Parameter Redundancy with Applications in Statistical Ecology

This thesis is concerned with parameter redundancy in statistical ecology models. If it is not possible to estimate all the parameters, a model is termed parameter redundant. Parameter redundancy commonly occurs when parameters are confounded in the model so that the model could be reparameterised in terms of a smaller number of parameters. In principle, it is possible to use symbolic algebra to determine whether or not all the parameters of a certain ecological model can be estimated using classical methods of statistical inference. We examine a variety of different ecological models: We begin by exploring models based on marking a number of animals and observing the same animals at future time points. These observations can either be when the animal is marked and then recovered dead in mark-recovery modelling, or when the animal is marked and then recaptured alive in capture-recapture modelling. We also explore capture-recapture-recovery models where both dead recoveries and alive recaptures can be observed in the same study. We go on to explore occupancy models which are used to obtain estimates of the probability of presence, or absence, for living species by the use of repeated detection surveys, where these models have the advantage that individuals are not required to be marked. A variety of different occupancy models are examined included the addition of season-dependent parameters, group-dependent parameters and species-dependent, along with other models. We investigate parameter redundancy by deriving general results for a variety of different models where the model's parameter dependencies can be relaxed suited to different studies. We also analyse how the results change for specific data sets and how sparse data influence whether or not a model is parameter redundant using procedures written in Maple. This theory on parameter redundancy is vital for the correct use of these ecological models so that valid statistical inference can be made