A simple permutation-type method for testing circular uniformity with correlated angular measurements

A simple method is provided for testing uniformity on the circle that allows dependence among repeated angular measurements on the same subject. Our null hypothesis is that the distribution of repeated angles is unaffected by rotation. This null can be evaluated with any test of uniformity by using a null reference distribution obtained by simulation, where each subject's vector of angles is rotated by a random amount. A new weighted version of the univariate Rayleigh test of circular uniformity is proposed.     

Consumer-resource theory predicts dynamic transitions between outcomes of interspecific interactions

Interactions between two populations are often defined by their interaction outcomes; that is, the positive, neutral, or negative effects of species on one another. Yet, signs of outcomes are not absolute, but vary with the biotic and abiotic contexts of interactions. Here, we develop a general theory for transitions between outcomes based on consumer–resource (C–R) interactions in which one or both species exploit the other as a resource. Simple models of C–R interactions revealed multiple equilibria, including one for species coexistence and others for extinction of one or both species, indicating that species' densities alone could determine the fate of interactions. All possible outcomes [(+ +), (+ −), (−−), (+ 0), (− 0), (0 0)] of species coexistence emerged merely through changes in parameter values of C–R interactions, indicating that variation in C–R interactions resulting from biotic and abiotic conditions could determine shifts in outcomes. These results suggest that C–R interactions can provide a broad mechanism for understanding context- and density-dependent transitions between interaction outcomes.     

Stable and invariant adjusted directed likelihoods

For the purpose of making inferences for a one-dimensional interestparameter, or constructing approximate complementary ancillariesor residuals, the directed likelihood or signed square rootof the likelihood ratio statistic can be adjusted so that theresulting modified directed likelihood is under ordinary repeatedsampling approximately standard normal with error of O(n^–3/2),conditional on a suitable ancillary statistic and hence unconditionally.In general, suitable specification of the ancillary statisticmay be difficult. We introduce two adjusted directed likelihoodswhich are similar to the modified directed likelihood but donot require the specification of the ancillary statistic. Theerror of the standard normal approximation to the distributionof these new adjusted directed likelihoods is O(n^–1),conditional on any reasonable ancillary statistic, which isstill an improvement over the unadjusted directed likelihoods.