Sampling animal association networks with the gambit of the group

Ecologists increasingly use network theory to examine animal association patterns. The gambit of the group (GoG) is a simple and useful assumption for accumulating the data necessary for a network analysis. The gambit of the group implies that each animal in a group is associating with every other individual in that group. Sampling is an important issue for networks in wild populations collected assuming GoG. Due to time, effort, and resource constraints and the difficulty of tracking animals, sampled data are usually a subset of the actual network. Ecologists often use association indexes to calculate the frequency of associations between individuals. These indexes are often transformed by applying a filter to produce a binary network. We explore GoG sampling using model networks. We examine assortment at the level of the group by a single dichotomous trait, along with many other network measures, to examine the effect of different sampling regimes, and choice of filter on the accuracy and precision with which measures are estimated. We find strong support for the use of weighted, rather than filtered, network measures and show that different filters have different effects depending on the nature of the sampling. We make several practical recommendations for ecologists planning GoG sampling.     

Adaptive changes in size and age at metamorphosis can qualitatively vary with predator type and available defenses

In many taxa the timing of metamorphosis is plastic in response to predation risk during the pre-metamorphic stage, and trends in both age and body size at metamorphosis have been the subject of much study. The responses to cues of predators are predominantly to be larger or equal-sized at the same age or older at metamorphosis. These observations are in direct contrast with existing theoretical treatments of this plasticity, which mostly predict earlier and smaller metamorphosis and never later and larger metamorphosis without invoking indirect effects on growth rate. Here we resolve the discrepancy between theory and observation using a dynamic state-dependent model that incorporates morphological and behavioral responses to predation risk. We allow prey to choose the optimal activity level and/or investment in defense over the growth period. We show that under certain conditions, metamorphosis at a larger size and later time is likely to be optimal. Our analysis allows us to make testable predictions about the changes in activity level of prey as they grow and how the effect of providing refuges will vary with predator type. Several of these predictions are supported by a meta-analysis of metamorphic responses to caged predators by larval amphibians and insects. Our predictions lead to insights about the feedback effects of antipredator responses on growth and subsequent implications for life history.     

Distribution-free two-sample comparisons in the case of heterogeneous variances

Behavioral ecologists are often faced with a situation where they need to compare the central tendencies of two samples. The standard tools of the t test and Mann–Whitney U test (equivalent to the Wilcoxon rank-sum test) are unreliable when the variances of the groups are different. The problem is particularly severe when sample sizes are different between groups. The unequal-variance t test (Welch test) may not be suitable for nonnormal data. Here, we propose the use of Brunner and Munzel’s generalized Wilcoxon test followed by randomization to allow for small sample sizes. This tests whether the probability of an individual from one population being bigger than an individual from the other deviates from random expectation. This probability may sometimes be a more clear and informative measure of difference between the groups than a difference in more commonly used measures of central tendency (such as the mean). We provide a recipe for carrying out a statistical test of the null hypothesis that this probability is 50% and demonstrate the effectiveness of this technique for sample sizes typical in behavioral ecology. Although the test is not available in any commercial software package, it is relatively straightforward to implement for anyone with some programming ability. Furthermore, implementations in R and SAS are freely available on the internet.     

Round your numbers in rank tests: exact and asymptotic inference and ties

Non-parametric statistical tests are commonly used in the behavioral sciences. Researchers need to be aware that non-parameteric methods involving ranks can perform unreliably as a result of very small amounts of noise added in the storage and manipulation of values by computers, causing spurious reduction in the number of ties. In order to avoid this problem, researchers should round values to an appropriate number of decimal places prior to the ranking procedure to ensure that data points whose values cannot be separated according to the precision of their measurement are recorded as having identical rank. We also recommend exact rather than asymptotic evaluation of p values in non-parametric statistical tests.     

Game theory, multi-modal signalling and the evolution of communication

We discuss how the theoretical framework related to selection pressures on multi-component and multi-modal signalling introduced by the article of Wilson et al. in this special issue could usefully be built both theoretically and empirically. Theoretically, we suggest that the game theory approach of Wilson et al. could be generalised using the methodology of adaptive dynamics in order to indicate evolutionary trajectories and paths of evolution. This might indicate the relative likelihood of finding different equilibriums empirically in situations where the game theory explorations of Wilson et al. suggest that multiple equilibriums may exist for a given system. We also suggest how the work of Wilson et al. could be extended theoretically and empirically to further capture the effects of receiver psychology on selective pressures on multi-component and multi-modal signals. We also highlight the assumptions and predictions of the existing theory that would most benefit from and would be most amenable to empirical testing.     

Good practice in testing for an association in contingency tables

The testing for an association between two categorical variables using count data is commonplace in the behavioral sciences. Here, we present evidence that influential biostatistical textbooks give contradictory and incomplete advice on good practice in the analysis of such contingency table data. We survey the statistical literature and offer guidance on such analyses. Specifically, we call for greater use of exact testing rather than tests which use an asymptotic chi-squared distribution. That is, we suggest that researchers take a conservative approach and only perform asymptotic testing where there is little doubt that it is appropriate. We recommend a specific criterion for such decision-making. Where asymptotic testing is appropriate, we recommend chi-squared over the G-test and recommend against the implementation of Yates (or any other) correction. We also provide advice on the effective use of exact testing for associations in contingency tables. Lastly, we highlight issues that need to be considered when using the commonly recommended Fisher’s exact test.     

Group size and relative competitive ability: geometric progressions as a conceptual tool

Contrary to the assumptions of many previous theoretical models, group size has recently been shown in experiments to have an effect on the relative (as well as absolute) competitive abilities of group members. Here we introduce a novel and effective mathematical tool for describing how relative competitive ability will change for any two specified individuals within a group as group size changes. We show that there is no simple general rule for describing how relative competitive ability will change with group size. A subsequent empirical test of the model helps to illustrate that very specific knowledge of the system under study is needed in order to produce robust predictions. Received: 23 December 1998 / Received in revised form: 26 July 1999 / Accepted: 2 October 1999     

Basic features,conjunctive searches,and the confusion effect in predator–prey interactions

The confusion effect describes the observed decrease in the likelihood that a predator will successfully catch any prey when attacking larger groups of moving prey. We introduce readers to the work of cognitive psychologists interested in human visual attention who have been studying their own version of the confusion effect for many years, developing methods and concepts that may be of fundamental utility to behavioral ecologists. In psychology, ‘basic features’ are characteristics unique to a target object in the visual field that no distracter objects share. Images containing targets with basic features are often less likely to induce the confusion effect in human subjects. Target objects with conjunctions of features, on the other hand, have no individual characteristics unique from distracters, but unique characteristics in combination. Such targets more often induce the confusion effect in humans. We propose the ‘basic feature’ (vs. conjunctions of features) as a new organizing concept for studies on the occurrence of the confusion effect in nature, potentially allowing predictions about which types of prey groups are likely to induce the confusion effect in predators.