Determining population growth across large scales is difficult because it is often impractical to collect data at large scales and over long timespans. Instead, the growth of a population is often only measured at a small, plot-level scale and then extrapolated to derive a mean field estimate. However, this approach is prone to error since it simplifies spatial processes such as the neighbourhood effects of density and dispersal. We present a novel approach that estimates how spatial processes derived from the effects of density and dispersal affect population growth between plot scales and landscape scales. The method is based on a scale transition theory and calculates a transition term to measure the spatial scaling of population growth, which we extend to unstable, expanding populations in order to assess whether landscape-scale population dynamics are different from those estimated at smaller spatial scales. We illustrate this approach using aerial imagery of eight locations in New Zealand experiencing non-native pine invasions. Analyses examined the dynamics at a plot scale (1 hectare) and compared this to estimates across entire landscapes (between 24 and 1600 hectares), in several cases for more than one time period. We used a Bayesian spatial random effects model to examine population growth and to account for neighbourhood effects and dispersal between plots in a rapidly changing system. 

We found that the estimates of the scale transition term were typically 10-25% of the mean field estimates, which led to mean field estimates of population growth extrapolated from plots being considerably higher than landscape estimates. The approach we have developed will not only have applications for predicting the populations’ growth of invasive species, but also for studies examining the scaling of landscape-scale phenomena.

We gathered imagery from eight invasion sites across the South Island of New Zealand for multiple time steps (2-4 points in time) using a combination of high resolution aerial imagery gathered from the Land Information New Zealand (LINZ) archives and high resolution satellite imagery downloaded from Google Earth. To detect the pine trees, we used an unsupervised, pixel-based classification method. First, we thresholded the imagery to separate out the dark-coloured trees against the light-coloured background vegetation (Ke and Quackenbush 2011). Then we segmented the pixels identified as trees using a process called watershedding in order to delineate the tree canopies (Komura et al. 2004, Wang et al. 2004, Deng et al. 2016). We extracted the centre point of each polygon identified as a tree, and for each site and time step, we generated a file of the point locations of every tree detected. To prepare the data derived from the image classification and detection methods for use in our population growth models, we first divided each site into a set of one hectare grid-cells, and counted the number of trees in each cell for each time step.