Calculates a kinship matrix using the Malecot Migration Model

Description

Calculates a kinship matrix using the Malecot Migration Model, in the form described by L. B. Jorde 1982.

Usage

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mal.phi(S, P, N, n)

Arguments

S

the sistematic pressure matrix, where the diagonal elements are 1-sk, with sk the sistematic pressure for the k-th population, and the non diagonal elements are 0

P

the column stochastic migration matrix, possibly obtained using col.sto on the "raw" migration matrix

N

the vector of effective populations, where each element is the population size for all the n populations divided by 3

n

the number of iterations needed to reach the equilibrium, calculated by the function Mal.eq

Details

The Malecot model is simply an iterative markow-chain-like process that gives rise to an asymptotic growth curve, so that an equilibrium is reached after a number of iterations.

Value

Returns a square and symmetrical matrix.

Note

...

Author(s)

Federico C. F. Calboli federico.calboli@helsinki.fi

References

Imaizumi, Y., N. E. Morton and D. E. Harris. 1970. Isolation by distance in artificial populations. Genetics 66: 569-582.

Jorde, L. B. 1982. The genetic structure of the Utah mormons: migration analysis. Human Biology 54(3): 583-597.

See Also

mal.eq for the function generating the number of cycles needed to reach the asymptotic value

Examples

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# using Swedlund data again...
data(S); data(P); data(N)
x<-mal.eq(S,P,N)
phi<-mal.phi(S,P,N,x)
phi