Population-genetic basis of haplotype blocks in the 5q31 region

We investigated patterns of nucleotide variation in the 5q31 region identified by Daly et al. as containing haplotype blocks, to determine whether the blocklike pattern requires the assumption of hotspots in recombination. Using extensive simulations that generate data matched to the Daly et al. data set in (a) the method of ascertainment of single-nucleotide polymorphisms, (b) the heterozygosity of ascertained markers, (c) the number of block boundaries, and (d) the diversity of haplotypes within blocks, we show that the patterns found in the Daly et al. data are not consistent with the assumption of uniform recombination in a population of constant size but are consistent either with the presence of hotspots in a population of constant size or with the absence of hotspots if there was a period of rapid population growth. We further show that estimates of local recombination rate can distinguish between population growth and hotspots as the primary cause of a blocklike pattern. Estimates of local recombination rates for the Daly et al. data do not indicate the presence of recombination hotspots.     

Non-Selective Evolution of Growing Populations

Non-selective effects, like genetic drift, are an important factor in modern conceptions of evolution, and have been extensively studied for constant population sizes (Kimura, 1955; Otto and Whitlock, 1997). Here, we consider non-selective evolution in the case of growing populations that are of small size and have varying trait compositions (e.g. after a population bottleneck). We find that, in these conditions, populations never fixate to a trait, but tend to a random limit composition, and that the distribution of compositions “freezes” to a steady state. This final state is crucially influenced by the initial conditions. We obtain these findings from a combined theoretical and experimental approach, using multiple mixed subpopulations of two Pseudomonas putida strains in non-selective growth conditions (Matthijs et al, 2009) as model system. The experimental results for the population dynamics match the theoretical predictions based on the Pólya urn model (Eggenberger and Pólya, 1923) for all analyzed parameter regimes. In summary, we show that exponential growth stops genetic drift. This result contrasts with previous theoretical analyses of non-selective evolution (e.g. genetic drift), which investigated how traits spread and eventually take over populations (fixate) (Kimura, 1955; Otto and Whitlock, 1997). Moreover, our work highlights how deeply growth influences non-selective evolution, and how it plays a key role in maintaining genetic variability. Consequently, it is of particular importance in life-cycles models (Melbinger et al, 2010; Cremer et al, 2011; Cremer et al, 2012) of periodically shrinking and expanding populations.     

On the Bayesian estimation of a closed population size in the presence of heterogeneity and model uncertainty

Summary .   We consider the estimation of the size of a closed population, often of interest for wild animal populations, using a capture–recapture study. The estimate of the total population size can be very sensitive to the choice of model used to fit to the data. We consider a Bayesian approach, in which we consider all eight plausible models initially described by Otis et al. (1978, Wildlife Monographs 62, 1–135) within a single framework, including models containing an individual heterogeneity component. We show how we are able to obtain a model-averaged estimate of the total population, incorporating both parameter and model uncertainty. To illustrate the methodology we initially perform a simulation study and analyze two datasets where the population size is known, before considering a real example relating to a population of dolphins off northeast Scotland.     

The significance of genetic erosion in the process of extinction

Summary The amount of genetic variation within a population is, among other things, related to population size. In small populations loss of genetic variation due to high levels of genetic drift and inbreeding may result in decline of individual fitness and increase the chance of population extinction. This chain of processes is known as genetic erosion. In this study we tested the genetic erosion hypothesis by investigating the relation between morphological variation and population size in two perennial, outbreeding plant species, Salvia pratensis and Scabiosa columbaria. To relate phenotypic variation to genetic variation the experiments were performed under common environmental conditions. For both species a positive correlation was observed between the amount of phenotypic variation and population size (Salvia r=0.915; Scabiosa r=0.703). Part of this variation is likely to have a genetic base, although maternal effects were present in the seedling and juvenile life stages. Differences between populations could in both species be attributed to parameters related to fitness, i.e. growth rate in Salvia and reproductive effort in Scabiosa. Discriminant functions reflecting these parameters did not however discriminate between large and small populations.Results are discussed in relation to the common environment approach and to electrophoretic results obtained earlier (Van Treuren et al. 1991).     

The Minimum Capture Proportion for Reliable Estimation in Capture–Recapture Models

Summary .   We derive estimates of the minimum capture proportion required to obtain a reliable estimate of the population size for several continuous and discrete-time capture–recapture models. The models considered are     , and     in the notation of Otis et al. , (1978, Wildlife Monograph 62 , 1–135). Numerical results with simulation studies are given, and two real examples for the model     are also considered. Potential applications of these results are suggested.     

The minimum capture proportion for reliable estimation in capture-recapture models.

We derive estimates of the minimum capture proportion required to obtain a reliable estimate of the population size for several continuous and discrete-time capture-recapture models. The models considered are M(0), M(t), M(b), M(h), M(ht), and M(tb) in the notation of Otis et al., (1978, Wildlife Monograph62, 1-135). Numerical results with simulation studies are given, and two real examples for the model M(h) are also considered. Potential applications of these results are suggested.     

Navigating the unknown: model selection in phylogeography. Models of population structure: tools for thinkers

Despite the widespread use and obvious strengths of model-based methods for phylogeographic study, a persistent concern for such analyses is related to the definition of the model itself. The study by Peter et al. (2010) in this issue of Molecular Ecology demonstrates an approach for overcoming such hurdles. The authors were motivated by a deceptively simple goal; they sought to infer whether a population has remained at a low and stable size or has undergone a decline, and certainly there is no shortage of software packages for such a task (e.g., see list of programs in Excoffier & Heckel 2006). However, each of these software packages makes basic assumptions about the underling population (e.g., is the population subdivided or panmictic); these assumptions are explicit to any model-based approach but can bias parameter estimates and produce misleading inferences if the model does not approximate the actual demographic history in a reasonable manner. Rather than guessing which model might be best for analyzing the data (microsatellite data from samples of chimpanzees), Peter et al. (2010) quantify the relative fit of competing models for estimating the population genetic parameters of interest. Complemented by a revealing simulation study, the authors highlight the peril inherent to model-based inferences that lack a statistical evaluation of the fit of a model to the data, while also demonstrating an approach for model selection with broad applicability to phylogeographic analysis.     

A stochastic model of mutant growth due to mutation in tumors,based on stem cell considerations

A stochastic model of the evolution of mutant subpopulations from stem cells in a human tumor system is derived. From the model, the growth of mutants (both stem cell mutants and overall mutants) due to mutation of tumor stem cells during growth is explored in detail. This allows one to relate the mutant stem cell and overall tumor mutant cell population sizes. The relation of these average sizes is derived for large tumor size and confirms the result of the model due to MacKillop et al. [4], which is based on three tumor cell subpopulations: stem, transitional, and end cells. Furthermore, the results of the stem cell statistics obtained are the same as those obtained from the filtered Poisson process approach [2].     

Growth and development of immature life stages ofPropylaea 14-punctata L. andCoccinella 7-punctata L. [Col.: Coccinellidae] simulated by the metabolic pool model

The conversion of aphid prey tissue (Acyrthosiphon pisum Harris) into predator biomass (immature life stages ofPropylaea 14-punctata L. andCoccinella 7-punctata L.) is calculated by plotting weight gain against assimilation (i.e. consumption minus egestion). This concept is added to the metabolic pool model byGutierrez et al. (1981) that enables the simulation of growth and development of a predator on a physiological basis. Physiological time is expressed in daydegrees above lower development thresholds for both species. Visual examination of observed and calculated values showed that the model satisfactorily describes the growth patterns of the above predators.      

Rapid evolution of wing size clines in Drosophila subobscura

Parallel latitudinal clines across species and continents provide dramatic evidence of the efficacy of natural selection, however little is known about the dynamics involved in cline formation. For example, several drosophilids and other ectotherms increase in body and wing size at higher latitudes. Here we compare evolution in an ancestral European and a recently introduced (North America) cline in wing size and shape in Drosophila subobscura. We show that clinal variation in wing size, spanning more than 15 degrees of latitude, has evolved in less than two decades. In females from Europe and North America, the clines are statistically indistinguishable however the cline for North American males is significantly shallower than that for European males. We document that while overall patterns of wing size are similar on two continents, the European cline is obtained largely through changing the proximal portion of the wing, whereas the North American cline is largely in the distal portion. We use data from sites collected in 1986/1988 (Pegueroles et al. 1995) and our 1997 collections to compare synchronic (divergence between contemporary populations that share a common ancestor) and allochronic (changes over time within a population) estimates of the rates of evolution. We find that, for these populations, allochronically estimated evolutionary rates within a single population are over 0.02 haldanes (2800 darwins), a value similar in magnitude to the synchronic estimates from the extremes of the cline. This paper represents an expanded analysis of data partially presented in Huey et al. (2000).     

Size-structured demographic models of coral populations

The demographic processes of growth, mortality, and the recruitment of young individuals, are the major organizing forces regulating communities in open systems. Here we present a size-structured (rather than age-structured) population model to examine the role of these different processes in space-limited open systems, taking coral reefs as an example. In this flux-diffusion model the growth rate of corals depends both on the available free-space (i.e. density-dependence) and on the particular size of the coral. In our analysis we progressively study several different forms of growth rate functions to disentangle the effects of free space and size-dependence on the model's stability. Unlike Roughgarden et al. [1985. Demographic theory for an open marine population space-limited recruitment. Ecology 66(1), 54-67], whose principal result is that the growth of settled organisms is destabilizing, we find that size-dependent growth rate often has the potential to endow stability. This is particularly true, if the growth rate is dependent on available free space (i.e. density dependent), but examples are given for growth rates that even lack this property. Further insights into reef system fragility are found through studying the sensitivity of the model steady state to changes in recruitment.     

An improved,simple, hydroponic method for growing<Emphasis Type="Italic">Arabidopsis thaliana</Emphasis>

Arabidopsis thaliana is one os the most studied plant model systems. Completing the genomic sequence ofA. thaliana has provided new opportunities for physiological and biochemical studies. While its small size is advantageous for genetic studies, the plant's low biomass makes it difficult to obtain enough plant material for biochemical and physiological research. The small size and rosette leaf structure, combined with the sensitivity of the apical meristem to flooding, make hydroponic growth of this model plant difficult. A few systems for hydroponic culture ofArabidopsis have been described. Gibeaut et al. (1997) introduced the use of rockwool forArabidopsis hydroponic culture. We have improved this system by introducing small-volume plastic containers with improved plugs to support the rockwool. This method is simpler than the original setup and provides improved germination and growth. The smaller containers enable the use of this system in growth chambers or small growth rooms for a large number of parallel experiments.     

Energy allocation in the cladoceran Daphnia magna Straus,under starvation and refeeding

Summary Models incorporating the energetics of individual daphnids (Cladocera) have been developed to predict the effect of environmental variables, particularly food availability, on population dynamics. One of them, that of Kooijman (1986), assumes that all assimilated energy enters a storage compartment prior to use in production and metabolism, and that under starvation the stores are used to support maintenance, reproduction and somatic growth, in that order of priority. This predicts that, under starvation, reproduction and growth will continue for a time, and that after they cease death will be immediate. Another model, that of McCauley et al. (1990), assumes that assimilated energy is used directly for maintenance and production, and that stores are accumulated to support maintenance metabolism under starvation. This predicts that growth and reproduction should cease immediately upon starvation and that death will not be immediate. We have carried out laboratory experiments, manipulating starvation time, on Daphnia magna to distinguish between these two models. The results support features of both models in that reproduction, but not growth, ceases upon starvation. We therefore developed a third model in which both maintenance and growth are supported from stores under starvation, with maintenance taking priority over growth under these conditions.     

Temporal dynamics of bacterial aging and rejuvenation

Single-celled organisms dividing by binary fission were thought not to age [1-4]. A 2005 study by Stewart et al. [5] reversed the dogma by demonstrating that Escherichia coli were susceptible to aging. A follow-up study by Wang et al. [6] countered those results by demonstrating that E. coli cells trapped in microfluidic devices are able to sustain robust growth without aging. The present study reanalyzed these conflicting data by applying a population genetic model for aging in bacteria [7]. Our reanalysis showed that in E. coli, as predicted by the model, (1) aging and rejuvenation occurred simultaneously in a population; (2) lineages receiving sequentially the maternal old pole converged to a stable attractor state; (3) lineages receiving sequentially the maternal new pole converged to an equivalent but separate attractor state; (4) cells at the old pole attractor had a longer doubling time than ones at the new pole attractor; and (5) the robust growth state identified by Wang et al. corresponds to our predicted attractor for lineages harboring the maternal old pole. Thus, the previous data, rather than opposing each other, together provide strong evidence for bacterial aging.     

Development of a biologically-based controlled growth and differentiation model for developmental toxicology

 A mathematical model is developed with a highly controlled birth and death process for precursor cells. This model is both biologically- and statistically-based. The controlled growth and differentiation (CGD) model limits the number of replications allowed in the development of a tissue or organ and thus, more closely reflects the presence of a true stem cell population. Leroux et al. (1996) presented a biologically-based dose-response model for developmental toxicology that was derived from a partial differential equation for the generating function. This formulation limits further expansion into more realistic models of mammalian development. The same formulae for the probability of a defect (a system of ordinary differential equations) can be derived through the Kolmogorov forward equations due to the nature of this Markov process. This modified approach is easily amenable to the expansion of more complicated models of the developmental process such as the one presented here. Comparisons between the Leroux et al. (1996) model and the controlled growth and differentiation (CGD) model as developed in this paper are also discussed. Received: 8 June 2001 / Revised version: 15 June 2002 / Published online: 26 September 2002 Keywords or phrases: Teratology – Multistate process – Cellular kinetics – Numerical simulation     

AN ANALYSIS OF PROCEDURES FOR IMPLEMENTING THE DYNAMIC RESPONSE METHOD

Abstract: A new method, the "dynamic response method," was developed (DeMaster et al. 1982) in an attempt to use time series data on relative population sizes to satisfy the requirements of the Marine Mammal Protection Act of 1972 for maintaining an "optimum sustainable population" of marine mammals. Three methods of implementing this approach were studied, using a computer simulation of stochastic population growth with density-dependence operating on first-year survival in the form of a generalized-logistic function. Methods developed by Gerrodette (1988) and Boveng et al. (1988) appeared to be less sensitive than desirable when used with the simulated population data. The third method, developed in this study, offers better protection against "Type II error" (failing to identify populations in the optimum sustainable population range), particularly when combined with Gerrodette's (1988) approach.     

Testing for association in the presence of population stratification: a simulation study comparing the S-TDT, STRAT and the GC

A novel approach for association testing in the presence of population stratification has been introduced by Pritchard et al. (2000a) and Pritchard et al. (2000b). The structured association approach is a two-tiered procedure that first estimates the population structure and then tests the null hypothesis H0: 'no association within subpopulations' in the second step. A power comparison of the stratified test for association (STRAT) (Pritchard et al., 2000b) and the Transmission-Disequilibrium-Test (TDT) (Spielman and Ewens, 1993a) in a simulation framework showed superiority of STRAT if allele frequencies or associations between allele and disease differ strongly in subpopulations. In more homogeneous situations, the TDT had greater power than STRAT. However, the TDT, based on family trios,that uses population controls, needs 50% more genotyping compared to STRAT. The Sib-Transmission-Disequilibrium-Test (S-TDT) needs the same amount of genotyping since it relays in its minimal configuration on pairs of siblings. This raises the question how the S-TDT (Spielman and Ewens, 1998a) performs compared to the population based methods STRAT and Genomic Controls (GC). In this paper, we present a simulation study accounting for two different models of population stratification in different settings of allele frequencies and under different risk models. The results showed that under a discrete as well as under an admixed population model, STRAT strongly outperformed the S-TDT and the GC when different alleles were associated in different subpopulations. In contrast, the S-TDT had greater power than STRAT when the same allele was associated in both subpopulations. Here, the GC was sometimes even more powerful than the S-TDT, depending on the population model and the allele frequency differences. A general recommendation for the use of one of the tests can therefore not be given.     

Validation of a Demographic Model for Woodland Caribou

Abstract: Wildlife population models are potentially valuable for conservation planning. Validation is necessary to ensure that models are sufficiently robust for predicting management outcomes consistent with conservation objectives. Sorensen et al. (2008) produced a model of woodland caribou (Rangifer tarandus) population growth rate that was recently modified and used as a predictive tool at several scales. We computed confidence intervals and evaluated the performance of this model using novel data. Confidence intervals were wide, and results suggested that the model may have a positive bias, resulting in over-estimation of population growth rates, as well as low predictive power. Wide confidence intervals mean that current understanding of factors governing woodland caribou herd dynamics is not sufficient for wildlife managers to make reliable projections of responses to management.     

On relationships between various distribution functions in balanced unicellular growth

The relationships between various size distributions in balanced exponential growth of a batch culture of microorganisms are presented. Starting from the partial differential integral equations (Eakmanet al., 1966; Fredricksonet al., 1967) derived for the growth of a microbial culture expressions are obtained for the growth rate of organisms of specific size and size range. These expressions were first obtained by Collins and Richmond (1962) by an entirely different method. Also derived are equations which link probability functions, which are basic to the growth of a microbial culture, with other size distributions that can be estimated experimentally.