One-dimensional stepping stone models, sardine genetics and Brownian local time
Publication
, Journal Article
Durrett, R; Restrepo, M
Published in: Annals of Applied Probability
February 1, 2008
Consider a one-dimensional stepping stone model with colonies of size M and per-generation migration probability v, or a voter model on ℤ in which interactions occur over a distance of order K. Sample one individual at the origin and one at L. We show that if Mv/L and L/K2 converge to positive finite limits, then the genealogy of the sample converges to a pair of Brownian motions that coalesce after the local time of their difference exceeds an independent exponentially distributed random variable. The computation of the distribution of the coalescence time leads to a one-dimensional parabolic differential equation with an interesting boundary condition at 0. © Institute of Mathematical Statistics, 2008.
Duke Scholars
Published In
Annals of Applied Probability
DOI
EISSN
1050-5164
ISSN
1050-5164
Publication Date
February 1, 2008
Volume
18
Issue
1
Start / End Page
334 / 358
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 4901 Applied mathematics
- 0104 Statistics
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Durrett, R., & Restrepo, M. (2008). One-dimensional stepping stone models, sardine genetics and Brownian local time. Annals of Applied Probability, 18(1), 334–358. https://doi.org/10.1214/07-AAP451
Durrett, R., and M. Restrepo. “One-dimensional stepping stone models, sardine genetics and Brownian local time.” Annals of Applied Probability 18, no. 1 (February 1, 2008): 334–58. https://doi.org/10.1214/07-AAP451.
Durrett R, Restrepo M. One-dimensional stepping stone models, sardine genetics and Brownian local time. Annals of Applied Probability. 2008 Feb 1;18(1):334–58.
Durrett, R., and M. Restrepo. “One-dimensional stepping stone models, sardine genetics and Brownian local time.” Annals of Applied Probability, vol. 18, no. 1, Feb. 2008, pp. 334–58. Scopus, doi:10.1214/07-AAP451.
Durrett R, Restrepo M. One-dimensional stepping stone models, sardine genetics and Brownian local time. Annals of Applied Probability. 2008 Feb 1;18(1):334–358.
Published In
Annals of Applied Probability
DOI
EISSN
1050-5164
ISSN
1050-5164
Publication Date
February 1, 2008
Volume
18
Issue
1
Start / End Page
334 / 358
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 4901 Applied mathematics
- 0104 Statistics
- 0102 Applied Mathematics