Semiparametric Bayesian modeling of density dependence
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Density dependence is a foundation of population biology. Analysis of population data with parametric models has long provided estimates of the maximum reproductive rate and the form of density dependence. These in turn determine the limit of sustainable harvest and the population's stability, respectively. However, standard parametric analyses of population data generate incorrect inferences of density dependence in noisy and short series. Therefore, there is a clear need for improved statistical methods for inferring density dependence. In this thesis, I developed new semiparametric Bayesian (SB) methods for estimating reproductive rates and for identifying forms of density dependence. Using simulated data, I validated the superiority of the SB methods to parametric alternatives. Then, I conducted SB analyses of 285 fish populations' datasets to estimate reproductive rates and to identify the forms of density dependence. I compared the results of the SB analyses with those based on standard parametric analyses of the same datasets. The SB analysis indicated that the forms of density dependence in 3.4% of the datasets are Allee effects, whereas the parametric analysis indicated 1.5%, suggesting that Allee effects are more than twice as often as previously thought. However, both the SB and the parametric model (the linear model) generated essentially the same estimates of the reproductive rates, indicating that the linear model may be a reasonable approach to inferring the reproductive rates of fish populations.