Assessing the response to genomic selection by simulation

Abstract

We propose a simulation approach to compute response to genomic selection on a multi-environment framework to provide breeders the number of entries that need to be selected from the population to have a defined probability of selecting the truly best entry from the population and the probability of obtaining the truly best entries when some top-ranked entries are selected. The goal of any plant breeding program is to maximize genetic gain for traits of interest. In classical quantitative genetics, the genetic gain can be obtained from what is known as "Breeder's equation". In the past, only phenotypic data were used to compute the genetic gain. The advent of genomic prediction (GP) has opened the door to the utilization of dense markers for estimating genomic breeding values or GBV. The salient feature of GP is the possibility to carry out genomic selection with the assistance of the kinship matrix, hence improving the prediction accuracy and accelerating the breeding cycle. However, estimates of GBV as such do not provide the full information on the number of entries to be selected as in the classical response to selection. In this paper, we use simulation, based on a fitted mixed model for GP in a multi-environmental framework, to answer two typical questions of a plant breeder: (1) How many entries need to be selected to have a defined probability of selecting the truly best entry from the population; (2) what is the probability of obtaining the truly best entries when some top-ranked entries are selected.

Fig. 1

The structure of selection cycles in the rye hybrid breeding program. The number of entries decreases due to selection in each GCA trial. In each cycle, inbred lines are crossed with two testers of the opposite gene pool

Fig. 2

Illustration of datasets used for the CYC and MY analyses. In CYC, the GCA1, GCA2, and GCA3 datasets from all cycles are combined. In MY, the dataset comprises the GCA1 data of the years 2016 to 2019

Fig. 3

Illustration of the selected entries for the GCA2 assessment. The transparent red cylinders illustrate the selected common entries in GCA1 and GCA2

Fig. 4

Plots of the probability of obtaining the m truly best entries based on the GBLUPs for each selected number of entries (expressed as percentage of N) from GCA1 assessment of each pool. The different coloured entries indicate the different numbers (m) of truly best entries

Fig. 5

Plots of the probability of obtaining the $m$ truly best entries based on the GBLUPs for each selected number of entries (expressed as percentage of N) of each cycle in the GCA2 assessment for each pool. The different coloured entries indicate the different numbers (m) of truly best entries. In general, the pollen pool has higher probability to obtain the truly best entries than the seed pool. In Cycle 4, both pools have a relatively lower probability to obtain the truly best entries compared to the other cycles