RESEARCH: Process & Systems Modelling
Modelling the risk of spread of alien species
The increasing presence of invasive alien species is widely recognised as a major threat to native biodiversity. In conjunction with Heriot-Watt University, models describing the spread of invasive species at the landscape scale were developed and fitted to data detailing the spread of invasive plants, using geo-referenced covariate information describing local temperature, elevation and habitat type. The use of Markov chain Monte Carlo sampling within a Bayesian framework facilitated statistical assessments of relative suitability of different habitats, and enabled predictions of future spread to account both for uncertainty in model parameters and for stochastic variability in the spread of the species. The methods, widely applicable to data on spatio-temporal expansion, are illustrated (see figure) by application to data on the spread of giant hogweed across Britain in the 20th Century.
The figure shows a map of posterior predicted risk (the estimated probability, conditional on the model and data) of 10X10km grid cells being colonised by giant hogweed between the end of 2000 (the last available data) and 2010. The climate and land use are assumed to remain constant over this 10 year period. Data on existing sites from the National Biodiversity Network http://www.nbn.org.uk/
Estimating optimum seed rates for winter wheat
Advice to farmers on the amount of seed to sow is based on trials in which varieties of a crop are grown at different seed rates. Conventionally, the relationships between seed rate and crop yield are estimated separately for each trial and variety: information on the optima is then combined informally. With HGCA support, we have developed a method for combining results from seed-rate trials and choosing economically optimum seed rates for a variety. This Bayesian method incorporates information on the anticipated value of the harvest, seed and management costs, and expert knowledge of the crop and the soil. It can also take account of differences such as sowing date, latitude and management practices. The methodology is of more general applicability, particularly in areas where decisions on optimal dosing must be tailored to particular circumstances.
The utility of sowing seed is taken to be the value of the grain minus the cost of the seed: the optimum rate is the point where the curve reaches a maximum. The plots show the expected utility for two sowing dates: later sowing requires a higher seed rate in order to achieve maximum expected utility.
Genetic diversity of Scots pine trees
Monoterpenes are a highly heritable group of phyto-chemicals that can be used as a surrogate measure of genetic diversity in Scots pine trees. Observed monoterpene diversity is surprisingly high at small as well as at large spatial scales. We have been simulating the patterns of monoterpene concentrations that arise from simple models of sexual recombination, dispersal, competition for space, and death. These simulated patterns allow us to assess whether observed levels of diversity are to be expected from the spatial population dynamics. The alternative hypothesis is that the diversity of monoterpenes, which are known to influence vulnerability of young trees to parasites, may be driven by the interaction between parasites and monoterpenes.
A simulated forest, with points representing the location of trees, and colour intensity for red green and blue indicating concentrations of three independent monoterpenes. Even with the small average dispersal of 10m for seeds and 100m for pollen, monoterpene diversity is high at small as well as at large spatial scales.
Understanding the effects of social hierarchy on disease dynamics
Many livestock diseases (e.g. paratuberculosis) also have wildlife hosts, and knowledge of disease dynamics in natural populations is often critical to the development of successful control strategies. A key challenge is to understand the epidemiological importance of interactions between individuals in natural populations. In conjunction with scientists at SAC, we have developed models to explore the effects of features of social hierarchy such as dominance on epidemiology. This work demonstrates that populations with a hierarchy have higher levels of disease than populations without a hierarchy. The biggest effects of hierarchy tend to be at points where the disease is close to extinction, suggesting that such effects should be considered in models being used to examine the impact of control strategies.
The figure shows contours of the difference in prevalence between a model with hierarchy and one without. The disease is expected to become extinct above the lines for models with (red) and without (green) a social hierarchy respectively.
OPA survey and modelling
Ovine Pulmonary Adenocarcinoma (OPA) is a contagious lung cancer of sheep caused by a viral infection. BioSS have been working with MRI and SAC to inform the choice of potential control strategies for OPA in a project involving laboratory science, field epidemiology and mathematical modelling. We have designed a major field study of 125 holdings, sampling over 3000 sheep throughout Scotland, to provide the first ever snap-shot of OPA prevalence in the field. These data are being combined with knowledge of Scottish sheep husbandry systems and modes of OPA transmission to parameterise an agent-based model of sheep management and OPA infection on Scottish hill, upland and lowland farms. The results of this project will enable much better advice to be given to farmers and vets on how to control the disease.
The sheep management system on a Scottish hill farm used by our agentbased model, with females (breeding ewes and one year old hoggs), tups (breeding males) and lambs.