Morphological variation associated with dispersal capacity in a tree‐killing bark beetle Dendroctonus ponderosae Hopkins

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含度量误差的黑龙江省主要树种生物量相容性模型

基于516株样木的生物量数据,采用非线性度量误差模型理论和方法,构建了黑龙江省15个主要树种(组)总生物量与地上、地下、树干、树冠、树枝、树叶6个分项生物量以及分项生物量间的相容性生物量模型,分别选出各树种总生物量和各分项生物量的最优模型,采用比值函数分级联合控制方程组构建了以总生物量为基础的相容性模型,并采用对数变换对总生物量模型消除异方差,采用加权回归对各分项生物量模型消除异方差.结果表明:本文所建的15个树种(组)相容性生物量模型中,总生物量的预估精度最高,达到90％以上;其次是地上部分生物量和树干生物量,预估精度在87.5％以上;地下部分、树冠、树枝和树叶生物量的预估精度相对较低,但绝大多数树种(组)的预估精度在80％以上;所有树种(组)总生物量、地上部分生物量、树干生物量模型的模拟效率(EF)值达0.9以上,绝大多数树种(组)的地下部分、树冠、树枝、树叶生物量模型的EF值在0.8以上.     

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.     

Quantifying individual variation in reaction norms: Mind the residual

Phenotypic plasticity is a central topic in ecology and evolution. Individuals may differ in the degree of plasticity (individual‐by‐environment interaction (I × E)), which has implications for the capacity of populations to respond to selection. Random regression models (RRMs) are a popular tool to study I × E in behavioural or life‐history traits, yet evidence for I × E is mixed, differing between species, populations, and even between studies on the same population. One important source of discrepancies between studies is the treatment of heterogeneity in residual variance (heteroscedasticity). To date, there seems to be no collective awareness among ecologists of its influence on the estimation of I × E or a consensus on how to best model it. We performed RRMs with differing residual variance structures on simulated data with varying degrees of heteroscedasticity and plasticity, sample size and environmental variability to test how RRMs would perform under each scenario. The residual structure in the RRMs affected the precision of estimates of simulated I × E as well as statistical power, with substantial lack of precision and high false‐positive rates when sample size, environmental variability and plasticity were small. We show that model comparison using information criteria can be used to choose among residual structures and reinforce this point by analysis of real data of two study populations of great tits (Parus major). We provide guidelines that can be used by biologists studying I × E that, ultimately, should lead to a reduction in bias in the literature concerning the statistical evidence and the reported magnitude of variation in plasticity.     

Exploring patterns of variation in clutch size–density reaction norms in a wild passerine bird

Negative density dependence of clutch size is a ubiquitous characteristic of avian populations and is partly due to within‐individual phenotypic plasticity. Yet, very little is known about the extent to which individuals differ in their degree of phenotypic plasticity, whether such variation has a genetic basis and whether level of plasticity can thus evolve in response to selection. Using 18 years of data of a Dutch great tit population (Parus major), we show that females reduced clutch size with increasing population density (slopes of the reaction norms), differed strongly in their average clutch size (elevations of the reaction norms) at the population‐mean density and that the latter variation was partly heritable. In contrast, we could not detect individual variation in phenotypic plasticity (‘I × E’). Level of plasticity is thus not likely to evolve in response to selection in this population. Observed clutch sizes deviated more from the estimated individual reaction norms in certain years and densities, implying that the within‐individual between‐year variance (so‐called residual variance) of clutch size was heterogeneous with respect to these factors. Given the observational nature of this study, experimental manipulation of density is now warranted to confirm the causality of the observed density effects. Our analyses demonstrate that failure to acknowledge this heterogeneity would have inflated the estimate of ‘I × E’ and led to misinterpretation of the data. This paper thereby emphasizes the fact that heterogeneity in residuals can provide biologically insightful information about the ecological processes underlying the data.     

Optimal sampling and estimation strategies under the linear model

In some cases model-based and model-assisted inferences canlead to very different estimators. These two paradigms are notso different if we search for an optimal strategy rather thanjust an optimal estimator, a strategy being a pair composedof a sampling design and an estimator. We show that, under alinear model, the optimal model-assisted strategy consists ofa balanced sampling design with inclusion probabilities thatare proportional to the standard deviations of the errors ofthe model and the Horvitz–Thompson estimator. If the heteroscedasticityof the model is 'fully explainable’ by the auxiliary variables,then this strategy is also optimal in a model-based sense. Moreover,under balanced sampling and with inclusion probabilities thatare proportional to the standard deviation of the model, thebest linear unbiased estimator and the Horvitz–Thompsonestimator are equal. Finally, it is possible to construct asingle estimator for both the design and model variance. Theinference can thus be valid under the sampling design and underthe model.