On fitness surfaces, adaptive landscapes and the "G-matrix"

This week we'll discuss two conceptual reviews in evolutionary quantitative genetics: Arnold et al. (2001), published in Genetica, and Steppan et al. (2002), published in TREE. Both two take the "Adaptive landscape" as their starting point, and Steppan et al. (2002) do also link the so-called "G-matrix" to the position of the population on the adaptive landscape and how it might affect evolutionary trajectories.

1. What exactly is a G-matrix? What do the diagonal elements mean? What does the off-diagonal elements mean? What can it be used for, and  how can one estimate the G-matrix?

2. Are genetic correlations really "constraints" in the sense that they can prevent a population from reaching a fitness optimum (an adaptive peak)? Why? Why not?

3. When do you expect a curved evolutionary trajectory and how is such a curved evolutionary trajectory related to genetic correlations?

4. Is the G-matrix really stable between generations? If not, on what time-scale (-s) can it change and why would it change? What is the role of pleiotropy and physical linkage in the stability of the G-matrix?

5. If two populations have G-matrices that are a/identical, b/proportional or c/unrelated to each other, how can one interpret these patterns?

Chapters 22 and 24: Thursday November 11 2010

These two chapters deal with some fundamental topics in quantitative genetics and evolutionary biology. Again, they are fairly technical in the details and sometimes the methods are a bit outdated, but the questions that are covered are still relevant and of great interest to evolutionary biologists.

In chapter 22, I would especially like to highlight Fig. 22.1 (p. 658) which shows how genotype-by-environment interactions ("G x E":s) can arise in several different ways, i. e. changed additive genetic variances between environments (B), changed rank ordering of genotypes (C) or a combination of changed additive genetic variances and changed rank ordering in the different environments (D). Discuss the evolutionary consequences of these different settings in terms of maintenance of genetic variation in heterogeneous environments. Is there any principal difference in terms of evolutionary consequences between scenario B and C, for instance?

(Hint: think of the character being "Fitness" (Y-axis), instead of an ordinary trait to answer this question).

In chapter 24, there is a principally interesting discussion about sex-specific additive genetic variances and the central role of the intersexual genetic correlation in "constraining" the evolution of sexual dimorphism (SD). How much of an "absolute" genetic constraint do you think the intersexual genetic correlation really is? Can sexual dimorphism ever evolve if the intersexual genetic correlation is equal to one? Can it become negative, and if so, how? And why would it become negative?

What is the relationship between sex-specific genetic variances and the intersexual genetic correlation? Can the sex-specific genetic variances differ between males and females, and the intersexual genetic correlation still be equal to one? Or is it impossible?

Also, try to think of the two sexes as different "environments" and the intersexual genetic correlation as the between-environment genetic correlation, as it was formulated by Falconer, and which is also discussed in chapter 22 (return to Fig. 22.1 and replace "Environment 1" with males and "Environment 2" with females.

Chapters 18 and 21 (Thursday November 4)

These two chapters are rather technical, and focussed on the statistical details of estimation procedures. I would encourage you to not "get drowned in the details" but try to see the bigger picture and the biological implications. Much has happened in the past decade, and the estimation procedures that are described have, to some extent, been replaced by more modern and powerful methods, such as the "Animal Model".


Nevertheless, there are some general and interesting questions that should be discussed:


Chapter 18: Why are heritability estimates from full-sib analyses often higher than those from parent-offspring regressions? Which genetic factors are responsible for the higher heritability estimates  obtained in full-sib analyses? Which procedures are preferrable: parent-offspring regression, half-sib analyses or full-sib analyses? Discuss and motivate!


Chapter 21: Which factors are responsible for genetic correlations between characters? How is it possible to explain the strong congruence between phenotypic and genetic correlations (Fig. 21.1) in a biologically meaningful way? How does "selection bias" influence the magnitude of genetic correlations (increasing or decreasing it)? Are there any a priori reasons to expect that genetic and phenotypic correlations should differ more for life-history traits than for morphological traits? If so, in what direction? Do we always expect trade-offs between life-history traits to be expressed as negative genetic correlations? Why? Why not?