Prospective evaluation of designs for analysis of variance without knowledge of effect sizes

Estimation of design power requires knowledge of treatment effect size and error variance, which are often unavailable for ecological studies. In the absence of prior information on these parameters, investigators can compare an alternative to a reference design for the same treatment(s) in terms of its precision at equal sensitivity. This measure of relative performance calculates the fractional error variance allowed of the alternative for it to just match the power of the reference. Although first suggested as a design tool in the 1950s, it has received little analysis and no uptake by environmental scientists or ecologists. We calibrate relative performance against the better known criterion of relative efficiency, in order to reveal its unique advantage in controlling sensitivity when considering the precision of estimates. The two measures differ strongly for designs with low replication. For any given design, relative performance at least doubles with each doubling of effective sample size. We show that relative performance is robustly approximated by the ratio of reference to alternative $\alpha $ quantiles of the $F$ distribution, multiplied by the ratio of alternative to reference effective sample sizes. The proxy is easy to calculate, and consistent with exact measures. Approximate or exact measurement of relative performance serves a useful purpose in enumerating trade-offs between error variance and error degrees of freedom when considering whether to block random variation or to sample from a more or less restricted domain.     

Designs with a priori information for nonmarket valuation with choice experiments: A Monte Carlo study

Good practice in experimental design is essential for choice experiments used in nonmarket valuation. We review the practice of experimental design for choice experiments in environmental economics and we compare it with advances in experimental design. We then evaluate the statistical efficiency of four different designs by means of Monte Carlo experiments. Correct and incorrect specifications are investigated with gradually more precise information on the true parameter values. The data generating process (DGP) is based on estimates from data of a real study. Results indicate that D-efficient designs are promising, especially when based on Bayesian algorithms with informative prior. However, if good quality a priori information is lacking, and if there is strong uncertainty about the real DGP—conditions which are quite common in environmental valuation—then practitioners might be better off with shifted designs built from conventional fractional factorial designs for linear models.     

Measuring the impact of dynamic antipredator traits on predator-prey-resource interactions

This article analyzes the limitations of the most widely used method for quantifying the impact of dynamic antipredator traits on food chain dynamics and discusses alternative approaches. The standard method for a predator-prey-resource chain estimates the effects of the prey's defensive behavior by comparing population densities or fitness measures in a "predator cue" treatment to those in a no-predator treatment. This design has been interpreted as providing a measure of the "nonconsumptive effect" of the predator on the prey and the "trait-mediated indirect effect" of the predator on the resource. Other approaches involve measurements of the impact of the behavior in the presence of functional predators. The questions addressed here are: (1) How consistent are the results of different approaches? (2) How time-dependent are their results? (3) How well do they correspond to theoretical measures of effect size? (4) How useful are the measurements in understanding system dynamics? A model of a tritrophic system in which the prey species adjusts a defensive trait adaptively is used to evaluate the experimental designs. Measures of changes in prey fitness or population density in a cue treatment generally include offsetting effects of the cost of the behavior and the benefit of more resources. This means that the sign of the effect, as well as its magnitude, may change depending on when the experiment is terminated. Because predation is not present in the cue treatment, few conclusions can be drawn about the impact of the behavior on population densities or fitness of the prey in a natural setting with predators. Cue experiments often do not accurately separate trait-mediated from density-mediated effects on the resource. Most scalar measures of effects are sensitive to experimental duration and initial densities. Use of a wider range of experimental designs to measure trait-related effects is called for.     

Sex ratio manipulation and decreased growth of male offspring of undernourished golden hamsters (Mesocricetus auratus)

Summary The theory that female mammals in poor condition may increase individual fitness by skewing the sex ratio of their offspring toward daughters and by investing more resources in daughters than in sons was tested in hamsters. Newly mated experimental females were food-restricted during pregnancy and lactation (RR) or during lactation only (AR). Controls received food ad libitum. Maternal body weights were assessed daily from mating to 25 days postpartum. Litter survival (% litters with at least one pup surviving on any day), litter size, offspring sex ratios (=% males), and pup weights were monitored daily from birth (Day 1) to Day 25. All control and AR dams gave birth 16 days after mating. Gestation was extended by 1–3 days for 35.4% of RR dams. RR dams weighed significantly less at parturition than controls and AR females. During lactation, AR females showed the greatest weight loss and control females the least. AR weight loss exceeded that of RR females, possibly because the former maintained larger litters. Survival was highest for controls, intermediate for AR, and lowest for RR litters. Mean sex ratio at birth was significantly less for RR (40.7%) than for control (49.6%) and AR (48.8%) litters. RR sex ratio did not change significantly postnatally. Sex ratios of control and AR litters never differed statistically from 50%. Control male pups were significantly heavier than their sisters throughout the experiment. No significant gender differences were observed for AR pup weights after Day 2 postpartum. RR female offspring weighed more than their brothers throughout the experiment, and this difference was statistically significant immediately prior to the time that pups began to feed independently (Days 14–17). RR female pup weights were similar to, and sometimes significantly greater than, weights of control daughters during the period of postnatal maternal investment. Control males were always heavier than males from the other treatments. Patterns of weight gain by AR and RR males varied with age. We conclude that underfed female hamsters are able to adjust the sex ratio of offspring prenatally and parental investment postnatally to favor daughters.     

Litter sex ratios in the golden hamster vary with time of mating and litter size and are not binomially distributed

Summary Pregnancy rates, litter sizes, and litter sex ratios vary strongly with the time in the estrous cycle at which female golden hamsters (Mesocricetus auratus) are mated. Early matings tend to produce relatively high pregnancy rates, large litters, and female-biased sex ratios, while late matings tend to produce low pregnancy rates, small litters, and male-biased sex ratios. Time of mating and litter size are therefore correlated, but each appears to have an independent effect on litter sex ratio: time of mating and sex ratio are positively correlated, holding litter size constant, while litter size and sex ratio are negatively correlated, holding time of mating constant. At each litter size greater than two, the variance of litter sex ratios is less than the binomial variance expected on the hypotheses of independent sampling with a constant probability of producing a male. The main features of the distribution of litter sex ratios can be generated from a causal model in which different probabilities of producing a male apply to early and late conceptions within each litter. The relationship between litter size and mean litter sex ratio is potentially consistent with several different models for the evolution of adaptive sex-ratio variation. Offrint request to: U.W. Huck     

A comparison of periodic survey designs employing multi-stage sampling

Sampling designs considered for a national scale environmental monitoring programme are compared. Specifically, design strategies designed to monitor one aspect of this environmental programme, agro-ecosystem health, are assessed. Two types of panel survey designs are evaluated within the framework of two-stage sampling. Comparisons of these designs are discussed with regard to precision, cost, and other issues that need to be considered in planning long-term surveys. To compare precision, the underlying variance of a simple estimator of mean difference is derived for each of the two designs. A variance and cost model accounting for the different rotational sampling schemes across designs are developed. Optimum stage allocation for each design are assessed with the variance-cost models. The best choice of design varied with the conditions underlying the variance model and the degree of other sources of survey error expected in the programme.     

Order restricted randomized designs and two sample inference

This paper develops a new design that relies on subjective judgment ranking to compare subsets of experimental units. This judgment ranking is used along with restricted randomization to improve statistical inference for the contrast between two levels of a treatment. The new design assigns the judgment ranked units in a subset to different treatments. Such an assignment translates the positive dependence among units within each subset into negative dependence for the estimators of treatment means, and hence leads to a reduction in variance for the contrast. For the proposed design, a test for the difference in means of two treatment levels is developed along with an associated confidence interval. It is shown that the null distribution of the proposed test is approximated reasonably well with the Student’s t-distribution for sample sizes as small as 6. A simulation study indicates that the proposed design is advantageous compared to its competitors in the literature for both high and low quality rankings. The new design’s advantage increases with the quality of rankings.     

Chromium recovery from solid leather waste by chemical treatment and optimisation by response surface methodology

The leather industry uses conventional tanning methods which cause environmental pollution due mainly to the presence of chromium. This study suggests a treatment for solid leather waste containing chromium as an ecological alternative to the pollution generated by tanneries. The study uses an original approach to the optimisation of chromium recovery by mathematical and statistical treatment of the experimental data. Several factors that influence recovery, such as temperature, concentration, time and solid/liquid ratio through acid and basic hydrolysis were analysed with the aid of experimental design. Tanning liquor was obtained by adjusting pH, alkalinity and concentration when hydrolysis finished. An appropriate response surface model was constructed using alkaline hydrolysis experiments with sodium hydroxide, leading to conditions for maximum recovery of Cr₂O₃. The optimal NaOH concentration (1.58%), temperature (63.7 °C), time (3 h) and solid/liquid ratio (1/70 g·mL^?1) were established. The results indicate that sodium hydroxide as an hydrolysis agent is a highly efficient means of recovering chromium from solid leather waste in order to produce tanning liquor.     

Detecting conservation benefits in spatially protected fish populations with meta-analysis of long-term monitoring data

Marine protected areas (MPA) produce a positive effect on fish populations, but this may be difficult to identify due to the high temporal variability of populations. Meta-analysis is an option for analysing data from different sources and sampling designs and it can address problems related to temporal and spatial variability in fish populations. We analysed fish abundance data from visual counts conducted in summer, from 1996 to 2002, in the MPA of Tabarca (Alicante, Spain). The results showed an overall positive effect of protection at the species and family levels. Overall abundance of fishes inside the reserve was, on average, 1.22 times higher than outside the reserve boundaries. Positive effect of protection was found for Boops boops, Diplodus annularis, Diplodus cervinus, Epinephelus marginatus, Epinephelus costae and Epinephelus aenus. Species of Labrids were not affected by protection, except for Thalassoma pavo and Symphodus ocellatus. Meta-analysis of temporal data allows evaluation of the protection MPA provide and is particularly useful when data sources have different experimental designs or sampling programs. The Tabarca MPA has benefited fish populations by increasing their abundance and we suggest that meta-analysis is a complementary tool for the management of MPAs.     

Synergy between pheromone trails and quorum thresholds underlies consensus decisions in the ant Myrmecina nipponica

Coordination of group actions in social organisms is often a self-organised process lacking central control. These collective behaviours are driven by mechanisms of positive feedback generated through information exchange. Understanding how different methods of communication generate positive feedback is an essential step in comprehending the functional mechanisms underlying complex systems. The Japanese small-colony ant, Myrmecina nipponica uses both pheromone trails and an apparent quorum response during consensus decisions over a new home. Both of these mechanisms have been shown to generate positive feedback and are effective means of selecting among mutually exclusive courses of action. In this study, I investigate how pheromone trails and quorum thresholds contribute to consensus decisions during house-hunting in this species through experimental manipulations of pheromone trails, colony size and environmental context. Results demonstrate that (1) providing colonies with pre-established pheromone trails increased the number of ants finding the new site and led to higher quorum thresholds and more rapid relocations, (2) experimentally halving colony size resulted in a proportional decrease in quorum thresholds and (3) colonies relocating long distances had higher quorums than those relocating short distances. Taken together, these data indicate that pheromone trails are important for recruitment and navigation during nest site selection, but that decision making is contingent on a quorum response. Such synergy between mechanisms of positive feedback may be a common means of optimising collective behaviours.     

Power and Sample Size Calculations for Linear Hypotheses Associated with Mixtures of Many Components using Fixed-Ratio Ray Designs

Response surface methodology, often supported by factorial designs, is the classical experimental approach that is widely accepted for detecting and characterizing interactions among chemicals in a mixture. In an effort to reduce the experimental effort as the number of compounds under study is increased, ray designs have been proposed to study combinations of chemicals. When interest is restricted to relevant mixing ratios, we are only interested in making inference along the specific rays of interest, as opposed to methods which use designs that require more experimental effort to support the estimation of a response surface over a broader experimental region. Methods have been developed for the test of additivity along multiple fixed-ratio rays. Of primary importance is the detection of interactions with reasonable power. The objective of this paper is to address power and sample size issues related to the hypothesis of no interaction.     

Two neighborhood-free plot designs for adaptive sampling of forests

Adaptive cluster sampling (ACS) has the potential of being superior for sampling rare and geographically clustered populations. However, setting up an efficient ACS design is challenging. In this study, two adaptive plot designs are proposed as alternatives: one for fixed-area plot sampling and the other for relascope sampling (also known as variable radius plot sampling). Neither includes a neighborhood search which makes them much easier to execute. They do, however, include a conditional plot expansion: at a sample point where a predefined condition is satisfied, sampling is extended to a predefined larger cluster-plot or a larger relascope plot. Design-unbiased estimators of population total and its variance are derived for each proposed design, and they are applied to ten artificial and one real tree position maps to estimate density (number of trees per ha) and basal area (the cross-sectional area of a tree stem at breast height) per hectare. The performances—in terms of relative standard error (SE%)—of the proposed designs and their non-adaptive alternatives are compared. The adaptive plot designs were superior for the clustered populations in all cases of equal sample sizes and in some cases of equal area of sample plots. However, the improvement depends on: (1) the plot size factor; (2) the critical value (the minimum number of trees triggering an expansion); (3) the subplot distance for the adapted cluster-plots, and (4) the spatial arrangement of the sampled population. For some spatial arrangements, the improvement is relatively small. The adaptive designs may be particularly attractive for sampling in rare and compactly clustered populations with critical value of 1, subplot distance equal to the diameter of initial circular plots, or plot size factor of 2.5 for an initial basal area factor of 2.     

Sexual selection in the zebra finch Taeniopygia guttata : condition, sex traits and immune capacity

The aim of this study was to test two hypotheses: (1) that condition-dependent secondary sexual traits reflect an individual's immune capacity and (2) that immune capacity and secondary sexual traits covary with primary sex traits, specifically ejaculate quality. We used the zebra finch Taeniopygia guttata as a study species, since the traits that females find attractive in males of this species, song rate and beak colour, are well established. A paired experimental design comprising 31 pairs of brothers was used; for each pair, one male was assigned to a control group provided with ad libitum food and no additional exercise, and the other male was assigned to an experimental group which experienced additional exercise and a reduced rate of food intake. After 11 weeks, the experimental group differed significantly from the control group in a range of variables, including body mass, haematocrit, granulocyte:lymphocyte (G:L) ratio and several primary sex traits, indicating that condition in this group was reduced. Birds in the experimental group showed a differential response to the treatment. We used the rank order in which birds could be captured by an experimenter as an index of condition. Birds easily caught were assumed to be in poorer condition than those which were more difficult to capture. Rank capture order was repeatable and was significantly correlated with the G:L ratio in the experimental group, but not in the control group. In the experimental group, rank capture order was correlated significantly with both secondary sex traits: birds in better condition had redder beaks and a higher song rate. However, beak colour and song rate did not covary significantly, suggesting that these two traits provide different types of information. Secondary sex traits did not covary with primary sex traits or any sperm features. Thus, there was no evidence for Trivers' sexual-competence hypothesis or the phenotype-linked fertility hypothesis. We used four assays of immune capacity, two general (G:L ratio and spleen mass) and two specific [antibody titres to sheep red blood cells (SRBCs) and Brucella abortus (BA)]. The G:L ratio was significantly higher in the experimental group, spleen mass (absolute and relative) did not differ between the groups, anti-SRBC antibody titres were significantly higher in the control group (contrary to expectation), and anti-BA antibody titres were close to being significantly lower in the experimental group. Within the experimental group, there was no evidence that antibody titres covaried with secondary sex traits. Although we demonstrated that beak colour and song rate were condition dependent, our experiment provided no evidence that either of these traits covaried with immune capacity or sperm features. Received: 9 February 1998 / Accepted after revision: 5 September 1998     

Long-term effects of yolk androgens on phenotype and parental feeding behavior in a wild passerine

Early growth conditions, such as exposure to maternally derived androgens in bird eggs, have been shown to shape offspring in ways that may have important long-term consequences for phenotype and behavior. Using an experimental approach, we studied the long-term effects of yolk androgens on several phenotypic traits and parental behavior in adult and female collared flycatchers (Ficedula albicollis). We elevated yolk androgen levels and monitored the experimental recruits the following breeding seasons. Androgen treatment had a sex-dependent effect on adult body condition, yolk androgen-treated males being heavier than control males when controlling for size, a result which may be caused potentially by selective mortality, physiological differences, or different life-history strategies. Androgen treatment did not however affect the expression of sexually selected plumage ornaments (forehead and wing patch size), UV coloration, or parental feeding rate in either sex. Our results suggest that yolk androgens are unlikely to affect sexual selection via plumage characteristics or contribute to breeding success via altered parental care. Yolk androgens do not seem to act as a means for female collared flycatchers to enhance the attractiveness of their sons. The lower return rate previously observed for androgen-treated male offspring compared to controls may therefore not be due to lower mating or breeding success, but may rather reflect lower survival or higher dispersal propensity of yolk androgen-treated males.     

Comparison of some homogeneity tests in analysis of over-dispersed binomial data

This paper compares the procedures based on the extended quasi-likelihood, pseudo-likelihood and quasi-likelihood approaches for testing homogeneity of several proportions for over-dispersed binomial data. The type I error of the Wald tests using the model-based and robust variance estimates, the score test, and the extended quasi-likelihood ratio test (deviance reduction test) were examined by simulation. The extended quasi-likelihood method performs less well when mean responses are close to 1 or 0. The model-based Wald test based on the quasi-likelihood performs the best in maintaining the nominal level. The score test performs less well when the intracluster correlations are large or heterogeneous. In summary: (i) both the quasilikelihood and pseudo-likelihood methods appear to be acceptable but care must be taken when overfitting a variance function with small sample sizes; (ii) the extended quasi-likelihood approach is the least favourable method because its nominal level is much too high; and (iii) the robust variance estimator performs poorly, particularly when the sample size is small.     

A meta-BACI approach for evaluating management intervention on chronic wasting disease in mule deer.

Advances in acquiring and analyzing the spatial attributes of data have greatly enhanced the potential utility of wildlife disease surveillance data for addressing problems of ecological or economic importance. We present an approach for using wildlife disease surveillance data to identify areas for (or of) intervention, to spatially delineate paired treatment and control areas, and then to analyze these nonrandomly selected sites in a meta-analysis framework via before-after-control impact (BACI) estimates of effect size. We apply these methods to evaluate the effectiveness of attempts to reduce chronic wasting disease (CWD) prevalence through intensive localized culling of mule deer (Odocoileus hemionus) in north-central Colorado, USA. Areas where surveillance data revealed high prevalence or case clusters were targeted by state wildlife management agency personnel for focal scale (on average <17 km2) culling, primarily via agency sharpshooters. Each area of sustained culling that we could also identify as unique by cluster analysis was considered a potential treatment area. Treatment areas, along with spatially paired control areas that we constructed post hoc in a case-control design (collectively called "management evaluation sites"), were then delineated using home range estimators. Using meta-BACI analysis of CWD prevalence data for all management evaluation sites, the mean effect size (change of prevalence on treatment areas minus change in prevalence on their paired control areas) was 0.03 (SE = 0.03); mean effect size on treatment areas was not greater than on paired control areas. Excluding cull samples from prevalence estimates or allowing for an equal or greater two-year lag in system responses to management did not change this outcome. We concluded that management benefits were not evident, although whether this represented true ineffectiveness or was a result of lack of data or insufficient duration of treatment could not be discerned. Based on our observations, we offer recommendations for designing a management experiment with 80% power to detect a 0.10 drop in prevalence over a 6-12-year period.     

Colony level sex allocation in a polygynous and polydomous ant

The colony-level sex allocation pattern of eusocial Hymenoptera has attracted much attention in recent studies of evolutionary biology. We conducted a theoretical and empirical study on this subject using the dolichoderine ant Technomyrmex albipes. This ant is unusual in having a dispersal polymorphism in both males and females. New colonies are founded by an alate female after mating with one or more alate males in the nuptial flight. In mature colonies, the reproductive role of the foundress queen is taken over by wingless offspring (supplementary reproductives). Mature colonies are extremely polygynous, with many wingless queens reproducing through intea-colonial mating with wingless males (inbreeding), and producing both alate and wingless sexuals. The population sex ratio of wingless sexuals was found to be extremely female-biased, while the population allocation ratio of alates was almost 1:1. This result suggests that there is local mate competition among wingless sexuals. A specific model for this extraordinary life cycle predicted that the asymmetry of regression relatedness (b _f/b _m) will disappear during the first few generations of wingless reproductives after the foundress dies. If colonies begin to produce alates after several wingless generations, this undermines the hypotheses for intercolonial sex ratio variation based on the relatedness asymmetry. We compared the magnitude of variation in sex ratios and other characteristics between two levels (within-colony-inter-nest and between-colony). Although there was considerable within-colony variation in all the examined characteristics, between-colony variances were always larger. This means that allocation is important at the whole-colony level, not that of the nest. There was no apparent correlation between the sex ratio of alates and colony size. Furthermore, partial correlation analysis indicated that neither the number of workers nor investment in alates explained the variation in the sex ratio of alates. The only factor which was significantly correlated with the sex ratio of alates was the sex ratio of wingless sexuals (a positive correlation). We conclude that both the alate and wingless sex ratios may be influenced by a common primary sex ratio at the egg stage, the variance of which may have genetic components. In the wingless sexuals, partial correlation analysis indicated that colony size and the number of workers explained the sex allocation ratio. The number of wingless females was strongly (positively) correlated with the total investment in wingless sexuals, while the number of males showed no such correlation. There is, however, no convincing explanation for the variation in sex allocation ratio of wingless sexuals, because the estimates of investment in wingless males may have a large sampling error. Correspondence to: K. Tsuji     

A new meta-analysis on the WTP/WTA disparity

This study reports a new meta-analysis of papers that elicit willingness-to-pay (WTP) and willingness-to-accept compensation (WTA) measures of value for the same good. We investigate the effects of type of good and several survey-design features on the WTP/WTA disparity, measured as the logarithm of the ratio of mean WTA to mean WTP. Confirming Horowitz and McConnell?s (2002) pioneering meta-analysis, we find the disparity is smaller for ordinary private goods than for public and non-market goods, that it is not solely an artifact of using hypothetical transactions or other weak experimental or survey methods, and that it is smaller for studies using student subjects. In addition, we find that the disparity is smaller when subjects have experience valuing the good in real markets or through repeated experimental trials. In contrast to Horowitz and McConnell, we find the disparity is significantly smaller in studies using incentive-compatible elicitation mechanisms. The disparity is smaller in more recent studies, an effect that is attributable only in part to changes in study characteristics.     

Inference about the ratio of means from Negative Binomial paired count data

We derive some statistical properties of the distribution of two Negative Binomial random variables conditional on their total. This type of model can be appropriate for paired count data with Poisson over-dispersion such that the variance is a quadratic function of the mean. This statistical model is appropriate in many ecological applications including comparative fishing studies of two vessels and or gears. The parameter of interest is the ratio of pair means. We show that the conditional means and variances are different from the more commonly used Binomial model with variance adjusted for over-dispersion, or the Beta-Binomial model. The conditional Negative Binomial model is complicated because it does not eliminate nuisance parameters like in the Poisson case. Maximum likelihood estimation with the unconditional Negative Binomial model can result in biased estimates of the over-dispersion parameter and poor confidence intervals for the ratio of means when there are many nuisance parameters. We propose three approaches to deal with nuisance parameters in the conditional Negative Binomial model. We also study a random effects Binomial model for this type of data, and we develop an adjustment to the full-sample Negative Binomial profile likelihood to reduce the bias caused by nuisance parameters. We use simulations with these methods to examine bias, precision, and accuracy of estimators and confidence intervals. We conclude that the maximum likelihood method based on the full-sample Negative Binomial adjusted profile likelihood produces the best statistical inferences for the ratio of means when paired counts have Negative Binomial distributions. However, when there is uncertainty about the type of Poisson over-dispersion then a Binomial random effects model is a good choice.     

整合分析中的非参数检验:重复取样检验法的实例应用

整合分析(meta-analysis)是对同一主题下多个独立实验结果进行综合的统计学方法。非参数检验整合分析——重复取样检验(resampling test)不考虑原文献数据的分布形式，故可在不知原文献数据分布形式时使用。其中的靴襻法(bootstrap)可用来给出总效应值的置信区间，但不能检验组内异质性是否显著。靴襻法与随机检验法(randomization test)可以有效弥补这一缺失，判断出组间差异性是否显著。实例应用表明，重复取样检验没有参数检验保守，又与参数检验的结果差异较小。