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*.     

Subset Selection of an Almost Best Treatment

A generalized goal using subset selection is discussed for the location parameter case. This goal is to select a non-empty subset from a set of k (k ≥ 2) treatments that contains at least one ε-best treatment with confidence level P*. For a set of treatments an ε-best treatment is defined as a treatment with location parameter on a distance less than or equal to ε(ε ≥o) from the best treatment, where best is defined as largest value of the location parameter. The efficiency of subset selection of an ε-best treatment relative to subset selection of the best treatment is investigated and is computed for some values of k and the confidence level for the Normal case as well as for the Logistic case.     

Simultaneous Selection of Extreme Populations: A Subset Selection Approach

The problem of selecting a “best” (largest mean, or smallest mean) population from a collection of k independent populations was formulated and solved by Bechhofer (1954). Gupta (1965) solved another important problem, that of selecting a subset of populations containing the “best” population from the original collection of populations. Since then many variations of the problem have been considered. Tong (1969) and Lewis (1980) have investigated the problem of selecting extreme populations (populations with a largest, and populations with a smallest, mean) with respect to one and two standard populations, respectively. In this paper we study the selection of extreme populations in absence of any standard population. We formulate subset-selection procedures when variances are known and equal, and also in the most general case when they are unknown and unequal. Nonexistence of a single-stage procedure is noted for this latter case (even if variances are equal). A two-stage procedure and some of its associated properties are discussed. Tables needed for application are provided, as is a worked example.     

Least Favorable Parameter Configurations for a Step‐down Subset Selection Procedure

Given a k‐dimensional vector X , k≥2, the range‐type statistic with J⊆I≡{1, …, k}, plays an important role in stepwise subset selection as well as in testing whether a<?tlb> prespecified subset of k populations exclusively consists of good ones. Although in previous papers least favorable parameter configurations (LFC's) for this statistic, which are worth knowing for the calculations of critical values, have been already shown to be from a small finite subset of the parameter space, further reduction has been conjectured. Under the assumption of a log‐concave and symmetric Lebesgue density with shift parameter, it is proved that in many cases the LFC can be uniquely given or, at least, found among only a few candidates. The resulting step‐down selection procedure will be illustrated for data from a balanced incomplete block design.     

THE EFFECT OF DELAYED POPULATION GROWTH ON THE GENETIC DIFFERENTIATION OF LOCAL POPULATIONS SUBJECT TO FREQUENT EXTINCTIONS AND RECOLONIZATIONS

I investigated the effects of delayed population growth on the genetic differentiation among populations subjected to local extinction and recolonization, for two different migration functions; (1) a constant migration rate, and (2) a constant number of migrants. A delayed period of population growth reduces the size of the newly founded populations for one or several generations. Whether this increases differentiation among local populations depends on the actual pattern of migration. With a constant migration rate, fewer migrants move into small populations than into large, thus providing ample opportunity for drift to act within a population. A prolonged period of population growth thus makes the conditions for enhanced differentiation between local populations less restrictive and also inflates the actual levels of differentiation. The effect depends on the relative magnitudes of k_e, the effective number of colonizers and k, the actual number of colonizers. When there is a constant number of migrants into a population per generation, migration into small populations is increased. This increase of migration in small populations counteracts the effects of genetic drift due to small population size. It increases the rate by which populations approach equilibrium, as small populations are swamped by migrants from larger populations closer to genetic equilibrium, and overall levels of differentiation are thus reduced. I also discuss situations for which the results of this paper are relevant.     

Identifying Signatures of Selection in Genetic Time Series

Both genetic drift and natural selection cause the frequencies of alleles in a population to vary over time. Discriminating between these two evolutionary forces, based on a time series of samples from a population, remains an outstanding problem with increasing relevance to modern data sets. Even in the idealized situation when the sampled locus is independent of all other loci, this problem is difficult to solve, especially when the size of the population from which the samples are drawn is unknown. A standard χ²-based likelihood-ratio test was previously proposed to address this problem. Here we show that the χ²-test of selection substantially underestimates the probability of type I error, leading to more false positives than indicated by its P-value, especially at stringent P-values. We introduce two methods to correct this bias. The empirical likelihood-ratio test (ELRT) rejects neutrality when the likelihood-ratio statistic falls in the tail of the empirical distribution obtained under the most likely neutral population size. The frequency increment test (FIT) rejects neutrality if the distribution of normalized allele-frequency increments exhibits a mean that deviates significantly from zero. We characterize the statistical power of these two tests for selection, and we apply them to three experimental data sets. We demonstrate that both ELRT and FIT have power to detect selection in practical parameter regimes, such as those encountered in microbial evolution experiments. Our analysis applies to a single diallelic locus, assumed independent of all other loci, which is most relevant to full-genome selection scans in sexual organisms, and also to evolution experiments in asexual organisms as long as clonal interference is weak. Different techniques will be required to detect selection in time series of cosegregating linked loci.     

The invariance of production per unit of food consumed in fish populations

The amount of biomass production per unit of food consumed (P/Q) represents an important quantity in ecosystem functioning, because it indicates how efficient a population transforms ingested food into biomass. Several investigations have noticed that P/Q remains relatively constant (or invariant) across fish population that feed at the same food-type level (carnivorous/herbivorous). Nevertheless, theoretical explanation for this invariant is still lacking. In this paper, we demonstrate that P/Q remains invariant across fish populations with stable-age distribution. Three key assumptions underpin the P/Q invariant: (1) the ratio between natural mortality M and von Bertalanffy growth parameter k (M/k ratio) should remain invariant across fish populations; (2) a parameter defining the fraction of ingested food available for growth needs to remain constant across fish that feed at the same trophic level; (3) third, the ratio between length at age 0 (\(l_0\)) and asymptotic length (\(l_\infty\)) should be constant across fish populations. The influence of these assumptions on the P/Q estimates were numerically assessed considering fish populations of different lifespan. Numerical evaluations show that the most critical condition highly relates to the first assumption, M/k. Results are discussed in the context of the reliability of the required assumption to consider the P/Q invariant in stable-age distributed fish populations.     

Molecular weight fractionation and the self-suppression of complex coacervation

A marked molecular weight fractionation accompanies the demixing or phase separation resulting from the complex coacervation of mixtures of aqueous solutions of salt-free isoionic unfractionated gelatins with pI's of 5 and 9. Viscosity studies show that the fractionation is such that the concentrated phase tends to maintain constant, homogeneous composition. A second feature, seen in phase volume and concentration measurements, is a marked self-suppression of coacervation intensity with increasing mixing concentration. These data were interpreted in terms of a dilute-phase aggregate model which assumes nearly equal electrostatic free energies of mixing in dilute aggregate and concentrated random phase. The driving force for phase separation is the entropy increase upon formation of the random phase but demixing also depends upon the polymer-solvent interaction parameter χ, in the same fashion as in simple coacervation. The dilute-phase aggregate model indicates that the sharp molecular weight selection takes place in the aggregate formation step and explains the self-suppression. Phase equilibria studies utilizing fractionated, paucidisperse high molecular weight gelatins, emphasize the requirement for concentrated phase homogeneity and indicate that aggregates of different molecular weight may act as different components, so that χP¹Q¹,P^kQ^k > 0, bringing about a separation of the system into three or more coexisting phases. The formation of several coexisting phases from a homologous polyelectrolyte system and the very marked requirement for phase homogeneity suggest that the phenomenon of complex coacervation is a very good model for some of the essential steps in the pre-biologic organization of polymeric polyions.     

Selection studies in sugarcane (Saccharum sp. hybrids)

Summary An approximate method to determine sample size for the estimation of population variance, ², is given. The estimate of ² is denoted as s² . Based on the assumption of a normal distribution for (s²/²–1), the sample size is approximately equal to 20,000 z² _p,/k²; where z is a standard normal deviate, p is the probability that s² ( 100¦s² – ²¦/²) is less than, or equal to, a critical value k, and k (measured as gDs²) is the desired precision of s² .The expected value of s², with respect to sample size, and the expected cumulative frequencies of s² over sample size for various k values are given. Their goodness of fit to the observed results was satisfactory except for populations that were different from normal. The observed values were taken from a study on four yield components in five sugarcane polycross progenies, grown in two contrasting environments over 2 years in three selection stages.The expected s² was found to be independent of the population coefficient of variance.Research suppoted in part by USDA, ARS, grant #12-14-5001-34. Published with the approval of the Director as Paper No. 412 in the Journal Series of the Experiment Station, Hawaiian Sugar Planters' Association.     

Optimal restricted phenotypic selection

Phenotypic selection is modified by introducing upper limits on the portion (P ₁) of individuals selected from a family as well as on the portion (P ₂) of family number that are allowed to contribute. At a preset selection proportion, P and P ₁, the maximum genetic gain is obtained by finding an optimum restriction on family number (P ₂ ^* ). A numerical procedure for solving the problem of optimization is developed for infinite populations. In small populations, maximum gain and P ₂ ^* can be found by simply comparing all possible P₂. Numerical examples are demonstrated for infinite breeding populations, assuming a normally-distributed family mean and within-family deviation. Selection and its simulation were applied to the fieldtest results of two tree species. Optimum restriction on family number is very close to P/P ₁, especially when heritability is low. In the real world of tree breeding, P ₂ ^* is given, or approximated, by P/P ₁+1/ _tm where m is the initial family number. The improvement of gain and the conservation of inbreeding effective population size are easy with high heritability and could be simultaneously obtained by using intense selection with a relatively low P ₁.     

Estimation of genetic variability and heritability for biofuel feedstock yield in several populations of switchgrass

Information on heritability and predicted gains from selection for increased biomass yield for ethanol production in switchgrass is limited and may vary among breeding populations. The purpose of this study was to estimate heritability and predicted gains from selection for higher biomass yield within a lowland ecotype switchgrass population, Southern Lowland 93 (SL‐93), and two upland ecotype switchgrass populations, Southern Upland Northern Upland Early Maturing (SNU‐EM) and Southern Upland Northern Upland Late Maturing (SNU‐LM). Narrow‐sense heritabilities (h_n²) for biomass yield in each of the three populations were estimated via progeny–parent regression analysis. Half‐sib (HS) progeny families from 130 randomly selected plants from the SL‐93 population were evaluated for biomass yield in replicated trials in 2002 and 2003. Clonal parent plants were evaluated for biomass yield in separate environments to provide unbiased h_n² estimates from progeny–parent regression. Yield differences were highly significant among SL‐93 HS progenies within and over years. For the SL‐93 population, h_n² estimates were 0.13 and 0.12 based on individual plant and phenotypic family mean (PFM) selection, respectively. Predicted genetic gains (ΔG) per selection cycle were 0.15 kg dry matter (dm) plant^?1 and 0.10 kg dm plant^?1 for PFM and individual plant selection methods, respectively. For the SNU‐EM and SNU‐LM populations, year and year × HS family effects were highly significant (P < 0.01) and the HS family effect over years was nonsignificant (P < 0.05). However, HS family effects were highly significant within respective years (P < 0.01). Estimates of h_n² for the SNU‐EM and SNU‐LM populations based on PFM and individual plant selection were similar, ranging from 0.44 to 0.47; ΔG per selection cycle ranged from 0.22 to 0.33 kg dm plant^?1. The magnitudes of the estimates of additive genetic variation suggest that selection for higher biomass yield should be possible. The substantial effect of environment on biomass yields in the upland populations and the failure of families to respond similarly over years stress the importance of adequately testing biomass yield over years to assess yield.     

Rio Grande Wild Turkey Habitat Selection in the Southern Great Plains

ABSTRACT We recorded telemetry locations from 1,129 radiotagged turkeys (Meleagris gallopavo intermedia) on 4 study areas in the Texas Panhandle and southwestern Kansas, USA, from 2000 to 2004. Analyses of telemetry locations indicated both sexes selected riparian vegetative zones. Females did not select grazed or nongrazed pastures for daily movements. However, females did select nongrazed pastures for nest sites on 2 study areas and males selected for grazed pastures at one study area during the breeding season. We compared nest sites (n = 351) to random sites using logistic regression, which indicated height of visual obstruction, percent canopy cover, and percent bare ground provided the highest predictive power (P ≤ 0.003) for characteristics describing nest-site selection. Nest-site vegetative characteristics between vegetative zones differed primarily in composition: upland zone nest sites had more (P ≤ 0.001) shrubs and riparian zone nest sites had more (P ≤ 0.001) grass. There were no differences in measured nest site vegetative characteristics between pasture types, but there were differences between available nesting cover in grazed and nongrazed pastures. Random plots in grazed pastures had less grass cover (P ≤ 0.001) and more bare ground (P = 0.002). Because of cattle impacts on average grass height and availability, grazing would likely have the highest impact on nesting in riparian zones due to turkey use of grass as nesting cover. An appropriate grazing plan to promote Rio Grande turkey nesting habitat would include grazing upland zones in the spring, when it likely has little impact on nesting-site selection, and grazing riparian zones following breeding season completion. Grazing at light to moderate intensities with periods of rest did not affect male turkey pasture use and may have continued to maintain open areas used by male turkeys for displaying purposes.     

Modeling Markovian biological systems via optimization operators

A general, computer-oriented method permitting to derive Markovian models with required (desired) properties is suggested and illustrated by examples. The method is based on the concept of a transition matrices generating (tmg) optimization operator, which is defined as a pair involving a (linear) transformation T and the associate optimization problem L _T . When the latter one is solved a set of transition matrices with required properties (ergodicity, regularity etc.) is get by starting from a sequence of probability vectors {P _k } which expresses the test data. Since the corresponding measurements are inevitably subjected to errors, it is not required that {P _k } be reached in the step-wise evolution of the process. Instead, it is required to minimize the so-called v-distance with respect to the probability vectors {P _k }. The optimization is performed by taking into account some constraints expressing the prior-known properties of the chain. This enables to solve the following problem: Given a sequence of (measured) probability vectors {P _k }, find a sequence of transition matrices {P _k } leading to the smallest v-distance with respect to {P _k } subject to given constraints. Some fundamental properties of the resulting Markov chains are emphasized, which are useful in modeling concrete biological systems. Thus, more realistic Markovian models are obtained starting from test data, as compared with the methods using conventional means.     

Microsatellite variation and population genetic structure of the red throat emperor on the Great Barrier Reef

Analysis (using three analytical approaches) of eight microsatellite markers from six locations in three geographic regions of the Great Barrier Reef (GBR), including populations that differed in demographic characteristics, showed no evidence of genetic stock structure in the red throat emperor Lethrinus miniatus. Measures of inter‐population differentiation were non‐significant (P ≥ 0·67). Using a Bayesian clustering approach, ‘admixture’ was detected (mean alpha values >1) with allele frequencies for each of the locations sampled being correlated equally with allele frequencies from all locations sampled. The number of populations (K) identified was one, based on the estimates of the probability of the data at various K values (K = 1, 2, 3, … 6). Additionally, alpha values did not stabilize to relatively constant values in any of the Bayesian analyses performed, indicating that there was no real genetic structure between locations. Analysis of genetic variation as detected by analysis of molecular variance (AMOVA) indicated that almost all of the variance in the data (99·74%, P ≤ 0·023) was within populations, rather than among populations (0·15%, P ≤ 0·176) or amongst regions sampled (0·10%, P ≤ 0·247) on the GBR. F_st statistics identified four individual loci having statistically significant differentiation among populations, but these were only related to one out of 12 pair‐wise comparisons where populations differed demographically. Given these results (albeit using neutral markers), together with the capacity of adults and larvae to be mobile between reefs on the inter‐connected GBR, it is considered unlikely that L. miniatus populations exist as distinct genetic stocks in the GBR. It is therefore not possible, using neutral markers, to reject the null hypothesis that the fishery be managed as a single panmictic stock.     

Origins of H-2 polymorphism in the house mouse. II. characterization of a model population and evidence for heterozygous advantage

Comparison of the rate of synonymous and nonsynonymous nucleotide substitutions suggests that certain regions of the functional H-2 genes, which are part of the mouse major histocompatibility complex (Mhc), are under strong positive selection pressure. Thus far, however, little evidence has been provided for the existence of such pressure in natural mouse populations. We have, therefore, initiated experiments designed to test the hypothesis of positive selection acting on H-2 loci. The experiments are being carried out on two natural mouse populations in Jerusalem, Israel. One population occupies a space of about 100 m² in a chicken coop, the other lives in a nearby field in which mouse stations providing food and shelter have been set up. Extensive typing of these two populations revealed the presence of only four H-2 haplotypes. Mice in the two populations breed continually all year around, yet population size varies seasonally, with population maxima in winter and minima in summer. The population in the chicken coop contains a relatively stable nucleus which may be organized in demes with an excess of females over males and limited territorial mobility. The rest of the mice stay in the population for a short time only and then either die or emigrate. The field population is smaller and more loosely organized than the chicken-coop population, with demes probably forming only during population maxima. For the rest of the time breeding in this population is probably panmictic. At a population minimum in the summer of 1984, H-2 homozygotes happened to predominate over heterozygotes. This situation, however, lasted for a short time only and thereafter there was a continuous, statistically highly significant increase in the proportion of H-2 heterozygotes of one or two types. The increase occurred in both populations but was more apparent in the chicken-coop population. This observation provides the first experimental evidence that heterozygous advantage might be one of the mechanisms maintaining high H-2 polymorphism in natural populations of the house mouse.     

An Asymptotically Optimal Adaptive Selection Procedure in the Proportional Hazards Model with Conditionally Independent Censoring

Assume k independent populations are given which are distributed according to R, …,R (ϑ_i ∈ Θ ⊆ R ). Taking samples of size n the population with the smallest ϑ-value is to be selected. Using the framework of Le Cam's decision theory (Le Cam , 1986; Strasser , 1985) under mild regularity assumptions, an asymptotically optimal selection procedure is derived for the sequence of localized models. In the proportional hazards model with conditionally independent censoring, an asymptotically optimal adaptive selection procedure is constructed by substituting the unknown nuisance parameter by a kernel estimator.     

The accumulation of mutations in asexual populations and the structure of genealogical trees in the presence of selection

We study the accumulation of unfavourable mutations in asexual populations by the process of Muller's ratchet, and the consequent inevitable decrease in fitness of the population. Simulations show that it is mutations with only moderate unfavourable effect that lead to the most rapid decrease in fitness. We measure the number of fixations as a function of time and show that the fixation rate must be equal to the ratchet rate once a steady state is reached. Large bursts of fixations are observed to occur simultaneously. We relate this to the structure of the genealogical tree. We derive equations relating the rate of the ratchet to the moments of the distribution of the number of mutations k per individual. These equations interpolate between the deterministic limit (an infinite population with selection present) and the neutral limit (a finite size population with no selection). Both these limits are exactly soluble. In the neutral case, the distribution of k is shown to be non-self-averaging, i.e. the fluctuations remain very large even for very large populations. We also consider the strong-selection limit in which only individuals in the fittest surviving class have offspring. This limit is again exactly soluble. We investigate the structure of the genealogical tree relating individuals in the same population, and consider the probability (T) that two individuals had their latest common ancestor T generations in the past. The function (T) is exactly calculable in the neutral limit and the strong-selection limit, and we obtain an empirical solution for intermediate selection strengths.     

Selection against immigrants in wild seabird populations

Immigration is a major demographic parameter shaping population dynamics and is an important driver of eco‐evolutionary patterns, but the fitness consequences for individuals following their settlement to a new population (immigrants) remain poorly tested in wild animal populations, particularly among long‐lived species. Here we show that immigrants have a lower fitness than residents in three wild seabird populations (wandering albatross Diomedea exulans, southern fulmar Fulmarus glacialoides, snow petrel Pagodroma nivea). Across all species and during a 32‐year period, immigrants made on average ?9 to 29% fewer breeding attempts, had 5–31% fewer fledglings, had 2–16% lower breeding success and produced 6–46% fewer recruits. Female immigration and male residency were also favored through differences in breeding performance. We provide evidence for selection against immigrants in wild populations of long‐lived species and our results are consistent with female‐biased dispersal in birds being driven by asymmetric limiting resources and the competitive ability of dispersers vs. non‐dispersers.     

An Integrated Formulation for Comparing Treatments with Binary Response with a Control

The problem of comparing k(≧2) bernoulli rates of success with a control is considered. An one-stage decision procedure is proposed for either (1) choosing the best among several experimental treatments and the control treatment when the best is significantly superior or (2) selecting a random size subset that contains the best experimental treatment if it is better than the control when the difference between the best and the remaining treatments is not significant. We integrate two traditional formulations, namely, the indifference (IZ) approach and the subset selection (SS) approach, by seperating the parameter space into two disjoint sets, the preference zone (PZ) and the indifference zone (IZ). In the PZ we insist on selecting the best experimental treatment for a correct selection (CS₁) but in the IZ we define any selected subset to be correct (CS₂) if it contains the best experimental treatment which is also better than the control. We propose a procedure R to guarantee lower bounds P₁* for P(CS₁≧PZ) and P₂* for P(CS₂≧IZ) simultaneously. A brief table on the common sample size and the procedure parameters is presented to illustrate the procedure R.