In ecological population management, years of animal counts are fit to nonlinear, dynamic models (e.g. the Ricker model) because the values of the parameters are of interest. The yearly counts are subject to measurement error, which inevitably leads to biased estimates and adversely affects inference if ignored. In the literature, often convenient distribution assumptions are imposed, readily available estimated measurement error variances are not utilized, or the measurement error is ignored entirely. In this thesis, ways to estimate the parameters of the Ricker model and perform inference while accounting for measurement error are investigated where distribution assumptions are minimized and estimated measurement error variances are utilized. To these ends, SIMEX and modified estimating equations (MEE) rather than likelihood methods are investigated for data on the abundance and log-abundance scales, and how inference is done via the parametric bootstrap and estimated standard errors from the modified estimating equations is shown. Subsequently, simulation studies are performed on the log-abundance scale under varying parameter values to learn how levels of measurement error variances (ranging from the realistically low value of 0.0025 to unrealistically high value of 0.025 ) affects the estimators and inference when measurement error is ignored, and how the methods perform accounting for it. It was found that the bias induced by measurement error depends on the true value of the parameter. Furthermore, the performances of SIMEX and MEE are associated with the true value of a and the level of measurement error variance. In particular, both methods perform best for a > 1 and low to moderate levels of measurement error variance, with the MEE estimators having high standard error and often poorer performance than those from SIMEX. It was also found that the MEE estimators contain singularities which attribute to its low precision and erratic behavior. These methods were then applied to actual moose count data with sample size more than double that of the simulations. It was found that both the SIMEX and MEE estimators performed well suggesting that sample size contributes to previous poor behavior.

Current eastern wild turkey (<I>Meleagris gallopavo silvestris</I>) harvest models assume density-independent population dynamics despite indications that populations are subject to a form of density dependence. I suggest that both density-dependent and independent factors operate simultaneously on wild turkey populations, where the relative strength of each is governed by population density. I attempt to estimate the form of the density dependence relationship in wild turkey population growth using the theta-Ricker model. Density-independent relationships are explored between production and rainfall and temperature correlates for possible inclusion in the harvest model. Density-dependent and independent effects are then combined in the model to compare multiple harvest strategies. To estimate a functional relationship between population growth and density, I fit the theta-Ricker model to harvest index time-series from 11 state wildlife agencies. To model density-independent effects on population growth, I explored the ability of rainfall, temperature, and mast during the nesting and brooding season to predict observed production indices for 7 states. I then built a harvest model incorporating estimates to determine their influence on the mean and variability of the fall and spring harvest. Estimated density-dependent growth rates produced a left-skewed yield curve maximized at ~40% of carrying capacity, with large residuals. Density-independent models of production varied widely and were characterized by high model uncertainty. Results indicate a non-linear density dependence effect strongest at low population densities. High residuals from the model fit indicate that extrinsic factors will overshadow density-dependent factors at most population densities. However, environmental models were weak, requiring more data with higher precision. This indicates that density-independence can be correctly and more easily modeled as random error. The constructed model uses both density dependence and density-independent stochastic error as a tool to explore harvest strategies for biologists. The inclusion of weak density dependence changes expected harvest rates little from density-independent models. However, it does lower the probability of overharvest at low densities. Alternatives to proportional harvesting are explored to reduce the uncertainty in annual harvests. / Ph. D.

This is a study of the effect of harvesting on a system with two competing species. The system is a Ricker-type model that extends the work done by Luis, Elaydi, and Oliveira to include the effect of harvesting on the system. We look at the uniform bound of the system as well as the isoclines and perform a stability analysis of the equilibrium points. We also look at the effects of harvesting on the stability of the system by looking at the bifurcation of the system with respect to harvesting.

This thesis consists of four papers, three papers about modelling animal populations and one paper about an area integral estimate for solutions of partial differential equations on non-smooth domains. The papers are: I. Å. Brännström, Single species population models from first principles. II. Å. Brännström and D. J. T. Sumpter, Stochastic analogues of deterministic single species population models. III. Å. Brännström and D. J. T. Sumpter, Coupled map lattice approximations for spatially explicit individual-based models of ecology. IV. Å. Brännström, An area integral estimate for higher order parabolic equations. In the first paper we derive deterministic discrete single species population models with first order feedback, such as the Hassell and Beverton-Holt model, from first principles. The derivations build on the site based method of Sumpter &amp; Broomhead (2001) and Johansson &amp; Sumpter (2003). A three parameter generalisation of the Beverton-Holtmodel is also derived, and one of the parameters is shown to correspond directly to the underlying distribution of individuals. The second paper is about constructing stochastic population models that incorporate a given deterministic skeleton. Using the Ricker model as an example, we construct several stochastic analogues and fit them to data using the method of maximum likelihood. The results show that an accurate stochastic population model is most important when the dynamics are periodic or chaotic, and that the two most common ways of constructing stochastic analogues, using additive normally distributed noise or multiplicative lognormally distributed noise, give models that fit the data well. The latter is also motivated on theoretical grounds. In the third paper we approximate a spatially explicit individual-based model with a stochastic coupledmap lattice. The approximation effectively disentangles the deterministic and stochastic components of the model. Based on this approximation we argue that the stable population dynamics seen for short dispersal ranges is a consequence of increased stochasticity from local interactions and dispersal. Finally, the fourth paper contains a proof that for solutions of higher order real homogeneous constant coefficient parabolic operators on Lipschitz cylinders, the area integral dominates the maximal function in the L2-norm.

Knowledge of offspring production (recruitment) is fundamental to understanding and forecasting the dynamics of a population. In this thesis, I focus on two demographic characteristics of fish stocks that are important to recruitment: population density and age structure. First, populations produce more recruits at low density, but quantifying this response has proven difficult. Using data from hundreds of populations of walleye (Sander vitreus), an economically important freshwater fish, I demonstrate that the growing-degree-day metric (a temperature index) is better than age at explaining variation in density-dependent growth and maturity both within and among populations. I then incorporate multi-lake measures of density-dependent life history change into a temperature-based biphasic model of growth and reproduction to predict sustainable rates of mortality for walleye throughout most of their range. Second, the age (or size) structure of a population may also affect recruitment because of positive effects of maternal age on offspring production and survival; however, evidence for these ‘maternal influences’ on recruitment is limited. Using both an analytical model and a meta-analysis of stock-recruitment data from 25 species of exploited marine fish, I show that (i) maximum reproductive rate increased with the mean age of adults in a population, and (ii) the importance of age structure increased with a species’ longevity. I then demonstrate a similar effect of maternal influences on reproductive rate in a detailed study of Lake Erie walleye. By highlighting the importance of fisheries-induced demographic change to recruitment, this thesis provides insight into past and present failures. However, it also demonstrates clearly the benefits of proactive management strategies that (i) identify and respect the limits of exploitation, (ii) protect from exploitation reproductively valuable individuals—principles that apply generally to any freshwater, marine, or terrestrial species that is of recreational, commercial, or conservation value.

Knowledge of offspring production (recruitment) is fundamental to understanding and forecasting the dynamics of a population. In this thesis, I focus on two demographic characteristics of fish stocks that are important to recruitment: population density and age structure. First, populations produce more recruits at low density, but quantifying this response has proven difficult. Using data from hundreds of populations of walleye (Sander vitreus), an economically important freshwater fish, I demonstrate that the growing-degree-day metric (a temperature index) is better than age at explaining variation in density-dependent growth and maturity both within and among populations. I then incorporate multi-lake measures of density-dependent life history change into a temperature-based biphasic model of growth and reproduction to predict sustainable rates of mortality for walleye throughout most of their range. Second, the age (or size) structure of a population may also affect recruitment because of positive effects of maternal age on offspring production and survival; however, evidence for these ‘maternal influences’ on recruitment is limited. Using both an analytical model and a meta-analysis of stock-recruitment data from 25 species of exploited marine fish, I show that (i) maximum reproductive rate increased with the mean age of adults in a population, and (ii) the importance of age structure increased with a species’ longevity. I then demonstrate a similar effect of maternal influences on reproductive rate in a detailed study of Lake Erie walleye. By highlighting the importance of fisheries-induced demographic change to recruitment, this thesis provides insight into past and present failures. However, it also demonstrates clearly the benefits of proactive management strategies that (i) identify and respect the limits of exploitation, (ii) protect from exploitation reproductively valuable individuals—principles that apply generally to any freshwater, marine, or terrestrial species that is of recreational, commercial, or conservation value.