Mark R. T. Dale

Utility of computer simulations in landscape genetics

Population genetics theory is primarily based on mathematical models in which spatial complexity and temporal variability are largely ignored. In contrast, the field of landscape genetics expressly focuses on how population genetic processes are affected by complex spatial and temporal environmental heterogeneity. It is spatially explicit and relates patterns to processes by combining complex and realistic life histories, behaviours, landscape features and genetic data. Central to landscape genetics is the connection of spatial patterns of genetic variation to the usually highly stochastic space–time processes that create them over both historical and contemporary time periods. The field should benefit from a shift to computer simulation approaches, which enable incorporation of demographic and environmental stochasticity. A key role of simulations is to show how demographic processes such as dispersal or reproduction interact with landscape features to affect probability of site occupancy, population size, and gene flow, which in turn determine spatial genetic structure. Simulations could also be used to compare various statistical methods and determine which have correct type I error or the highest statistical power to correctly identify spatio‐temporal and environmental effects. Simulations may also help in evaluating how specific spatial metrics may be used to project future genetic trends. This article summarizes some of the fundamental aspects of spatial–temporal population genetic processes. It discusses the potential use of simulations to determine how various spatial metrics can be rigorously employed to identify features of interest, including contrasting locus‐specific spatial patterns due to micro‐scale environmental selection.

Spatial patterns of shrub encroachment in neighbouring grassland communities in the Pyrenees: floristic composition heterogeneity drives shrub proliferation rates

We studied the role of floristic composition and associational resistance in shrub dynamics by comparing spatial patterns of shrub cover after prescribed burning in neighbouring grassland communities with different palatability. The study focused on the shrub Cytisus balansae ssp. europaeus (G. López and Jarvis) Muñoz Garmendia. Seven two-dimensional transects (20xa0×xa00.5xa0m) were established to monitor shrub cover for at least 10xa0years after prescribed burning. Shrub cover and spatial patterns were assessed in each transect. Floristic similarity between transects and Cytisus associations with different species were estimated. Over an entire transect, shrub cover and shrub scale of pattern and patch size were lowest in the unpalatable Festuca eskia grasslands and highest in F. paniculata grasslands. At short distances, we found negative associations between Cytisus and most of the grasses, except for F. nigrescens and Agrostis capillaris, which showed positive associations with Cytisus. Thus, the effects of associational resistance on shrub encroachment were not as marked as expected, F. eskia grasslands showing the lowest shrub encroachment rates after fire. By contrast, Cytisus was positively associated with the most palatable grasses in the site, namely F. nigrescens and A.xa0capillaris. We conclude that differences in floristic composition drive shrub encroachment rates in these spatially heterogeneous communities.

How Spatial Heterogeneity of Cover Affects Patterns of Shrub Encroachment into Mesic Grasslands

We used a multi-method approach to analyze the spatial patterns of shrubs and cover types (plant species, litter or bare soil) in grassland-shrubland ecotones. This approach allows us to assess how fine-scale spatial heterogeneity of cover types affects the patterns of Cytisus balansae shrub encroachment into mesic mountain grasslands (Catalan Pyrenees, Spain). Spatial patterns and the spatial associations between juvenile shrubs and different cover types were assessed in mesic grasslands dominated by species with different palatabilities (palatable grass Festuca nigrescens and unpalatable grass Festuca eskia). A new index, called RISES (“Relative Index of Shrub Encroachment Susceptibility”), was proposed to calculate the chances of shrub encroachment into a given grassland, combining the magnitude of the spatial associations and the surface area for each cover type. Overall, juveniles showed positive associations with palatable F. nigrescens and negative associations with unpalatable F. eskia, although these associations shifted with shrub development stage. In F. eskia grasslands, bare soil showed a low scale of pattern and positive associations with juveniles. Although the highest RISES values were found in F. nigrescens plots, the number of juvenile Cytisus was similar in both types of grasslands. However, F. nigrescens grasslands showed the greatest number of juveniles in early development stage (i.e. height<10 cm) whereas F. eskia grasslands showed the greatest number of juveniles in late development stages (i.e. height>30 cm). We concluded that in F. eskia grasslands, where establishment may be constrained by the dominant cover type, the low scale of pattern on bare soil may result in higher chances of shrub establishment and survival. In contrast, although grasslands dominated by the palatable F. nigrescens may be more susceptible to shrub establishment; current grazing rates may reduce juvenile survival.

Spatial Analysis of Wildlife Distribution and Disease Spread

Many of the interactions between organisms depend on the distance or the ease of movement (accessibility) between them which can be based on the concept of the neighbors or of the neighborhoods of given individuals. A number of different statistical approaches have been developed (Fortin and Dale 2005; Perry 1995) to address the definitions of neighbors and neighborhoods in order to implement measures of those characteristics that are most important to the interactions under study. In particular, the numbers of neighbors (however defined) and their distances can be combined into measures of aggregation, dispersion or crowding (Lloyd 1967), which can have clear effects on important demographic processes, such as the spread of disease, beyond the simple effect of distance to the nearest organisms of the same or different kinds.

Dealing with spatial autocorrelation

Introduction The familiar procedures of parametric statistics are based on the assumption of independence of the individual observations in the data under scrutiny, but in ecological data the assumption of independence is often violated and we need to understand the effects of a lack of independence. A lack of independence can arise because, in the natural world, things (samples, observations, etc.) that are closer together sometimes have a tendency to be more similar than those that are further apart, a phenomenon known to geographers as ‘Toblers Law’ (Tobler 1970, and see Chapters 1 and 3). We refer to this lack of independence as ‘spatial dependence’ in the data (see Chapter 1), whatever the cause. One source of this phenomenon is autocorrelation in the data due to causal interactions within the measured variable itself; for example, in studying species distribution and abundance, the abundance of a single species may be spatially autocorrelated because of constraints on the organisms mobility and dispersal. This kind of autocorrelation is sometimes called ‘true autocorrelation’ (see Chapter 1), but it might be more accurate to refer to it as ‘inherent autocorrelation’ (‘autogenic’ might be even more accurate, perhaps, but more unwieldy). The descriptor is to distinguish this phenomenon from ‘induced spatial dependence’ (see Chapter 1), where the observed variable (e.g. species abundance) has a functional dependence on an underlying variable (e.g. soil moisture or nutrient content), which is itself autocorrelated (cf. Legendre et al . 2002).