Abstract
We introduce a spatially explicit model for the competition between type a and type b alleles. Each vertex of the d-dimensional integer lattice is occupied by a diploid individual, which is in one of three possible states or genotypes: aa, ab or bb. We are interested in the long-term behavior of the gene frequencies when Mendel's law of segregation does not hold. This results in a voter type model depending on four parameters; each of these parameters measures the strength of competition between genes during meiosis. We prove that with or without a spatial structure, type a and type b alleles coexist at equilibrium when homozygotes are poor competitors. The inclusion of a spatial structure, however, reduces the parameter region where coexistence occurs.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1880-1920 |
| Number of pages | 41 |
| Journal | Annals of Applied Probability |
| Volume | 19 |
| Issue number | 5 |
| DOIs | |
| State | Published - Oct 2009 |
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Keywords
- Annihilating branching process
- Non-Mendelian segregation
- Voter model
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
Spatially explicit non-mendelian diploid model. / Lanchier, Nicolas; Neuhauser, C.
In: Annals of Applied Probability, Vol. 19, No. 5, 10.2009, p. 1880-1920.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Spatially explicit non-mendelian diploid model
AU - Lanchier, Nicolas
AU - Neuhauser, C.
PY - 2009/10
Y1 - 2009/10
N2 - We introduce a spatially explicit model for the competition between type a and type b alleles. Each vertex of the d-dimensional integer lattice is occupied by a diploid individual, which is in one of three possible states or genotypes: aa, ab or bb. We are interested in the long-term behavior of the gene frequencies when Mendel's law of segregation does not hold. This results in a voter type model depending on four parameters; each of these parameters measures the strength of competition between genes during meiosis. We prove that with or without a spatial structure, type a and type b alleles coexist at equilibrium when homozygotes are poor competitors. The inclusion of a spatial structure, however, reduces the parameter region where coexistence occurs.
AB - We introduce a spatially explicit model for the competition between type a and type b alleles. Each vertex of the d-dimensional integer lattice is occupied by a diploid individual, which is in one of three possible states or genotypes: aa, ab or bb. We are interested in the long-term behavior of the gene frequencies when Mendel's law of segregation does not hold. This results in a voter type model depending on four parameters; each of these parameters measures the strength of competition between genes during meiosis. We prove that with or without a spatial structure, type a and type b alleles coexist at equilibrium when homozygotes are poor competitors. The inclusion of a spatial structure, however, reduces the parameter region where coexistence occurs.
KW - Annihilating branching process
KW - Non-Mendelian segregation
KW - Voter model
UR - http://www.scopus.com/inward/record.url?scp=73949151249&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=73949151249&partnerID=8YFLogxK
U2 - 10.1214/09-AAP598
DO - 10.1214/09-AAP598
M3 - Article
AN - SCOPUS:73949151249
VL - 19
SP - 1880
EP - 1920
JO - Annals of Applied Probability
JF - Annals of Applied Probability
SN - 1050-5164
IS - 5
ER -