Masting,mixtures and modes: are two models better than one?

A key hypothesis in population ecology is that synchronous and intermittent seed production, known as mast seeding, is driven by the alternating allocation of carbohydrates and mineral nutrients between growth and reproduction in different years, i.e. ‘resource switching’. Such behaviour may ultimately generate bimodal distributions of long‐term flower and seed production, and evidence of these patterns has been taken to support the resource switching hypothesis. Here, we show how a widely‐used statistical test of bimodality applied by many studies in different ecological contexts may fail to reject the null hypothesis that focal probability distributions are unimodal. Using data from five tussock grass species in South Island, New Zealand, we find clear evidence of bimodality only when flowering patterns are analyzed with probabilistic mixture models. Mixture models provide a theory oriented framework for testing hypotheses of mast seeding patterns, enabling the different responses underlying medium‐ and high‐ versus non‐ and low‐flowering years to be modelled more realistically by associating these with distinct probability distributions. Coupling theoretical expectations with more rigorous statistical approaches will empower ecologists to reject null hypotheses more often.     

Model selection as a tool for phylogeographic inference: an example from the willow Salix melanopsis

Phylogeographic inference has typically relied on analyses of data from one or a few genes to provide estimates of demography and population histories. While much has been learned from these studies, all phylogeographic analysis is conditioned on the data, and thus, inferences derived from data that represent a small sample of the genome are unavoidably tenuous. Here, we demonstrate one approach for moving beyond classic phylogeographic research. We use sequence capture probes and Illumina sequencing to generate data from >400 loci in order to infer the phylogeographic history of Salix melanopsis, a riparian willow with a disjunct distribution in coastal and the inland Pacific Northwest. We evaluate a priori phylogeographic hypotheses using coalescent models for parameter estimation, and the results support earlier findings that identified post‐Pleistocene dispersal as the cause of the disjunction in S. melanopsis. We also conduct a series of model selection exercises using IMa2, Migrate‐n and ?a?i. The resulting ranking of models indicates that refugial dynamics were complex, with multiple regions in the inland regions serving as the source for postglacial colonization. Our results demonstrate that new sources of data and new approaches to data analysis can rejuvenate phylogeographic research by allowing for the identification of complex models that enable researchers to both identify and estimate the most relevant parameters for a given system.     

Ecologists should not use statistical significance tests to interpret simulation model results

Simulation models are widely used to represent the dynamics of ecological systems. A common question with such models is how changes to a parameter value or functional form in the model alter the results. Some authors have chosen to answer that question using frequentist statistical hypothesis tests (e.g. ANOVA). This is inappropriate for two reasons. First, p‐values are determined by statistical power (i.e. replication), which can be arbitrarily high in a simulation context, producing minuscule p‐values regardless of the effect size. Second, the null hypothesis of no difference between treatments (e.g. parameter values) is known a priori to be false, invalidating the premise of the test. Use of p‐values is troublesome (rather than simply irrelevant) because small p‐values lend a false sense of importance to observed differences. We argue that modelers should abandon this practice and focus on evaluating the magnitude of differences between simulations. Synthesis Researchers analyzing field or lab data often test ecological hypotheses using frequentist statistics (t‐tests, ANOVA, etc.) that focus on p‐values. Field and lab data usually have limited sample sizes, and p‐values are valuable for quantifying the probability of making incorrect inferences in that situation. However, modern ecologists increasingly rely on simulation models to address complex questions, and those who were trained in frequentist statistics often apply the hypothesis‐testing approach inappropriately to their simulation results. Our paper explains why p‐values are not informative for interpreting simulation models, and suggests better ways to evaluate the ecological significance of model results.     

Selection of evolutionary models for phylogenetic hypothesis testing using parametric methods

Recent molecular studies have incorporated the parametric bootstrap method to test a priori hypotheses when the results of molecular based phylogenies are in conflict with these hypotheses. The parametric bootstrap requires the specification of a particular substitutional model, the parameters of which will be used to generate simulated, replicate DNA sequence data sets. It has been both suggested that, (a) the method appears robust to changes in the model of evolution, and alternatively that, (b) as realistic model of DNA substitution as possible should be used to avoid false rejection of a null hypothesis. Here we empirically evaluate the effect of suboptimal substitution models when testing hypotheses of monophyly with the parametric bootstrap using data sets of mtDNA cytochrome oxidase I and II (COI and COII) sequences for Macaronesian Calathus beetles, and mitochondrial 16S rDNA and nuclear ITS2 sequences for European Timarcha beetles. Whether a particular hypothesis of monophyly is rejected or accepted appears to be highly dependent on whether the nucleotide substitution model being used is optimal. It appears that a parameter rich model is either equally or less likely to reject a hypothesis of monophyly where the optimal model is unknown. A comparison of the performance of the Kishino–Hasegawa (KH) test shows it is not as severely affected by the use of suboptimal models, and overall it appears to be a less conservative method with a higher rate of failure to reject null hypotheses.     

Statistical challenges in null model analysis

This review identifies several important challenges in null model testing in ecology: 1) developing randomization algorithms that generate appropriate patterns for a specified null hypothesis; these randomization algorithms stake out a middle ground between formal Pearson–Neyman tests (which require a fully‐specified null distribution) and specific process‐based models (which require parameter values that cannot be easily and independently estimated); 2) developing metrics that specify a particular pattern in a matrix, but ideally exclude other, related patterns; 3) avoiding classification schemes based on idealized matrix patterns that may prove to be inconsistent or contradictory when tested with empirical matrices that do not have the idealized pattern; 4) testing the performance of proposed null models and metrics with artificial test matrices that contain specified levels of pattern and randomness; 5) moving beyond simple presence–absence matrices to incorporate species‐level traits (such as abundance) and site‐level traits (such as habitat suitability) into null model analysis; 6) creating null models that perform well with many sites, many species pairs, and varying degrees of spatial autocorrelation in species occurrence data. In spite of these challenges, the development and application of null models has continued to provide valuable insights in ecology, evolution, and biogeography for over 80 years.     

Model selection in ecology and evolution

Recently, researchers in several areas of ecology and evolution have begun to change the way in which they analyze data and make biological inferences. Rather than the traditional null hypothesis testing approach, they have adopted an approach called model selection, in which several competing hypotheses are simultaneously confronted with data. Model selection can be used to identify a single best model, thus lending support to one particular hypothesis, or it can be used to make inferences based on weighted support from a complete set of competing models. Model selection is widely accepted and well developed in certain fields, most notably in molecular systematics and mark-recapture analysis. However, it is now gaining support in several other areas, from molecular evolution to landscape ecology. Here, we outline the steps of model selection and highlight several ways that it is now being implemented. By adopting this approach, researchers in ecology and evolution will find a valuable alternative to traditional null hypothesis testing, especially when more than one hypothesis is plausible.     

Integrating coalescent and ecological niche modeling in comparative phylogeography

Understanding the factors that contribute to the formation of population genetic structure is a central goal of phylogeographic research, but achieving this goal can be complicated by the stochastic variance inherent to genetic processes. Statistical approaches to testing phylogeographic hypotheses accommodate this stochasticity by evaluating competing models of putative historical population structure, often by simulating null distributions of the expected variance. The effectiveness of these tests depends on the biological realism of the models. Information from the fossil record can aid in reconstructing the historical distributions of some taxa. However, for the majority of taxa, which lack sufficient fossils, paleodistributional modeling can provide valuable spatial-geographic data concerning ancestral distributions. Paleodistributional models are generated by projecting ecological niche models, which predict the current distribution of each species, onto a model of past climatic conditions. Here, we generate paleodistributional models describing the suitable habitat during the last glacial maximum for lineages from the mesic forests of the Pacific Northwest of North America, and use these models to generate alternative phylogeographic hypotheses. Coalescent simulations are then used to test these hypotheses to improve our understanding of the historical events that promoted the formation of population genetic structure in this ecosystem. Results from Pacific Northwest mesic forest organisms demonstrate the utility of these combined approaches. Paleodistribution models and population genetic structure are congruent across three amphibian lineages, suggesting that they have responded in a concerted manner to environmental change. Two other species, a willow and a water vole, despite being currently codistributed and having similar population genetic structure, were predicted by the paleodistributional model to have had markedly different distributions during the last glacial maximum. This suggests that congruent phylogeographic patterns can arise from incongruent ancestral distributions. Paleodistributional models introduce a much-needed spatial-geographic perspective to statistical phylogeography. In conjunction with coalescent models of population genetic structure, they have the potential to improve our understanding of the factors that promote population divergence and ultimately produce regional patterns of biodiversity.     

Revisiting Amazonian phylogeography: insights into diversification hypotheses and novel perspectives

The Amazon Basin harbors one of the richest biotas on Earth, such that a number of diversification hypotheses have been formulated to explain patterns of Amazonian biodiversity and biogeography. For nearly two decades, phylogeographic approaches have been applied to better understand the underlying causes of genetic differentiation and geographic structure among Amazonian organisms. Although this research program has made progress in elucidating several aspects of species diversification in the region, recent methodological and theoretical developments in the discipline of phylogeography will provide new perspectives through more robust hypothesis testing. Herein, we outline central aspects of Amazonian geology and landscape evolution as well as climate and vegetation dynamics through the Neogene and Quaternary to contextualize the historical settings considered by major hypotheses of diversification. We address each of these hypotheses by reviewing key phylogeographic papers and by expanding their respective predictions. We also propose future directions for devising and testing hypotheses. Specifically, combining the exploratory power of phylogeography with the statistical rigor of coalescent methods will greatly expand analytical inferences on the evolutionary history of Amazonian biota. Incorporation of non-genetic data from Earth science disciplines into the phylogeographic approach is key to a better understanding of the influence of climatic and geophysical events on patterns of Amazonian biodiversity and biogeography. In addition, achieving such an integrative enterprise must involve overcoming issues such as limited geographic and taxonomic sampling. These future challenges likely will be accomplished by a combination of extensive collaborative research and incentives for conducting basic inventories.     

Conditional Rejection Probabilities of Student's t‐test and Design Adaptations

For clinical trials with interim analyses conditional rejection probabilities play an important role when stochastic curtailment or design adaptations are performed. The conditional rejection probability gives the conditional probability to finally reject the null hypothesis given the interim data. It is computed either under the null or the alternative hypothesis. We investigate the properties of the conditional rejection probability for the one sided, one sample t‐test and show that it can be non monotone in the interim mean of the data and non monotone in the non‐centrality parameter for the alternative. We give several proposals how to implement design adaptations (that are based on the conditional rejection probability) for the t‐test and give a numerical example. Additionally, the conditional rejection probability given the interim t‐statistic is investigated. It does not depend on the unknown σ and can be used in stochastic curtailment procedures. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Guidelines for a priori grouping of species in hierarchical community models

Recent methodological advances permit the estimation of species richness and occurrences for rare species by linking species‐level occurrence models at the community level. The value of such methods is underscored by the ability to examine the influence of landscape heterogeneity on species assemblages at large spatial scales. A salient advantage of community‐level approaches is that parameter estimates for data‐poor species are more precise as the estimation process “borrows” from data‐rich species. However, this analytical benefit raises a question about the degree to which inferences are dependent on the implicit assumption of relatedness among species. Here, we assess the sensitivity of community/group‐level metrics, and individual‐level species inferences given various classification schemes for grouping species assemblages using multispecies occurrence models. We explore the implications of these groupings on parameter estimates for avian communities in two ecosystems: tropical forests in Puerto Rico and temperate forests in northeastern United States. We report on the classification performance and extent of variability in occurrence probabilities and species richness estimates that can be observed depending on the classification scheme used. We found estimates of species richness to be most precise and to have the best predictive performance when all of the data were grouped at a single community level. Community/group‐level parameters appear to be heavily influenced by the grouping criteria, but were not driven strictly by total number of detections for species. We found different grouping schemes can provide an opportunity to identify unique assemblage responses that would not have been found if all of the species were analyzed together. We suggest three guidelines: (1) classification schemes should be determined based on study objectives; (2) model selection should be used to quantitatively compare different classification approaches; and (3) sensitivity of results to different classification approaches should be assessed. These guidelines should help researchers apply hierarchical community models in the most effective manner.     

Statistical phylogeography: methods of evaluating and minimizing inference errors

Nested clade phylogeographical analysis (NCPA) has become a common tool in intraspecific phylogeography. To evaluate the validity of its inferences, NCPA was applied to actual data sets with 150 strong a priori expectations, the majority of which had not been analysed previously by NCPA. NCPA did well overall, but it sometimes failed to detect an expected event and less commonly resulted in a false positive. An examination of these errors suggested some alterations in the NCPA inference key, and these modifications reduce the incidence of false positives at the cost of a slight reduction in power. Moreover, NCPA does equally well in inferring events regardless of the presence or absence of other, unrelated events. A reanalysis of some recent computer simulations that are seemingly discordant with these results revealed that NCPA performed appropriately in these simulated samples and was not prone to a high rate of false positives under sampling assumptions that typify real data sets. NCPA makes a posteriori use of an explicit inference key for biological interpretation after statistical hypothesis testing. Alternatives to NCPA that claim that biological inference emerges directly from statistical testing are shown in fact to use an a priori inference key, albeit implicitly. It is argued that the a priori and a posteriori approaches to intraspecific phylogeography are complementary, not contradictory. Finally, cross-validation using multiple DNA regions is shown to be a powerful method of minimizing inference errors. A likelihood ratio hypothesis testing framework has been developed that allows testing of phylogeographical hypotheses, extends NCPA to testing specific hypotheses not within the formal inference key (such as the out-of-Africa replacement hypothesis of recent human evolution) and integrates intra- and interspecific phylogeographical inference.     

In support of null hypothesis significance testing

Many criticisms have been levelled at null hypothesis significance testing (NHST). It is argued here that although there is reason to doubt that data subjected only to NHST have been subjected to sufficient analysis, the search for clear answers to well-formulated questions derived from substantive hypotheses is well served by NHST. To reliably draw inferences from data, however, NHST may need to be complemented by additional methods of analysis, such as the use of confidence intervals and of estimates of the degree of association between independent and dependent variables. It is argued that these should be seen as complements of, rather than as substitutes for, NHST since they do not directly test the strength of evidence against a null hypothesis.     

Integrating species distribution models (SDMs) and phylogeography for two species of Alpine Primula

The major intention of the present study was to investigate whether an approach combining the use of niche-based palaeodistribution modeling and phylo-geography would support or modify hypotheses about the Quaternary distributional history derived from phylogeographic methods alone. Our study system comprised two closely related species of Alpine Primula. We used species distribution models based on the extant distribution of the species and last glacial maximum (LGM) climate models to predict the distribution of the two species during the LGM. Phylogeographic data were generated using amplified fragment length polymorphisms (AFLPs). In Primula hirsuta, models of past distribution and phylogeographic data are partly congruent and support the hypothesis of widespread nunatak survival in the Central Alps. Species distribution models (SDMs) allowed us to differentiate between alpine regions that harbor potential nunatak areas and regions that have been colonized from other areas. SDMs revealed that diversity is a good indicator for nunataks, while rarity is a good indicator for peripheral relict populations that were not source for the recolonization of the inner Alps. In P. daonensis, palaeo-distribution models and phylogeographic data are incongruent. Besides the uncertainty inherent to this type of modeling approach (e.g., relatively coarse 1-km grain size), disagreement of models and data may partly be caused by shifts of ecological niche in both species. Nevertheless, we demonstrate that the combination of palaeo-distribution modeling with phylogeographical approaches provides a more differentiated picture of the distributional history of species and partly supports (P. hirsuta) and partly modifies (P. daonensis and P. hirsuta) hypotheses of Quaternary distributional history. Some of the refugial area indicated by palaeodistribution models could not have been identified with phylogeographic data.     

Inference in ecology and evolution

Most ecologists and evolutionary biologists continue to rely heavily on null hypothesis significance testing, rather than on recently advocated alternatives, for inference. Here, we briefly review null hypothesis significance testing and its major alternatives. We identify major objectives of statistical analysis and suggest which analytical approaches are appropriate for each. Any well designed study can improve our understanding of biological systems, regardless of the inferential approach used. Nevertheless, an awareness of available techniques and their pitfalls could guide better approaches to data collection and broaden the range of questions that can be addressed. Although we should reduce our reliance on significance testing, it retains an important role in statistical education and is likely to remain fundamental to the falsification of scientific hypotheses.     

Rivers,not refugia,drove diversification in arboreal,sub‐Saharan African snakes

The relative roles of rivers versus refugia in shaping the high levels of species diversity in tropical rainforests have been widely debated for decades. Only recently has it become possible to take an integrative approach to test predictions derived from these hypotheses using genomic sequencing and paleo‐species distribution modeling. Herein, we tested the predictions of the classic river, refuge, and river‐refuge hypotheses on diversification in the arboreal sub‐Saharan African snake genus Toxicodryas. We used dated phylogeographic inferences, population clustering analyses, demographic model selection, and paleo‐distribution modeling to conduct a phylogenomic and historical demographic analysis of this genus. Our results revealed significant population genetic structure within both Toxicodryas species, corresponding geographically to river barriers and divergence times from the mid‐Miocene to Pliocene. Our demographic analyses supported the interpretation that rivers are indications of strong barriers to gene flow among populations since their divergence. Additionally, we found no support for a major contraction of suitable habitat during the last glacial maximum, allowing us to reject both the refuge and river‐refuge hypotheses in favor of the river‐barrier hypothesis. Based on conservative interpretations of our species delimitation analyses with the Sanger and ddRAD data sets, two new cryptic species are identified from east‐central Africa. This study highlights the complexity of diversification dynamics in the African tropics and the advantages of integrative approaches to studying speciation in tropical regions.     

cati: an R package using functional traits to detect and quantify multi‐level community assembly processes

Community ecologists are active in describing species by their functional traits, quantifying the functional structure of plant and animal assemblages and inferring community assembly processes with null‐model analyses of trait distribution and functional diversity indices. Intraspecific variation in traits and effects of spatial scale are potentially important in these analyses. Here, we introduce the R package cati (Community Assembly by Traits: Individuals and beyond) available on CRAN, for the analysis of community assembly with functional traits. cati builds on a recent approach to community assembly that explicitly incorporates individual differences in community assembly analyses and decomposes phenotypic variations across scales and organizational levels, based on three phenotypic variance ratios, termed the T‐statistics. More generally, the cati package 1) calculates a variety of single‐trait and multi‐trait indices from interspecific and intraspecific trait measures; 2) it partitions functional trait variation among spatial and taxonomic levels; 3) it implements a palette of flexible null models for detecting non‐random patterns of functional traits. These patterns can be used to draw inferences about hypotheses of community assembly such as environmental filtering and species interactions. The basic input for cati is a data frame in which columns are traits, rows are species or individuals, and entries are the measured trait values. The cati package can also incorporate a square distance matrix into analyses, which could include phylogenetic or genetic distances among individuals or species. Users select from a variety of functional trait metrics and analyze these relative to a null model that specifies trait distributions in a regional source pool.     

On the power of some binomial modifications of the Bonferroni multiple test

Widely used in testing statistical hypotheses, the Bonferroni multiple test has a rather low power that entails a high risk to accept falsely the overall null hypothesis and therefore to not detect really existing effects. We suggest that when the partial test statistics are statistically independent, it is possible to reduce this risk by using binomial modifications of the Bonferroni test. Instead of rejecting the null hypothesis when at least one of n partial null hypotheses is rejected at a very high level of significance (say, 0.005 in the case of n = 10), as it is prescribed by the Bonferroni test, the binomial tests recommend to reject the null hypothesis when at least k partial null hypotheses (say, k = [n/2]) are rejected at much lower level (up to 30-50%). We show that the power of such binomial tests is essentially higher as compared with the power of the original Bonferroni and some modified Bonferroni tests. In addition, such an approach allows us to combine tests for which the results are known only for a fixed significance level. The paper contains tables and a computer program which allow to determine (retrieve from a table or to compute) the necessary binomial test parameters, i.e. either the partial significance level (when k is fixed) or the value of k (when the partial significance level is fixed).     

Paleodistributions and comparative molecular phylogeography of leafcutter ants (Atta spp.) provide new insight into the origins of Amazonian diversity

The evolutionary basis for high species diversity in tropical regions of the world remains unresolved. Much research has focused on the biogeography of speciation in the Amazon Basin, which harbors the greatest diversity of terrestrial life. The leading hypotheses on allopatric diversification of Amazonian taxa are the Pleistocene refugia, marine incursion, and riverine barrier hypotheses. Recent advances in the fields of phylogeography and species-distribution modeling permit a modern re-evaluation of these hypotheses. Our approach combines comparative, molecular phylogeographic analyses using mitochondrial DNA sequence data with paleodistribution modeling of species ranges at the last glacial maximum (LGM) to test these hypotheses for three co-distributed species of leafcutter ants (Atta spp.). The cumulative results of all tests reject every prediction of the riverine barrier hypothesis, but are unable to reject several predictions of the Pleistocene refugia and marine incursion hypotheses. Coalescent dating analyses suggest that population structure formed recently (Pleistocene-Pliocene), but are unable to reject the possibility that Miocene events may be responsible for structuring populations in two of the three species examined. The available data therefore suggest that either marine incursions in the Miocene or climate changes during the Pleistocene--or both--have shaped the population structure of the three species examined. Our results also reconceptualize the traditional Pleistocene refugia hypothesis, and offer a novel framework for future research into the area.