Interacting populations in heterogeneous environments

To optimally manage a metapopulation, managers and conservation biologists can favor a type of habitat spatial distribution (e.g. aggregated or random). However, the spatial distribution that provides the highest habitat occupancy remains ambiguous and numerous contradictory results exist. Habitat occupancy depends on the balance between local extinction and colonization. Thus, the issue becomes even more puzzling when various forms of relationships - positive or negative co-variation - between local extinction and colonization rate within habitat types exist. Using an analytical model we demonstrate first that the habitat occupancy of a metapopulation is significantly affected by the presence of habitat types that display different extinction-colonization dynamics, considering: (i) variation in extinction or colonization rate and (ii) positive and negative co-variation between the two processes within habitat types. We consequently examine, with a spatially explicit stochastic simulation model, how different degrees of habitat aggregation affect occupancy predictions under similar scenarios. An aggregated distribution of habitat types provides the highest habitat occupancy when local extinction risk is spatially heterogeneous and high in some places, while a random distribution of habitat provides the highest habitat occupancy when colonization rates are high. Because spatial variability in local extinction rates always favors aggregation of habitats, we only need to know about spatial variability in colonization rates to determine whether aggregating habitat types increases, or not, metapopulation occupancy. From a comparison of the results obtained with the analytical and with the spatial-explicit stochastic simulation model we determine the conditions under which a simple metapopulation model closely matches the results of a more complex spatial simulation model with explicit heterogeneity.

Use of anisotropic modelling in electrical impedance tomography: description of method and preliminary assessment of utility in imaging brain function in the adult human head.

Electrical Impedance Tomography (EIT) is an imaging method which enables a volume conductivity map of a subject to be produced from multiple impedance measurements. It has the potential to become a portable non-invasive imaging technique of particular use in imaging brain function. Accurate numerical forward models may be used to improve image reconstruction but, until now, have employed an assumption of isotropic tissue conductivity. This may be expected to introduce inaccuracy, as body tissues, especially those such as white matter and the skull in head imaging, are highly anisotropic. The purpose of this study was, for the first time, to develop a method for incorporating anisotropy in a forward numerical model for EIT of the head and assess the resulting improvement in image quality in the case of linear reconstruction of one example of the human head. A realistic Finite Element Model (FEM) of an adult human head with segments for the scalp, skull, CSF, and brain was produced from a structural MRI. Anisotropy of the brain was estimated from a diffusion tensor-MRI of the same subject and anisotropy of the skull was approximated from the structural information. A method for incorporation of anisotropy in the forward model and its use in image reconstruction was produced. The improvement in reconstructed image quality was assessed in computer simulation by producing forward data, and then linear reconstruction using a sensitivity matrix approach. The mean boundary data difference between anisotropic and isotropic forward models for a reference conductivity was 50%. Use of the correct anisotropic FEM in image reconstruction, as opposed to an isotropic one, corrected an error of 24 mm in imaging a 10% conductivity decrease located in the hippocampus, improved localisation for conductivity changes deep in the brain and due to epilepsy by 4-17 mm, and, overall, led to a substantial improvement on image quality. This suggests that incorporation of anisotropy in numerical models used for image reconstruction is likely to improve EIT image quality.