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Indirect genetic effects between non-relatives

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Background

Traditional quantitative genetics is based on so-called direct genetic effects. That is, trait expression of a focal individual is determined only by its own genes. In the simplest case (ignoring genetic dominance, epigenetics etc.), the non-genetic effects on an individual’s trait expression are considered to be environmental. However, in potentially many situations, the environment of an individual includes conspecifics. An indirect genetic effect (IGE) occurs whenever the expression of a focal individual’s trait A is partly dependent on the extent to which the other individuals in its environment are expressing the trait A, or the extent by which they express another trait (trait B) that affects trait A in the focal individual. One can view such an indirect genetic effect as a situation in which the environment has genes.
A special case of an IGE is the maternal genetic effect, where the trait expression of the offspring is dependent on the mother’s genes. For example, mammalian offspring are often nurtured by their mothers during a substantial amount of time. If genes affect the capacity of females to care for their offspring, we may have an IGE of the mother on its offspring (e.g. on offspring growth). This IGE is separate from the offspring’s own (direct) genetic effect on its trait expression. Maternal genetic effects are a special case of IGE, because the focal individual (the offspring) is related to the other individual that has an IGE on its trait expression. Traditional quantitative genetics has long recognized this form of an IGE, but it considers any effect of non-relatives as purely environmental. Researchers such as Moore, Wolf and others have argued that this view is restrictive and may give a misguided conception of the evolutionary dynamics. If an IGE between unrelated individuals indeed operates, and the traits involved (e.g. trait ‘A’ in the example above) are under selection, then both the direct and the indirect genetic effect will evolve. Relative to a scenario where there is only a direct genetic effect, evolution will either speed up if direct and indirect genetic effects are positively correlated, but will slow down in case direct and indirect genetic effects are not aligned (Wolf et al. 1998, TREE 13: 64–69).

Specifics

Perhaps the clearest example of an IGE between non-relatives relate to the framework of “interacting phenotypes” promoted by Moore, Brodie III & Wolf (1997, Evolution 51: 1351–1362), which is perhaps easiest to apply when dealing with behavioural interactions. If we are studying aggression, where two individuals interact, it may be so that a relatively ‘shy’ individual will react aggressively when confronted with an aggressive individual, whereas its behaviour is much “milder” when facing another “shy” phenotype. Obviously, this may also be the other way around. The quantification of aggression may thus not only depend on the focal individual’s genes, but also on its adversary’s (Wilson et al. (2009, Proc. Roy. Soc. B 276: 533–541). Another example would be when two unrelated individual birds of the opposite sex form a pair. Together these individuals provide care for their offspring (feeding, defense of the brood). Clearly, this is a situation where the expression of these “care” traits of one individual is likely to depend on the trait expression of its partner. In this type of interaction we are concerned with two or more individuals expressing a trait in a reciprocal fashion (Moore et al. 1997). One can derive the expected evolutionary dynamics by modifying the trait heritability to take into account both direct and indirect genetic effect (e.g. Bijma & Wade 2008, J. Evol. Biol).
Another scenario for an IGE between unrelated individuals includes interactions that are non-reciprocal. In this case, trait A of a focal individual is partly determined by trait B of another individual, but trait B is itself not affected by trait A. Brommer & Rattiste (2008, Evolution 62-9: 2326–2333) considered the interaction where a male affects its partner’s reproductive trait as such a non-reciprocal interaction. Only the female can reproduce and can therefore express a reproductive trait (seasonal timing of reproduction, fecundity), but a male may have an indirect effect through several other traits (e.g. related to feeding his partner, preparing and defending the nest site). This interaction can be considered non-reciprocal, because the expression of the female trait (reproduction) cannot affect male trait expression prior to it.

Implementation

It is clear that the above sketched interactions between unrelated individuals are potentially complex and difficult to quantify, especially since it is often not known which trait(s) of the other individuals affect our focal trait. However, we can circumvent this issue by quantifying the effect an individual has on other individuals’ expression of the trait of interest. In order to be effective, each (or most) of the individuals will need to have interacted with at least two other individuals. In this case, we can use the identity of the individuals as random effects in order to quantify their indirect effect.
This approach is perhaps easiest to follow by considering an example. Consider a reproductive trait that is expressed once a year (e.g. fecundity). Males and females form a pair to reproduce each year, but also regularly divorce between reproductive seasons, such that many males have mated with several females (and vice versa). In this case, we can model fecundity (of a pair in a given year) and can include female and male identity as random effects. In ASReml, we can link both male and female to the pedigree, and we can therefore also model the genetic effects of both. Lastly, we can model the genetic correlation between male and female effects. In this case, we can argue that the trait (fecundity) is to always be assigned to the female (who is the only one that can reproduce), such that there is a direct (female) genetic effect and an indirect (male) genetic effect. In other situations, we can distinguish between a focal individual (for which the quantified behaviour for that particular data line is the response) and the interacting individual(s). Wilson et al. (2009, Proc.Roy.Soc.B) provide an example of such an analysis based on repeated pairwise testing in mice.

Notice

When conducting these kind of analyses, we are dealing with so-called "crossed" random effects. It is clear that if each individual has interacted with only one individual, there is no crossing (the effects of the two individuals are confounded with each other). Hence, we cannot seperate their effects. For example, we are interested in male and female effects on reproduction, and there is complete monogamy. Ideally, of course, every individual has been interacting with at least two other individuals such that none of the individual-specific effects are confounded with another individual. Without a specific design (which is difficult in wild animals), we are lucky to find that a "sizeable" fraction of the population has interacted with two or more individuals. It is, however, not clear how large such a "sizeable" fraction should be in order to conclude that there is power in separating the individual-specific effects. For example, when we are dealing with male and female effects in a species that lives relatively short (few repeated records, relatively little "crossing"), we may not find evidence of a significant male effect on reproduction. Is this finding real, or is it because of low power in separating the male effect from the female effect? In Brommer & Rattiste (2008, Evolution), a subset of pairs where at least one of the pair members has bred with another individual was used (i.e., the 'lifelong monogamous' pairs were omitted from the analyses). In this study, the omitted subset was relatively small because the study organism was long-lived. However, similar data restrictions in short-lived organisms are likely to lead to strong reduction in the proportion of individuals that are selected for analysis, increasing the possibility that any inferences made are not representative for the population as a whole. These are issues that would be worthwhile to explore in simulations.

Example code

Below is pasted the ASReml code for the analysis of male and female effects on a reproductive trait (Brommer & Rattiste 2008, Evolution). The modelling approach was to conduct testing of hierarchical models of increasing complexity. The different parts of the code presented below relate to the models presented in the article. Each consecutive step is tested using a Likelihood Ratio Test (-2 times the difference in Log(Likelihood) tested against a chi-square distribution with the number of degrees of freedom equal to the number of (co)variances additionally included).
ASREML model for female and male effects on laying date
#next section describes data file, each column heading must be indented
  FEMALE		!P #for genetic analysis, otherwise !A
  DAY	  	 # continuous response variable
  MALE		!P #for genetic analysis, otherwise !A
  YEAR		!I
  FixedEffect		!I

ped.ped  !alpha !make  !skip 1       # pedigree file with qualifiers, 'skip' = nr of lines to skip

sexes_pair.asd  !dopart 7 !skip 1 # data file, 'dopart' specifies which part of the code below is to be run

!part 1	     # conventional mixed model with repeated measures and no causal effects
############################################################################
DAY  ~  mu  FixedEffect
#Model statement above
#Variance structure model below
0 1 0   !STEP 0.001               #  1 error univariate error structure, no random structures

!part 2	     # conventional mixed model with repeated measures and year effects
############################################################################
DAY  ~  mu  FixedEffect  !r  YEAR

0 1 1   !STEP 0.001               #  1 error univariate error structure, 1 random structures

YEAR 1                     
YEAR 0 ID  0.1  

!part 3	     # conventional mixed model with repeated measures: year and only female effects
############################################################################
DAY ~  mu  FixedEffect  !r  YEAR  ide(FEMALE)

0 1 2   !STEP 0.001               #  1 error univariate error structure, 2 random structures

YEAR 1                     
YEAR 0 ID  0.1  

ide(FEMALE) 1                     
ide(FEMALE) 0 ID  0.1            

!part 4	     # conventional mixed model with repeated measures: year, male and female effects
############################################################################
DAY  ~  mu  FixedEffect  !r  YEAR  ide(FEMALE)  ide(MALE)

0 1 3   !STEP 0.001               #  1 error univariate error structure, 3 random structures

YEAR 1                     
YEAR 0 ID  0.1 

ide(FEMALE) 1                     
ide(FEMALE) 0 ID  0.1            

ide(MALE) 1                         
ide(MALE) 0 ID 0.1       

!part 5	     # conventional mixed model with repeated measures: year, male and female effects
############################################################################
DAY  ~  mu  FixedEffect  !r  YEAR  FEMALE  ide(FEMALE)  ide(MALE)

0 1 4   !STEP 0.001               #  1 error univariate error structure, 4 random structures

YEAR 1                     
YEAR 0 ID  0.1 

FEMALE 1                     
FEMALE 0 ID  0.1 

ide(FEMALE) 1                     
ide(FEMALE) 0 ID  0.1            

ide(MALE) 1                         
ide(MALE) 0 ID 0.1       

!part 6	     # animal model with repeated measures; year, female G and PE effects and male G and PE effects
############################################################################
DAY  ~  mu  FixedEffect  !r  YEAR  FEMALE  ide(FEMALE)  MALE  ide(MALE) 

0 1 5   !STEP 0.001               #  1 error univariate error structure, 5 random structures

YEAR 1                     
YEAR 0 ID  0.1 

FEMALE 1
FEMALE 0 ID 0.1

ide(FEMALE) 1                     
ide(FEMALE) 0 ID  0.1            

MALE 1
MALE 0 ID 0.1

ide(MALE) 1                         
ide(MALE) 0 ID 0.1   

!part 7	     # animal model with repeated measures; year, female G and PE effects and male G and PE effects including genetic correlation between FEMALE and MALE
############################################################################
DAY  ~  mu  FixedEffect  !r  !{ FEMALE MALE !}  YEAR  ide(FEMALE)  ide(MALE)

1 1 4   !STEP 0.001               #  1 error univariate error structure, 4 random structures

0 0 ID 0.1      !S2==1                  # for error only matrix is I of size number of observations (0 to count)

YEAR 1                     
YEAR 0 ID  0.1 

FEMALE 2 
2 0 US
0.1
0.1 0.1
FEMALE

ide(FEMALE) 1                     
ide(FEMALE) 0 ID  0.1            

ide(MALE) 1                         
ide(MALE) 0 ID 0.1



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