A Selection Procedure for Selecting Good Exponential Populations

Consider k independent exponential populations with location parameters μ₁,…, μ_k and a common scale parameter or standard deviation θ. Let μ_(k) be the largest of the μ's and define a population to be good if its location parameter exceeds μ_(k) –Δ₁. A selection procedure is proposed to select a subset of the k populations which includes the good populations with probability at least P*, a pre-assigned value. Simultaneous confidence intervals, that can be derived with the proposed selection procedure, are discussed. Moreover, if populations with locations below μ_(k) –δ₂, (δ₂ > δ₁) are “bad”, a selection procedure is proposed and a sample size is determined so that the probability of omitting a “good” population or selecting a “bad” population is at most 1 – P*.     

Continuous and discrete extreme climatic events affecting the dynamics of a high-arctic reindeer population

Climate at northern latitudes are currently changing both with regard to the mean and the temporal variability at any given site, increasing the frequency of extreme events such as cold and warm spells. Here we use a conceptually new modelling approach with two different dynamic terms of the climatic effects on a Svalbard reindeer population (the Brøggerhalvøya population) which underwent an extreme icing event (“locked pastures”) with 80% reduction in population size during one winter (1993/94). One term captures the continuous and linear effect depending upon the Arctic Oscillation and another the discrete (rare) “event” process. The introduction of an “event” parameter describing the discrete extreme winter resulted in a more parsimonious model. Such an approach may be useful in strongly age-structured ungulate populations, with young and very old individuals being particularly prone to mortality factors during adverse conditions (resulting in a population structure that differs before and after extreme climatic events). A simulation study demonstrates that our approach is able to properly detect the ecological effects of such extreme climate events.     

Subset Selection for Exponential Populations: Determination of the Selection Constant

Given are k(≧2) exponential populations differing only in their location parameter. One wishes to choose the best one, that is the population with the largest value of the location parameter. A possible method for solving this problem is to select a subset of the k populations of size at least one which includes the best population with a required confidence P*(k^?1 ≤ P* ≤1). In this paper the required selection constant is determined for different values of k and P*. Also an approximation for the selection constant is derived. A comparison with the exact results is made.     

Robustness of Selection Procedures

In the article Bechhofers Indifference-zone formulation for selecting the t populations with the t highest means is considered in a set of non-normal distributions. Selection rules based on the sample mean, the 10% and the 20% trimmed means, two estimators proposed by Tiku (1981) for valuating the smallest and highest accepted sample values higher, the sample median and a linear combination of quantile estimators, two adaptive procedures and a ranksum procedure are investigated in a large scale simulation experiment in respect of their robustness against deviations from an assumed distribution. Robustness is understood as a small percentage of the difference β_A-β between the actual probability of incorrect selection β_A and the nominal β-value. We obtained a relatively good robustness for the classical sample mean selection rule and useful derivations for the employment of other selection rules in an area of practical importance.     

Genome size variation in Chenopodium quinoa (Chenopodiaceae)

The extent and significance of intraspecific genome size variation were analysed in quinoa (Chenopodium quinoa Willd.), a pseudocereal important for human consumption in the Andean region of South America. Flow cytometry, with propidium iodide as the DNA stain, was used to estimate the genome size of 20 quinoa accessions from Ecuador, Peru, Bolivia, Argentina, Chile and the USA. Limited genome size variation was found among the analysed accessions. The differences between the accessions were statistically significant but the maximum inter-accession difference between the populations with the largest and the smallest genome reached only 5.9%. The largest genome was found in population C4 from Chile (mean 3.077 pg/2C) and the smallest in the Peruvian population P2 (mean 2.905 pg/2C). The variation was not correlated with collection site; however, the quinoa accessions analysed in this study belonged to three distinct geographical groups: northern highland, southern highland and lowland.     

Quantitative methods for defining mast‐seeding years across species and studies

Abstract: Although there is a quantitative method that is commonly used for identifying mast‐seeding behaviour of a plant population based on the coefficient of variation (i.e. CV is standard deviation/mean>1), there is no general quantitative method for delineating “mast” as opposed to “non‐mast” years. Mast years are, however, described qualitatively as years when “large”, “unusually large” and “high” seed production occurs. The use of a consistent and generally applicable method for delineating mast years across species and plant populations is important for synthesizing knowledge of the causes and consequences of mast seeding, which could be confounded by using different methods among studies. We examine six quantitative methods for identifying mast years: four methods from the literature and two methods developed here. We use 36 seed production datasets covering a variety of species with ≥10 years of data to test the performance of these six methods. For each method, we quantify the percentage of the datasets to which the method could be successfully applied, the magnitude of the mast year relative to the mean, the frequency of mast years and the occurrence of consecutive mast years. The majority of the methods failed to meet the criteria for a suitable method. The best method used the number of standard deviates (standardized deviate method) of the annual mean seed production from the long‐term mean of the dataset to identify mast‐seeding years. General results from the standardized deviate method include that the occurrence of mast‐seeding years is largely unrelated to plant population CV, but similar across species and data collection methods.     

Selection of a rapidly maturing population of Globodera rostochiensis by continuous cultivation of early potatoes in Ayrshire, Scotland

Development of three G. rostochiensis populations was compared after 2, 3, 4, 5 and 13 wk at 12 and 15 °C on cv. Pentland Crown. The Jameston Farm (JF) and Skelmorlie populations originated from Ayrshire, Scotland, the former where early potatoes are grown annually, the latter from a farm where potatoes are grown in a conventional manner. The Feltwell population was originally from Norfolk, England. At 12 °C, nematodes from the JF population penetrated roots and developed more quickly than nematodes from the other populations. The JF population also produced the most cysts, which were the largest and contained most embryonated eggs. At 15 °C, differences between the populations were less marked, but JF nematodes invaded roots quickest and produced cysts with most eggs. These results are consistent with the hypothesis that the annual practice of early planting and harvesting to control losses caused by G. rostochiensis in Ayrshire is selecting a nematode population adapted genetically to the procedure.     

Application of statistical selection procedures for selecting the mutant with the highest enzyme activity from a set of mutants of the species Aspergillus niger

The enzyme Glucoamylase [1,4-α-D-glucan-glucohydrolase EC 3.2.1.3] is very important for the food industry. It is used for producing glucose, ethanol and beer, as well as in technological processes that require the decomposition of starch. Eight mutants of the species Aspergillus niger are evaluated and tested with respect to their production of Glucoamylase and proved to be suitable. The task is to find the mutant showing the highest enzyme activity with a given precision. Conventionally, this kind of multiple decision problem is handled by the analysis of variance (Model I), which tests the homogeneity of the population means, but in this case the results do not supply the desired information. Provided that the enzyme activities of the mutants are different, selection procedures can be used to choose the mutant with the “best” or at least a “good” level of activity. In this paper, a short methodical summary about the two classes of selection procedures is given, i.e. the indifference zone (and d-correct) procedures and the subset procedures. By the example of the selection of a mutant with high enzyme activity the planning of experiments is shown. Depending on suppositions about the variances, different selection rules are applied. Starting with the subset procedure of GUPTA, the number of mutants is reduced to seven. The following application of the d-correct procedures of BECHHOFER, DUNNETT and SOBEL allow us to calculate the necessary sample size of n = 49. Then the mutant whose sample has the largest mean will be selected as a “good” one with a given precision of d = 4 [u/l] and a probability of correct selection of (1–β) = 0.9

1 This application is result of a cooperation between the Dept. of Food of the Technical University, Berlin, and the Dept. of Biotechnology of the Higher Institute of Food and Flavour Industry, Plovdiv, sponsored by the DAAD andthe TU Berlin.

     

A Two-stage Design for Comparing Clinical Trials

A two-stage design is proposed to choose among several experimental treatments and a standard treatment in clinical trials. The first stage employs a selection procedure to select the best treatment, provided it is better than the standard. The second stage tests the hypothesis between the best treatment selected at the first stage (if any) and the standard treatment. All the treatments are assumed to follow normal distributions and the best treatment is the one with the largest population mean. The level and the power are defined and they are used to set up equations to solve unknown first stage sample size, second stage sample size, and procedure parameters. The optimal design is the one that gives the smallest average sample size. Numerical results are presented to illustrate the improvement of one design as compared to existing one stage design.     

Yearly changes in dispersal and life-history traits of Monochamus alternatus Hope with reference to its outbreak

The Japanese pine sawyer, Monochamus alternatus Hope, is the primary vector of the pinewood nematode, Bursaphelenchus xylophilus (Steiner et Buhrer) Nickle, the causative agent of pine wilt disease in East Asia. The range of B. xylophilus expands through the dispersal capability of its vectors and transport of host trees infested with the pathogenic nematode and its vector. Outbreaks of M. alternatus populations occur together with the epidemics of pine wilt disease, because the insect reproduces on host trees recently killed by the disease. We measured some dispersal and life-history traits of adults for four years to determine the change in flight capability and life history of a field population of beetles in relation to an outbreak. The population monitored exhibited an outbreak and subsequent collapse. The greatest mean body mass, largest area of hind wings, smallest wing load, and shortest preoviposition period were observed in the year of outbreak. By contrast, there was no difference in the ovariole number between pre-outbreak (latent) and outbreak years. The greatest mean hind wing area and smallest wing load suggest likely result in greater flight performance. As other studies showed, adult body mass is related positively to the flight performance and oviposition rate. Moreover, a shortened preoviposition period leads to a high reproduction rate. Thus, adults in outbreak populations are “superdispersers” because they are likely to have enhanced flight capability and reproduction power. This suggests that M. alternatus populations at the onset of a population outbreak enhance the expansion rate of B. xylophilus range more than those during the latent and pre-outbreak periods.     

Theoretical Modifications of Reciprocal Recurrent Selection

Reciprocal recurrent selection (RRS), which assumes overdominant loci to be important, alters two genetically different populations to improve their crossbred mean. Individual plants from two populations (A and B) are selfed and also crossed with plants from the reciprocal female tester population (B and A, respectively). Selection is based on the mean of crossbred families, and the selected individuals are randomly mated within A and B to form new populations.—We propose two alternatives to RRS. The first (RRS-I) uses, as the tester of population A, a population (LB) that is derived from population B by family selection for low yield. The second (RRS-II) is similar to RRS-I, but also uses, as the tester of B, a population (LA) that is derived from population A by family selection for low yield.—The expected crossbred means of RRS, RRS-I, and RRS-II were compared, assuming equal σP, at several cycles of selection for incomplete and complete dominance, and for several cases of overdominance (depending on the gene frequencies in A and B, and on the equilibrium gene frequency).—The choice of selection method depends on the importance of the effects of overdominant loci compared to loci exhibiting incomplete or complete dominance. If overdominance is unimportant, RRS-II is the best selection method, followed by RRS-I and RRS. If overdominance is important, both RRS and RRS-I are superior to RRS-II; RRS is preferred to RRS-I if the effects of overdominant loci are sufficiently important. If the genetic model is a mixture of levels of dominance at different loci, a combination of selection systems is suggested.     

A Two-Stage Test for Distinguishing Random,Pseudo-Random and Nonrandom Mating Populations

There is no such an implication that a population in Hardy-Weinberg equilibrium must have undergone random mating. Therefore, it is unequivocal that the usual tests for “Hardy-Weinberg equilibrium” are indeed tests for “random union of gametes” but not for “random mating”. In this paper, utilizing population characteristics expressed in equilibrium state (equilibrium or disequilibrium) and mating behavior (random or nonrandom), a two-stage testing procedure for distinguishing random, pseudo-random and nonrandom mating populations is proposed. At the first stage, a population is tested for Hardy-Weinberg equilibrium. If insignificant result (i.e., in equilibrium) is obtained, then to a second stage the population is further tested for mating behavior. Random mating-pairs data are needed here for analysis instead of random individuals for usual Hardy-Weinberg equilibrium tests. Since distinguishing the three types of mating populations depends on the combined results of two stages, the probability of correct determination of the two-stage tests is discussed by simulation studies.     

Selection against demographic stochasticity in age-structured populations

It has been shown that differences in fecundity variance can influence the probability of invasion of a genotype in a population; i.e., a genotype with lower variance in offspring number can be favored in finite populations even if it has a somewhat lower mean fitness than a competitor. In this article, Gillespie's results are extended to population genetic systems with explicit age structure, where the demographic variance (variance in growth rate) calculated in the work of Engen and colleagues is used as a generalization of "variance in offspring number" to predict the interaction between deterministic and random forces driving change in allele frequency. By calculating the variance from the life-history parameters, it is shown that selection against variance in the growth rate will favor a genotypes with lower stochasticity in age-specific survival and fertility rates. A diffusion approximation for selection and drift in a population with two genotypes with different life-history matrices (and therefore different mean growth rates and demographic variances) is derived and shown to be consistent with individual-based simulations. It is also argued that for finite populations, perturbation analyses of both the mean and the variance in growth rate may be necessary to determine the sensitivity of fitness to changes in the life-history parameters.     

Comparison of asymptotic population growth rates with heterogeneous variances

This report explores how the heterogeneity of variances affects randomization tests used to evaluate differences in the asymptotic population growth rate, λ. The probability of Type I error was calculated in four scenarios for populations with identical λ but different variance of λ: (1) Populations have different projection matrices: the same λ may be obtained from different sets of vital rates, which gives room for different variances of λ. (2) Populations have identical projection matrices but reproductive schemes differ and fecundity in one of the populations has a larger associated variance. The two other scenarios evaluate a sampling artifact as responsible for heterogeneity of variances. The same population is sampled twice, (3) with the same sampling design, or (4) with different sampling effort for different stages. Randomization tests were done with increasing differences in sample size between the two populations. This implies additional differences in the variance of λ. The probability of Type I error keeps at the nominal significance level (α = .05) in Scenario 3 and with identical sample sizes in the others. Tests were too liberal, or conservative, under a combination of variance heterogeneity and different sample sizes. Increased differences in sample size exacerbated the difference between observed Type I error and the nominal significance level. Type I error increases or decreases depending on which population has a larger sample size, the population with the smallest or the largest variance. However, by their own, sample size is not responsible for changes in Type I errors.     

Optimum operating mode for a class of fermentation

This paper is concerned with optimization of the operating mode of a fermentor. Combining the various modes of operation—batch, semibatch, and continuous—the operating pattern which maximizes the desired metabolic product in a single fermentor is determined by using Kelley's transformation method with Pontryagin's maximum principle. Kelley's transformation method is a device which avoids the singular situation which occurs when the usual procedure of selecting the optimal control function by the maximum principle breaks down. This is the case in the problem considered in this paper. For lysine fermentation, the best operating mode depends on the fermentor capacity and operating time. The results of this study are summarized thus: (i) when the operating time is “long enough,” optimal conditions require that continuous operation follows either semibatch and/or batch operation, and (ii) when the fermentor capacity becomes “large enough,” semibatch operation becomes important.     

An iterative approach from the standpoint of the additive hypothesis to the dendrogram problem posed by molecular data sets

The problem of constructing a dendrogram depicting phylogenetic relationships for a collection of contemporary species is considered. An approach was developed based on the additive hypothesis in which each “length” between two species can be described by the shortest sum of lengths for the individual links on the dendrogram topology which connect the two species. The additive hypothesis holds equally well if the dendro gram is replaced by its corresponding (rootless) network. Network topologies are defined set theoretically in terms of the initial, contemporary species, and a coefficient is defined for each point of any conceivable network. It is proved mathematically that each point of an additive network gives a coefficient value of zero, whereas each point not belonging to an additive network gives a coefficient value greater than zero. This suggests an iterative procedure in which “false” network points are replaced by “true” ones, or more generally in which “very false” network points are replaced by “nearly true” ones. The first procedure follows from the mathematical proof and the second is confirmed by simulation. Since most real data sets are not additive in the strict sense, a real data example was presented in which the iterative procedure produced a plausible network topology.     

Population cytology of the genus Phaulacridium

Twenty seven populations of the grasshopper Phaulacridium marginale were sampled from South Island, New Zealand. An analysis of the chiasma frequency data showed that populations differed significantly for this metric. The populations appeared to fall into two distinct size groups. Morphological measurements confirmed this and a reanalysis of the chiasma frequency data revealed that although the two groups differed significantly for both mean cell chiasma frequency and between cell variances, there was no difference between populations within a group. Analysis of climatological data suggests that the “larger” individuals show different environmental (habitat) preferences from the smaller, which are restricted to one region of South Island. The taxonomic status of Ph. marginale as a single species is called into question.     

Variance component analysis of bristle characters in local populations of Drosophila melanogaster.

The genetic variabilities of sternopleural and abdominal bristle numbers existing in local natural populations were assessed. Using second chromosome lines of Drosophila melanogaster extracted from three natural populations in Japan (the Ishigakijima, Ogasawara and Aomori populations), experiments were conducted to estimate the components of genetic variances, additive and dominance variances. The following results were obtained: For both sternopleural and abdominal bristle numbers, the additive genetic variances (sigma 2A) were much larger than the dominance variances (sigma 2D) especially in the southern populations. For example, in the Ishigakijima population, for females sternopleural bristle numbers of the inversion-free chromosome group, the additive and dominance variances were estimated to be 1.255 +/- 0.2034 and 0.0552 +/- 0.0180, respectively. The magnitudes of the estimates of additive genetic variances were nearly equal from north to south. By comparing the additive genetic variances of the inversion-free chromosome group with those of the In(2L)t-carrying chromosome group, it was inferred that sufficient number of generations to achieve the equilibrium state has not passed since the introduction of a single or a small number of the In(2L)t-carrying chromosomes to the Ishigakijima population.     

Monogamy Has a Fixation Advantage Based on Fitness Variance in an Ideal Promiscuity Group

We consider an ideal promiscuity group of females, which implies that all males have the same average mating success. If females have concealed ovulation, then the males’ paternity chances are equal. We find that male-based monogamy will be fixed in females’ promiscuity group when the stochastic Darwinian selection is described by a Markov chain. We point out that in huge populations the relative advantage (difference between average fitness of different strategies) determines primarily the end of evolution; in the case of neutrality (means are equal) the smallest variance guarantees fixation (absorption) advantage; when the means and variances are the same, then the higher third moment determines which types will be fixed in the Markov chains.