Defining spatial overlap with marine traffic

A quantitative measure of risk associated to vessel traffic can be considered as a monotonic function of the number of vessels and the probability of encountering a whale^39,70. As described above, the relative amount of time allocated to each grid-cell can be obtained from 1/ν_i. Therefore, as a measure of risk we calculated the relative probability of vessel encountering whale (RPVEW)^39,69 by combining N_i, ν_i and VD_i as follows.

where Pwi=Ni∑i=1n(Ni) corresponds to the probability of observing a whale within each grid-cell i relative to all other grid cells n, Pti=1νi∑i=1n(1νi) corresponds to the time allocated to each grid-cell i relative to all other grid cells n, and Pvi=VDi∑i=1n(VDi) corresponds to the observed number of vessels within grid-cell i relative to all other grid cells n. fleets. Finally, to generate quantitative estimates on the degree of overlap between blue whale distribution and vessel traffic we used the Shoener's D and Warren's I similarity statistics⁷¹. These statistics range from 0, indicating no overlap, to 1, indicating distributions are identical. To use these statistics, the variables N_i times 1/ν_i and VD_i were rescaled to range between 0 and 1 and inputted to the nicheOverlap function from the R package dismo^72,73. A schematic representation of our workflow can be found as a Supplementary Figure ^S5 online.