Evidential statistics as a statistical modern synthesis to support 21st century science

During the 20th century, population ecology and science in general relied on two very different statistical paradigms to solve its inferential problems: error statistics (also referred to as classical statistics and frequentist statistics) and Bayesian statistics. A great deal of good science was done using these tools, but both schools suffer from technical and philosophical difficulties. At the turning of the 21st century (Royall in Statistical evidence: a likelihood paradigm. Chapman & Hall, London, 1997 ; Lele in The nature of scientific evidence: statistical, philosophical and empirical considerations. The University of Chicago Press, Chicago, pp 191–216, 2004a ), evidential statistics emerged as a seriously contending paradigm. Drawing on and refining elements from error statistics, likelihoodism, Bayesian statistics, information criteria, and robust methods, evidential statistics is a statistical modern synthesis that smoothly incorporates model identification, model uncertainty, model comparison, parameter estimation, parameter uncertainty, pre-data control of error, and post-data strength of evidence into a single coherent framework. We argue that evidential statistics is currently the most effective statistical paradigm to support 21st century science. Despite the power of the evidential paradigm, we think that there is no substitute for learning how to clarify scientific arguments with statistical arguments. In this paper we sketch and relate the conceptual bases of error statistics, Bayesian statistics and evidential statistics. We also discuss a number of misconceptions about the paradigms that have hindered practitioners, as well as some real problems with the error and Bayesian statistical paradigms solved by evidential statistics.     

Configural Frequency Analysis as a Parametric Method for the Search of Types and Antitypes

The article introduces Parametric Configural Frequency Analysis (CFA). It is argued that there are two types of parameters that can be of importance in CFA models. The first is effect parameters that are estimated from the data. This type of parameter is involved in almost all models of Classical, nonparametric CFA. The second type involves a priori or distributional parameters that can be used for estimation of expected frequencies. These parameters are specified a priori rather than estimated from data. A combination of models from Classical CFA and Parametric CFA is introduced as Semi-Parametric CFA. Data examples illustrate the new CFA models in comparison with the Classical CFA. Interpretational issues are discussed.     

The Distribution of the Number of Maxima in a Cyclic Sequence

A simple statistical method is presented which tests for non-randomness in a cyclic sequence. The distribution of the statistic is tabulated for short sequences, and a large sample approximation is derived. Significant values of the statistic are given for sequences of length up to 52. Easily used computer programs to carry out appropriate calculations are presented.     

The Distribution of the Number of Maxima in a Cyclic Sequence

A simple statistical method is presented which tests for non-randomness in a cyclic sequence. The distribution of the statistic is tabulated for short sequences, and a large sample approximation is derived. Significant values of the statistic are given for sequences of length up to 52. Easily used computer programs to carry out appropriate calculations are presented.     

Erroneous behaviour of MixSIR, a recently published Bayesian isotope mixing model: a discussion of Moore & Semmens (2008)

The application of Bayesian methods to stable isotopic mixing problems, including inference of diet has the potential to revolutionise ecological research. Using simulated data we show that a recently published model MixSIR fails to correctly identify the true underlying dietary proportions more than 50% of the time and fails with increasing frequency as additional unquantified error is added. While the source of the fundamental failure remains elusive, mitigating solutions are suggested for dealing with additional unquantified variation. Moreover, MixSIR uses a formulation for a prior distribution that results in an opaque and unintuitive covariance structure.     

hierfstat,a package for r to compute and test hierarchical F‐statistics

The package hierfstat for the statistical software r , created by the R Development Core Team, allows the estimate of hierarchical F‐statistics from a hierarchy with any numbers of levels. In addition, it allows testing the statistical significance of population differentiation for these different levels, using a generalized likelihood‐ratio test. The package hierfstat is available at http://www.unil.ch/popgen/softwares/hierfstat.htm .     

Experimental realization and optimalization of a fluorescence correlation spectroscopy apparatus

Fluorescence Correlation Spectroscopy is an elegant technique for measuring lateral diffusion on cell membranes. It is based on the extraction of kinetic information from spontaneous fluctuations in number density of fluorescent molecules. As with most methods of noise analysis, one has to be careful about posssible (instrumental) distortion. Conversely, the intrinsic stochastic character of this technique permits some improvements on the S/N ratio. We describe some experiments on the optimization of this S/N ratio, and on the measurement of the instrumental distortion.     

A test for a shift in the boundary of the geographical range of a species

One predicted impact of climate change is a poleward shift in the boundaries of species ranges. Existing methods for identifying such a boundary shift based on changes in the observed pattern of occupancy within a grid of cells are sensitive to changes in the overall rate of sightings and their latitudinal distribution that are unconnected to a boundary shift. A formal test for a boundary shift is described that allows for such changes. The test is applied to detect northward shifts in the northern boundary of the Essex skipper (Thymelicus lineola) butterfly and the European goldfinch (Carduelis carduelis) in Great Britain. A shift is detected in the latter case but not in the former. Results from a simulation study are presented showing that the test performs well.     

Intelligent design and mathematical statistics: a troubled alliance

The explanatory filter is a proposed method to detect design in nature with the aim of refuting Darwinian evolution. The explanatory filter borrows its logical structure from the theory of statistical hypothesis testing but we argue that, when viewed within this context, the filter runs into serious trouble in any interesting biological application. Although the explanatory filter has been extensively criticized from many angles, we present the first rigorous criticism based on the theory of mathematical statistics.

Some African fossil foot bones: a note on the interpolation of fossils into a matrix of extant species

Certain fossil foot bones (a terminal toe phalanx from Olduvai, specimens of tali from Spy, Skhūl, Olduvai, Kromdraai, Songhor and Rusinga) have been investigated by other workers using the multivariate statistical approach. The conclusions of their studies have, in the main, been based upon examination of early canonical variates alone. It is demonstrated here that if the full analyses (generalized distances) are taken into account, then almost exactly opposite conclusions obtain. The terminal toe phalanx from Olduvai is widely different from those of modern men; the Neandertal tali differ more from modern human bones than previously realized; the specimens from Olduvai, Kromdraai, Songhor and Rusinga are all completely dissimilar from both African ape and modern human tali.     

microsatellite analyser (MSA): a platform independent analysis tool for large microsatellite data sets

In molecular ecology the analysis of large microsatellite data sets is becoming increasingly popular. Here we introduce a new software tool, which is specifically designed to facilitate the analysis of large microsatellite data sets. All common microsatellite summary statistics and distances can be calculated. Furthermore, the microsatellite analyser (msa ) software offers an improved method to deal with inbred samples (such as Drosophila isofemale lines). Executables are available for Windows and Macintosh computers.     

High variation in developmental instability under non-normal developmental error: a Bayesian perspective

The developmental mechanisms behind developmental instability (DI) are only poorly understood. Nevertheless, fluctuating asymmetry (FA) is often used a surrogate for DI. Based on statistical arguments it is often assumed that individual levels of FA are only weakly associated with the underlying DI. Patterns in FA therefore need to be interpreted with caution, and should ideally be transformed into patterns in DI. In order to be able to achieve that, assumptions about the distribution of developmental errors must be made. Current models assume that errors during development are additive and independent such that they yield a normal distribution. The observation that the distribution of FA is often leptokurtic has been interpreted as evidence for between-individual variation in DI. This approach has led to unrealistically high estimates of between-individual variation in DI, and potentially incorrect interpretations of patterns in FA, especially at the individual level. Recently, it has been suggested that the high estimates of variation in DI may be biased upward because either developmental errors are log-normal or gamma distributed and/or low measurement resolution of FA. A proper estimation of the amount (and shape) of heterogeneity in DI is crucial for the interpretation of patterns in FA and their transformation into patterns in DI. Yet, incorrect model assumptions may render misleading inferences. We therefore develop a statistical model to evaluate the sensitivity of results under the normal error model against the two alternative distributions as well as to investigate the importance of low measurement resolution. An analysis of simulated and empirical data sets indicated that bias due to misspecification of the developmental error distribution can be substantial, yet, did not appear to reduce estimates of variation in DI in empirical data sets to a large extent. Effects of low measurement resolution were neglectable. The importance of these results are discussed in the context of the interpretation of patterns in FA.     

Unifying ecosystem responses to disturbance into a single statistical framework

Natural ecosystems are currently experiencing unprecedented rates of anthropogenic disturbance. Given the potential ramifications of more frequent disturbances, it is imperative that we accurately quantify ecosystem responses to severe disturbance. Specifically, ecologists and managers need estimates of resistance and recovery from disturbance that are free of observation error, not biased by temporal stochasticity and that standardize disturbance magnitude among many disparate ecosystems relative to normal interannual variability. Here, I propose a statistical framework that estimates all four components of ecosystem responses to disturbance (resistance, recovery, elasticity and return time), while resolving all of the issues described above. Coupling autoregressive time series with exogenous predictors (ARX) models with impulse response functions (IRFs) allows researchers to statistically subject all ecosystems to similar levels of disturbance, estimate lag effects and obtain standardized estimates of resistance to and recovery from disturbance that are free from observation error and stochastic processes inherent in raw data.     

Phenology of Zamia boliviana (Zamiaceae), a threatened species from a seasonally dry biodiversity hotspot in South America

Dioecy, a character common to all cycads, requires obligatory outcrossing. The absence of potential reproductive mates of the opposite sex renders individuals effectively sterile. Therefore, reproductive synchrony is essential for the reproductive success of cycads. Here, we describe the reproductive phenology, morphology, and lifespan of strobili of Zamia boliviana (Cycadales, Zamiaceae), an endemic cycad in South America. We examined the variation in timing of maturation between polliniferous and ovuliferous individuals in two Z. boliviana populations. Lifespan of polliniferous and ovuliferous strobili was based on direct observations and systematic measurements of strobili development. Phenological study covered three reproductive cohorts in two distinct cycad populations. Lifespan of polliniferous strobili was comprised of four phases and lasted 50 days until the cycle's completion, while ovuliferous strobili underwent seven phases that extended over 330 days until seed dehiscence. Both sexes produced strobili during the dry season. We identified a seasonally synchronous pattern in the reproductive phenology of Z. boliviana, with a major overlap in the phases of emergence, pollen release, and strobili receptivity between sexes, populations, and subsequent years. Reproductive events of Z. boliviana followed the seasonality of the Cerrado vegetation and climate. Synchrony between the period of strobili production and reproductive activity peaks was found in both sexes, but seed dehiscence occurred in the dry season. Our study provides relevant and new biological data for Z. boliviana in its natural habitat, demonstrating a temporal distinction between the lifespan of polliniferous and ovuliferous strobili and the necessary overlap between the release and receptivity of pollen.     

Simultaneous modeling of multivariate heterogeneous responses and heteroskedasticity via a two-stage composite likelihood

Multivariate heterogeneous responses and heteroskedasticity have attracted increasing attention in recent years. In genome-wide association studies, effective simultaneous modeling of multiple phenotypes would improve statistical power and interpretability. However, a flexible common modeling system for heterogeneous data types can pose computational difficulties. Here we build upon a previous method for multivariate probit estimation using a two-stage composite likelihood that exhibits favorable computational time while retaining attractive parameter estimation properties. We extend this approach to incorporate multivariate responses of heterogeneous data types (binary and continuous), and possible heteroskedasticity. Although the approach has wide applications, it would be particularly useful for genomics, precision medicine, or individual biomedical prediction. Using a genomics example, we explore statistical power and confirm that the approach performs well for hypothesis testing and coverage percentages under a wide variety of settings. The approach has the potential to better leverage genomics data and provide interpretable inference for pleiotropy, in which a locus is associated with multiple traits.