EVoluTioN iN SPACE 195
where pm is the allele’s frequency in the migrants and p is its frequency in the focal
population before migration. The right side of Equation 8.1 shows that the change
in allele frequency is proportional to two quantities: the migration rate, m, and the
difference in allele frequencies between the local population and the migrants,
(pm – p). For example, say that a population has an allele frequency of p = 0.25, and
it receives immigrants at a rate m = 0.1 from another population whose allele fre-
quency is 0.75. Equation 8.1 tells us that the change in allele frequency is 0.05, so
migration will cause the allele frequency in the focal population to increase from
p = 0.25 to 0.3. The population has become more genetically similar to the popu-
lation that is the source of the migrants. The higher the migration rate between
populations, the quicker genetic differences between them are erased.
In populations that are spatially continuous, there are no distinct populations
and so the migration rate cannot be used. Instead, we measure gene flow with the
migration variance, symbolized by σm^2. FIGURE 8.5 plots the distribution of places
where Texas spiny lizards (Sceloporus olivaceus) reproduced relative to where they were
born. These data were collected by painstakingly marking young lizards where they
hatched, then locating them again after they had become sexually mature and estab-
lished territories where they reproduced [3]. The variance of this distribution gives an
estimate of σm^2. Roughly speaking, σm (the square root of the migration variance) is
equal to the average distance between the birthplaces of a parent and its offspring.
Over the course of many generations, migration can cause genes to diffuse
across a landscape in a way similar to how a cloud of smoke disperses by diffu-
sion. The migration variance measures the speed of that diffusion. The units of
the migration variance depend on how we choose to measure space; for example,
σm^2 might be in units of square kilometers if we are studying moose but in units of
square millimeters if we are studying protozoa. (The Appendix explains variances
and how they are calculated.)
The migration rate and migration variance are measured in several ways. Direct
methods measure gene flow by following individuals, as in the study of the liz-
ard. This approach is useful if we need a snapshot of dispersal over a short period
of time. It does, however, have limitations. The evolutionary effects of gene flow
are typically averaged over many generations, and a short-term estimate may not
be representative. Another problem is that some individuals do not reproduce suc-
cessfully after they disperse, so they do not contribute to genetic mixing. And if an
individual is not found, we don’t know if it dispersed so far that we could not find it,
or if it simply died.
These considerations motivate indirect methods that use genetic data to esti-
mate gene flow. The mixing of individuals from populations with different allele
frequencies generates a systematic deviation from the Hardy-Weinberg ratios: it Futuyma Kirkpatrick Evolution, 4e
Sinauer Associates
Troutt Visual Services
Evolution4e_08.05.ai Date 11-17-2016Frequency–500 –250 0 250 500
Distance (m)σm^2 = 9800 m^2
σm = 99 m0.060.080.100.040.0200.12Sceloporus olivaceusFIGURE 8.5 Distribution of dispersal distanc-
es of the Texas spiny lizard (Sceloporus oliva-
ceus, inset) in a population in Austin, Texas.
The birthplaces of individuals are centered at
0, and distribution shows the places where
they established territories and presumably
reproduced. (The original data are reported
as absolute distances. This figure assumes
that half of the individuals dispersed to the
left and half to the right, which is why the
distribution is exactly symmetrical.) The vari-
ance of this distribution equals the dispersal
variance, σm^2 = 9800 m^2. This corresponds to
an average movement of roughly σm = 99 m
per generation. (Based on data from [3].)08_EVOL4E_CH08.indd 195 3/23/17 9:12 AM