Saddlepoint Approximations to the Moments of Multitype Age‐Dependent Branching Processes,with Applications

Summary This article proposes saddlepoint approximations to the expectation and variance–covariance function of multitype age‐dependent branching processes. The proposed approximations are found accurate, easy to implement, and much faster to compute than by simulating the process. Multiple applications are presented, including the analyses of clonal data on the generation of oligodendrocytes from their immediate progenitor cells, and on the proliferation of Hela cells. New estimators are also constructed to analyze clonal data. The proposed methods are finally used to approximate the distribution of the generation, which has recently found several applications in cell biology.     

Linear Mixed Model Selection for False Discovery Rate Control in Microarray Data Analysis

Summary In a microarray experiment, one experimental design is used to obtain expression measures for all genes. One popular analysis method involves fitting the same linear mixed model for each gene, obtaining gene‐specific p‐values for tests of interest involving fixed effects, and then choosing a threshold for significance that is intended to control false discovery rate (FDR) at a desired level. When one or more random factors have zero variance components for some genes, the standard practice of fitting the same full linear mixed model for all genes can result in failure to control FDR. We propose a new method that combines results from the fit of full and selected linear mixed models to identify differentially expressed genes and provide FDR control at target levels when the true underlying random effects structure varies across genes.     

Open Capture–Recapture Models with Heterogeneity: II. Jolly–Seber Model

Summary Estimation of abundance is important in both open and closed population capture–recapture analysis, but unmodeled heterogeneity of capture probability leads to negative bias in abundance estimates. This article defines and develops a suite of open population capture–recapture models using finite mixtures to model heterogeneity of capture and survival probabilities. Model comparisons and parameter estimation use likelihood‐based methods. A real example is analyzed, and simulations are used to check the main features of the heterogeneous models, especially the quality of estimation of abundance, survival, recruitment, and turnover. The two major advances in this article are the provision of realistic abundance estimates that take account of heterogenetiy of capture, and an appraisal of the amount of overestimation of survival arising from conditioning on the first capture when heterogeneity of survival is present.     

Phylogeny,diversification patterns and historical biogeography of euglossine orchid bees (Hymenoptera: Apidae)

The orchid bees constitute a clade of prominent insect pollinators distributed throughout the Neotropical region. Males of all species collect fragrances from natural sources, including flowers, decaying vegetation and fungi, and store them in specialized leg pockets to later expose during courtship display. In addition, orchid bees provide pollination services to a diverse array of Neotropical angiosperms when foraging for food and nesting materials. However, despite their ecological importance, little is known about the evolutionary history of orchid bees. Here, we present a comprehensive molecular phylogenetic analysis based on ～4.0 kb of DNA from four loci [cytochrome oxidase (CO1), elongation factor 1‐α (EF1‐α), arginine kinase (ArgK) and RNA polymerase II (Pol‐II)] across the entire tribe Euglossini, including all five genera, eight subgenera and 126 of the approximately 200 known species. We investigated lineage diversification using fossil‐calibrated molecular clocks and the evolution of morphological traits using disparity‐through‐time plots. In addition, we inferred past biogeographical events by implementing model‐based likelihood methods. Our dataset supports a new view on generic relationships and indicates that the cleptoparasitic genus Exaerete is sister to the remaining orchid bee genera. Our divergence time estimates indicate that extant orchid bee lineages shared a most recent common ancestor at 27–42 Mya. In addition, our analysis of morphology shows that tongue length and body size experienced rapid disparity bursts that coincide with the origin of diverse genera (Euglossa and Eufriesea). Finally, our analysis of historical biogeography indicates that early diversification episodes shared a history on both sides of Mesoamerica, where orchid bees dispersed across the Caribbean, and through a Panamanian connection, thus reinforcing the hypothesis that recent geological events (e.g. the formation of the isthmus of Panama) contributed to the diversification of the rich Neotropical biota. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 100 , 552–572.     

Molecular systematics of Selenops spiders (Araneae: Selenopidae) from North and Central America: implications for Caribbean biogeography

The Caribbean region includes a geologically complex mix of islands, which have served as a backdrop for some significant studies of biogeography, mostly with vertebrates. Here, we use the tropical/subtropical spider genus Selenops (Selenopidae) to obtain a finer resolution of the role of geology in shaping patterns of species diversity. We obtained a broad geographic sample from over 200 localities from both the islands and American mainland. DNA sequence data were generated for three mitochondrial genes and one nuclear gene for eleven outgroup taxa and nearly 60 selenopid species. Phylogenetic analysis of the data revealed several biogeographic patterns common to other lineages that have diversified in the region, the most significant being: (1) a distinct biogeographic break between Northern and Southern Lesser Antilles, although with a slight shift in the location of the disjunction; (2) diversification within the islands of Jamaica and Hispaniola; (3) higher diversity of species in the Greater Antilles relative to the Lesser Antilles. However, a strikingly unique pattern in Caribbean Selenops is that Cuban species are not basal in the Caribbean clade. Analyses to test competing hypotheses of vicariance and dispersal support colonization through GAARlandia, an Eocene–Oligocene land span extending from South America to the Greater Antilles, rather than over‐water dispersal. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 101 , 288–322.     

Sufficiency of the number of segregating sites in the limit under finite-sites mutation

We show that the number of segregating sites is a sufficient statistic for the scaled mutation parameter (θ) in the limit as the number of sites tends to infinity and there is free recombination between sites. We assume that the mutation parameter at each site tends to zero such than the total mutation parameter (θ) is constant in the limit. Our results show that Watterson’s estimator is the maximum likelihood estimator in this case, but that it estimates a composite parameter which is different for different mutation models. Some of our results hold when recombination is limited, because Watterson’s estimator is an unbiased, method-of-moments estimator regardless of the recombination rate. The quantity it estimates depends on the details of how mutations occur at each site.     

On Haldane's formulation of Luria and Delbrück's mutation model

Two formulations of Luria and Delbrück's mutation model have been in common use since the 1940s. While mathematicians focused their attention on the formulation of Lea and Coulson that assumes asynchronous cell growth, biologists found more appealing the formulation of Haldane that assumes synchronous cell growth. This article attempts to solve several outstanding issues for the latter formulation. First, it provides an exact, closed-form expression for the mutant distribution by correcting a minor error in the literature. Second, it presents a novel algorithm for computing the mutant distribution, which leads to novel methods for computing point and interval estimates of mutation rates based on the maximum likelihood principle. Third, it critically examines existing methods based on the mean number of mutants. Finally, it compares the two formulations to underline their strengths and shortcomings.     

A mathematical framework for inferring connectivity in probabilistic neuronal networks

We describe an approach for determining causal connections among nodes of a probabilistic network even when many nodes remain unobservable. The unobservable nodes introduce ambiguity into the estimate of the causal structure. However, in some experimental contexts, such as those commonly used in neuroscience, this ambiguity is present even without unobservable nodes. The analysis is presented in terms of a point process model of a neuronal network, though the approach can be generalized to other contexts. The analysis depends on the existence of a model that captures the relationship between nodal activity and a set of measurable external variables. The mathematical framework is sufficiently general to allow a large class of such models. The results are modestly robust to deviations from model assumptions, though additional validation methods are needed to assess the success of the results.     

The log multinomial regression model for nominal outcomes with more than two attributes

An estimate of the risk or prevalence ratio, adjusted for confounders, can be obtained from a log binomial model (binomial errors, log link) fitted to binary outcome data. We propose a modification of the log binomial model to obtain relative risk estimates for nominal outcomes with more than two attributes (the "log multinomial model"). Extensive data simulations were undertaken to compare the performance of the log multinomial model with that of an expanded data multinomial logistic regression method based on the approach proposed by Schouten et al. (1993) for binary data, and with that of separate fits of a Poisson regression model based on the approach proposed by Zou (2004) and Carter, Lipsitz and Tilley (2005) for binary data. Log multinomial regression resulted in "inadmissable" solutions (out-of-bounds probabilities) exceeding 50% in some data settings. Coefficient estimates by the alternative methods produced out-of-bounds probabilities for the log multinomial model in up to 27% of samples to which a log multinomial model had been successfully fitted. The log multinomial coefficient estimates generally had lesser relative bias and mean squared error than the alternative methods. The practical utility of the log multinomial regression model was demonstrated with a real data example. The log multinomial model offers a practical solution to the problem of obtaining adjusted estimates of the risk ratio in the multinomial setting, but must be used with some care and attention to detail.