October 2nd, 2020
The Biofortified Baseline
1. Introduction to the problem
Crop by region
IITA-Cassava Biorfortified
Problem specification
Currently, seventy (70) parents are used. Too few parents or too many parents may affect the rate of genetic gain over time.
Breeding strategy component tackled
Crossing, Evaluation, Selection
Breeders’ equation terms tackled
r, \(\sigma_g\), L
\(\Delta_g = (i * \sigma_g * r)/L\)
Hypothesis
Using the optimal number of parents, crosses and progeny will help sustain the rate of genetic gain over time.
2. Materials and methods
Treatments
| Treatment | Description |
|---|---|
| Optimal numbers | A grid of different nParents= c(12, 24, 48, 96), nCrosses = c(25, 50, 100, 200, 250, 500, 1000, 1250) [n(n-1)/2], nProgeny = c(1000, 500, 250, 125, 100, 50, 25, 20) thus restricting Total Number of F1 to 25,000; the current program size. Parents recycled from PYT and AYT (mixed crossing block). |
| Optimal recycle strategy | From the grid above, largest nCrosses possible per nParents ([n(n-1)/2]) to compare recycling new parents at PYT, AYT and PYT+AYT. The nProgeny is determined by nF1/nCrosses (nF1 = 25,000). |
| Optimal F1 size | From the results above, we selected the optimal nParents and its largest possible nCrosses ([n(n-1)/2]) to study the effect of the size of F1 by reducing the current baseline (100%) to 80%, 60%, 40% and 20% by reducing nProgeny per Cross. |
Simulation procedure
A 20 year burn-in period was modeled using the baseline. The burn-in was followed by a 60 years period of breeding to measure rates of genetic gain for all treatments. Genetic gain was measured by assessing changes in genetic merit at F1 and is presented relative to the mean at F1. Genotype-by-year interaction variance was assumed to be equivalent to genetic variance (based on average correlation between locations being equal to 0.5). 40 replications done.
3.0 What we know already about IP = cycle length
The current recycling strategy (parents from PYT-UYT), could be changed to recyling 50% parents at PYT and 50% parents at AYT to provide a balance between speed an accuracy.
3.1 Best recycling strategy given the grid
Comparing the best crossing block composition at year 20, year 40, year 60
In all scenarios, the mixed crossing block is the best. For the mixed crossing block, a plateau forms at 24 parents. (15-30)
3.2 Optimal nParents and nCrosses
Comparing optimal numbers at year 20, year 40 and year 60 
The higher the number of parents, the lower the genetic gain. The optimal nCrosses for nParents = 24 for this pipeline is 250.
3.3 Optimal size of F1
Comparing 100%, 80%, 60%, 40% and 20% of the current F1 size. nParents = 24, nCrosses = 250, nProgeny= c(100, 80, 60, 40, 20) 
Compared to the current baseline, reducing the F1 size by upto 80% only had about 6% reduction in genetic gain
4. Conclusion
Data suggest an optimal nParents = 24 if looking to up to 60 years. In line with nParents = 15-30, previously recommended.
Optimal recycling strategy is 50% PYT and 50% AYT
Reducing the F1 size by up to 80% did not affect the rate of genetic gain much.
We recommend a reduction of the current nParents of 70 to between 20-30. Additionally we recommend that for population improvement, for the program to keep a smaller F1 size than the current.