  Under models of isolation-by-distance, population structure is determined by
the probability of identity-by-descent between pairs of genes according to the
geographic distance between them. Well established analytical results indicate
that the relationship between geographical and genetic distance depends mostly
on the neighborhood size of the population, $N_b = 4{\pi}{\sigma}^2 D_e$, which
represents a standardized measure of dispersal. To test this prediction, we
model local dispersal of haploid individuals on a two-dimensional torus using
four dispersal kernels: Rayleigh, exponential, half-normal and triangular. When
neighborhood size is held constant, the distributions produce similar patterns
of isolation-by-distance, confirming predictions. Considering this, we propose
that the triangular distribution is the appropriate null distribution for
isolation-by-distance studies. Under the triangular distribution, dispersal is
uniform within an area of $4{\pi}{\sigma}^2$ (i.e. the neighborhood area),
which suggests that the common description of neighborhood size as a measure of
a local panmictic population is valid for popular families of dispersal
distributions. We further show how to draw from the triangular distribution
efficiently and argue that it should be utilized in other studies in which
computational efficiency is important
