The tempo of avian diversification during the Quaternary

It is generally assumed that the Quaternary was a period of heightened diversification in temperate vertebrate organisms. Previous molecular systematics studies have challenged this assertion. We re-examined this issue in north temperate birds using log-lineage plots and distributions of sister-taxon distances. Log-lineage plots support earlier conclusions that avian diversification slowed during the Quaternary. To test plots of empirical sister-taxon distances we simulated three sets of phylogenies: constant speciation and extinction, a pulse of recent speciation, and a pulse of recent extinction. Previous opinions favour the model of recent speciation although our empirical dataset on 74 avian comparisons failed to reject a distribution derived from the constant and extinction models. Hence, it does not appear that the Quaternary was a period of exceptional rates of diversification, relative to the background rate.     

Model Diagnostic Plots for Repeated Measures Data

In the analysis of repeated measurements, multivariate regression models that account for the correlations among the observations from the same subject are widely used. Like the usual univariate regression models, these multivariate regression models also need some model diagnostic procedures. Though these models have been widely used, not many studies have been performed in model diagnostic areas. In this paper, we propose simple residual plots to investigate the goodness of model fit for repeated measures data. Here, we mainly focus on the mean model diagnostics. The proposed residual plots are based on the quantile‐quantile(Q–Q) plots of a χ² distribution and a normal distribution. In particular, the proposed model is useful in comparing several models simultaneously. The proposed method is illustrated using two examples. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On plotting species abundance distributions

1. There has been a revival of interest in species abundance distribution (SAD) models, stimulated by the claim that the log-normal distribution gave an underestimate of the observed numbers of rare species in species-rich assemblages. This led to the development of the neutral Zero Sum Multinomial distribution (ZSM) to better fit the observed data. 2. Yet plots of SADs, purportedly of the same data, showed differences in frequencies of species and of statistical fits to the ZSM and log-normal models due to the use of different binning methods. 3. We plot six different binning methods for the Barro Colorado Island (BCI) tropical tree data. The appearances of the curves are very different for the different binning methods. Consequently, the fits to different models may vary depending on the binning system used. 4. There is no agreed binning method for SAD plots. Our analysis suggests that a simple doubling of the number of individuals per species in each bin is perhaps the most practical one for illustrative purposes. Alternatively rank-abundance plots should be used. 5. For fitting and testing models exact methods have been developed and application of these does not require binning of data. Errors are introduced unnecessarily if data are binned before testing goodness-of-fit to models.     

Trivial and non-trivial applications of entropy maximization in ecology: a reply to Shipley

Entropy maximization (EM) is becoming an increasingly popular modelling technique in ecology, but its potential and limitations are still poorly understood. In our previous contribution (Haegeman and Loreau 2008), we showed that even a trivial application of EM can yield predictions that provide an excellent fit to empirical data. In his response, Shipley (2009) distinguishes two different versions of the EM procedure, an information-theoretical version and a combinatorial version, to justify a trivial application of EM. Here we first provide a brief user's guide to EM to clarify the various steps involved in the procedure. We then show that the information-theoretical and combinatorial rationales for EM are but complementary views on the same procedure. Lastly, we attempt to identify the conditions that lead to trivial and non-trivial applications of EM. We discuss how non-trivial applications of EM can yield valuable new insights in ecology.     

Inferring phenomenological models of first passage processes

Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often infeasible. Instead, here we propose a systematic framework for building phenomenological models of such networks from experimental data, focusing on accurately approximating the time it takes to complete the process, the First Passage (FP) time. Our phenomenological models are mixtures of Gamma distributions, which have a natural biophysical interpretation. The complexity of the models is adapted automatically to account for the amount of available data and its temporal resolution. The framework can be used for predicting behavior of FP systems under varying external conditions. To demonstrate the utility of the approach, we build models for the distribution of inter-spike intervals of a morphologically complex neuron, a Purkinje cell, from experimental and simulated data. We demonstrate that the developed models can not only fit the data, but also make nontrivial predictions. We demonstrate that our coarse-grained models provide constraints on more mechanistically accurate models of the involved phenomena.     

Species richness and range size of the terrestrial mammals of the world: biological signal within mathematical constraints

We explore global spatial diversity patterns for terrestrial mammals using as a tool range-diversity plots. These plots display simultaneously information about the number of species in localities and their spatial covariance in composition. These are highly informative, as we show by linking range-diversity plots with maps and by highlighting the correspondences between well defined regions of the plots with geographical regions or with taxonomic groups. Range-diversity plots are mathematically constrained by the lines of maximum and minimum mean covariance in species composition. We show how regions in the range-diversity plot corresponding to the line of maximum covariance correspond to large continental masses, and regions near the lower limit of the range-diversity plot correspond to archipelagos and mountain ranges. We show how curves of constant covariance correspond to nested faunas. Finally, we show that the observed distribution of the covariance range has significantly longer tails than random, with clear geographic correspondences. At the scale of our data we found that range-diversity plots reveal biodiversity patterns that cannot be replicated by null models, and correspond to conspicuous terrain features and taxonomic groupings.     

New Phylogenetic Models Incorporating Interval-Specific Dispersal Dynamics Improve Inference of Disease Spread

Phylodynamic methods reveal the spatial and temporal dynamics of viral geographic spread, and have featured prominently in studies of the COVID-19 pandemic. Virtually all such studies are based on phylodynamic models that assume—despite direct and compelling evidence to the contrary—that rates of viral geographic dispersal are constant through time. Here, we: (1) extend phylodynamic models to allow both the average and relative rates of viral dispersal to vary independently between pre-specified time intervals; (2) implement methods to infer the number and timing of viral dispersal events between areas; and (3) develop statistics to assess the absolute fit of discrete-geographic phylodynamic models to empirical datasets. We first validate our new methods using simulations, and then apply them to a SARS-CoV-2 dataset from the early phase of the COVID-19 pandemic. We show that: (1) under simulation, failure to accommodate interval-specific variation in the study data will severely bias parameter estimates; (2) in practice, our interval-specific discrete-geographic phylodynamic models can significantly improve the relative and absolute fit to empirical data; and (3) the increased realism of our interval-specific models provides qualitatively different inferences regarding key aspects of the COVID-19 pandemic—revealing significant temporal variation in global viral dispersal rates, viral dispersal routes, and the number of viral dispersal events between areas—and alters interpretations regarding the efficacy of intervention measures to mitigate the pandemic.     

Parameter estimation for bursting neural models

This paper presents work on parameter estimation methods for bursting neural models. In our approach we use both geometrical features specific to bursting, as well as general features such as periodic orbits and their bifurcations. We use the geometry underlying bursting to introduce defining equations for burst initiation and termination, and restrict the estimation algorithms to the space of bursting periodic orbits when trying to fit periodic burst data. These geometrical ideas are combined with automatic differentiation to accurately compute parameter sensitivities for the burst timing and period. In addition to being of inherent interest, these sensitivities are used in standard gradient-based optimization algorithms to fit model burst duration and period to data. As an application, we fit Butera et al.'s (Journal of Neurophysiology 81, 382-397, 1999) model of preB?tzinger complex neurons to empirical data both in control conditions and when the neuromodulator norepinephrine is added (Viemari and Ramirez, Journal of Neurophysiology 95, 2070-2082, 2006). The results suggest possible modulatory mechanisms in the preB?tzinger complex, including modulation of the persistent sodium current.     

Modeling denitrification in aquatic sediments

Sediment denitrification is a major pathway of fixed nitrogen loss from aquatic systems. Due to technical difficulties in measuring this process and its spatial and temporal variability, estimates of local, regional and global denitrification have to rely on a combination of measurements and models. Here we review approaches to describing denitrification in aquatic sediments, ranging from mechanistic diagenetic models to empirical parameterizations of nitrogen fluxes across the sediment-water interface. We also present a compilation of denitrification measurements and ancillary data for different aquatic systems, ranging from freshwater to marine. Based on this data compilation we reevaluate published parameterizations of denitrification. We recommend that future models of denitrification use (1) a combination of mechanistic diagenetic models and measurements where bottom-waters are temporally hypoxic or anoxic, and (2) the much simpler correlations between denitrification and sediment oxygen consumption for oxic bottom waters. For our data set, inclusion of bottom water oxygen and nitrate concentrations in a multivariate regression did not improve the statistical fit.     

A Simulation Study Comparing Epidemic Dynamics on Exponential Random Graph and Edge-Triangle Configuration Type Contact Network Models

We compare two broad types of empirically grounded random network models in terms of their abilities to capture both network features and simulated Susceptible-Infected-Recovered (SIR) epidemic dynamics. The types of network models are exponential random graph models (ERGMs) and extensions of the configuration model. We use three kinds of empirical contact networks, chosen to provide both variety and realistic patterns of human contact: a highly clustered network, a bipartite network and a snowball sampled network of a “hidden population”. In the case of the snowball sampled network we present a novel method for fitting an edge-triangle model. In our results, ERGMs consistently capture clustering as well or better than configuration-type models, but the latter models better capture the node degree distribution. Despite the additional computational requirements to fit ERGMs to empirical networks, the use of ERGMs provides only a slight improvement in the ability of the models to recreate epidemic features of the empirical network in simulated SIR epidemics. Generally, SIR epidemic results from using configuration-type models fall between those from a random network model (i.e., an Erdős-Rényi model) and an ERGM. The addition of subgraphs of size four to edge-triangle type models does improve agreement with the empirical network for smaller densities in clustered networks. Additional subgraphs do not make a noticeable difference in our example, although we would expect the ability to model cliques to be helpful for contact networks exhibiting household structure.     

Modeling the synergistic effect of high pressure and heat on inactivation kinetics of Listeria innocua: a preliminary study

The survival curves of Listeria innocua CDW47 by high hydrostatic pressure were obtained at four pressure levels (138, 207, 276, 345 MPa) and four temperatures (25, 35, 45, 50 degrees C) in peptone solution. Tailing was observed in the survival curves. Elevated temperatures and pressures substantially promoted the inactivation of L. innocua. A linear and two non-linear (Weibull and log-logistic) models were fitted to these data and the goodness of fit of these models were compared. Regression coefficients (R2), root mean square (RMSE), accuracy factor (Af) values and residual plots suggested that linear model, although it produced good fits for some pressure-temperature combinations, was not as appropriate as non-linear models to represent the data. The residual and correlation plots strongly suggested that among the non linear models studied the log-logistic model produced better fit to the data than the Weibull model. Such pressure-temperature inactivation models form the engineering basis for design, evaluation and optimization of high hydrostatic pressure processes as a new preservation technique.     

The significance of assemblage-level thinning for species richness

1 A unimodal relationship between species richness and primary productivity is commonly reported. To explain this pattern, the mechanisms proposed in the many hypotheses are generally complex and almost all are without a strong empirical foundation. Here we evaluate the role of self-thinning in plant assemblages: assemblage-level thinning.
2 We developed a simple two-parameter model of species richness that predicts that plant species richness will be determined by a unimodal relationship between total plant density and above-ground biomass. This model provides a very narrowly defined set of testable quantitative predictions, and thus is the first falsifiable model of assemblage-level thinning. We fit this model to the species richness–above-ground biomass data from 14 empirical studies that are often cited as evidence of a general diversity–productivity relationship. In addition, we compared our model to two other models, one more flexible and one more constrained than our own.
3 We found that our model of species richness explained a substantial and statistically significant portion of the species richness observed in 11 of the 14 empirical studies of species richness–biomass patterns. Therefore, given the conservative nature of our model, and the number of previously published data sets explained by this model, we argue that assemblage-level thinning not only provides a viable and exceedingly parsimonious explanation, but may also be a widespread phenomenon.     

A Variance-Component Framework for Pedigree Analysis of Continuous and Categorical Outcomes

Variance-component methods are popular and flexible analytic tools for elucidating the genetic mechanisms of complex quantitative traits from pedigree data. However, variance-component methods typically assume that the trait of interest follows a multivariate normal distribution within a pedigree. Studies have shown that violation of this normality assumption can lead to biased parameter estimates and inflations in type-I error. This limits the application of variance-component methods to more general trait outcomes, whether continuous or categorical in nature. In this paper, we develop and apply a general variance-component framework for pedigree analysis of continuous and categorical outcomes. We develop appropriate models using generalized-linear mixed model theory and fit such models using approximate maximum-likelihood procedures. Using our proposed method, we demonstrate that one can perform variance-component pedigree analysis on outcomes that follow any exponential-family distribution. Additionally, we also show how one can modify the method to perform pedigree analysis of ordinal outcomes. We also discuss extensions of our variance-component framework to accommodate pedigrees ascertained based on trait outcome. We demonstrate the feasibility of our method using both simulated data and data from a genetic study of ovarian insufficiency.     

The Co-Occurrence of Species and the Co-Diversity of Sites in Neutral Models of Biodiversity

Patterns of co-occurrence of species are widely used to assess the fit of ecological neutral models to empirical patterns. The mathematically equivalent patterns of co-diversity of sites, in contrast, have been considered only indirectly and analyses normally are focused on the spatial distribution of species richness, rather than on the patterns of species sharing. Here we use two analytical tools (range-diversity plots and rank plots) to assess the predictions of simple neutral models in relation to patterns of co-occurrence and co-diversity. Whereas a fully stochastic null model predicts zero average among species and among sites, neutral models generate systems with low levels of covariance among species and high levels of positive covariance among sites. These patterns vary with different combinations of dispersal and speciation rates, but are always linked to the shape, symmetry, and spread of the range-size and species-richness frequency distributions. Non-homogeneous patterns of diversity and distribution arise in neutral models because of the spatial arrangement of sites and their concomitant similarity, which is reflected also in the spread of the range-size frequency distribution. The nearly null covariance among species, in contrast, implies low variance in species richness of sites and very slim frequency distributions. In real world assemblages of Mexican volant and non-volant mammals, patterns of range-size and species-richness frequency distribution are similar to those generated by neutral models. However, when the comparison includes the covariance both for species (co-occurrence) and for sites (co-diversity), empirical patterns differ significantly from the predictions of neutral models. Because of the mathematical links between the covariance in the distribution of species and the variance of species-richness values and between the covariance in species sharing among sites and the variance of range-size values, a full understanding of patterns of diversity calls for the simultaneous analysis of co-occurrence and co-diversity.     

Intraspecific interactions affect the spatial pattern of a dominant shrub in a semiarid shrubland: A prospective approach

Dispersal, physical conditions and biotic interactions contribute to determine the spatial distribution of individuals in plant populations. Much of what we know has been learned from studies that retrospectively posit mechanisms presumed to have generated the observed spatial patterns. Here we present a prospective approach. We start by measuring spatial demographic effects and evaluate if they can generate observed spatial patterns. We evaluated the influence of interactions among conspecifics on vital rates, demography and spatial distribution of Croton aff. wagneri, a dominant shrub in dry Andean ecosystems. Recruitment, survival and growth varied in relation with distance to conspecifics neighbours and with their summed cover. We built a spatial individual-based model and simulated its population dynamics in 30 × 30 m plots for a 30-year period. We compared the predicted spatial pattern from these demographic models with that observed among plants in 16 independent plots with the same area. Simulated populations mimicked observed spatial patterns, although in plots at high elevations the simulated populations did not reproduce the observed inhibition at small scales. Observed and simulated patterns indicated differences between elevations in maximum aggregation and location of the distances with higher aggregation. We discuss how consideration of critical seed and juvenile stages and interspecific interactions could further improve our understanding of spatial pattern and recommend that these factors be considered in future models.     

Goodness of Fit of Probability Distributions for Sightings as Species Approach Extinction

Estimating the probability that a species is extinct and the timing of extinctions is useful in biological fields ranging from paleoecology to conservation biology. Various statistical methods have been introduced to infer the time of extinction and extinction probability from a series of individual sightings. There is little evidence, however, as to which of these models provide adequate fit to actual sighting records. We use L-moment diagrams and probability plot correlation coefficient (PPCC) hypothesis tests to evaluate the goodness of fit of various probabilistic models to sighting data collected for a set of North American and Hawaiian bird populations that have either gone extinct, or are suspected of having gone extinct, during the past 150 years. For our data, the uniform, truncated exponential, and generalized Pareto models performed moderately well, but the Weibull model performed poorly. Of the acceptable models, the uniform distribution performed best based on PPCC goodness of fit comparisons and sequential Bonferroni-type tests. Further analyses using field significance tests suggest that although the uniform distribution is the best of those considered, additional work remains to evaluate the truncated exponential model more fully. The methods we present here provide a framework for evaluating subsequent models.     

Rooting the Animal Tree of Life

Identifying our most distant animal relatives has emerged as one of the most challenging problems in phylogenetics. This debate has major implications for our understanding of the origin of multicellular animals and of the earliest events in animal evolution, including the origin of the nervous system. Some analyses identify sponges as our most distant animal relatives (Porifera-sister hypothesis), and others identify comb jellies (Ctenophora-sister hypothesis). These analyses vary in many respects, making it difficult to interpret previous tests of these hypotheses. To gain insight into why different studies yield different results, an important next step in the ongoing debate, we systematically test these hypotheses by synthesizing 15 previous phylogenomic studies and performing new standardized analyses under consistent conditions with additional models. We find that Ctenophora-sister is recovered across the full range of examined conditions, and Porifera-sister is recovered in some analyses under narrow conditions when most outgroups are excluded and site-heterogeneous CAT models are used. We additionally find that the number of categories in site-heterogeneous models is sufficient to explain the Porifera-sister results. Furthermore, our cross-validation analyses show CAT models that recover Porifera-sister have hundreds of additional categories and fail to fit significantly better than site-heterogenuous models with far fewer categories. Systematic and standardized testing of diverse phylogenetic models suggests that we should be skeptical of Porifera-sister results both because they are recovered under such narrow conditions and because the models in these conditions fit the data no better than other models that recover Ctenophora-sister.     

Use of additive models to represent trends in a barley field trial

Even when a field experiment has been designed with care, subsequent examination of the plot values may reveal additional unforeseen trends. In this paper we examine data from a barley pathology field trial and show that additive models provide a flexible representation of environmental trends, in one or two dimensions. Such models smooth out noise in the observed data, rather than fit an equation specified in advance. This approach tends to increase the precision of treatment comparisons relative to a classical analysis of variance. We recommend the use of residual plots to explore experimental data for underlying trends, and additive models to display these trends and estimate treatment effects.     

Ecology and multilevel selection explain aggression in spider colonies

Progress in sociobiology continues to be hindered by abstract debates over methodology and the relative importance of within‐group vs. between‐group selection. We need concrete biological examples to ground discussions in empirical data. Recent work argued that the levels of aggression in social spider colonies are explained by group‐level adaptation. Here, we examine this conclusion using models that incorporate ecological detail while remaining consistent with kin‐ and multilevel selection frameworks. We show that although levels of aggression are driven, in part, by between‐group selection, incorporating universal within‐group competition provides a striking fit to the data that is inconsistent with pure group‐level adaptation. Instead, our analyses suggest that aggression is favoured primarily as a selfish strategy to compete for resources, despite causing lower group foraging efficiency or higher risk of group extinction. We argue that sociobiology will benefit from a pluralistic approach and stronger links between ecologically informed models and data.