We have a draft/working system in place where we can scale queen and individual worker variances. We are seeing some discrepancies though and one reason for that is that we assume certain types of relatedness between workers in a colony and between colonies, however these are expected relatedness coefficients, which will vary due to the random recombination and segregation, but also due to background / past IBS relatedness.
However, since we are in a simulation we know the QTL genotypes, so we could easily use these to further fine-scale these variances.
The idea is that with a workersFUN of sum we have a_{w_s,t} = sum(a_{w,t}) and we assumed that Var(a_{w_s,t}) = n_w * Var(a_{w,t}) + covariances and expected relatedness kicks in covariances but these are expected and the first term and covariances are off due to background / past IBS relatedness.
We can extend by denoting a_{w_i,t} = x_{w_i} \alpha_t and similarly for all workers with a full matrix of QTL genotypes X_{w}. Then we are trying to look at the overall variance of Var(a_{w_s,t}). Since we know that Var(a_{w_s,t}) = Var(sum(a_{w_i,t})) = Var(sum(X_{w_i} \alpha_t)) and we actually have both X_{w_i} and \alpha_t then Var(a_{w_s,t} | X_{w_i}, \alpha_t) = Var(sum(X_{w_i} \alpha_t) | X_{w_i}, \alpha_t) = \alpha_t^T 1^t X_{w_i} X_{w_i}^T 1 \alpha_t, which will be a scalar.
Hmm, is this just within the colony or across all of the colonies!? We can take the above logic and compute both within and between colony quantities. The goal is to get the right amount of between colony variance, so that is Var(a_c) where a_c is a vector of colony genetic values. TODO: work this out ... might need an example to work with ...
We have a draft/working system in place where we can scale queen and individual worker variances. We are seeing some discrepancies though and one reason for that is that we assume certain types of relatedness between workers in a colony and between colonies, however these are expected relatedness coefficients, which will vary due to the random recombination and segregation, but also due to background / past IBS relatedness.
However, since we are in a simulation we know the QTL genotypes, so we could easily use these to further fine-scale these variances.
The idea is that with a
workersFUNofsumwe havea_{w_s,t} = sum(a_{w,t})and we assumed thatVar(a_{w_s,t}) = n_w * Var(a_{w,t}) + covariancesand expected relatedness kicks incovariancesbut these are expected and the first term and covariances are off due to background / past IBS relatedness.We can extend by denoting
a_{w_i,t} = x_{w_i} \alpha_tand similarly for all workers with a full matrix of QTL genotypesX_{w}. Then we are trying to look at the overall variance ofVar(a_{w_s,t}). Since we know thatVar(a_{w_s,t}) = Var(sum(a_{w_i,t})) = Var(sum(X_{w_i} \alpha_t))and we actually have bothX_{w_i}and\alpha_tthenVar(a_{w_s,t} | X_{w_i}, \alpha_t) = Var(sum(X_{w_i} \alpha_t) | X_{w_i}, \alpha_t) = \alpha_t^T 1^t X_{w_i} X_{w_i}^T 1 \alpha_t, which will be a scalar.Hmm, is this just within the colony or across all of the colonies!? We can take the above logic and compute both within and between colony quantities. The goal is to get the right amount of between colony variance, so that is
Var(a_c)wherea_cis a vector of colony genetic values. TODO: work this out ... might need an example to work with ...