Computational geometry applied to develop new metrics of road and edge effects and their performance to understand the distribution of small mammals in an Atlantic forest landscape

Roads negatively affect many vertebrate species, whereas edge effect may favor some generalist species. This study aims to: 1) present a new way to calculate "line integral effects", represented by LIE and AVLIE, through new computer software, making this concept accessible to a broad audience of researchers interested in the study of Road Ecology and Tropical Forest Ecology; and, 2) test the performance of LIE and AVLIE indices, applied to road effect (LIE_road and AVLIE_road) and to edge effect (LIE_edge and AVLIE_edge), other road effect indices and forest area, using a data set on small mammal abundance in a human modified landscape in the Brazilian Atlantic Forest. Road and edge effects were represented by new metrics: Line Integral Effect (LIE) and Average Integral Effect (AVLIE), calculated using Line Integral from Differential Calculus of Several Variables through new free software developed by the second author. LIE_road and LIE_edge measure the total sum of the effect of roads (represented by lines) and edges (polygons), respectively, in relation to the forest fragment (point). AVLIE_road and AVLIE_edge measure the average of road and edge effect, respectively, in relation to the same sampling point. We used generalized linear regression models to explore the relationships between the abundance of the two groups of small mammals (forest specialists and habitat generalists) and the independent variables representing road, edge and forest effects. For forest specialists, the best model included AVLIE_road (negatively associated with abundance) and AVLIE_edge (negatively associated), while for habitat generalists, the best model included AVLIE_road (negatively associated) and LIE_edge (positively associated). Thus, there are more small mammals where road effect is lower. Forest fragments with higher edge effect showed more habitat generalists and less forest specialists. LIE and AVLIE could be useful metrics to explore edge effect separately to road effect on wildlife in forest fragments.