Mapping Averaged Pairwise Information (MAPI): a new exploratory tool to uncover spatial structure

Abstract

Visualisation of spatial networks based on pairwise metrics such as (dis)similarity coefficients provides direct information on spatial organisation of biological systems. However, for large networks, graphical representations are often unreadable as nodes (samples), and edges (links between samples) strongly overlap. We present a new method, MAPI, allowing translation from spatial networks to variation surfaces. MAPI relies on (i) a spatial network in which samples are linked by ellipses and (ii) a grid of hexagonal cells encompassing the study area. Pairwise metric values are attributed to ellipses and averaged within the cells they intersect. The resulting surface of variation can be displayed as a colour map in Geographical Information System (GIS), along with other relevant layers, such as land cover. The method also allows the identification of significant discontinuities in grid cell values through a nonparametric randomisation procedure. The interest of MAPI is here demonstrated in the field of spatial and landscape genetics. Using simulated test data sets, as well as observed data from three biological models, we show that MAPI is (i) relatively insensitive to confounding effects resulting from isolation by distance (i.e. over-structuring), (ii) efficient in detecting barriers when they are not too permeable to gene flow and, (iii) useful to explore relationships between spatial genetic patterns and landscape features. MAPI is freely provided as a PostgreSQL/PostGIS data base extension allowing easy interaction with GIS or the r software and other programming languages. Although developed for spatial and landscape genetics, the method can also be useful to visualise spatial organisation from other kinds of data from which pairwise metrics can be computed.