### Abstract

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 which represents a standardized measure of gene flow. To test this prediction, we model local dispersal of haploid individuals on a two-dimensional landscape using seven dispersal kernels: Rayleigh, exponential, half-normal, triangular, gamma, Lomax and Pareto. 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 over the neighborhood area which suggests that the common description of neighborhood size as a measure of an effective, local panmictic population is valid for popular families of dispersal distributions. We further show how to draw random variables from the triangular distribution efficiently and argue that it should be utilized in other studies in which computational efficiency is important.

Original language | English (US) |
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Article number | 1848 |

Journal | PeerJ |

Volume | 2016 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2016 |

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### Keywords

- Correlograms
- Fine scale
- Identity-by-descent
- Individual based
- Kinship coefficients
- Neighborhood size
- Simulation
- Triangular distribution

### ASJC Scopus subject areas

- Neuroscience(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Agricultural and Biological Sciences(all)

### Cite this

*PeerJ*,

*2016*(3), [1848]. https://doi.org/10.7717/peerj.1848