Sexual selection and canine dimorphism in New World monkeys.

Social and ecological factors are important in shaping sexual dimorphism in Anthropoidea, but there is also a tendency for body-size dimorphism and canine dimorphism to increase with increased body size (Rensch's rule) (Rensch: Evolution Above the Species Level. London: Methuen, 1959.) Most ecologist interpret Rensch's rule to be a consequence of social and ecological selective factors that covary with body size, but recent claims have been advanced that dimorphism is principally a consequence of selection for increased body size alone. Here we assess the effects of body size, body-size dimorphism, and social structure on canine dimorphism among platyrrhine monkeys. Platyrrhine species examined are classified into four behavioral groups reflecting the intensity of intermale competition for access to females or to limiting resources. As canine dimorphism increases, so does the level of intermale competition. Those species with monogamous and polyandrous social structures have the lowest canine dimorphism, while those with dominance rank hierarchies of males have the most canine dimorphism. Species with fission-fusion social structures and transitory intermale breeding-season competition fall between these extremes. Among platyrrhines there is a significant positive correlation between body size and canine dimorphism However, within levels of competition, no significant correlation was found between the two. Also, with increased body size, body-size dimorphism tends to increase, and this correlation holds in some cases within competition levels. In an analysis of covariance, once the level of intermale competition is controlled for, neither molar size nor molar-size dimorphism accounts for a significant part of the variance in canine dimorphism. A similar analysis using body weight as a measure of size and dimorphism yields a less clear-cut picture: body weight contributes significantly to the model when the effects of the other factors are controlled. Finally, in a model using head and body length as a measure of size and dimorphism, all factors and the interactions between them are significant. We conclude that intermale competition among platyrrhine species is the most important factor explaining variations in canine dimorphism. The significant effects of size and size dimorphism in some models may be evidence that natural (as opposed to sexual) selection also plays a role in the evolution of increased canine dimorphism.

Distributed Feature Selection in Large n and Large p Regression Problems

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (in the sample space) or vertically (in the feature space), and the challenge arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. For sample space partitioning, I propose a MEdian Selection Subset AGgregation Estimator ({\em message}) algorithm for solving these issues. The algorithm applies feature selection in parallel for each subset using regularized regression or Bayesian variable selection method, calculates the `median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in sample size, and has theoretical guarantees. I provide extensive experiments to show excellent performance in feature selection, estimation, prediction, and computation time relative to usual competitors.

While sample space partitioning is useful in handling datasets with large sample size, feature space partitioning is more effective when the data dimension is high. Existing methods for partitioning features, however, are either vulnerable to high correlations or inefficient in reducing the model dimension. In the thesis, I propose a new embarrassingly parallel framework named {\em DECO} for distributed variable selection and parameter estimation. In {\em DECO}, variables are first partitioned and allocated to m distributed workers. The decorrelated subset data within each worker are then fitted via any algorithm designed for high-dimensional problems. We show that by incorporating the decorrelation step, DECO can achieve consistent variable selection and parameter estimation on each subset with (almost) no assumptions. In addition, the convergence rate is nearly minimax optimal for both sparse and weakly sparse models and does NOT depend on the partition number m. Extensive numerical experiments are provided to illustrate the performance of the new framework.

For datasets with both large sample sizes and high dimensionality, I propose a new "divided-and-conquer" framework {\em DEME} (DECO-message) by leveraging both the {\em DECO} and the {\em message} algorithm. The new framework first partitions the dataset in the sample space into row cubes using {\em message} and then partition the feature space of the cubes using {\em DECO}. This procedure is equivalent to partitioning the original data matrix into multiple small blocks, each with a feasible size that can be stored and fitted in a computer in parallel. The results are then synthezied via the {\em DECO} and {\em message} algorithm in a reverse order to produce the final output. The whole framework is extremely scalable.