Fitness (often denoted w in
population genetics models) is a central
idea in
evolutionary theory. It describes
the capability of an individual of certain
genotype to reproduce, and usually is equal to the
proportion of the individual's
genes in all the
genes of the next generation. If differences in individual
genotypes affect fitness, then the frequencies of the genotypes
will change over generations; the genotypes with higher fitness
become more common. This process is called
natural selection.
An individual's fitness is manifested through its
phenotype. As phenotype is affected by both genes
and environment, the fitnesses of different individuals with the
same genotype are not necessarily equal, but depend on the
environment in which the individuals live. However, since the
fitness of the genotype is an averaged quantity, it will reflect
the reproductive outcomes of all individuals with that
genotype.
As fitness measures the quantity of the
copies of the
genes of an individual in the next generation, it doesn't really
matter how the genes arrive in the next generation. That is, for an
individual it is equally "beneficial" to reproduce itself, or to
help relatives with similar genes to reproduce, as long as similar
amount of copies of individual's genes get passed on to the next
generation. Selection which promotes this kind of helper behavior
is called
kin selection.
The concept is particularly difficult to understand and frequently
misunderstood;
J.B.S. Haldane when discussing it with
John Maynard Smith is reported to have
described it as "a bugger".
Measures of fitness
There are two commonly used measures of fitness; absolute fitness
and relative fitness.
Absolute fitness
Absolute fitness (w_{\mathrm{abs}}) of a
genotype is defined as the
ratio between the
number of individuals with that genotype after selection to those
before selection. It is calculated for a single
generation and may be calculated from absolute
numbers or from frequencies. When the fitness is larger than 1.0,
the genotype increases in frequency; a ratio smaller than 1.0
indicates a decrease in frequency.
- {w_{\mathrm{abs}}} = } \over {N_{\mathrm{before}}}}
Absolute fitness for a genotype can also be calculated as the
product of the proportion
survival times the average
fecundity.
Relative fitness
Relative fitness is quantified as the
average number of surviving progeny of a particular genotype
compared with average number of surviving progeny of competing
genotypes after a single generation, i.e. one genotype is
normalized at w=1 and the fitnesses of other genotypes are measured
with respect to that genotype. Relative fitness can therefore take
any nonnegative value, including 0.
While researchers can usually measure relative fitness, absolute
fitness is more difficult. It is often difficult to determine how
many individuals of a genotype there were immediately after
reproduction.
The two concepts are related, and both of them are equivalent when
they are divided by the
mean fitness, which is
weighted by
genotype
frequencies.
- {\frac{w_{abs}}{\overline{w}_{abs}} =
\frac{w_{rel}}{\overline{w}_{rel}}}
Because fitness is a
coefficient, and a
variable may be multiplied by it several times, biologists may work
with "log fitness" (particularly so before the advent of
computers). By taking the
logarithm of fitness each term may be added rather
than multiplied. A
fitness
landscape, first conceptualized by
Sewall Wright, is a way of visualising fitness
in terms of a three-dimensional surface on which peaks correspond
to local fitness maxima; it is often said that natural selection
always progresses uphill but can only do so locally. This can
result in suboptimal local maxima becoming stable, because natural
selection cannot return to the less-fit "valleys" of the landscape
on the way to reach higher peaks.
The related concept of
genetic load
measures the overall fitness of a population of individuals of many
genotypes whose fitnesses vary, relative to a hypothetical
population in which the most fit genotype has become
fixed.
Maynard-Smith's Definition
As another example we may mention the definition
of fitness given by Maynard Smith in the following way: "Fitness is
a property, not of an individual, but of a class of individuals –
for example homozygous for allele A at a particular locus. Thus the
phrase ’expected number of offspring’ means the average number, not
the number produced by some one individual. If the first human
infant with a gene for levitation were struck by lightning in its
pram, this would not prove the new genotype to have low fitness,
but only that the particular child was unlucky." This measure is
certainly useful in breeding programs, but hardly as a basis of a
model of an evolution selecting individuals, because evolution
would hardly know if the individual may be selected or not.
Hartl's Definition
Yet another possible measure has been formulated:
"The fitness of the individual - having an array x of phenotypes -
is the probability, s(x), that the individual will be included
among the group selected as parents of the next generation." Then,
the
mean fitness may be determined as a
mean over the set of individuals in a large population.
- P(m) = \int s(x) N(m - x)\, dx
where N is the
probability distribution
function of phenotypes in the population, and m is its
centre of gravity. This measure is a
suitable basis of a model of an evolution selecting individuals. It
may in principle take even the stroke of the lightning into
consideration. In the case N is a Gaussian it is fairly easily
proved that the
average
information (
information
entropy,
disorder, diversity) of a
large population may be maximized by
Gaussian adaptation - keeping the mean
fitness constant - in accordance with
recapitulation, the
central limit theorem, the
Hardy-Weinberg law and the
second law of thermodynamics.
This is in contrast to
Fisher's
fundamental theorem of natural selection.
History
The
British
sociologist Herbert
Spencer coined the phrase "survival of the fittest" (though
originally, and perhaps more accurately, "survival of the best
fitted") in his 1851 work Social
Statics and later used it to characterise what Charles Darwin had called natural selection. The British
biologist
J.B.S. Haldane was the first to quantify fitness, in
terms of the
modern
evolutionary synthesis of Darwinism and
Mendelian genetics starting with his 1924
paper
A
Mathematical Theory of Natural and Artificial Selection.
The next further advance was the introduction of the concept of
inclusive fitness by the British
biologist
W.D. Hamilton in 1964 in his paper on
The Evolution of Social
Behavior.
Notes
Further reading
- Sober, E. (2001). The Two Faces of
Fitness. In R. Singh, D. Paul, C. Krimbas, and J. Beatty (Eds.),
Thinking about Evolution: Historical, Philosophical, and
Political Perspectives. Cambridge University Press,
pp.309-321. Full text
See also
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