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.     

Towards accurate estimation of the proportion of true null hypotheses in multiple testing

BACKGROUND: Biomedical researchers are now often faced with situations where it is necessary to test a large number of hypotheses simultaneously, eg, in comparative gene expression studies using high-throughput microarray technology. To properly control false positive errors the FDR (false discovery rate) approach has become widely used in multiple testing. The accurate estimation of FDR requires the proportion of true null hypotheses being accurately estimated. To date many methods for estimating this quantity have been proposed. Typically when a new method is introduced, some simulations are carried out to show the improved accuracy of the new method. However, the simulations are often very limited to covering only a few points in the parameter space. RESULTS: Here I have carried out extensive in silico experiments to compare some commonly used methods for estimating the proportion of true null hypotheses. The coverage of these simulations is unprecedented thorough over the parameter space compared to typical simulation studies in the literature. Thus this work enables us to draw conclusions globally as to the performance of these different methods. It was found that a very simple method gives the most accurate estimation in a dominantly large area of the parameter space. Given its simplicity and its overall superior accuracy I recommend its use as the first choice for estimating the proportion of true null hypotheses in multiple testing.     

The selectivity of K+ ion channels: testing the hypotheses

How K⁺ channels are able to conduct certain cations yet not others remains an important but unresolved question. The recent elucidation of the structure of NaK, an ion channel that conducts both Na⁺ and K⁺ ions, offers an opportunity to test the various hypotheses that have been put forward to explain the selectivity of K⁺ ion channels. We test the snug-fit, field-strength, and over-coordination hypotheses by comparing their predictions to the results of classical molecular dynamics simulations of the K⁺ selective channel KcsA and the less selective channel NaK embedded in lipid bilayers. Our results are incompatible with the so-called strong variant of the snug-fit hypothesis but are consistent with the over-coordination hypothesis and neither confirm nor refute the field-strength hypothesis. We also find that the ions and waters in the NaK selectivity filter unexpectedly move to a new conformation in seven K⁺ simulations: the two K⁺ ions rapidly move from site S4 to S2 and from the cavity to S4. At the same time, the selectivity filter narrows around sites S1 and S2 and the carbonyl oxygen atoms rotate 20°−40° inwards toward the ion. These motions diminish the large structural differences between the crystallographic structures of the selectivity filters of NaK and KcsA and appear to allow the binding of ions to S2 of NaK at physiological temperature.     

Dangers in testing statistical hypotheses

Most experiments are intended for the estimation of the size of effects rather than for the testing of a hypothesis of whether or not an effect occurs. Hypothesis testing is often inapplicable, is over-used and is likely to lead to misinterpretations of results. The two types of error possible in hypothesis testing are discussed. Whereas Type I error is usually examined as a matter of course, Type II error is almost always ignored. Investigations in which zero differences are important should recognise the possibility of Type II error in their interpretation. A nonsignificant result should not be interpreted as evidence of a lack of effect. Statistical significance is not synonymous with economic or scientific importance. The importance of choosing the most appropriate design is emphasised and some suggestions are made as to how important sources of error can be avoided.     

A powerful truncated tail strength method for testing multiple null hypotheses in one dataset

This article re-analyses a prey-predator model with a refuge introduced by one of the founders of population ecology Gause and his co-workers to explain discrepancies between their observations and predictions of the Lotka-Volterra prey-predator model. They replaced the linear functional response used by Lotka and Volterra by a saturating functional response with a discontinuity at a critical prey density. At concentrations below this critical density prey were effectively in a refuge while at a higher densities they were available to predators. Thus, their functional response was of the Holling type III. They analyzed this model and predicted existence of a limit cycle in predator-prey dynamics. In this article I show that their model is ill posed, because trajectories are not well defined. Using the Filippov method, I define and analyze solutions of the Gause model. I show that depending on parameter values, there are three possibilities: (1) trajectories converge to a limit cycle, as predicted by Gause, (2) trajectories converge to an equilibrium, or (3) the prey population escapes predator control and grows to infinity.     

The inheritance of resistance alleles in multiple sclerosis

Multiple sclerosis (MS) is a complex trait in which alleles at or near the class II loci HLA-DRB1 and HLA-DQB1 contribute significantly to genetic risk. HLA-DRB1*15 and HLA-DRB1*17-bearing haplotypes and interactions at the HLA-DRB1 locus increase risk of MS but it has taken large samples to identify resistance HLA-DRB1 alleles. In this investigation of 7,093 individuals from 1,432 MS families, we have assessed the validity, mode of inheritance, associated genotypes, and the interactions of HLA-DRB1 resistance alleles. HLA-DRB1*14-, HLA-DRB1*11-, HLA-DRB1*01-, and HLA-DRB1*10-bearing haplotypes are protective overall but they appear to operate by different mechanisms. The first type of resistance allele is characterised by HLA-DRB1*14 and HLA-DRB1*11. Each shows a multiplicative mode of inheritance indicating a broadly acting suppression of risk, but a different degree of protection. In contrast, a second type is exemplified by HLA-DRB1*10 and HLA-DRB1*01. These alleles are significantly protective when they interact specifically in trans with HLA-DRB1*15-bearing haplotypes. HLA-DRB1*01 and HLA-DRB1*10 do not interact with HLA-DRB1*17, implying that several mechanisms may be operative in major histocompatibility complex-associated MS susceptibility, perhaps analogous to the resistance alleles. There are major practical implications for risk and for the exploration of mechanisms in animal models. Restriction of antigen presentation by HLA-DRB1*15 seems an improbably simple mechanism of major histocompatibility complex-associated susceptibility.     

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.     

STORM: software for testing hypotheses of relatedness and mating patterns

Storm is a software package that allows users to test a variety of hypotheses regarding patterns of relatedness and patterns of mate choice and/or mate compatibility within a population. These functions are based on four main calculations that can be conducted either independently or in the hypothesis-testing framework: internal relatedness; homozygosity by loci; pairwise relatedness; and a new metric called allele inheritance, which calculates the proportion of loci at which an offspring inherits a paternal allele different from that inherited from its mother. STORM allows users to test four hypotheses based on these calculations and Monte Carlo simulations: (i) are individuals within observed associations or groupings more/less related than expected; (ii) do observed offspring have more/less genetic variability (based on internal relatedness or homozygosity by loci) than expected from the gene pool; (iii) are observed mating pairs more/less related than expected if mating is random with respect to relatedness; and (iv) do observed offspring inherit paternal alleles different from those inherited from the mother more/less often than expected based on Mendelian inheritance.     

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.     

Testing of one of the hypotheses of the inheritance of human fingerprints

A hypothesis claiming that the total phenotypes of finger patterns are controlled by three independent two-allele loci A, L and W with the complete dominance in each was analysed in this work. By means of the population genetics methods, non-accordance of the hypothesis examined to the observed distributions of total phenotypes A, L, W, AL, LW, ALW was revealed on the material of five populations (3060 men). On the basis of the segregation analysis method applied to 210 complete families (the total number of children-532), the hypothesis of one-locus heredity with the complete dominance of total phenotypes A and W was rejected, the reliability of this conclusion being 0.999 and 0.95, respectively. The hypothesis of the L pattern being genetically controlled by one locus with the complete dominance gave, when examined, the contradictory results, due to monomorphism of the character.     

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.     

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.