Towards an integrated approach to stochastic process-based modelling : with applications to animal behaviour and spatio-temporal spread

Using example applications from our recent research we illustrate the development of an integrated approach to modelling biological processes based on stochastic modelling techniques. The goal of this programme of research is to provide a suite of mathematical and statistical methods to enable models to play a more central role in the development of scientific understanding of complex biological systems. The resulting framework should allow models to both inform, and be informed by data collection, and enable probabilistic risk assessments to reflect inherent variability and uncertainty in current knowledge of the system in question. We focus on discrete state-space Markov processes as they provide a general and flexible framework to both describe and infer the behaviour of a broad range of systems. Unfortunately the non-linearities required to model many real-world systems typically mean that such discrete state-space stochastic processes are intractable to analytic solution, necessitating the use of simulation and analytic approximations. We show how to formulate stochastic process-based models within this framework and discuss the representation of spatial and temporal heterogeneity. Simple population models are developed and used to illustrate these concepts. We describe how to simulate from such models, and compare them with their deterministic counterparts. In addition, we discuss two methods, closure schemes and linearization about steady-states, which can be used to obtain analytic insights into model behaviour. We outline how to conduct parameter estimation for such models when, as is typically the case for biological and agricultural systems, only partial observations are available. Having focused on familiar population-level models in introducing our integrated approach, its wider applicability is illustrated by two contrasting applications from our recent research. The first example combines the development and analysis of an agent-based model describing grazing in heterogeneous environments, with parameter inference based on data generated using a transponder system in a behavioural experiment on dairy cows. The second example makes use of large-scale data describing bio-geographical features of the landscape and the spatio-temporal spread of an alien plant to estimate the parameters of a stochastic model of dispersal and establishment.