# Presentation of "Incorporation of Competitive Effects in Forest Tree or Animal Breeding Programs" by Muir in Genetics (2005)

Timothée Flutre

► To cite this version:

Timothée Flutre. Presentation of "Incorporation of Competitive Effects in Forest Tree or Animal Breeding Programs" by Muir in Genetics (2005). Doctoral. Journal club of WP4 in the MoBiDiv project, France. 2023, pp.41. hal-04099164

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Submitted on 16 May 2023

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Distributed under a Creative Commons Attribution 4.0 International License
"Incorporation of Competitive Effects in Forest Tree or Animal Breeding Programs"
Muir, Genetics (2005)

Timothée Flutre

16/05/2023
# Outline

## Introduction

## Theory

## Experimental validation

## Discussion
## Introduction

- Theory

- Experimental validation

- Discussion
IGEs not used in breeding

* the impacts of the genes of one individual on the performance of other individuals are generally ignored

* relative efficiency of BLUP-based selection index compared to mass selection: theoretical advantages not confirmed, or even worse, possibly because competition is ignored
Case of animals: breeding vs housing

► limit or ban suffering or injury to animals in breeding

► change management practices or update selection schemes
# Objectives

* examine and compare alternative methods of incorporating competitive interactions in plant and animal breeding programs

* theory, simulations, and a biological experimentation
# Outline

## Introduction

## Theory

Experimental validation

## Discussion
Group of *n* unrelated individuals:

$$ 
\begin{aligned}
P_i &= P_{D,i} + \sum_{j \neq i}^{n-1} P_{S,j} \\
&= A_{D,i} + E_{D,i} + \sum_{j \neq i}^{n-1} (A_{S,j} + E_{S,j})
\end{aligned}
$$

* Pᵢ: observed phenotypic value of individual *i*

* A<sub>D,i</sub>: heritable direct effect (breeding value) of *i*

* E<sub>D,i</sub>: nonheritable direct effect of *i*

* A<sub>S,j</sub>: heritable social/indirect effect (breeding value) of *j*

* E<sub>S,j</sub>: nonheritable indirect effect of *j*
Expected change in the mean from selection on individual records:

$$ \Delta\mu = \frac{\bar{I}}{\sigma_P} (\sigma_{A_D}^2 + (n-1)\sigma_{A_{DS}}) $$

where $\bar{I}$ is the standardized selection differential (selection intensity)

Competition for a limited resource:

* $\sigma_{A,DS} < 0$

* positive selection can reduce rather than increase the mean
Expected change in the mean from selection on groups:

$$ \Delta\mu = \frac{1}{n} \frac{\bar{I}_{gr}}{\sigma_{\bar{P}_{gr}}} (\sigma_{A_D}^2 + 2(n-1)\sigma_{A_{DS}} + (n-1)^2\sigma_{A_S}^2) $$

► always positive
About group selection

the term group selection is used henceforth to refer to
selection among groups, with the group as the unit of
selection

Concretely, each group is selected based on its mean:

$$
\bar{P}_{gr} = \frac{1}{n} \sum_{i=1}^{n} P_i
$$
More theory and experiments

* exp.: Wade on randomly formed groups

* exp.: Goodnight comparing individual vs group selection

* theory: Griffing: group selection becomes more efficient as the average relationship within groups increases

* exp.: Muir, Craig and Muir
Needed improvements

Group selection is based entirely on between-group variation and ignores within-group variation. The optimal index would separate the direct and associative effects and weight each according to the variance-covariance structure of the genetic parameters.
Competition by distance (trees)

<figure><img src="image_2.png" /></figure>

Influence of tree *i* on *j*: $c_{i \to j} \propto \left(\frac{1}{d_{ij}}\right)^2 a_{p,i}$

► phenotypic associative effect of tree *i*: $p,i = a_{g,i} + a_{e,i}$
Competition within a pen (animals)

Assume all animals interact equally:

* same as above with distance set to 1 within a pen and zero between pens
$$ \mathbf{y} = X\beta + Z_D\mathbf{d}_g + Z_A\mathbf{a}_g + Z_A\mathbf{a}_e + \epsilon $$

$$ V \begin{bmatrix} \mathbf{D} \\ \mathbf{A}^g \\ \mathbf{A}^e \\ \varepsilon \end{bmatrix} = \begin{bmatrix} \mathbf{G}\sigma_D^2 & \mathbf{G}\sigma_{A^g,D} & 0 & 0 \\ \mathbf{G}\sigma_{A^g,D} & \mathbf{G}\sigma_{A^g}^2 & 0 & 0 \\ 0 & 0 & \mathbf{I}\sigma_{A^e}^2 & 0 \\ 0 & 0 & 0 & \mathbf{I}\sigma_e^2 \end{bmatrix}. $$

ReML algorithm to estimate the parameters and mixed-model equations to compute the BLUPs
Optimal index

$$I_i = eBLUP(d_{g,i}) + (n-1) eBLUP(a_{g,i})$$
Relative efficiency of group vs index-based selection

Simulations with 512 individuals in 32 groups of size 16.

Four methods:

1. (K) group selection with groups composed of full sibs

2. (R) group selection with groups composed of random individuals

3. (D) individual selection using a model with only direct effects

4. (C) individual selection with a model with associative genetic effects
Relative efficiency of group vs index-based selection

<table><thead><tr><th>Magnitude of<br>associative<br>effects</th><th>Method <sup>a</sup></th><th>Response<br>per<br>generation</th><th>SE</th><th>Relative<br>efficiency<sup>b</sup></th></tr></thead><tbody><tr><td rowspan="4">Large<sup>c</sup></td><td>C</td><td>0.721</td><td>0.021</td><td>3.03</td></tr><tr><td>D</td><td>-0.229</td><td>0.004</td><td>-0.96</td></tr><tr><td>K</td><td>0.509</td><td>0.011</td><td>2.13</td></tr><tr><td>R</td><td>0.238</td><td>0.002</td><td>1.00</td></tr><tr><td rowspan="4">Small<sup>d</sup></td><td>C</td><td>0.098</td><td>0.002</td><td>3.69</td></tr><tr><td>D</td><td>0.054</td><td>0.001</td><td>2.00</td></tr><tr><td>K</td><td>0.078</td><td>0.002</td><td>2.88</td></tr><tr><td>R</td><td>0.027</td><td>0.001</td><td>1.00</td></tr></tbody></table>

<sup>a</sup> C, competitive effects BLUP, two random effects model; D, animal model with direct effects only; K, group selection composed of kin; R, group selection composed of random individuals.

<sup>b</sup> Relative to R.

$$c \sigma_D^2 = 69, \sigma_{A^c,D} = -30, \sigma_{A^c}^2 = 45.5, \sigma_e^2 = 69.$$

$$d \sigma_D^2 = 68, \sigma_{A^d,D} = -5, \sigma_{A^d}^2 = 1.3, \sigma_e^2 = 68.$$
Relative efficiency of group vs index-based selection

► $\rho_{D,A} = -0.54$

► $\sigma_D^2/(\sigma_D^2 + \sigma_A^2 + \sigma_\epsilon^2) = 0.38$

► $(\sigma_D^2 + \sigma_A^2)/(\sigma_D^2 + \sigma_A^2 + \sigma_\epsilon^2) = 0.62$

<figure><img src="image_3.png" /></figure>
Relative efficiency of group vs index-based selection

► $\rho_{D,A} = -0.53$

► $\sigma_D^2/(\sigma_D^2 + \sigma_A^2 + \sigma_\epsilon^2) = 0.495$

► $(\sigma_D^2 + \sigma_A^2)/(\sigma_D^2 + \sigma_A^2 + \sigma_\epsilon^2) = 0.505$

<figure><img src="image_4.png" /></figure>
Relative efficiency of group vs index-based selection

► individual selection with DGEs and IGEs (C) always best

► 2nd best is group selection composed of full-sibs (K)

► group selection in random groups (R) always positive but inefficient when $\sigma_{A_g}^2$ small

► individual selection with only DGEs (D) always sub-optimal and even detrimental when $\sigma_{A_g}^2$ high
Impact of group size

Simulations with groups of size 16 versus 4 (for the same progeny size: 256).

Correlations between estimated and true genetic effects.

► both direct and associative effects were estimated more precisely in small groups than in large, but the difference was small
# Outline

## Introduction

## Theory

## Experimental validation

## Discussion
Japanese quail:

* short generation time (6 weeks)

* can be individually tagged (pedigree)

* very aggressive and cannibalistic (IGE)
Experimental design

► 3 rooms: 1 for brooding and 2 for growing and breeding

► each room has 6 rows

► each row has 12 cages (61x61cm)
Competition for resources

Restrict access to food:

► 15.2 cm per cage

► once a day

⇒ 240 g / day

► adequate to meet all nutritional requirements provided the
birds did not waste feed

► in some cages, some birds dominating the social order
restricted access to the feeder
G1: choice of the optimal density

<figure><img src="image_5.png" /><figcaption>FIGURE 6.—Mean body weight at 42 days by group (pen) size.</figcaption></figure>

Choice of 16 birds.
G1: choice of the optimal density

<figure><img src="image_6.png" /><figcaption>FIGURE 7.—Mean percentage of mortality by group size.</figcaption></figure>

Choice of 16 birds.
The next two generations were devoted to parameter estimation. In each of two rooms, 24 sires were each mated to two dams at random. Females were placed in individual mating cages and a male was placed with each female and was rotated between the two females twice a week. Eggs were marked and collected for 2 weeks and kept in a cooler. After 2 weeks, they were incubated as a group. Upon hatching chicks within a sire family were toe clipped, left or right, to distinguish the dam families, moved to the brooding room, and caged by sire half-sib family. At 2 weeks of age the chicks were wing banded and randomly allocated to grow-out cages, 16 per cage, and up to 12 cages, depending on numbers hatched. If not enough birds were available to fill an additional cage, those extra birds were discarded. At 6 weeks of age, the birds were sexed and weights were recorded. This process was replicated three times. As birds reached 12 weeks of age, random males and fe- males were selected to replace the breeders and data for the second generation were collected.
$$ 
\begin{bmatrix} \hat{\boldsymbol{\sigma}}_{D}^{2} & \hat{\boldsymbol{\sigma}}_{Ag,D} \\ \hat{\boldsymbol{\sigma}}_{Ag,D} & \hat{\boldsymbol{\sigma}}_{Ag}^{2} \end{bmatrix} = \begin{bmatrix} 33.7 & -5.5 \\ -5.5 & 2.87 \end{bmatrix} \\ 
\hat{\boldsymbol{\sigma}}_{\epsilon}^{2} = 124.5.
$$

$$ \text{▶ } \rho_{D,A} = -0.56 $$

$$ \text{▶ } \sigma_D^2/(\sigma_D^2 + \sigma_A^2 + \sigma_\epsilon^2) = 0.21 $$

$$ \text{▶ } (\sigma_D^2 + \sigma_A^2)/(\sigma_D^2 + \sigma_A^2 + \sigma_\epsilon^2) = 0.23 $$
Selection scheme for weight

to large and negative (−0.56). Using these estimates of
the genetics parameters, and starting with the adults of
the second generation, birds in each room were selected
on the basis of solutions from a model that included an
index with either direct and associative effects (C-BLUP)
or only direct effects (D-BLUP). Within a selection
method, sires and dams were kept for breeding until
replaced with an animal with a higher breeding value.
Selected birds were kept in holding cages for another
4 weeks to become fully sexual mature, i.e., 10 weeks of
age, before being used as replacements. Mating was
therefore with overlapping generations. Matings be-
tween full- and half-sibs were avoided. The experiment
was continued for 23 hatches, approximately six genera-
tions.
At the termination of the experiment, feed efficiency was measured with the feed restrictors removed. At 2 weeks of age, 60 birds from each line were randomly chosen, weighed, and placed in five cages (12 per cage). Feed was weighed into each trough and birds were allowed to feed continuously. Feed was replaced when the feeders were almost empty. At 6 weeks of age, food was removed 24 hr prior to the birds being weighed. The entire experiment was replicated three times.
Change in weight along hatches per scheme

<figure><img src="image_7.png" /></figure>
Change in DGEs along hatches per scheme

<figure><img src="image_8.png" /></figure>
Change in IGEs along hatches per scheme

<figure><img src="image_9.png" /></figure>
Change in mortality per scheme

Mortality was highly variable and the regression of per-
centage of mortality on hatch number showed a slight
reduction in mortality with C-BLUP ($b = -0.06 \pm 0.15$
deaths/hatch) while mortality increased with D-BLUP
($b = 0.32 \pm 0.15$ deaths/hatch). The difference between
regression coefficients was tested by the interaction of
method by hatch and was found to be significant ($P <
0.05$). These results are consistent with the above find-
ings that the associative effects were made worse with
selection using D-BLUP and better with selection on
the index from C-BLUP.
Final efficiency

<figure><img src="image_10.png" /></figure>

6.65g of food to get 1g (?) of weight: the lower, the better
# Outline

## Introduction

## Theory

## Experimental validation

## Discussion
► even if variation due to associative effects is small relative to the environmental variance, the impact of associative effects on group performance can be dramatic, particularly if group size is large

► with D-BLUP feed conversion efficiency can be improved only if feed efficiency is included in the selection program

► because of the biology of most traits, it is difficult to envision a situation in which the genetic correlation between direct and associative effects would be positive

► cases of complementarity, altruism?
Among many others:

* Bijma P, Muir WM, Van Arendonk JAM. 2006. Multilevel Selection 1: Quantitative Genetics of Inheritance and Response to Selection. Genetics. 175(1):277-288. doi:10.1534/genetics.106.062711.

* Ellen ED, Muir WM, Teuscher F, Bijma P. 2007. Genetic Improvement of Traits Affected by Interactions Among Individuals: Sib Selection Schemes. Genetics. 176(1):489-499. doi:10.1534/genetics.106.069542.