Modelling diet composition dynamics among North Sea predatory fish using a length-structured partial ecosystem model

Multispecies fisheries management approaches must take account of the array of trophic interactions within the ecosystem. Studies of the gut contents of fish stocks in the North Sea show decadal changes in diet composition, as might be expected when the relative abundances of prey species change. In this paper we explore the extent to which a simple model of prey consumption deployed within a dynamic multi-species population model is able to capture those changes. We make use of a length-structured partial-ecosystem model (FishSUMS) in which the relative preferences of predators for prey are set by a combination of species weightings and predator-to-prey length ratios. The model allows for diets to evolve over the lifetime of the predator species as well as in response to changes in the available prey. Eleven commercially important North Sea species were included in the model with full length structure, together with other trophic resources represented in less detail. The model was simultaneously tuned to various sources of data, including time series of stock biomass and landings. We show that, despite the simplicity of the representation of the predation process, it is capable of capturing some of the large observed changes in diet in four predator species that were sampled during the Year of the Stomach projects in 1981 and 1991: cod, haddock, whiting and saithe. We also quantify how much of the biomass is lost to the fishery, to predation by explicitly-modelled species, and to unspecified mortality

From individuals to populations: changing scale in process algebra models of biological systems

The problem of changing scale in models of a system is relevant in many different fields. In this thesis we investigate the problem in models of biological systems, particularly infectious disease spread and population dynamics. We investigate this problem using the process algebra \emph{Weighted Synchronous Calculus of Communicating Systems} (WSCCS). In WSCCS we can describe the different types of individual in a population and study the population by placing many of these individuals in parallel. We present an algorithm that allows us to rigorously derive mean field equations (MFE) describing the average change in the population. The algorithm takes into account the Markov chain semantics of WSCCS such that as the system being considered becomes larger, the approximation offered by the MFE tends towards the mean of the Markov chain. The traditional approach to developing population level equations of a system involves making assumptions about the behaviour of the entire population. Our approach means that the population level dynamics explained by the MFE are a direct consequence of the behaviour of individuals, which is more readily observed and measured than the behaviour of the population. In this way we develop MFE models of several different systems and compare the equations obtained to the traditional mathematical models of the system

From Individuals to Populations: A Symbolic Process Algebra Approach to Epidemiology

Is it possible to symbolically express and analyse an individual-based model of disease spread, including realistic population dynamics? This problem is addressed through the use of process algebra and a novel method for transforming process algebra into Mean Field Equations. A number of stochastic models of population growth are presented, exploring different representations based on alternative views of individual behaviour. The overall population dynamics in terms of mean field equations are derived using a formal and rigorous rewriting based method. These equations are easily compared with the traditionally used deterministic Ordinary Differential Equation models and allow evaluation of those ODE models, challenging their assumptions about system dynamics. The utility of our approach for epidemiology is confirmed by constructing a model combining population growth with disease spread and fitting it to data on HIV in the UK population

Studying the effects of adding spatiality to a process algebra model

We use NetLogo to create simulations of two models of disease transmission originally expressed in WSCCS. This allows us to introduce spatiality into the models and explore the consequences of having different contact structures among the agents. In previous work, mean field equations were derived from the WSCCS models, giving a description of the aggregate behaviour of the overall population of agents. These results turned out to differ from results obtained by another team using cellular automata models, which differ from process algebra by being inherently spatial. By using NetLogo we are able to explore whether spatiality, and resulting differences in the contact structures in the two kinds of models, are the reason for this different results. Our tentative conclusions, based at this point on informal observations of simulation results, are that space does indeed make a big difference. If space is ignored and individuals are allowed to mix randomly, then the simulations yield results that closely match the mean field equations, and consequently also match the associated global transmission terms (explained below). At the opposite extreme, if individuals can only contact their immediate neighbours, the simulation results are very different from the mean field equations (and also do not match the global transmission terms). These results are not surprising, and are consistent with other cellular automata-based approaches. We found that it was easy and convenient to implement and simulate the WSCCS models within NetLogo, and we recommend this approach to anyone wishing to explore the effects of introducing spatiality into a process algebra model

Deriving Mean Field Equations from Large Process Algebra Models

In many domain areas the behaviour of a system can be described at two levels: the behaviour of individual components, and the behaviour of the system as a whole. Often deriving one from the other is impossible, or at least intractable, especially when realistically large systems are considered. Here we present a rigorous algorithm which, given an individual based model in the process algebra WSCCS describing the components of a system and the way they interact, can produce a system of mean field equations which describe the mean behaviour of the system as a whole. This transformation circumvents the state explosion problem, allowing us to handle systems of any size by providing an approximation of the system behaviour. From the mean field equations we can investigate the transient dynamics of the system. This approach was motivated by problems in biological systems, but is applicable to distributed systems in general

Process Algebra Models of Population Dynamics

It is well understood that populations cannot grow without bound and that it is competition between individuals for resources which restricts growth. Despite centuries of interest, the question of how best to model density dependent population growth still has no definitive answer. We address this question here through a number of individual based models of populations expressed using the process algebra WSCCS. The advantage of these models is that they can be explicitly based on observations of individual interactions. From our probabilistic models we derive equations expressing overall population dynamics, using a formal and rigorous rewriting based method. These equations are easily compared with the traditionally used deterministic Ordinary Differential Equation models and allow evaluation of those ODE models, challenging their assumptions about system dynamics. Further, the approach is applied to epidemiology, combining population growth with disease spread

From Individuals to Populations: a mean field semantics for process algebra

A new semantics in terms of Mean Field Equations is presented for WSCCS (Weighted Synchronous Calculus of Communicating Systems). The semantics captures the average behaviour of the system over time, but without computing the entire state space, therefore avoiding the state space explosion problem. This allows easy investigation of models with large numbers of components. The new semantics is shown to be equivalent to the standard Discrete Time Markov Chain semantics of WSCCS as the number of processes tends to infinity. The method of deriving the semantics is illustrated with examples drawn from biology and from computing

Modelling the sensitivity of suspended sediment profiles to tidal current and wave conditions

Seawater turbidity due to suspended particulate material (SPM) is an important property of a marine ecosystem, determining the underwater light environment and many aspects of biological production and ecology. SPM concentrations are largely determined by patterns of sediment resuspension from the seabed due to shear stress caused by waves and currents. Hence planning for the construction of large scale offshore structures which will alter regional hydrodynamics needs to consider the consequences for SPM concentrations. Here we develop a one-dimensional (vertical) model of SPM dynamics which can be used to scope the effects of changes in wave and tidal current properties at a site. We implement the model for a number of sites off the east coast of Scotland where we have extensive data sets to enable numerical parameter optimisation. The model performs well at simulating fluctuations in turbidity varying from flood-ebb tidal cycles, spring-neap cycles, storm wave events, and an annual cycle of SPM concentration which is attributed to seasonal consolidation of seabed sediments. Sensitivity analysis shows that, for the range of seabed sediment types in the study (water depth 16 – 50 m; mud content 0.006 – 0.380 proportion by weight), relatively large (50%) attenuations of tidal current speed are required to produce changes in water column turbidity which would be detectable by observations given the variability in measurements. The model has potential for application to map the large scale sensitivity of turbidity distributions to the installation of wave and tidal energy extraction arrays

Modelling wave-current interactions off the east coast of Scotland

Densely populated coastal areas of the North Sea are particularly vulnerable to severe wave conditions, which overtop or damage sea-defences leading to dangerous flooding. Around the shallow southern North Sea, where the coastal margin is low-lying and population density is high, oceanographic modelling has helped to develop forecasting systems to predict flood risk. However coastal areas of the deeper northern North Sea are also subject to regular storm damage but there has been little or no effort to develop coastal wave models for these waters. Here we present a high spatial resolution model of northeast Scottish coastal waters, simulating waves and the effect of tidal currents on wave propagation, driven by global ocean tides, far-field wave conditions, and local air pressure and wind stress. We show that the wave- current interactions and wave-wave interactions are particularly important for simulating the wave conditions close to the coast at various locations. The model can simulate the extreme conditions experienced when high (spring) tides are combined with sea-level surges and large Atlantic swell. Such a combination of extremes represents a high risk for damaging conditions along the Scottish coast