Download Fitness and Quantitative Genetics in Ecology: Lecture 25 from IB150 Spring Semester 2002 and more Exams Ecology and Environment in PDF only on Docsity!
IB 372
Ecology and evolution
Lecture 28 - Finish
quantitative genetics,
and fitness
Are God and Nature then at strife, That Nature lends such evil dreams? So careful of the type she seems, So careless of the single life; That I, considering everywhere Her secret meaning in her deeds, And finding that of fifty seeds She often brings but one to bear... A. E. Tennyson
Lecture syllabus 13 Oct Lecture 20 - Genetic Variation and random mating 15 Oct Lecture 21 - Random mating continued, linkage disequilibrium 17 Oct Lecture 22 - Inbreeding 20 Oct Lecture 23 - Mutation and migration 22 Oct Lecture 24 - Genetic Drift 24 Oct Lecture 25 - Drift-migration equilibrium and F-stats 27 Oct Lecture 26 - F-stats, selection intro, quantitative genetics I 29 Oct Lecture 27 - Quantitative Genetics II 31 Oct SECOND MID-TERM EXAM (lectures 13-27) 3 Nov Lecture 28 - Finish Quantitative Genetics, Fitness 5 Nov Lecture 29 - Artificial selection 7 Nov Lecture 30 - Natural Selection 10 Nov Lecture 31 - Sexual Selection 12 Nov Lecture 32 - Geographic variation 14 Nov Lecture 33 - Molecular Evolution 17 Nov Lecture 34 - Species and Speciation 19 Nov Lecture 35 - Allopatric speciation 21 Nov Lecture 36 - The genetics of speciation 28 Dec Lecture 37 - Sympatric speciation 1 Dec Lecture 38 - The fossil record 3 Dec Lecture 39 - Macroevolution 5 Dec Lecture 40 - Macroevolution 8 Dec Lecture 36 - Human population structure 10 Dec Semester review
Readings
DF, Chapter 17, pp. 408-408; Chapter 11, pp. 247- C & H, Chapter 3, pp. 67-69; Chapter 6, pp. 189-
Note: we will soon return in detail to the equation for artificial selection that we briefly covered last time.
A LOD score is a ratio on a log10 scale of the probability that there is andthe probability that there isn’t an association between a trait and a particular marker. Don’t sweat this; a high LOD score means that there is a really small chance of an association by chance alone.
Lo 407
Med 859
Hi 234
Diseaserisk AA AG GG
p = 3.78 x 10 - fromcontingency 2
Lo 76 89 103
Med 299 329 301
Hi 59 65 43
Diseaserisk AA AG GG
p = 0. from contingency ^2
p = 0.
p = 0.
p = 10 -
QTL
mapping
A Single IGF1 Allele Is a Major Determinant of Small Size in Dogs Nathan B. Sutter,1 Carlos D. Bustamante,2 Kevin Chase,3 Melissa M. Gray,4 Keyan Zhao,5 Lan Zhu,2 Badri Padhukasahasram,2 Eric Karlins,1 Sean Davis,1 Paul G. Jones,6 Pascale Quignon,1 Gary S. Johnson,7 Heidi G. Parker,1 Neale Fretwell,6 Dana S. Mosher,1 Dennis F. Lawler,8 Ebenezer Satyaraj,8 Magnus Nordborg,5 K. Gordon Lark,3 Robert K. Wayne,4 Elaine A. Ostrander1* Science 6 April 2007: Vol. 316. no. 5821, pp. 112 - 115
“The fitness of a genotype is the average lifetime contribution of individuals of that genotype to the population after one or more generations…” Futuyma (p. 272). Assume a parthenogenetic (female only) organism.
For genotype A, probability of an egg surviving to be an adult of reproductive age (VIABILITY) is 0.05, and the average number of eggs laid (FECUNDITY) is 60. Then fitness of A is 0.05 x 60 = 3.
Assume also a genotype B with viability of 0.10 and a fecundity of 40, so fitness of B is 0.10 x 40 = 4. Can we use these numbers to tell us about evolution?
Yes - we can plot increase in numbers of each genotype.
The graphs look a lot like the graphs of exponential population growth from ecology - and that’s what they are. R 0 , a per capita growth rate, is called the net reproductive rate.
Absolute and relative fitnesses
R 0 values so far are absolute fitnesses.
But relative fitnesses are often more convenient for algebra (and for thinking simply).
Relative fitnesses are denoted using w (or W). The highest fitness is often set to 1.0, and the others are scaled against the highest W. For example, W (^) A has a fitness of 3/4 = 0.75 (while W (^) B is of course 4/4 = 1.0).
Relative fitnesses throw away all ecological information on whether the population is growing, stable, or shrinking, but they are perfectly OK for looking at whether B will replace A.
Another variation on measuring fitnesses is the idea of the coefficient of selection or selection coefficient s.
One can represent the relative fitness of A as either W (^) A = 0.75 or
s = 1 - 0.75 = 0.25.
You can think of s as a measure of selection “against” a genotype.
Why would one want to do this?
Algebraic simplicity! Sometimes equations just work out “cleaner looking” using s, and sometimes with w. One of the goals of the algebra of population genetics is to manipulate as many w or s terms to values of 0 or 1, so that terms “disappear” from equations.
A very useful concept for relative fitnesses is the idea of average or mean fitness. mean = x (^) i /N or p (^) i x (^) i
mean = (2 + 2 + 3 + 3 + 3)/5 = 2.
or mean = 2/5 + 2/5 + 3/5 + 3/5 + 3/
(2/5)(2) + (3/5)(3) = 2.
So going back to Futuyma, if the frequency of A is 0. and of B were 0.8, then
w = (0.2)(0.75) + (0.8)(1.0) = 0.
Fig. 12. Components of natural selection that may affect the fitness of a sexually reproducing organism (Futuyma)
Lifetime fitness is the result of fitness differences at different stages of the life cycle. Thus there are different components of fitness. We may often study only one at a time if that tells us what we need to know.
Fitness of geographic populations of Drosophila serrata in Australia
R (^0)
Sydney 107
Brisbane 144
Cairns 93
Port Moresby 66
Rabaul 15
Under ideal lab conditions (unlimited food), at 25°C (77 °F), assuming a generation length of 20 days. These are obviously maximum absolute fitnesses.
Birch, L. C., Th. Dobzhansky, P. O. Elliott, R. C. Lewontin. 1963. Relative Fitness of Geographic Races of Drosophila serrata. Evolution 17: 72-83.
Can we predict population growth for each strain (at least in the lab) from these data?
Relative fitness of geographic populations of Drosophila serrata in Australia
R 0 w
Sydney 107 107/144 = 0.
Brisbane 144 144/144 = 1.
Cairns 93 93/144 = 0.
Port Moresby 66 66/144 = 0.
Rabaul 15 15/144 = 0.
Three common approaches to measuring fitnesses.
- Measure survival, fecundity, and other components as the ecological variables they are.
- Calculate relative fitnesses from association of genotypes with e.g. diseases.
Calculate relative fitnesses from genotype frequencies (in cases where we cannot do survival experiments).
Assume we have a parthenogenetic lizard population with two genotypes, AA and Aa. A parasitic nematode exists in the population, and the mortality m is 0.10 (10% of lizards with worms die before reproduction). We observe these genotype data:
It is immediately apparent that worms are more common in AA - it is susceptible to worms.
AA Aa Sum With worms 90 10 100 No worms 50 50 100 With worms 0.90 0.10 1. No worms 0.50 0.50 1.
Calculate relative fitnesses from genotype frequencies.
We need a number known as Relative Risk (RR), for which we can use the ratio of the genotype frequencies. Relative Risk of worms for the AA genotype can be based on genotype frequencies (= probabilities), so 0.90/0.50 = 1.80.
AA Aa Sum With worms 90 10 100 No worms 50 50 100 With worms 0.90 0.10 1. No worms 0.50 0.50 1. R R 1.
If RR is 1, then AA is as likely to have worms as not
- no risk related to genotype.
Modiano et al. observed significant differences in genotype frequencies for -hemoglobin alleles in people in Burkina Faso.
Table 1 Genotype frequencies in healthy (control) subjects (fc), malaria (diseased) patients (fd), and the relative risk of malaria for the four genotypes where the relative risk is statistically significant (Modiano et al., 2001).
Sample Genotype AA AC AS CC Healthy subjects (fc) 0.6641 0.2172 0.0954 0. Malaria patients (fd) 0.8036 0.1641 0.0275 0. Relative risk (RR) 2.070 0.7075 0.2681 0.
(RR were calculated slightly differently from what we did. Also, the genotypes SS and CS are rare and require a different calculation for w.)
The decline in the frequency of the melanic
form at one British locality Hedrick, P.
- Genetics of Populations 3rd ed. Jones and Bartlett.
p' = p 2 w (^) CC + pqw (^) Cc
w
w
CC 1-s
Cc 1-s cc 1
Can we predict population growth at Caldy Commons from these data?
Three common approaches to measuring fitnesses
- Measure survival, fecundity, and other components as the ecological variables they are.
- Calculate relative fitnesses from association of genotypes with e.g. diseases.
- Calculate relative fitnesses from change in allele frequency over time.
So, R and w values for discrete traits can be measured. But what about continuous variation? We can use the slope of the regression of w (or R or s) on a trait, called a selection gradient. We use relative fitness, but scaled so mean fitness is 1.00.
WIKELSKI, MARTIN, AND L. MICHAEL ROMERO. 2003. Body Size, Performance and Fitness in Galapagos Marine Iguanas. INTEGR. COMP. BIOL., 43:376–386. SVL means “snout-vent (anus) length, a standard measure of length for lizards.
group of 10 hatchlings)
slope = 0.
