Problems with the statistical testing of panbiogeographic hypotheses

Abstract

Croizat regarded generalised tracks as having a statistical basis, their degree of justification being directly related to the number of individual tracks consistent with them. In order to be logically valid, however, such an approach needs to have an explicit statistical basis. Page (1987) attempts to provide this, proposing the following protocol. Tracks are treated as geographic minimum-spanning trees which in turn are represented numerically as binary connectivity matrices. The statistical significance of similarities between two connectivity matrices is assessed using a permutation-test of association, a test that was developed for comparing distancematrices. The null hypothesis for this test is defined by the set of alternative connectivity matrices corresponding to all possible permutations of the track-vertices. There are however, a number of problems with this statistical test when applied to connectivity matrices derived from panbiogeographic tracks, and these render invalid the procedure advocated by Page.     

The use of parsimony in testing phylogenetic hypotheses

With the advance of cladistic theory differences in principle between it and other systematic techniques are few but of fundamental importance. In the mechanics of classification they are confined to ranking and the rejection of paraphyletic taxa. In cladistic analysis, leading to cladograms, trees and phylogeny reconstruction, inconsistencies in apparent synapomorphies are said to be resolved using Popper's hypothetico-deductive method together with the principle of parsi However, not only do cladists not use Popper's methodology, which is inconsistent with parsimony, but their use of parsimony is invalid as a test of phylo The only accepted extrinsic test of a classification is that enunciated by John Stuart Mill. It has been claimed that cladistic classifications yield the best results when judged by Mill's criteria, but this is only possibly the case with analytic classifications produced by numerical techniques. No satisfactory test exists in normal (synthetic) cladism for distinguishing synapomorphy from homoplasy. The effects of this are particularly dire in cladograms and classifications involving fossils in which a Stufenreihe arrangement is adopted.     

On testing hypotheses concerning standardized mortality ratios

This paper describes tests of hypotheses concerning the equality of any k standardized mortality ratios (or, equivalently, of any k indirect adjusted rates) from p(≥k) populations. The distinction is made between the situation where the standard population is chosen independently of the p populations and one where the standard is formed by pooling all p populations. Different test procedures are required for these two situations. When the pooled standard is used, the appropriate test procedure is applicable only when k = p. Experimental evidence is given showing that when the pooled standard is used both test procedures lead to the same conclusion concerning the hypothesis for the case k = p. The recommendation is made, therefore, to use the “incorrect” test procedure when the standard is a pooled one even when k < p.     

Extending conventional priors for testing general hypotheses in linear models

We consider that observations come from a general normal linearmodel and that it is desirable to test a simplifying null hypothesisabout the parameters. We approach this problem from an objectiveBayesian, model-selection perspective. Crucial ingredients forthis approach are ‘proper objective priors’ to beused for deriving the Bayes factors. Jeffreys-Zellner-Siow priorshave good properties for testing null hypotheses defined byspecific values of the parameters in full-rank linear models.We extend these priors to deal with general hypotheses in generallinear models, not necessarily of full rank. The resulting priors,which we call ‘conventional priors’, are expressedas a generalization of recently introduced ‘partiallyinformative distributions’. The corresponding Bayes factorsare fully automatic, easily computed and very reasonable. Themethodology is illustrated for the change-point problem andthe equality of treatments effects problem. We compare the conventionalpriors derived for these problems with other objective Bayesianproposals like the intrinsic priors. It is concluded that bothpriors behave similarly although interesting subtle differencesarise. We adapt the conventional priors to deal with nonnestedmodel selection as well as multiple-model comparison. Finally,we briefly address a generalization of conventional priors tononnormal scenarios.     

The inheritance procedure: multiple testing of tree-structured hypotheses

Hypotheses tests in bioinformatics can often be set in a tree structure in a very natural way, e.g. when tests are performed at probe, gene, and chromosome level. Exploiting this graph structure in a multiple testing procedure may result in a gain in power or increased interpretability of the results.We present the inheritance procedure, a method of familywise error control for hypotheses structured in a tree. The method starts testing at the top of the tree, following up on those branches in which it finds significant results, and following up on leaf nodes in the neighborhood of those leaves. The method is a uniform improvement over a recently proposed method by Meinshausen. The inheritance procedure has been implemented in the globaltest package which is available on www.bioconductor.org.     

Experimental models for testing hypotheses about cumulative cultural evolution

The rapid appearance (over evolutionary time) of the cognitive skills and complex inventions of modern humans has been attributed to “cumulative cultural evolution” (CCE), the accumulation of knowledge and skills over generations. To date, researchers have only been able to speculate about the reasons for the apparent absence of this phenomenon in nonhumans, and it has not been possible to test hypotheses regarding the mechanisms underlying it. Here, we show that it is possible to demonstrate CCE under laboratory conditions by simulating generational succession through the repeated removal and replacement of human participants within experimental groups. We created “microsocieties” in which participants were instructed to complete simple tasks using everyday materials. In one of our procedures, participants were instructed to build a paper aeroplane which flew as far as possible, and in the other, they were instructed to construct a tower of spaghetti which was as tall as possible. We show that, in both cases, information accumulates within the groups such that later generations produce designs which are more successful than earlier ones. These methods offer researchers a window to understanding CCE, allowing for experimental manipulation and hypothesis testing.     

Sexual segregation in western grey kangaroos: testing alternative evolutionary hypotheses

In sexually dimorphic ungulates, sexual segregation is hypothesized to have evolved because of sex-specific differences in body size and/or reproductive strategies. We tested these alternative hypotheses in kangaroos, which are ecological analogues of ungulates. Kangaroos exhibit a wide range of body sizes, particularly among mature males, and so the effects of body size and sex can be distinguished. We tested predictions derived from these hypotheses by comparing the distribution of three sex–sex size classes of western grey kangaroos Macropus fuliginosus , in different habitats, and the composition of groups of kangaroos, across seasons. In accordance with the predation risk-reproductive strategy hypothesis, during the non-breeding season, females, which were more susceptible to predation than larger males, and were accompanied by vulnerable young-at-foot, were over-represented in secure habitats. Large males, which were essentially immune to predation, occurred more often than expected in nutrient-rich habitat, and small males, which faced competing demands of predator avoidance and feeding, were intermediate between females and large males in their distribution across habitats. During the breeding season, females continued to be over-represented in secure habitats when their newly emerged pouch young were most vulnerable to predation. All males occupied these same habitats to maximize their chances of securing mates. Consistent with the social hypotheses, groups composed of individuals of the same sex, irrespective of body size, were over-represented in the population during the non-breeding season, while during the breeding season all males sought females so that mixed-sex groups predominated. These results indicate that body size and reproductive strategies are both important, yet independent, factors influencing segregation in western grey kangaroos.     

Multiple hypotheses testing of fish incidence patterns in an urbanized ecosystem

Ecological and evolutionary theories have focused traditionally on natural processes with little attempt to incorporate anthropogenic influences despite the fact that humans are such an integral part of virtually all ecosystems. A series of alternate models that incorporated anthropogenic factors and traditional ecological mechanisms of invasion to account for fish incidence patterns in urban lakes was tested. The models were based on fish biology, human intervention, and habitat characteristics. However, the only models to account for empirical patterns were those that included fish invasiveness, which incorporated species-specific information about overall tolerance and fecundity. This suggests that species-specific characteristics are more important in general distributional patterns than human-mediated dispersal. Better information of illegal stocking activities is needed to improve human-mediated models, and more insight into basic life history of ubiquitous species is needed to truly understand underlying mechanisms of biotic homogenization.     

Using statistical equivalence testing in clinical biofeedback research

The technique of statistical equivalence testing is described and recommended for use in clinical biofeedback research. Equivalence testing is valuable in aiding the interpretation of negative results or statistically significant results where effects are small in clinical terms. The method is also useful for establishing the similarity of treatment groups at baseline or for showing that the effect of a potentially confounding variable is tolerably small. Finally, equivalence testing is recommended as a method for documenting the equivalence of biofeedback therapy to proven conventional medical therapies in clinical equivalence trials. Examples, drawn from published literature, are provided.     

Some further remarks on testing hypotheses concerning standardized mortality ratios

In testing the equality of any k standardized mortality ratios from p(?k) populations, Kupper and Kleinbaum (1971) pointed out that different test procedures are required for the two situations where the standard population is chosen independently of the p populations and where the standard is formed by pooling all p populations. Unfortunately, the test they propose for the latter situation is applicable only when k = p. The purpose of this paper is to describe an alternative procedure based on the general theories of Wald (1943) and Neyman (1949) which can be used if the standard is a pooled one even when k < p.     

The choice of a statistic for testing hypotheses regarding seasonality

This paper discusses statistical methods for testing hypotheses of seasonality in births across one year, using monthly frequencies. It argues that the Freedman test, a variant of the Kolmogorov-Smirnov one-sample test, and the Edwards test and its modifications are most appropriate for this purpose. These tests take into account the order of the monthly frequencies and have a higher power than the ordinary chi-square goodness-of-fit test, regarding seasonality. The paper addresses some points mentioned in earlier papers by McCullough, and O'Brien and Holbert.     

Morphometric testing of structural hypotheses of the supraorbital region in modern humans

Our understanding of the functional morphology of the primate supraorbital region is based largely on previous morphometric and in vivo mechanical tests of hypotheses in non-human anthropoids. Prior tests of two structural hypotheses explaining morphological variation in the supraorbital region, the craniofacial size hypothesis and the spatial hypothesis, did not fully consider modern humans. We extend these previous findings to include modern humans by conducting morphometric tests of these two hypotheses in a sample of adult Melanesian crania. Morphometric correlates of structural predictions for the craniofacial size and spatial hypotheses were developed and compared to measurements of the supraorbital region via bivariate product-moment correlations. Measurements of the supraorbital region are significantly correlated with a craniofacial size estimate across individuals from this Melanesian sample. This result supports the prediction of the craniofacial size hypothesis that the magnitude of the supraorbital region is proportional to craniofacial size. The predicted link between the degree of neural-orbital disjunction and the magnitude of the supraorbital region, explicated in the spatial hypothesis, receives mixed support in the correlation analysis. These two results agree with previous research indicating that support for the craniofacial size and spatial hypotheses can be found across and within anthropoid primate species, including modern humans. Correlational support for both the craniofacial size and spatial hypotheses suggests multiple factors influence variation in the modern human supraorbital region. Thus, a single hypothesis cannot fully account for modern human variation in this region. The low bivariate correlation coefficients in this study further question whether existing hypotheses can adequately explain morphological variation in the supraorbital region in a primate population sample. Novel functional, structural, behavioral and developmental ideas must be explored if we are to better understand morphological variation in the modern human supraorbital region.