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 24 and 25: On the effects of short- and long-term selection on genetic variance

These chapters are rather technical and very mathematical. However, there are some interesting and general messages, that deserves to be carefully considered. Here are some questions to consider:

1. Which two main models about genetic variance have been developed and which assumptions underly them?

2. Sometimes, an initial increase in genetic variance is observed in an early stage of the selection experiment? Which of the two models can explain this, and what is the reason by behind such an increase in additive genetic variance?

3. What time frames are we talking about here we say "short-term" and "long-term"?

4. How do a/the effect size of loci and b/the number of loci affect the selection plateau?

5. How is allele frequency dynamics and hence additive genetic variance changing over time in "mixed models", i. e. genetic architectures characterized by a few loci of major effect and many loci of small effect?

Chapters 4 and 14 in second volyme ("Selection")

These two chapters in the second volume (available on the web) are rather basic, and they deal with the non-adaptive processes of evolution (genetic drift, mutation and recombination, chapter 4), and the adaptive process of evolution (i. e. selection, chapter 14), and how to analyze the effects of these processes. Two concepts strike me as being very important in these chapters and worthy of discussion: Realized heritability and asymmetric selection response. Both are parameters that kan be estimated from artificial selection experiments in the laboratory, and difficulties in how to interpret them are discussed in chapter 14.

I encourage you to search for additional litterature on asymmetric selection responses (e. g. in ISI-databases). What kind of theories are there to explain these asymmetric selection responses? Can realized heritabilities and asymmetric selection responses ever be estimated in natural populations, or can we only study them in laboratory settings?

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?

Chapters 7 and 17

These two chapters are rather technical, but I encourage you to think beyond the details and formulas and try to think of the biological implications and the bigger picture. Chapter 17, on parent-offspring regression, is a bit out-dated, as methods to estimate quantitative genetic parameters have been developed a lot since 1998, particularly the so-called "Animal Model".

Chapter 7, however, contains some general information that has important biological and evolutionary implications also today. I would particularly like to highlight the crucial evolutionary role of assortative mating, an underestimated evolutionary force. I say "underestimated", because assortative mating might be perceived as uninteresting and unimportant, since it only changes genotype frequences, not allele frequencies. Assortative mating (=positive correlation between the characters of mates), increases the frequency of homozygotes in a population, and hence "flattens" the trait distribution and increases the additive genetic variance. This is because extreme individuals at the tails of the trait distributions (homozygotes) increase at the expense of individuals close to the mean (heterozygotes); a higher frequency of homozygotes are produced when parents mate assortatively.

How can then assortative mating affect the additive genetic variance and the response to selection? In chapter 7, consider Figs. 7.7 (theory) and Example 4 (empirical results from an experiment on assortative mating experiment on Drosophila).

In Fig. 7 it can be seen that with a relative moderate phenotypic correlation between the traits of parents (r = 0.5), the additive genetic variance increases and becomes twice the amount as under the situation of random mating (r = 0)! This is a huge amount, and it happens without any particular molecular mechanism or changed gene experession etc., it simply an effect of the fact that "likes mates with like", which results in a higher frequency of homozygotes in the population.

Note that, interestingly, with disassortative mating (r < 0),  the additive genetic variance does not decrease as much, but instead hovers around 90 % of the expected variance under random mating (Fig. 7.7). These theoretical expectations are largely confirmed in the experiment presented in Example 4. 


Discuss the evolutionary implications of assortative mating as a means of increasing the additive genetic variance without affecting allele frequencies! Can you think of any implications in conservation biology, for instance, in terms of population "rescue" of small populations threatened by genetic drift?

 

First meeting: Chapters 1 and 4 in "Lynch & Walsh"

Our first meeting with the GENECO course will take place in the Ecology Building (Lund University) on Thursday, October 21 2010 (10.00 - 12.00). During this meeting, we will discuss chapter 1 (p. 3-17) and chapter 4 (p. 51-79). After this meeting, I expect the participants to be able to define and explain these terms:

- Homozygous effects
- Dominance coefficient
- Additive effect
- Average excess
- Breeding value
- Additive genetic variance

In particular, you should be able to explain how the link between breeding values and additive genetic variance, and how these terms are related to each other.

I also want you to discuss, in particular, the second paragraph on p. 17, about the relationship between molecular genetics and quantitative genetics. How do Lynch & Walsh counter the frequent criticism from molecular geneticists that quantitative genetics is "phenomenological", "missing the boat" or "cheating"? To what extent is it justified to ignore the details, studied by molecular geneticists, and focus on phenotypes? Do we actually need any information about mechanisms at all, to quantify and study patterns of resemblance between relatives? Would quantitative genetics work independent of the genetic material (i. e. whether it is DNA, RNA or any other self-replicating hereditary substance)? Why? Why not?

I recommend you to register your name at "Blogger" to participate in the discussion and comment on the posts below. Alternatively, you might sign with your name, but without being registered at Blogger. In any case, use this forum as a means to put forward your questions during the course.