Steelhead trout exhibit highly variable population dynamics that are driven by the vast life history variability of individuals that results in a complex system with highly non-linear dynamics for both individuals and populations. In this dissertation, I consider three different projects with the aim of understanding both individual processes and population dynamics using mathematical and statistical tools. In each chapter I develop new mathematical and statistical methodology that incorporates the biological knowledge about steelhead life history in order to answer different questions about the individual and population dynamics observed in nature.
The first project focuses on the development and application of methodology to better explain the observed adult returns in the Carmel River. To do this, I incorporate knowledge about conditional migration strategies into a life history model. In this work, I discover a decreasing trend in mean stream temperature that is coupled with a decreasing trend in mean length of individuals. One of the primary goals of this chapter is to test the scientific hypothesis that the inclusion of life history attributes would improve the predictions of adult returns. I demonstrate that the mechanistic inclusion of life history attributes into the mathematical model does significantly improve the ability to predict adult returns.
In the second project, I develop a Physiologically Structured Population Model (PSPM) for steelhead trout. The PSPM framework allows me to account for the biological processes driving the life history of steelhead through their entire lifetime. A benefit of this framework is that the resultant population dynamics arise solely from the interactions between individuals and their environment. The model captures the wide variability of life histories that are observed in nature. With this model, I explore the effects that size-dependent mortality and competition have on the population dynamics. I also explore the effects of three different temperature regimes on the population dynamics, highlighting the non-linear nature of the system.
The last project is the development of a Bayesian Semi-parametric model that describes the relationship between temperature and individual consumption that determines growth. Developing a state-space model that incorporates a Gaussian Process prior for the temperature-consumption relationship allows the data to determine the shape of the relationship and account for both measurement error and process stochasticity. I first test the model with simulated data with different levels of data availability, measurement error and process stochasticity. This application demonstrates that the total number of temporal measurements affects the performance of the model more than the number of individuals. I then apply the model to experimental data from a growth experiment of steelhead trout. The results demonstrate the ability of the model to describe the growth of individuals as well as to capture individual consumption. The model shows agreement between the shape of the temperature-consumption function that I predict and the relationship that is commonly used for steelhead.
