The past week or two I’ve been wrestling with the data we have on white-tailed deer density and vegetation in Michigan’s Upper Peninsula in an attempt to find some solid statistical relationships that we might use in our ecological-economic simulation model. However, I seem to be encountering similar issues to previous researchers, notably (as Weisberg and Bugmann put it) “the weak signal-to noise ratio that is characteristic of ungulate-vegetation systems”, that “multiple factors need to be considered, if we are to develop a useful, predictive understanding of ungulate-vegetation relationships”, and that “ungulate-vegetation interactions need to be better understood over multiple scales”.
Hobbs suggests that one of the problems slowing species distribution research is a preoccupation with statistical power that he calls “the tyranny of power”. This tyranny arises, he suggests, because traditional statistical methods that are powerful at smaller scales become less useful at larger extents. There are at least three reasons for this including,
- small things are more amenable to study by traditional methods than large things
- variability increases with scale (extent)
- potential for bias increases with scale (extent)
“The implication of the tyranny of power is that many of the traditionally sanctioned techniques for ecological investigation are simply not appropriate at large-scales… This means that inferences at large-scales are likely to require research designs that bear little resemblance to the approaches many of us learned in graduate school.” Hobbs p.230
However, this tyranny may simply be because, as Fortin and Dale point out, “most study areas contain more than one ecological process that can act at different spatial and temporal scales”. That is, the processes are non-stationary in time and space. Leaving time aside for now, spatial non-stationarity has already been found to be present in our study area with regards the processes we’re considering. For example, Shi and colleagues found that Geographically Weighted Regression (GWR) models are better at predicting white-tailed deer densities than an ordinary least-squares regression model for the entirety of our study area.
Hobbs’ argument suggests that it’s often useful analyse ecological data from large regions by partitioning them into smaller, more spatially homogenous areas. The idea is that these smaller patches are more likely to be governed by the same ecological process. But how should these smaller regions be selected? A commonly used geographical division is the ecoregion. Ecoregions divide land into areas of similar characteristics such as climate, soils, vegetation and topography. For our study area we’ve found that relationships between deer densities and predictor variables do indeed vary by Albert’s ecoregions. But we think that there might be more useful ways to divide our study area that take into account variables that are commonly believed to strongly influence spatial deer distributions. In Michigan’s UP the prime example is the large snow fall is received each winter and which hinders deer movement and foraging.
We’re beginning to examine how GWR and spatial boundary analysis might be used to delineate these areas (at different scales) in the hope of refining our understanding about the interaction of deer and vegetation across our large (400,000 ha) landscape. In turn we should be able to better quantify some of these relationships for use in our model.