Multiple paternity and the number of offspring: A model reveals two major groups of species.

Parentage analyses via microsatellite markers have revealed multiple paternity within the broods of polytocous species of mammals, reptiles, amphibians, fishes and invertebrates. The widespread phenomenon of multiple paternity may have attending relationships with such evolutionary processes as sexual selection and kin selection. However, just how much multiple paternity should a species exhibit? We developed Bayesian null models of how multiple paternity relates to brood sizes. For each of 114 species with published data on brood sizes and numbers of sires, we compared our null model estimates to published frequencies of multiple paternity. The majority of species fell close to our null model, especially among fish and invertebrate species. Some species, however, had low probabilities of multiple paternity, far from the predictions of the null model, likely due to sexual selection and environmental constraints. We suggest a major division among species' mating systems between those with close to random mating and high levels of multiple paternity, and those with constraints that produce low levels of multiple paternity.

Nonlinear spatial and temporal decomposition provides insight for climate change effects on sub-Arctic herbivore populations.

Global temperatures are increasing, affecting timing and availability of vegetation along with relationships between plants and their consumers. We examined the effect of population density, herd body condition in the previous year, elevation, plant productivity and phenology, snow, and winter onset on juvenile body mass in 63 semi-domesticated populations of Rangifer tarandus throughout Norway using spatiotemporal generalized additive models (GAMs) and varying coefficient models (VCMs). Optimal climate windows were calculated at both the regional and national level using a novel nonlinear climate window algorithm optimized for prediction. Spatial and temporal variation in effects of population and environmental predictors were considered using a model including covariates decomposed into spatial, temporal, and residual components. The performance of this decomposed model was compared to spatiotemporal GAMs and VCMs. The decomposed model provided the best fit and lowest prediction errors. A positive effect of herd body condition in the previous year explained most of the deviance in calf body mass, followed by a more complex effect of population density. A negative effect of timing of spring and positive effect of winter onset on juvenile body mass suggested that a snow free season was positive for juvenile body mass growth. Our findings suggest early spring onset and later winter permanent snow cover as reinforcers of early-life conditions which support more robust reindeer populations. Our methodological improvements for climate window analyses and effect size measures for decomposed variables provide important contributions to account for, measure, and interpret nonlinear relationships between climate and animal populations at large scales.

Modeling the Effect of HIV/AIDS Stigma on HIV Infection Dynamics in Kenya.

Stigma toward people living with HIV/AIDS (PLWHA) has impeded the response to the disease across the world. Widespread stigma leads to poor adherence of preventative measures while also causing PLWHA to avoid testing and care, delaying important treatment. Stigma is clearly a hugely complex construct. However, it can be broken down into components which include internalized stigma (how people with the trait feel about themselves) and enacted stigma (how a community reacts to an individual with the trait). Levels of HIV/AIDS-related stigma are particularly high in sub-Saharan Africa, which contributed to a surge in cases in Kenya during the late twentieth century. Since the early twenty-first century, the United Nations and governments around the world have worked to eliminate stigma from society and resulting public health education campaigns have improved the perception of PLWHA over time, but HIV/AIDS remains a significant problem, particularly in Kenya. We take a data-driven approach to create a time-dependent stigma function that captures both the level of internalized and enacted stigma in the population. We embed this within a compartmental model for HIV dynamics. Since 2000, the population in Kenya has been growing almost exponentially and so we rescale our model system to create a coupled system for HIV prevalence and fraction of individuals that are infected that seek treatment. This allows us to estimate model parameters from published data. We use the model to explore a range of scenarios in which either internalized or enacted stigma levels vary from those predicted by the data. This analysis allows us to understand the potential impact of different public health interventions on key HIV metrics such as prevalence and disease-related death and to see how close Kenya will get to achieving UN goals for these HIV and stigma metrics by 2030.

Estimating a Key Parameter of Mammalian Mating Systems: The Chance of Siring Success for a Mated Male.

Studies of multiple paternity in mammals and other animal species generally report proportion of multiple paternity among litters, mean litter sizes, and mean number of sires per litter. It is shown how these variables can be used to produce an estimate of the probability of reproductive success for a male that has mated with a female. This estimate of male success is more informative about the mating system that alternative measures, like the proportion of litters with multiple paternity or the mean number of sires per litter. The probability of success for a mated male can be measured both theoretically and empirically, and gives an estimate of the intensity of sperm competition and of a male's "confidence of paternity" upon mating. The probability of success for mated males for ten "exemplar" species of mammals is estimated and they are compared for insights into the functioning of their mating systems.

Multiple paternity and number of offspring in mammals.

Many cooperative social attributes are being linked to characteristics of mating systems, particularly to the rate of multiple paternity that typifies a population. Under the logic that greater offspring production by females should engender greater competition among males to mate with females, it is predicted that multiple paternity should increase with litter sizes. We tested the predicted positive association of multiple paternity and litter size with a meta-analysis of 59 species of mammals. The probability of multiple paternity and mean litter size were positively correlated, but not significantly (Zr = 0.202). Also, the mean number of sires of litters increased with mean litter size, but not significantly (Zr = 0.235). We developed a combinatorial formula for the influence of number of male mates and litter size on the probability of multiple paternity. We used Bayesian Markov chain Monte Carlo simulations to generate an expectation for the form of the relationship between the probability of multiple paternity and mean litter size. Under the assumption of random samplings of numbers of mates, the expected association of the probability of multiple paternity and mean litter sizes among species was positive, curvilinear and relatively high. However, the empirical probabilities of multiple paternities were much less than expected, suggesting that behavioural factors (such as mating-associated behaviours) or ecological characteristics (such as population density) probably limit the number of male mates for reproductive females. The probability of multiple paternity in a population is an estimate of mating patterns that does not closely reflect the number of sires of individual litters. We suggest use of the estimated probability of mating success for males as an alternative measure of their contribution to the mating system.

How much multiple paternity should we expect? A study of birds and contrast with mammals.

Parentage analyses via molecular markers have revealed multiple paternity within the broods of polytocous species, reshaping our understanding of animal behavior, ecology, and evolution. In a meta-analysis of multiple paternity in bird and mammal species, we conducted a literature search and found 138 bird and 64 mammal populations with microsatellite DNA paternity results. Bird populations averaged 19.5% multiple paternity and mammals more than twice that level (46.1%). We used a Bayesian approach to construct a null model for how multiple paternity should behave at random among species, under the assumption that all mated males have equal likelihood of siring success, given mean brood size and mean number of sires. We compared the differences between the null model and the actual probabilities of multiple paternity. While a few bird populations fell close to the null model, most did not, averaging 34.0-percentage points below null model predictions; mammals had an average probability of multiple paternity 13.6-percentage points below the null model. Differences between bird and mammal species were also subjected to comparative phylogenetic analyses that generally confirmed our analyses that did not adjust for estimated historical relationships. Birds exhibited extremely low probabilities of multiple paternity, not only compared to mammals but also relative to other major animal taxa. The generally low probability of multiple paternity in birds might be produced by a variety of factors, including behaviors that reflect sexual selection (extreme mate guarding or unifocal female choice) and sperm competition (e.g., precedence effects favoring fertilization by early or late matings).

Semiparametric model selection for identification of environmental covariates related to adult groundfish catches and weights.

Ecologists and fisheries managers are interested in monitoring economically important marine fish species and using this data to inform management strategies. Determining environmental factors that best predict changes in these populations, particularly under rapid climate change, are a priority. I illustrate the application of the least squares-based spline estimation and group LASSO (LSSGLASSO) procedure for selection of coefficient functions in single index varying coefficient models (SIVCMs) on an ecological data set that includes spatiotemporal environmental covariates suspected to play a role in the catches and weights of six groundfish species. Temporal trends in variable selection were apparent, though the selection of variables was largely unrelated to common North Pacific climate indices. These results indicate that the strength of an environmental variable's effect on a groundfish population may change over time, and not necessarily in-step with known low-frequency patterns of ocean-climate variability commonly attributable to large-scale regime shifts in the North Pacific. My application of the LSSGLASSO procedure for SIVCMs to deep water species using environmental data from various sources illustrates how variable selection with a flexible model structure can produce informative inference for remote and hard-to-reach animal populations.

Spatiotemporally explicit model averaging for forecasting of Alaskan groundfish catch.

Fisheries management is dominated by the need to forecast catch and abundance of commercially and ecologically important species. The influence of spatial information and environmental factors on forecasting error is not often considered. I propose a forecasting method called spatiotemporally explicit model averaging (STEMA) to combine spatial and temporal information through model averaging. I examine the performance of STEMA against two popular forecasting models and a modern spatial prediction model: the autoregressive integrated moving averages with explanatory variables (ARIMAX) model, the Bayesian hierarchical model, and the varying coefficient model. I focus on applying the methods to four species of Alaskan groundfish for which catch data are available. My method reduces forecasting errors significantly for most of the tested models when compared to ARIMAX, Bayesian, and varying coefficient methods. I also consider the effect of sea surface temperature (SST) on the forecasting of catch, as multiple studies reveal a potential influence of water temperature on the survival and growth of juvenile groundfish. For most of the preferred models, inclusion of SST in the model improved forecasting of catch. It is advisable to consider both spatial information and relevant environmental factors in forecasting models to obtain more accurate projections of population abundance. The STEMA method is capable of accounting for spatial information in forecasting and can be applied to various types of data because of its flexible varying coefficient model structure. It is therefore a suitable forecasting method for application to many fields including ecology, epidemiology, and climatology.