# Simple geometric model of range-shift errors

A free pdf of Chaper 7 of Niche Modelling can be downloaded. Entitled ‘Bias’, a simple geometric model of range-shift illustrates my take on the problems of range-shift models. The model can be used to estimate exaggeration of reduction in range area due to climate change. The basic range-shift model is like a simple Venn diagrams seen in the chapter excerpt below.

Chapter 7

When climate change shifts climates over a landscape (dashed to solid circle) the response of a species to that change can be described in one of three ways: dispersing to the new range, the occupying intersection of the circles, or the union of the circles. Depending on dispersal characteristics, there can be either no change in extinctions, increase (intersection), or decrease (union) depending on the assumptions made about the nature of dispersal.

The error model uses a small number of parameters: width, shift and proportions. Each of these parameters have error terms. The error terms in the geometric model represent sources of error such as:

1. Width error: Model overfitting
2. Shift error: Differential response of species to climate change
3. Proportional error: Truncation of range due to map boundaries