## 1.1 What is Participatory Plant Bredding ?

### 1.1.1 Decentralize the selection

The following development is adapted from Rex (2002) and Gallais (1990).

When considering multiple environments for evaluation and selection, the phenotypic value of a trait of any individual in a given environment can be written as the sum of its random genetic effect (or overall genetic potential, $$G$$ ), the random environmental effect ($$E$$) and the random interaction ($$G \times E$$), i.e. : $$P = G + E + G \times E + e$$ with $$e$$ the random residual effect within each environment following a normal distribution $$N(0, \sigma^2)$$.

In classical centralized breeding, the objective is to predict the overall genetic potential ($$G$$) of the candidates for selection to detect the highest values assuming that this potential would express in all farmers’ fields. These genetic potentials are predicted based on the average phenotypic values over all testing environments (usually experimental stations) and therefore the broad sense heritability for prediction is :

$$h^2_{sl} = \frac{var(G)}{var(G) + \frac{1}{nE} (var(E) + var(G \times E)) + \frac{1}{nEnR} (var(e))}$$

with $$nE$$ (resp. $$nR$$) the number of environments (resp. the number of replicates in each environment). As environmental effect and $$G \times E$$ interactions limit prediction accuracy, the option is to increase the number of environments and to use environments that are homogeneous and similar and that minimize $$G \times E$$ interactions.

On the contrary, in decentralized on farm breeding, it has been shown that the environments are very contrasted due to diverse pedo-climatic conditions associated to various agroecological farming practices, and that $$G \times E$$ interactions can be strong (Desclaux et al. 2008). Therefore, the prediction of the overall genotypic value ($$G$$) is not interesting and the objective is rather to predict the «local» genetic value of genotype $$i$$ in environment $$j$$, $$Gloc_{ij}$$ which also includes the interaction with the local environment, i.e.: $$Gloc_{ij} = G_i + (G \times E)_{ij}$$

Then, the genetic variance in each local environment can be written as: $$var(Gloc) = var(G) + var(G \times E)$$ and the heritability to predict the local genetic values based on the phenotypic values observed in the local environments is:

$$h^2_{sl} = \frac{var(Gloc)}{var(Gloc) + \frac{1}{nR} var(e)} = \frac{var(G) + var(G \times E)}{var(G) + var(G \times E) + \frac{1}{nR} var(e)}$$

It can be noted that the $$G \times E$$ interactions contributes to both denominator and numerator therefore leading to no limiting effect on prediction accuracy. Hence, when facing a wide diversity of agroecological environment and practices, decentralized breeding is a key point to select adapted varieties to local agro-systems.

### 1.1.2 Involve all actors in the breeding decision process

All actors are part of the breeding programme : farmers, technicians, researchers, facilitators, consumers … Such involvements empower all actors and may better answer the real needs of actors (Sperling et al. 2001).

### References

Desclaux, D., J. M. Nolot, Y. Chiffoleau, C. Leclerc, and E. Gozé. 2008. “Changes in the Concept of Genotype X Environment Interactions to Fit Agriculture Diversification and Decentralized Participatory Plant Breeding: Pluridisciplinary Point of View.” Euphytica 163: 533–46.

Gallais, A. 1990. Théorie de la sélection en amélioration des plantes. Masson. Sciences Agronomiques.

Rex, B. 2002. Breeding for quantitative traits in plants. Stemma Press, Woodbury, Minnesota.

Sperling, L., J.A. Ashby, M.E. Smith, E. Weltzien, and S. McGuire. 2001. “A Framework for Analyzing Participatory Plant Breeding Approaches and Results.” Euphytica 122 (3): 439–50.