Mapping between number of female children and number of female adults

[davidrpugh]

@markeschaffer

I need to get the number of female adults of each genotype and then normalize to get the population shares for the plots. Our system of recurrent relations currently tracks male adults and female children. How do I convert between number of female children and number of female adults?

I think the share of adult females of a given genotype in period t+1 must equal the share of female children from period t. Thus perhaps I just need to normalize the number of female children of each genotype in period t by the total number of female children in period t. These share will then be the adult shares for females in period t+1.

Thoughts?

[markeschaffer]

David,

“I think the share of adult females of a given genotype in period t+1 must equal the share of female children from period t.”

Not so, or at least not quite. The reason is that not all female children from period t survive to be adults at time t+1, because of differential matching.

Options are to calculate the numbers of selected female children from period t (=those selected to be adult females/wives at t+1), and to switch to tracking genotypes of adult males (almost the same thing).

[davidrpugh]

@markeschaffer

OK, I think I understand why the population shares of female and adult children need not match up. Not sure I understand how to calculate the number of selected female children from period t. Intuitively, I suppose that one would multiply the number of female children of a given genotype by the relevant screening and signaling probabilities?

Example: denote by fGA the number of female children with genotype GA in period t. Then the number of selected female children with genotype GA would be something like `eG * dA * fGA + (1 - eg) * (1 - dA) * fGA' (i.e., those female children with genotype GA that accurately signal A and are selected by the G males; plus the number of female children with genotype GA that mimic having the a allele and are incorrectly selected by g males).

Thoughts?

[markeschaffer]

Maybe the easiest way is to use the new formulation of the model and get it from the distribution of family types U_ijk(t+1)? Just add the number of families where female #1 is A (j=0,2) and the number of families where female #2 is A (k=0,2).

[davidrpugh]

@markeschaffer

Indeed. That is much easier. Thanks.

[davidrpugh]

@markeschaffer

I can now generate time series for the number of families in each of the 64 possible family configurations for the one male two female version of the model. I am a bit confused about aggregation. We want to total number of female adults carrying the A allele of the alpha gene.

I think this should be computed as follows...

 number adult females = (2 * number of familes where both females carrying A allele + 
                         number of families where only first female carrying A allele +
                         number of families where only second female carrying A allele)

...is this correct?

[markeschaffer]

Yes, that's right.

M

-------- Original message -------- Subject: Re: [population-ecology-approach] Mapping between number of female children and number of female adults (#37) From: "David R. Pugh" notifications@github.com To: davidrpugh/population-ecology-approach population-ecology-approach@noreply.github.com CC: "Schaffer, Mark" M.E.Schaffer@hw.ac.uk

@markeschafferhttps://github.com/markeschaffer

I can now generate time series for the number of families in each of the 64 possible family configurations for the one male two female version of the model. I am a bit confused about aggregation. We want to total number of female adults carrying the A allele of the alpha gene.

I think this should be computed as follows...

number adult females = (2 * number of familes where both females carrying A allele + number of families where only first female carrying A allele + number of families where only second female carrying A allele +

...is this correct?

— Reply to this email directly or view it on GitHubhttps://github.com/davidrpugh/population-ecology-approach/issues/37#issuecomment-60439483.

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[davidrpugh]

@markeschaffer

Great. Thanks. As soon as I can figure out how to group the data appropriately then we will be in business!

[davidrpugh]

@markeschaffer

Would it be equivalent to compute the number of female adults as...

 number adult females = (number of families where at least first female carries A allele +
                         number of families where at least second female carries A allele)

...I think that this will double count the number of families where both females carry the A allele (which is what we want).

[markeschaffer]

Yes, if you mean this:

number of adult F = (number of families where #1 female is A) + (number of families where #2 female is A).