Download Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness

Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness, Selection, and Adaptation
I. Defining Fitness
What is fitness?
Imagine a simple case where a population consists of individuals who have phenotype z1 and
individuals who have phenotype z2. The offspring of these individuals always have a phenotype
identical to their parent. What determines which of these individuals ultimately predominates
within the population?
Case 1: Annual organisms
Assume individuals survive to reproduce with probability l(z) and that surviving indidviduals
produce, on average, m(z) offspring. How do the relative frequencies of the types change over
time?
Start by determining the number of individuals of each type in the next generation
(1a)
(1b)
What do equations (1) tell us about the fate of the two phenotypes?
(2a)
(2b)
 The quantity W entirely determines the relative abundances of the two phenotypes at any
point in the future and is thus a complete description of fitness
Conclusion: For annual organisms, the change in frequencies of types depends on only the
product of the survival and fertility of the types. Thus, NS may favor decreased fertility or
decreased survival if doing so increases their product (fitness) through the presence of
fundamental life history trade-offs
Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness, Selection, and Adaptation
Case 2: Fitness in perennial organisms with age structure
Assume individuals survive to age x with probability lx and produce an expected number of
offspring equal to mx in age x. How do the relative frequencies of the types change over time?
Phenotype z2
Phenotype z1
x
lx
mx
lxmx
x
lx
mx
lxmx
1
1.00
0.00
0.00
1
1.00
1.00
1.00
2
0.75
0.00
0.00
2
0.75
0.67
0.50
3
0.50
1.00
0.50
3
0.00
0.00
0.00
4
0.25
4.00
1.00
4
0.00
0.00
0.00
How many offspring is an individual expected to produce over its lifetime?
k
l m
x 1
x
x
For annual organisms we found that this quantity, R0, which combines survival and fertility is
equal to fitness and completely determines how the frequency of genotypes/phenotypes changes
over time through selection.
However, for perennial organisms with age structure this simple quantity, R0, does not
completely describe fitness. If a stable age distribution has been reached, we can however,
describe fitness using another relatively simple quantity:
where τ is the generation time:
Calculating r for the example shown above reveals an important point: In age structured
populations, generation time is a fundamental component of fitness. Specifically, even though
individuals of the two phenotypes produce, on average, identical numbers of offspring, the
growth rate of z2 is greater. Also, note the remarkable fact that once z2 becomes fixed in the
population, individuals die at younger ages  the population has evolved early senescence, a
fundamental shift in life history
Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness, Selection, and Adaptation
Conclusion: In perennial populations with age structure, natural selection favors phenotypes
that increase r. Thus, NS favors phenotypes with effects on life histories that increase r,
potentially favoring reductions in survival and/or fertility.
II. How do we connect fitness to evolution?
We would like to predict how the phenotype distribution of the population will change over time.
A reasonable starting point would be to predict the mean phenotype of the population in the next
generation. How can we do this?
i. The number of individuals in the next generation that will be produced by individuals with
phenotype
in the current generation is:
ii. The total number of individuals in the next generation is:
iii. The frequency of individuals in the next generation that will be produced by individuals with
phenotype in the current generation is:
iv. We can now use this information to calculate the mean phenotype in the next generation
v. However, we need to relate the phenotype of offspring (zo) to the phenotype of their parent.
We will assume the following linear relationship:
vi. With this assumption the mean in the next generation is:
Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness, Selection, and Adaptation
vii. And the change in the mean over a single generation is:
(1)
LECTURE 2 ENDED HERE WHEN TIME RAN OUT
I. How else could we write equation (1)?
(2)
or
(3)
where:
G = additive genetic variance
Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness, Selection, and Adaptation
II. What do these expressions tell us about evolution by natural selection?
W
z
Q1: What determines the rate of evolution?
Q2: What determines the direction of evolution?
Q3: What role does phenotypic variation play?
Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness, Selection, and Adaptation
III. How does adaptation influence ecology?
We saw in section two that phenotypic variation for a trait influencing fitness causes the
population mean phenotype to evolve. Can we also predict how population size will change in a
phenotypically variable and evolving population?
The total population size in the next generation is:
Doing some simple algebra:
(4)
 The change in population size depends on the mean ***absolute*** fitness of the population.
How does mean fitness change over time?
Equation (1) is valid for any trait. What if the trait of interest were fitness itself?
The frequency of individuals with absolute fitness W in the next generation is:
 The population mean ***absolute*** fitness of the population in the next generation is
Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness, Selection, and Adaptation
 The change in the population mean ***absolute*** fitness over a generation is:
(5)
This is essentially Fisher's fundamental theorem of natural selection: the change in population
mean fitness is proportional to the additive genetic variance for fitness.
Note that equation (5) is simply equation (1) where the trait (z) of interest is fitness (W) itself.
What can we learn about the interface between ecology and evolution by combining
equations (4) and (5)?
Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness, Selection, and Adaptation
IV. How can we use the theory to predict/understand adaptation in the real world?
What quantities would we want to measure?
How could we measure them?
What assumptions must we make?
How could we standardize the data so that selection could be compared across studies?
Total fitness vs. Fitness components and the realities of studying NS in natural pops
A. Measuring heritability
The heritability of a population, h2, can be estimated by calculating the slope of the linear
regression of mid-parent phenotype on offspring phenotype. Although sufficient for the purposes
of this class, this is a crude approach and much more sophisticated methods exist.
B. Estimating the strength and form of selection
Directional Selection
i. Binary fitness data (e.g., survived vs. died) can be easily analyzed by simply estimating the
difference between the mean of the surviving individuals and the mean of the entire population
prior to selection. The result is an estimate of the selection differential S appearing in equation
(2) of section II. Multiplying the selection differential by the heritability yields a prediction for
the change in the trait mean over a single generation.
ii. Continuous fitness data (e.g., fertility, seed set, growth rate, etc) can be analyzed by
calculating the slope of the regression of relative fitness (or a component of fitness) on trait
value. This slope is equal to the selection gradient β appearing in equation (3) of section II.
Multiplying this selection gradient by the additive genetic variance G, yields a prediction for the
change in the trait mean over a single generation.
Warnings and conventions
i. Warning: Fitness data rarely conforms to the assumptions of linear regression. Thus, it is often
tempting to transform the fitness data. DO NOT do this. Transforming the fitness data yields
incorrect prediction.
ii. Convention: Trait values are generally transformed into units of phenotypic standard
deviations. Although this does not influence the accuracy of prediction, it facilitates comparison
across studies where traits may have very different units of measurement.
LECTURE #3 ENDED HERE WHEN TIME RAN OUT
Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness, Selection, and Adaptation
IV. Where do genetic constraints fit into the framework we have developed?
The only way genetic constraints can be manifested in our current framework is as limited or
absent additive genetic variance.
How else could genetic constraints be manifested in the real world?
What if selection acts on multiple traits?
(6)
where is now a vector of population means for a suite of traits, G is now the additive genetic
variance-covariance matrix, and β is now a vector of selection gradients.
Expanding (6) for insight yields:
Remembering linear algebra ("rows into columns") this yields:
What do these equations suggest about the nature of genetic constraints?
Which components of the G matrix comprise the genetic constraints?
Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness, Selection, and Adaptation
V. A concrete example with two traits and a single bivariate phenotypic optimum
Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness, Selection, and Adaptation
VI. Estimating the G-matrix
This can be accomplished in many ways, but all involve complicated breeding designs and
statistical techniques. If you are interested in finding more information on how G-matrices are
estimated, check out the following references:
VII. Estimating selection gradients
Lecture Notes for Evolutionary Ecology 548. Lecture #2: Fitness, Selection, and Adaptation
Appendix 1. Some Important Parameters and Variables for Evolutionary Ecology
Symbol
Meaning
z
The phenotype of an individual
The population mean phenotype
The number of individuals in the population
The number of individuals in the population with phenotype z
The frequency of individuals in the population with phenotype z
The number of offspring produced by an individual with phenotype z
The average number of offspring produced by individuals within the population
The number of offspring produced by an individual with phenotype z relative to
the average number produced by individuals within the population
Heritability. The slope of the parent offspring regression. The proportion of
2
h
phenotypic variation attributable to the additive action of genes