Fig. 1: An example showing how centroid distance (cd) and mean distance (md) are computed. | Nature Communications

Fig. 1: An example showing how centroid distance (cd) and mean distance (md) are computed.

From: Species invasiveness and community invasibility of North American freshwater fish fauna revealed via trait-based analysis

Fig. 1: An example showing how centroid distance (cd) and mean distance (md) are computed.The alternative text for this image may have been generated using AI.

The p and q individual native and non-native fish species in a n-dimensional trait space (here n = 2) are represented by blue and red circles. Vector Yj represents the position of non-native species j and vector Xj is the position of its nearest native species. dj is the distance between Xj and Yj. md is the mean distance between all non-native species and their nearest native neighbors. CX and CY (triangles) are the centroids of the p native species and q non-native species, with [CXi] and [CYi] representing the coordinates of the centroids according to all traits, i.e., [CX1, CX2,…, CXn], [CY1, CY2,…, CYn]. Here, CX = [CXi] and CY = [CYi], where CXi and CYi are the mean value of trait i for native and non-native species. cd is the distance between the centroids for native (CX) and non-native (CY) species.

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