Journal of Heredity 2014:105(4):457–465
doi:10.1093/jhered/esu024
Advance Access publication May 2, 2014
© The American Genetic Association 2014. All rights reserved.
For permissions, please e-mail: [email protected]
Heterozygote Advantage in a Finite
Population: Black Color in Wolves
Philip W. Hedrick, Daniel R. Stahler, and Dick Dekker
From the School of Life Sciences, Arizona State University, LSA-E, Tempe, AZ 85287 (Hedrick); Yellowstone Wolf Project,
Yellowstone Center for Resources, Yellowstone National Park, WY (Stahler); and 3819-112 A Street NW, Edmonton,
Alberta, Canada (Dekker).
Address correspondence to Philip W. Hedrick at the address above, or e-mail: [email protected].
Abstract
There is a striking color polymorphism for wolves in the Yellowstone National Park where approximately half the wolves are
black. The genetic basis for this polymorphism is known, and fitnesses of the genotypes are estimated. These estimates suggest that there is strong heterozygote advantage but substantial asymmetry in the fitness differences of the 2 homozygotes.
Theoretically, such fitnesses in a finite population are thought to reduce genetic variation at least as fast as if there were no
selection at all. Because the color polymorphism has remained at about the same frequency for 17 years, about 4 generations,
we investigated whether this was consistent with the theoretical predictions. Counter to this general expectation of loss, given
the initial frequency of black wolves, the theoretical expectation in this case was found to be that the frequency would only
decline slowly over time. For example, if the effective population size is 20, then the expected black allele frequency after 4
generations would be 0.191, somewhat less than the observed value of 0.237. However, nearly 30% of the time the expected
frequency is 0.25 or greater, consistent with the contemporary observed frequency. In other words and in contrast to general
theoretical predictions, because of the short period of time in evolutionary terms and the relatively weak selection at low
frequencies, the observed variation and the predicted theoretical variation are not inconsistent.
Subject areas: Conservation genetics and biodiversity
Key words: defensin, genetic drift, heterozygote advantage, polymorphism, predation
Heterozygote advantage, where the heterozygote at a locus
with 2 alleles has a higher fitness than both homozygotes, was
first shown theoretically by Fisher (1922) to maintain a genetic
polymorphism at a stable equilibrium. Subsequently, the view
of the genome that many loci were polymorphic and that heterozygote advantage was the major type of selection maintaining this variation became widespread (Dobzhansky 1955;
Lewontin 1974). However, Robertson (1962) showed that in a
finite population, given that there was heterozygote advantage
and asymmetry in the fitnesses of the 2 homozygotes, genetic
variation could be lost as least as fast as from genetic drift than
if there were no differential selection at all. There are a number of examples of heterozygote advantage having substantial
asymmetry in the fitness of homozygotes (Hedrick 2012), and
theory predicts that they would generally not result in longterm genetic polymorphism in small populations.
Black color in wolves (Canis lupus) (Figure 1) is found in
relatively high frequency in some North American populations such as Denali National Park, Alaska (Mech et al. 2003),
Jasper National Park, Alberta, Canada (Dekker 1986, 1998),
the Northern Territories, Canada (Musiani et al. 2007), and
the Yellowstone National Park, WY (Anderson et al. 2009).
Anderson et al. (2009) examined the molecular basis of
this color variation and found that the dominant allele KB
(for simplicity here, we will symbolize this allele as K) at the
beta-defensin protein locus resulted in black color in wolves
(homozygotes for the recessive allele ky, symbolized as k
here, are gray). Anderson et al. (2009) provided evidence suggesting that this is the same allele that determines black color
in over 30 breeds of black dogs. Consequently, and based
on molecular evolution support, Anderson et al. (2009) suggested that the black K allele was introgressed from dogs into
wolves and that the black coloration in Kk heterozygotes and
KK homozygotes was adaptive for wolves in forested areas
because of concealment advantage during predation.
Subsequently, Coulson et al. (2011) estimated that in the
Yellowstone National Park wolf population, about half of
which are black, that there was a quite asymmetrical heterozygote advantage at this locus. The largest selective difference
identified by Coulson et al. (2011) was between black heterozygotes, which had the highest fitness, and black homozygotes,
which had the lowest fitness, but which have indistinguishable
black color. Because these 2 genotypes have the same black
color, this large difference in fitness is apparently not associated
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Journal of Heredity
Figure 1. Photo of 8 gray and 8 black wolves in a pack in Yellowstone National Park.
with the hypothesis of concealment advantage in forested habitats but with “some other function of the gene, perhaps via its
role in cellular immunity” (Coulson et al. 2011). In other words,
dominance of the allele black K for color appears to change
for fitness-related measures with the gray genotype kk and the
black heterozygotes Kk having the most similar fitnesses.
Here we examine the expected frequency of the allele
causing black color in Yellowstone wolves using the relative
fitness values estimated from the data of Coulson et al. (2011)
and its change over time. We compare these predictions to the
observed frequency of this allele from the founding of the
population in 1995–1996 to the present population and discuss the comparison of these expectations and observations.
Table 1 The estimated values of the annual survival rate, annual
recruitment rate, generation length, and mean lifetime reproductive
success for the 3 different color genotypes in the Yellowstone
National Park wolf population (Coulson et al. 2011) and the relative
mean fitness values based on the mean lifetime reproductive success
Data
(Coulson T, personal communication). The bottom line of
Table 1 gives these relative fitness values for genotypes kk,
Kk, and KK, which are 0.779, 1.0, and 0.013, respectively.
The low fitness of KK homozygotes is particularly striking.
For the 280 wolves sampled for Coulson et al. (2011), only
12 (4.3%) were KK. Of these only 3 (2 females, 1 male) were
breeders. Out of these 3 KK breeders, 1 female produced no
surviving pups in her tenure, the other female produced only
1 surviving pup, and the male produced only 1 surviving pup.
These facts support the greatly reduced lifetime reproductive
success of KK individuals estimated by Coulson et al. (2011)
and the very low relative fitness value of KK in Table 1.
Table 2 gives the estimated annual frequencies of the 2
color phenotypes for 17 years in Yellowstone National Park
Coulson et al. (2011) estimated the difference in annual survival rate, annual recruitment rate, generation length, and
lifetime reproductive success for the 3 different color genotypes: gray homozygotes (kk), black heterozygotes (Kk), and
black homozygotes (KK) in a large sample (280) of wolves
from Yellowstone National Park (Table 1). For all these fitness measures, the black homozygote had the lowest value
and the black heterozygotes had slightly higher values than
the gray homozygote. Because the lifetime reproductive success is a function of the other 3 measures, a good estimate
of the relative fitnesses of the 3 genotypes is possible using
the relative lifetime reproductive successes of the genotypes
458
Genotype
kk
Kk
KK
Color
Gray
Black
Black
Annual survival rate
Annual recruitment rate
Generation length
Mean lifetime reproductive success
Mean fitness
0.75
0.24
4.5
1.83
0.779
0.77
0.28
4.9
2.35
1
0.47
0.08
2.4
0.031
0.013
Hedrick et al. • Heterozygote Advantage in Wolves
Table 2 The annual documented number of breeders and
numbers and frequencies of gray and black wolves in the
Yellowstone wolf population from 1996 to 2012 and the estimate
of the black allele K using these phenotypic frequencies and
expression (Equation 4b) when s1 = 0.05 and s2 = 0.63, the relative
survival values given 2 years of the annual survival rates in Table 1
Numbers
Frequency
Year
Breeders
Gray
Black
Gray
Black
K
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
Average
7
18
14
14
17
19
26
32
37
37
35
28
40
33
32
—
—
25.9
20
37
41
37
73
76
86
108
107
58
68
86
52
43
56
60
44
61.9
17
32
41
35
41
55
59
60
60
57
68
80
70
47
43
42
38
49.7
0.541
0.536
0.500
0.514
0.640
0.580
0.593
0.643
0.641
0.504
0.500
0.515
0.426
0.478
0.571
0.588
0.537
0.547
0.459
0.464
0.500
0.486
0.360
0.420
0.407
0.357
0.359
0.496
0.500
0.485
0.574
0.522
0.429
0.412
0.463
0.453
0.274
0.277
0.305
0.294
0.203
0.245
0.236
0.201
0.203
0.302
0.305
0.294
0.366
0.323
0.252
0.239
0.277
0.269
based on the year-end surveys in November–December from
1996 to 2012. These numbers include pups that survived the
summer and fall to their first winter. This does not include
1995 because more wolves were translocated into the population in 1996 (see Discussion below). From 1996 to 2012, the
estimated frequency of black wolves in the population has
been rather stable and varied from 0.36 in 2000, 2003, and
2004 to 0.57 in 2008 with means for these surveys of 0.547
gray and 0.453 black wolves.
VonHoldt et al. (2008) estimated the effective population
size (Ne) in the Yellowstone population for 1997 to 2004, and
the average for these 8 years was 17.9. The effective population size is highly correlated with the annual number of successful breeders. Therefore, another measure of the effective
population size can be obtained from the mean number of
breeders (Table 2). The mean number of breeders from 1996
to 2010 was 25.9. The mean total number of wolves over
this period was 61.9 gray wolves plus 49.7 black wolves plus
2.3 wolves of unknown color for a mean number of 113.9
wolves total. Therefore, we will explore the effects of an
effective population size of 10 and larger below to determine
the potential influence of genetic drift.
we can calculate the expected change in the frequency of
allele K as
∆q =
pq ( s1 p − s2 q )
1 − s1 p 2 − s2 q 2
(1)
Both alleles k and K are expected to be maintained because both
w11 and w22 are <1. The expected equilibrium frequency of K is
qe =
s1
s1 + s2 (2)
(Hedrick 2011). In this case from Table 1, s1 = 0.221 and
s2 = 0.987, making the expected equilibrium for allele K equal
to qe = 0.183.
To examine the impact of the effective population size
(Ne) on the expected frequency and distribution of K, we will
use the probability transition matrix method (Hedrick 2011).
With this approach, the probability of i K alleles out of 2Ne
alleles in generation t + 1, given that there were j K alleles in
generation t, is
Pij =
(2 N e !)
(1 − q ′ )2 N e −i (q ′ )i
(2 N e −1)! i !
(3)
In this expression, the frequency of K is q = j/2Ne before
selection and the frequency of K after selection is q′ = q +
Δq, where Δq is calculated from Equation 1 above. To find
the expected frequency and distribution of K over time, this
matrix can be multiplied by the allele-frequency vector for a
given generation containing all 2Ne + 1 possible population
states to produce the distribution of population states in the
next generation.
Although the genotype is known for many wolves, when
only the phenotypic frequencies of gray and black wolves are
known, then the following approach can be used to estimate
the frequency of K. After viability selection, the frequency of
gray wolves (x) is
x=
p 2 (1 − s1 )
1 − s1 p 2 − s2 q 2
(4a)
where s1 and s2 are the amount of viability selection against
genotypes kk and KK. After manipulation, this equation
results in the quadratic expression
p 2[ s1(1 − x ) − s2 x −1] + p (2 s2 x ) + x (1 − s2 ) = 0
(4b)
which gives an estimate for the frequency p of the gray allele
k, and the frequency of the black allele K is q = 1 − p.
Model
Let us assume that genotypes kk, Kk, and KK have relative
fitnesses w11 = 1 – s1, w12 = 1, and w22 = 1 − s2, respectively, where s1 and s2 indicate the level of selection against
homozygotes kk and KK, respectively, and that the frequencies of alleles k and K are p and q. Using traditional population genetic approaches in a large population (Hedrick 2011),
Results
The expected change in the frequency of K per generation
in a large population when the fitnesses of genotypes kk,
Kk, and KK are 0.779, 1.0, and 0.013, respectively, is given in
Figure 2. As expected, there is no change in the frequency
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Journal of Heredity
0.1
0
∆q
(0.779 1 0.013)
(1 1 0.013)
-0.1
-0.2
-0.3
-0.4
-0.5
0
0.2
0.4
0.6
0.8
1
q
Figure 2. The expected change in the frequency of K and Δq for different initial frequencies q when the fitnesses of genotypes
kk, Kk, and KK are 0.779, 1, and 0.013, respectively (upper curve) and 1, 1, 0.013, respectively (lower curve). For reference, the
broken line indicates when the expected change in allele frequency is 0.
of K when it is equal to 0.183, there is an increase in frequency below this equilibrium, and there is a decrease above
it, indicating a stable polymorphism. Notice that the decrease
in allele frequency per generation above the equilibrium is
much greater than the increase below the equilibrium.
As mentioned earlier, in a small population, the combined effect of genetic drift and asymmetrical heterozygote
advantage selection can cause some counterintuitive results
(Robertson 1962). To understand this, let us compare this situation to when there is only genetic drift (s1 = s2 = 0). For the
genetic drift only situation, genetic variation is expected to be
lost from the population at a rate of 1/(2Ne) per generation.
When there is symmetry of selection against homozygotes,
s1 = s2, then genetic variation is retained in the population
longer than when there is no selection and the rate of loss
is < 1/(2Ne) per generation. When there is asymmetry of
heterozygote advantage selection, then genetic variation can
be lost faster than if there were genetic drift only, or no selection at all. This effect can be understood using a measure
called the retardation factor (Robertson 1962), which is 1/
(2Ned) where d is the observed asymptotic decline (decay) in
heterozygosity per generation for a given type of selection.
In general, the retardation factor is a function of the
expected equilibrium in a large population for different levels of selection against the homozygotes and genetic drift,
as well as the amount of selection and the effective population size (Robertson 1962; Hedrick 2012). If the expected
equilibrium is near 0.5, then the retardation factor becomes
very large when Ne (s1 + s2) is large, indicating that genetic
variation is lost much more slowly than when only genetic
drift is acting. On the other hand, when s1 < s2 so that the
460
equilibrium is low in frequency, then the retardation factor is
small and genetic variation is lost more quickly than if there
were just genetic drift. As pointed out by Robertson (1962),
generally when qe < 0.2 (s2 > 4s1), the retardation factor is less
than that when there is only genetic drift.
This surprising prediction can be understood from the
expected change in allele frequency given in Figure 2. Overall,
the general effect of this selection when there is homozygote
fitness asymmetry is much like selection against a recessive
genotype KK with fitnesses of 1, 1, and 0.013 for genotypes
kk, Kk, and KK, respectively (see Figure 2) and pushes the
frequency of K downward to low frequencies. When K is
rare, the expected size of Δq increasing K up from near 0 is
small because nearly all K alleles are in heterozygotes and the
selective difference in fitness between heterozygote Kk and
the common kk homozygote of s1 is small so that genetic
drift becomes more important. As a result, of these 2 factors,
the net effect is a faster loss of variation than if no selection
at all were present.
For more insight, we can examine the retardation factor
more closely for the fitness values estimated and when the fitness of kk is 5% below and 5% above the estimate of 0.779
for different effective population values (Figure 3). First,
when w11 is 0.779 as estimated and there are low Ne values,
genetic variation is lost faster than under genetic drift only.
When Ne becomes 20, the retardation factor becomes greater
than 1, and when Ne is 50, it is significantly greater than 1. On
the other hand, if selection is less against the homozygote kk
(0.818, 1, and 0.013), then even with Ne = 50, there is little
retention of genetic variation compared with no selection.
While if there is more selection against the homozygote kk
Hedrick et al. • Heterozygote Advantage in Wolves
10
Retardation factor
8
6
(0.740 1 0.013)
4
(0.779 1 0.013)
2
(0.818 1 0.013)
0
10
20
30
40
50
Effective population size
Figure 3. The retardation factor for different effective population sizes (Ne) when the fitness of genotype kk is 5% less
(selection is more) than the estimate (0.740), the estimate (0.779), or 5% greater (selection is less) than the estimate (0.818), and
the fitnesses of genotypes Kk and KK are 1 and 0.013. In these cases, the expected equilibria of K in an infinite population are
0.209, 0.183, and 0.156. The broken line indicates the retardation factor of 1 when there is no differential selection.
(0.740, 1, and 0.013) so that symmetry in homozygote fitnesses is increased, then there is substantial retention even
with Ne = 30.
As we discussed above, the number of black KK homozygotes was very low, and as a result, it was difficult to estimate fitness for genotype KK precisely. In order to explore
the sensitivity of our results to variation in this estimate, we
assumed as an example that the fitness of genotype KK was
0.2, or 0.2/0.013 = 15.4-fold higher than the estimate used
above and the stable equilibrium for the K allele in an infinite
population was 0.216 for these fitness values. In this case,
the retardation factor was increased somewhat because heterozygote advantage selection was more balanced. However,
the effect was much less than the 5% decrease in the fitness
of genotype kk to 0.740 examined in Figure 3 which had
a very similar equilibrium value in an infinite population of
0.209. This suggests that our results are less sensitive to a
large increase in the fitness of KK than a small decrease in
the fitness of kk.
What is the expected impact of finite population size on
the frequency of the K allele given the estimated selection
on the 3 genotypes? Figure 4 gives the expected mean frequency of the K allele when the initial frequency is 0.25, and
the effective population size is either 10 or 40. After 10 generations (assuming 4-year generations, Coulson et al. 2011;
Stahler et al. 2013), the mean frequency has been reduced
substantially to 0.116 when Ne = 10 and to 0.171 when
Ne = 40.
For comparison, the estimated observed frequencies are
given using Equation 4b and s1 = 0.05 and s2 = 0.63, the relative survival rates for 2 years, given the annual survival rates
in Table 1. The average of these estimated frequencies of
the K allele over the 17 years is 0.269 (Table 1). In 2011, the
estimated frequency was 0.239, and the expected frequency
in 2011 was somewhat lower for Ne = 10 at 0.179 and for
Ne = 40 at 0.197.
However, even though the expected mean declines, the
expected distribution over replicate populations quickly
becomes quite broad. Figure 5 gives the expected distribution of the black K allele when its initial frequency is 0.25
and the Ne = 20. After 4 generations, the mean frequency is
0.191, but nearly 30% of the time the expected frequency is
0.25 or greater. In other words, the observed value of 0.237
is not unlikely in these circumstances. By generation 10, the
mean frequency has declined to 0.152, but about 20% of the
time the expected frequency is 0.25 or greater, and 11.2% of
the time the K allele has been lost.
Discussion
When there is heterozygote advantage with extreme asymmetry
in a finite population, genetic variation is expected to be lost as
least as fast as when there is only genetic drift (Robertson 1962).
Although the estimated relative fitnesses for color genotypes
in the Yellowstone population of wolves show heterozygote
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Journal of Heredity
0.4
Observed
Frequency
0.3
0.2
Ne = 40
Ne = 10
0.1
0
1995
2005
2015
2025
2035
Year
Figure 4. The frequency of K observed in the Yellowstone population from 1996 to 2012 and the mean frequency expected
when the fitnesses of genotypes kk, Kk, and KK are 0.779, 1, and 0.013, respectively, the initial frequency in 1995 is 0.25, the
effective population size is 10 or 40, and the generation length is 4 years.
0.2
Proportion
0.15
Gen. 1
Gen. 4
0.1
Gen. 10
0.05
0
0
0.1
0.2
0.3
0.4
0.5
q
Figure 5. The expected change in the distribution of the frequency of K over time (shown as q) at generations 1 (solid line), 4
(broken line), and 10 (dotted line) when the effective population size is 20 and the initial frequency of K is 0.25.
advantage with extreme asymmetry, the observed frequencies of
these genotypes appear to be relatively stable over the 17 years
(about 4 generations) of monitoring varying from a frequency
for K of 0.20 in 2000, 2003, and 2004 to 0.37 in 2008 with a
462
mean of 0.269. Here we examined, given the estimated relative
fitnesses and a small effective population size, how the theoretical expectation of the change in color allele frequencies compared with the allele frequencies observed at this color gene.
Hedrick et al. • Heterozygote Advantage in Wolves
Is the relative stability of allele frequencies observed consistent with theoretical expectations? Given the estimated
relative fitnesses and the initial frequency, the amount of
change in the frequency of the color alleles from selection is
not expected to be large per generation, the largest changes
are expected at much higher allele frequencies. Even with
a small effective population size of 20 after 4 generations,
nearly 30% of the time the frequency is as high or higher as
the initial frequency. In other words, in this case the action of
selection does not appear very strong and there has not been
enough time for the allele frequencies to be greatly reduced
by the combination of selection and genetic drift. Therefore,
even though there is an expectation for loss of genetic variation in this situation based on the theory of Robertson
(1962), counter to these general predictions, a detailed examination of this example provides an understanding for these
counterintuitive results.
To understand the temporal pattern in the frequency of
the color variants, it is important to examine the frequencies in the founders of the Yellowstone population that consisted of 3 independent groups (Table 3). The 14 wolves (6
gray and 8 black) translocated in 1995 came from near Jasper
National Park, Alberta, Canada and formed 3 packs. The first
group of 17 wolves (12 gray and 5 black) translocated in 1996
came from north of Fort St John, British Columbia, Canada
and formed 4 packs. Finally, in late 1996, 10 wolf pups (7
gray and 3 black) from the Sawtooth Mountains in northwest Montana were translocated. The genotypes for these 40
wolves are given in Table 3 (the genotype of one 1995 black
individual is not clear).
The 1995 and 1996 groups included adults and were
known to form packs and produce progeny that survived.
On the other hand, only 2 (both gray) of the 10 pups translocated in late 1996 were known to reproduce (VonHoldt
et al. 2008), and the others dispersed and died from various
causes. Therefore, to calculate the initial frequency below we
will use the 30 wolves translocated from Canada and the 2
gray wolves from Montana that consisted of 20 kk, 11 Kk,
and 1 KK wolves, making the initial frequency of alleles k and
Table 3 The observed and expected (under Hardy–Weinberg
proportions) numbers of the 3 genotypes that determine color in
the Yellowstone wolf population for the 40 genotyped founders
and 255 wolves born in the population over the period from 1998
to 2009.
Genotype or allele
kk
Kk
KK
Color
Gray
Black
Black
6
12
7
20
6
5
3
11
Founders—1995
Founders—1996
Founders—late 1996
Founders (1995, 1996,
2 grays from late 1996)
Observed
Expected
1998–2009
Observed
Expected
0.625 0.344
0.635 0.324
138
105
0.541 0.412
0.558 0.378
k
K
0.692
0.853
0.850
0.797
0.308
0.147
0.150
0.203
0.031
0.041
12
0.747
0.047
0.064
0.253
1
0
0
1
K, 0.797 and 0.203, respectively. For comparison, the genotypes of 255 wolves born in the population from 1998 to
2009 are also given in Table 3. The frequencies of alleles k
and K in this group are 0.747 and 0.253, somewhat higher
but not significantly different from the frequencies in the 30
founder wolves.
Field studies of the wolf population in and around Jasper
National Park, Alberta, Canada and its color morphs have
been carried out for many decades (Table 4). For example,
Cowan (1947) reported that 55% of the wolves in this area
were black and Carbyn (1973) found that 46% were black.
Dekker (1986, 1998) has studied wolves and their color for
over 30 years in Jasper National Park very near where the
group of 14 wolves translocated to Yellowstone in 1995 were
captured. Of the wolves he categorized for color between
1965 and 1984, 53% were black (Dekker (1986) and in a single pack he followed from 1979 to 1998, 73% were black
(Dekker (1998). In his most recent surveys from 1999 to
2013, Dekker (personal communication) documented that
82% were black, suggesting that the proportion of black
wolves might even be increasing in recent years. In other
words, the high proportion of black in the 14 wolves taken
from this area for translocation to Yellowstone in 1995
appears to reflect the high proportion of black wolves in this
area and were not an unusual sample.
Stahler et al. (2013) found that female black heterozygote wolves had significantly lower reproductive success
(0.75) than gray females. This differs from Coulson et al.
(2011) who found that the annual recruitment rate for
gray wolves was less (0.86) than black heterozygotes. The
2 samples were not identical, for example, Stahler et al.
(2013) examined just females and Coulson et al. (2011)
examined both sexes, perhaps explaining the difference in
estimates. In addition, the statistical analysis approach used
by Coulson et al. (2011) differed from the observed annual
reproductive success reported in the study by Stahler et al.
(2013). However if gray wolves had a higher fitness relative
to black heterozygotes because of a higher reproductive
success, then the maintenance of variation by heterozygote advantage might be influenced. For example, if gray
homozygotes and black heterozygotes do not have significantly different fitnesses, then the expected change in allele
frequency is always negative, although this value is not large
(Figure 2).
Table 4 The number of wolves of different colors observed
in and around Jasper National Park and the frequency of black
wolves
Years
Frequency
Gray Black White of black
Citation
1940s
1969–1972
1965–1984
1979–1998
1999–2013
36
31
59
39
12
44
26
70
115
56
—
—
3
3
—
0.550
0.456
0.530
0.732
0.823
Cowan (1947)
Carbyn et al. (1993)
Dekker (1986)
Dekker (1988)
Dekker (personal
communication)
463
Journal of Heredity
In addition, it appears that there might be nonrandom
mating among different color phenotypes in the Yellowstone
population. For 172 known breeding pairs, there was a 27%
excess of black–gray pairs and a complement deficiency of
gray–gray and black–black pairs. Such negative-assortative
mating is known to result in a stable polymorphism and
might substantially influence the maintenance of the allele
frequencies in this case. The impact of this factor is now
under investigation.
Here we have used fitness values based on the analysis of Coulson et al. (2011) of 280 wolves, virtually all the
animals in Yellowstone population during this period. This
analysis clearly showed a strong heterozygote advantage for
black heterozygotes during this time period and that the 2
homozygotes had quite different (asymmetric) fitness values.
As Coulson et al. (2011) suggested, selection values might
change over time. In addition, other factors, such as nonrandom mating and gene flow, might have impacts on genetic
variation at the K locus. Fortunately, the Yellowstone Wolf
Project will continue its long-term, detailed monitoring and
study of this wolf population so that our projections can
be reevaluated in the future, and further information can be
included in future evolutionary analysis. Overall, color polymorphism in Yellowstone wolves is already an important
case study for understanding evolutionary and conservation
genetics and is likely to become more important in the future.
As we mentioned earlier, Anderson et al. (2009) concluded that the black allele arose in dogs and spread into
wolves, potentially thousands of years ago. Given that the
wolf population size was large as has been estimated by
genetic analysis (Leonard et al. 2005) and the fitness estimates of Coulson et al. (2011), the black allele could have
been expected to increase from a low frequency in wolves.
This expectation occurs because initially all the black alleles
would be in heterozygotes and the fitness of the heterozygote Kk is higher than that of the ancestral homozygote
kk. Further, even in a finite population and given these fitnesses, the average frequency would be expected to increase
initially somewhat. However, after this initial increase, the
expectation is that in a small population, not unlike that in
a population with no selection, that the black allele would
eventually be lost (based on simulations similar to those discussed above). The overall impact of genetic drift, gene flow
between dogs and wolves, the timing of these events, and
the actual selection values during this period are not known.
In other words, it is possible that given these fitness values
that the black allele could have entered the wolf population
and increased, but the actual dynamics are based on a number of unknown factors.
Better concealment is assumed to provide a fitness advantage in ambush predators. However, wolves are primarily
coursing predators and ambush has little to do with their
hunting behavior. In addition, wolves are generally not secretive, and they live in conspicuous groups, howl and scent
mark regularly, prefer to travel in open, and easy to traverse
landscape features like game trails, roads, valley bottoms, and
ridgelines. In other words, the hypothesis of a concealment
advantage from dark coat color in forested areas is probably
464
not a primary factor influencing coat color frequencies in
wolves. Supporting this conclusion, Dekker (2009) stated
that “in my 40 years of field observations in Jasper National
Park, black wolves are at all times more visible than grey
ones, even among the trees.” On the other hand, it is possible
that the beta-defensin gene that determines black color in
wolves might have pleiotropic effects on disease resistance
or other immunologically related traits (Coulson et al. 2011)
and result in fitness trade-offs as described for single genes in
sheep (Johnston et al. 2013).
Funding
Ullman Professorship to P.W.H.; National Science Foundation
(DEB-0613730, DEB-1021397, DEB-1245373) to D.R.S.;
Yellowstone National Park.
Acknowledgments
We appreciate the comments of several anonymous reviewers. D.R.S. acknowledges support from many donors through the Yellowstone Park Foundation.
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Received January 24, 2014; First decision February 10, 2014;
Accepted March 20, 2014
Corresponding editor: Robert Wayne
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