the tall goldenrod,Solidago altissima

Summary As clonal plants grow they move through space. The movement patterns that result can be complex and difficult to interpret without the aid of models. We developed a stochastic simulation model of clonal growth in the tall goldenrod, Solidago altissima. Our model was calibrated with field data on the clonal expansion of both seedlings and established clones, and model assumptions were verified by statistical analyses.When simulations were based on empirical distributions with long rhizome lengths, there was greater dispersal, less leaf overlap, and less spatial aggregation than when simulations were based on distributions with comparatively short rhizome lengths. For the field data that we utilized, variation in rhizome lengths had a greater effect than variation for either branching angles or rhizome initiation points (see text). We also found that observed patterns of clonal growth in S. altissima did not cause the formation of fairy rings. However, simulations with an artificial distribution of branching angles demonstrate that fairy rings can result solely from a plant's clonal morphology.Stochastic simulation models that incorporated variation in rhizome lengths, branching angles, and rhizome initiation points produced greater dispersal and less leaf overlap than deterministic models. Thus, variation for clonal growth parameters may increase the efficiency of substrate exploration by increasing the area covered and by decreasing the potential for intraclonal competition. We also demonstrated that ramet displacements were slightly, but consistently lower in stochastic simulation models than in random-walk models. This difference was due to the incorporation of details on rhizome bud initiation into stochastic simulation models, but not random-walk models. We discuss the advantages and disadvantages of deterministic, stochastic simulation, and random-walk models of clonal growth.     

数量遗传学中一种新的求综合性状的方法

本文运用申农(Shannon)提供的最大熵原理,提出一种构成单一综合性状的新方法,并以此与数量遗传学中的多元统计法作了比较。在作多元遗传分析吋,常用多元统计法求出多个数量性状的综合性状,再对这些相互关联的基本性状作主成份分析或用典范相关进行遗传分析。本文提出了不同于多元统计学的另一种新的方法——最大熵法求出多个数量性状的单一综合性状值。它具有数学结构简单,过程明晰,结果简明等优点。     

大兴安岭林区针叶林的生长方程及火灾林木死亡率

本文用随机模拟的方法建立了北方针叶林的生长方程及其受到火灾侵害后的林木死亡率,定量地研究了火灾对这种林分变动的影响．     

The posterior probability distribution of alignments and its application to parameter estimation of evolutionary trees and to optimization of multiple alignments

How to sample alignments from their posterior probability distribution given two strings is shown. This is extended to sampling alignments of more than two strings. The result is first applied to the estimation of the edges of a given evolutionary tree over several strings. Second, when used in conjunction with simulated annealing, it gives a stochastic search method for an optimal multiple alignment.Correspondence to: L. Allison     

Time and biosequences

In this paper we discuss and demonstrate the importance of several factors relative to the relationship between time and evolution of biosequences. In both quantitative and qualitative measurements of the genetic distances, the compositional constraints of the nucleotide sequences play a very important role. We demonstrate that when homologous sequences significantly differ in base composition we get erratic branching order and/or wrong evaluation of the evolutionary rates. We must consider that every gene may have a different evolutionary dynamic along its sequence, generally linked to its functional constraints; this too can seriously affect its clocklike behavior. We report some cases showing how these factors can affect the quantitative measurements of the genetic distances of biosequences. Presented at the NATO Advanced Research Workshop onGenome Organization and Evolution, Spetsai, Greece, 16–22 September 1992