THE EvoluTion of BiologiCAl DivERsiTy 493
affected by current and future environmental changes, such as the global climate
change that is now under way as a result of human use of fossil fuels.Estimating and Modeling Changes in
Biological DiversityIn most evolutionary studies, “diversity” refers to the number of taxa, such as
genera or species. (The latter is often called species richness.) Over long time
scales or large areas, diversity is often estimated by compiling records, such as
the publications or museum specimens that have been accumulated by many
investigators, into faunal or floral lists of species. Changes in diversity over time
are analyzed in two major ways: by paleontology and by phylogenetic analysis
of living species.
Both approaches begin with a simple model of change in diversity over time.
The number of taxa (N) changes over time by speciation and extinction. These
events are analogous to the births and deaths of individual organisms in a popula-
tion, so models of population growth have been adapted to describe changes in
taxonomic diversity. Suppose there are N species alive at a given time. We use S to
represent the speciation rate, that is, the probability that one of the species “gives
birth” to a second species in a short time period that is dt long. (For these purposes,
dt is often 1 year.) E represents the extinction rate. Then on average, the number
of new species that appear by speciation during that short time period equals the
product of the speciation rate, the number of species that can speciate, and the
length of the interval: S N dt. Following the same logic, the number of species that
become extinct is E N dt. The change in the number of species during that inter-
val is the number of new species minus the number of extinctions. Putting this
together and rearranging the terms, we find that the rate of change in the number
of species per unit of time is19.1Here D is the net diversification rate, which is the speciation rate minus the extinc-
tion rate: D = S – E. The number of species will on average increase if the specia-
tion rate is greater than the extinction rate, that is, if D > 1. If D is negative, the
number of species will decline. This model can also be used to describe changes in
the number of higher taxonomic categories such as genera or families. In that case,
S represents the rate of origination of new taxa rather than the rate of speciation
for individual species. Once again, D is the diversification rate: the average rate
per taxon of an increase or decrease in diversity.
If the diversification rate D remains constant, then the number of species will
grow or shrink exponentially (FIGURE 19.2). But just as competition for resources
can act as a density-dependent brake on growth of a population, the diversifica-
tion rate may decrease as the result of diversity-dependent factors, factors such
as competition for food or space that become more intense as the diversity (num-
ber) of competing taxa increases. The diversity may then attain an equilibrium
at K species. Of course, this model is a great oversimplification of reality because
changes in the environment and in organisms themselves are likely to change
rates of origination and extinction, and consequently the rate of diversification,
over time. Nevertheless, it provides a framework for thinking about differences
in diversity.
In Chapter 18 we noted that two world regions might differ in species diver-
sity because of differences in the time since diversification began, in the rateDNdN
dt= S – E)N=(Futuyma Kirkpatrick Evolution, 4e
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Evolution4e_19.02.ai Date 12-12-20165 10 15 20Logistic
growthExponential
growth25 30510152025300
Time (My)Number of speciesKFIGURE 19.2 Two models for the change
in species diversity through time. In both,
we follow the number of species in a
clade that starts with just a single species.
In this example, the diversification rate is
D = 0.2/million years, which means there is
a 20 percent chance that one species will
have two descendant species after 1 My.
With exponential growth, the diversifica-
tion rate stays constant and the number of
species in the clade grows exponentially.
With logistic growth, the diversification
rate decreases as the number of species
increases. In this example, the equilibrium
is K = 20 species in the clade.19_EVOL4E_CH19.indd 493 3/22/17 1:42 PM