Some Initial Thoughts on Breeding Designs

This week I don’t particularly have any papers to review, just some thoughts.  In the past few weeks I have been showing the power of contextual analysis as a means of measuring the strength of multilevel selection in natural populations.  The problem, of course, is that a selection analysis is, correctly, strictly a phenotypic analysis of selection.  Mathematically this can be illustrated with the breeder’s equation:

R = G P-1S

Selection analyses, including contextual analysis only apply to the blue P-1S part of the equation. This is why the Molofsky data can be used both as an analysis of community ecology, or (mis) interpreted as community selection acting on species richness (when fitness is defined as below ground biomass of the reed canary grass).  The big determinant of whether it is community ecology or evolution by community selection is in the G matrix, which is not measured in selection analysis.

Actually, at this point, it is probably worth reiterating the famous list made by Lewontin in his article on the Units of Selection (R. C. Lewontin 1970, Ann. Rev. Ecol. Syst 1:1 – yes that citation is real).   In that paper Lewontin lists the properties of a population that are necessary and sufficient for evolution by natural selection.  To quote him exactly:

1. Different individuals in a population have different morphologies, physiologies, and behaviors (phenotypic variation).

2. Different phenotypes have different rates of survival and reproduction in different environments (differential fitness).

3. There is a correlation between parents and offspring in the contribution of each to future generations (fitness is heritable).

(Lewontin 1970 Ann. Rev. Ecol. Syst 1:1)

The rather mundane point is that if we are really going to think about the evolution of contextual traits, we need to understand what we mean by the heritability of these types of traits.  There are actually two problems, a conceptual problem:  What do we mean by the heritability of contextual traits, and a practical one:  how do we measure the heritability of contextual traits.

The conceptual problem of what do we mean by the heritability of a contextual trait is actually pretty straightforward.  Consider a contextual trait such as population density.  Then the heritability variance for population density would simply be covariance between the population density the parent experienced and the population density the offspring experienced.  Aside:  Note that I am calling it heritable variance, rather than the additive genetic variance.  As discussed earlier this is additive genetic variance has a very specific definition, which under most circumstances does not cover contextual traits.  Indeed, it is not at all clear to me that the term “genetic” necessarily applies to all causes of heritability of contextual traits, thus, I go with the generic term “heritable variance”.

In any case, this line of reasoning can be applied to any contextual trait:  The heritable variance is the covariance between the parental (or weighted? average parental) value of the trait and the offspring value of the trait.  That is fine for a conceptual definition of the heritable variation for a contextual trait, not so good from a practical perspective.

The problem is that our standard methods of estimating heritability and additive genetic variance specifically remove the effects of interactions among individuals and environmental effects.  Consider a classic method of estimating additive genetic variance, the half sib breeding design.  In this design a set of males (sires) are each mated to a set of females (dams):

Standard half sib breeding design.  A set of sires (blue squares) are each mated to a set of Dams (pink circles).  Each dam produces a set of full sib offspring (green dots).  A nested analysis of variance is used to divide the total variance among the offspring into variance among sires (covariance of half sibs), and variance among dams with sires (covariance of full sibs).  The additive genetic variance is 4 times the variance among sire half sib families.

There are a couple of things that should be obviously wrong with this.  The traditional half sib breeding design was designed for the agricultural industry.  In agriculture the breeder has control over the mating system, and as a result starting with the assumption of random mating makes sense.  Nature is not like that there is localized mating.  Thus, individuals that live physically close to each other are more likely to mate than ones that are physically widely separated.  Thus, in the traditional half sib breeding design dams are randomly assigned to sires.  In nature it won’t be like this.  So, perhaps the first thing we should reconsider is whether dams should be assigned to sires randomly given each dam an equal probability of being chosen, or perhaps it would be better to choose mates based on their probability of actually mating in nature.

The second thing is that technically the design could be reversed (each dam mated to multiple sires).  Besides a number of technical problems, the real reason we do this is that there are “maternal effects”.  Thus, at least in animals, the mother contributes a lot of “stuff” to the offspring that the father does not contribute.  These include cytoplasm – mitochondria are mostly maternally inherited, and potentially vertically transmitted pathogens, and this influence of the mother continues past birth.  For example, in mammals the female, but not the male, nurses the young, so there is much more potential for non-genetic resemblance between mothers and offspring than between fathers and offspring.

This is all fine if we are interested in only traits of the individual, but if we consider things like quality of mothers milk to be a contextual trait, then we are designing this trait out of our experimental design.  This becomes more extreme if we are using contextual traits such as neighborhood characteristics as the contextual trait.  In standard quantitative genetics we would be careful to randomize the environments in which the offspring are raised – we might, for example plant offspring in random order in a field or randomize the position of pots.  This is in fact destroying the very covariance we are interested in.  The covariance among contextual traits in parents and offspring is as often as not driven by the ecology of the setting, and it is this ecology, and thus the covariance that we destroy when we randomize the environments in which we raise the offspring.

Of course, randomization is the hallmark of good experimental design, so it would seem that measuring the heritability of contextual traits is at some level at odds with good experimental design.  Is all lost?  I don’t think so.  I think it just means that we need to carefully think through what it is we want to measure, and to preserve the ecological associations that we think are important, but randomizing what we can.  For example, we could collect seeds from not only our experimental offspring, but also from the neighborhood of the seed parent.  Then we could plant neighborhoods randomly in the field, and have each experimental offspring surrounded by the offspring of its parent’s neighbors.