Data from: Using semidefinite programming to optimize unequal deployment of genotypes to a clonal seed orchard

Tree breeders must often consider the conservation of genetic diversity,
while at the same time, maximizing response to selection. In the case of
seed orchards, the buyer of seed wants maximum performance, while
satisfying a restriction, sometimes legislated, on the diversity deployed
to the forest. Optimal selection will not completely avoid kinship but
rather maximize gain while imposing a constraint on average relatedness.
Here, we present the application of semidefinite programming (SDP) as a
flexible approach to optimize the deployment of genotypes to a clonal seed
orchard. We formulate the selection problem as an SDP, where average
breeding value is to be maximized, while imposing constraints on
relatedness, as well as maximum and minimum contributions from each
candidate. An open-source solver, SDPA, was embedded into a tool designed
to make the optimization of seed orchards by SDP simple and flexible. Case
studies optimizing seed orchards for Scots pine and loblolly pine
illustrate how this flexibility can be used to impose additional
constraints on the scion material available from some candidate genotypes
and optimize selection even when related candidates have varying degrees
of coancestry among them. Additional situations where SDP can be employed
are discussed.