Download Genetic modelling: an analysis of a colour polymorphism in the

<onlogical Journal o j the Linnean .Socie(y i 19841, 80: 4 3 7 4 4 5 . With 2 figures
Genetic modelling: an analysis of a colour
polymorphism in the Snow Goose
(Anser caerulescens)
BRUCE RATTRAY AND FRED COOKE
Department of Biolou, Queen's University, Kingston, Ontario, Canada
Received M a y 1983, accepted f o r puhlication August 1983
Previous studif\ of colour polymorphism in the Snow Goose ! , h e r cnerulescenJ failed to considrr and
reject alternative hypothrses to that of a single locus with incomplete dominance. Utilizing data
from a long-term study of a wild population, we test the validity of these earlier results by
considering two alternatives: (1; a single locus with multiple allelism and (2) a threshold
polygenic system. O u r analyses corroborate the original model, but emphasize the importance of
testing all plausible hypotheses.
KEY WORDS:
Lesser Snow Geese - genetic modelling
-
polymorphism
~
Anser caerulescens
CONTENTS
Introduction
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Methods .
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Genetic models
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Data collection and analysis .
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Results
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Single locus with incomplete dominance
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Single locus with an allelic series ,
Threshold polygenic .
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Discussion
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Acknowledgemrnts
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Referencrs
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4-12
INTRODUCTION
'The mechanisms of plumage and coat coloration have been known for some
time (see Fox, 1976), although, the genetic systems controlling these processes
have been more difficult to determine. I n most cases the proposed mechanism
has not been shown to provide a unique explanation for the observed pattern of
inheritance. Indeed, Bergston & Owen (1973) note that equally adequate
alternatives are often distinguished solely on the basis of presumed differences in
the simplicity of the hypothesis (i.e. Occam's razor). Claiming expediency as
justification, it has become common practice to shortcut the comprehensive
definition of potential hypotheses by jumping to those considered, a p i o n , to be
002'C4082/84/040437
+ 09 $03 011
4i7
0 1984 T h r
Linntan Societ) 01 London
438
BY RATTRAY AND F. COOKE
most likely. Studies of wild populations exacerbate this problem. Due to
increased logistical difficulties, the field worker is willing to be ‘realistic’ and test
one or two of the more plausible hypotheses. Unfortunately, even if this best
guess proves to be an adequate explanation, the issue remains unresolved until
the alternatives are tested and rejected (Medawar, 1969; Willson, 1981; Grant
& Price, 1981).
I n this paper we address the problem of the adequacy and uniqueness of an
hypothesis by resolving potential genetic models for a colour polymorphism in
the snow goose (Anser caerulescens). Earlier work on this species has suggested that
a single locus, two allele system with incomplete dominance controls the
polymorphism and plumage variation (Cooke & Cooch, 1968). However, faced
with the limitations of a field study, researchers failed to rule out a polygenic
mode of inheritance. Edwards (1960) discussed the conditions under which a
polygenic model may mimic the pattern of inheritance expected from a major
gene(s). Indeed, so general is the explanatory power of the threshold polygenic
model that, although it is often invoked when nothing else appears to fit, it is
seldom considered (and then rejected) when something else will do.
I n this study of a different population, we tested the validity of the
conclusions of Cooke & Cooch’s previous (1968) study. I n that study, they
postulated the simplest genetic model consistent with the data without ruling
out alternative more complex explanations. Below, we consider not only their
original hypothesis, but also examine two alternatives-single
locus with
multiple allelism and a threshold polygenic model.
METHOD
Genetic models
Since 1968, a long term study ofthe population biology ofthe snow goose has been
in operation a t La Perouse Bay (58”24’N, 94’24’W) 25 miles east of Churchill,
Manitoba. The data used in this paper were collected between 1973 and 1979,
and sufficient information is available to allow the testing of multiple allelic and
polygenic models.
The Snow Goose is a colonial nester, with the La Perouse Bay colony varying in
size from two to four thousand breeding pairs. I n addition to a
colour dimorphism manifested in both adults and goslings (white and blue),
continuous variation exists in the extent of pigmentation on the belly of adults of
the blue colour phase. This variation may be quantified using a modified
version of the scoring system suggested by Cooke & Cooch (1968). Blue phase
birds with all white bellies are classified as class 2, birds with all dark bellies,
breast and lower neck are class 6. Classes 3, 4, and 5 are arbitrary intermediates
with increasing amounts of dark plumage on the underside (see Fig. 1).
Goslings, however, may be scored only as either white or blue.
Figure 1 . Plumage coloration of snow geese. Two plumage types exist: white (A) and blue (B-F).
Although a continuum exists in the amount of pigmentation found on the belly of blue adults,
colour classes may be assigned to quantify this variation: A, Colour class 1 , B, colour class 2; C, 3;
D, 4; E, 5; F, 6.
440
B. RATTRAY AND F. COOKE
The hypotheses may be stated as follows.
(1) Single locus with incomplete dominance-Cooke
& Cooch (1968)
suggested that the polymorphism is controlled by a single locus with two alleles
and incomplete dominance. Hence ‘Blue’ birds are either homozygous dominant
(BB) or heterozygotes (Bb). As ‘B’ is incompletely dominant with respect to ‘b’,
darker bellied birds are predominantly but not exclusively homozygous
dominant (plumage classes 5 and 6). Heterozygotes are phenotypically light
bellied (classes 2 to 4) and white birds are homozygous recessive.
(2) Single locus with multiple allelism-the plumage variation within the blue
colour phase may also be explained by the existence of an allelic series at a
single locus. Hence, the plumage continuum could be a consequence of the
interaction of a set of ‘n’ alleles; the simplest case consists of three alleles and a
dosage effect. For example: ‘go’does not produce any pigmentation, while ‘B”
and ‘B2’produce X , and X, units of pigment, respectively. The production of
any one allele is then cumulative with respect to the production of the second
allele found at the locus.
(3) Threshold polygene-if we assume additive interactions among loci,
variation within the blue phase may be accounted for by the small, cumulative
effects of ‘k’ loci. However, the explanation of the polymorphism itself requires
the existence of a threshold such that individuals exceeding this critical value
exhibit the blue phase plumage. The amount of pigmentation on the belly will
then increase as the extent to which the threshold is exceeded becomes larger.
Data collection and analysis
The field season runs from early May to August, with two principal periods of
data collection. At hatch (late June) the phenotypes of both parents and their
goslings are scored and recorded. In August, during their flightless moult, adults
and young of the year are marked with a coded colour band. This allows for
individual identification of birds over successive years. This system has been
employed since 1972; currently over one-third of the colony residents are
individually marked.
Cooke & Mirsky (1972) have previously demonstrated that certain aspects of
the breeding biology of this species, principally non-random mating, precludes
the use of gene frequency analysis. Moreover, they observed the phenomenon of
two or more females laying eggs in the same nest. Such intraspecific parasitism
(or dumping) results in families of questionable genetic integrity. Hence, when
examining pedigrees a confounding effect is introduced, allowing for the ad hoe
explanation of anomolous observations. Consequently, two of the more
traditional techniques for genetic analysis (gene frequency and pedigrees)
cannot be utilized in this study.
However, if we consider all possible mating combinations as disjunct classes,
we may tabulate the results of individual pedigrees to provide an offspring
colour ratio per mating type (i.e. the ratio of the number of white to blue
goslings per mating type). If we assume that the probability of a female either
parasitizing or being parasitized is independent of her colour class, then
although the values of the ratio per mating type may change, this will have no
effect on comparisons among mating types. Therefore, any trends existing in the
colour offspring ratios will be independent of the dump phenomenon. Finally, as
COLOUR POLYMORPHISM I N SNOW GEESE
44 1
Mirsky (1972) and Finney (1975) have shown that larger clutches are more
likely to contain dumped eggs, nests with more than five eggs were excluded
from the analyses.
RESULTS
Single locus with incomplete dominance
In a Blue by Blue cross involving two heterozygote birds (Bb), one would
expect a 3 : 1 (blue to white) ratio in the offspring. Considering a set of
randomly sampled Blue x Blue crosses, this ratio (now calculated for the
population) should vary from 3 : 1 (blue to white) to zero, depending upon the
proportion of heterozygotes present. Since the model postulates incomplete
dominance, the proportion of heterozygotes present in light bellied birds should
approach 100°/o and then decline to some low frequency in the dark bellied
plumage classes. This gradient should be reflected in the offspring colour ratio
when calculated per plumage class (e.g. 3 x 3, 4 x 4).Table 1 gives the results
of such a set of crosses and clearly shows the predicted trend (P<0.05). Cooke &
Cooch (1968), observed similar results using data from a different population.
If the polymorphism and the plumage variation are determined as suggested
above, then given White x Blue matings which produced at least one white
gosling (i.e. the blue parent is an heterozygote), the distribution of the number
of white offspring per nest should approximate a truncated binomial
distribution (Hogben, 1931; Mirsky, 1972). This is a direct consequence of the
postulated independence of a gosling's colour relative to the colour(s) of its
siblings. A comparison of the observed and expected distributions of white
offspring shows no significant differences between them (Table 2) (P>0.50).
Single locus with an allelic series
Traditionally, multiple allelism is distinguished from multiple loci by observing
segregation rather than random assortment of the genes. Even if linkage is
present, recombination between loci must occur at some low frequency.
Unfortunately, such a test is rarely possible due to the difficulty of finding
appropriate families. In this study, mature plumages of complete families were
never obtained. Almost all observations consist of a single daughter and her
Table 1 . Offspring colour ratio: Blue x Blue matings
Offspring
N0
Mating
nc\ts
2x2
3x3
4x4
5x5
hx6
0
12
14
112
I44
~-
No. White
No Blue
Rdtlo*
White Blue
~~
~
21
81
37
9
54
352
40 1
520
-
1 : 2.6
1 : 4.3
1 : 10.8
1 : 57.8
*A11 crosses, except 3 x 3, h a w ratios significantly different from 1 : 3 (PiO.01).
Rank
correlation
~
P<0.05
B. RATTRAY AND F. COOKE
442
Table 2. Number of nests containing four offspring in which 1, 2, 3 or all 4 are
white
Number of White offspring
Mating
Number of
crosses
6x 1
Observed
Expected
5x 1
Observed
Expected
4x 1
Observed
Expected
3x1
Observed
Expected
Probability of
observation
2
3
4
6
5.07*
7
7.6
3
5.07
3
1.26
P>0.50
9
10.68
18
16
7
10.68
6
2.64
P>0.50
21
25.88
45
38.8
23
25.88
8
6.46
P>0.50
12
18
18
9
12
6
3
P>0.50
1
19
40
97
45
12
*Expected values were calculated on the basis of a truncated binomial as observations of zero white
offspring were not made (From Hogben, 1931.); e.g. Where f=no. of offspring (family size), r=no. of
recessives ( i x . whites), P,,= probability of family size ‘s’ having ‘r‘ recessives:
S!
parents. Despite this limitation, these data are sufficient to allow testing of this
hypothesis.
Consider first a three allele, single locus model. Regardless of dominance
specifications, this model cannot account for a gradient of offspring colour ratios
related to parental phenotype (Table 1). Although it does allow for a 3 : 1 ratio
(blue to white) in the offspring of 3 x 3 matings, it requires 4 x 4,5 x 5 and 6 x 6
matings to produce blue goslings only. The observed trend could be accounted
for by postulating a larger number of alleles. This, however, leads to a second
prediction: with an increase in the number of alleles, a correlation between
parental and offspring plumage (i.e. the extent of belly pigmentation) should be
observed. For a fixed range in the variation of the phenotype, an increase in the
number of codominant alleles requires the difference in the dosage provided by
any two consecutive alleles to be reduced. It follows that the average change in
phenotype measured by comparing homozygotes to heterozygotes must also
decrease. As the effect of the heterozygote is reduced, the result should be a tighter
relationship between parental plumage and that of their offspring. This may be
tested by regressing the colour class of blue phase offspring on the average
colour class of their parents (i.e. the midparent (Fig. 2)). No significant
relationship is found (P>0.10).
Threshold polygenic
Given that quantitative variation is observed in plumage coloration, the
probability of a future gosling being blue should increase with the magnitude of
the parental deviation from the threshold. Moreover, we would expect these
probabilities to be reflected in the calculated offspring colour ratios of crosses
involving birds of similar plumage (e.g. 3 x 3, 4 x 4). Threshold inheritance
COLOUR POLYMORPHISM I N SNOW GEESE
2.
.
7
.
5
6.
I
I
I
40
45
50
‘2
.
443
u
55
60
Midporent colour score
Figure 2 Regression of blue offspring colour class on midparent colour class. Y=3.65+0 33 X,
N = 62. Not significant a t the
level.
predicts a positive correlation between the offspring colour ratio and the colour
class of the parents. Like the single locus, incomplete dominance model, a model
of threshold inheritance predicts a positive correlation between the offspring
colour ratio and parental colour class. The two can be distinguished by
considering only offspring colour ratios from heterozygous parents. Here, the
threshold model-in contrast to the single locus model-still predicts a strong
correlation between offspring colour ratio and parental colour class. The
offspring colour ratios calculated for each parental colour class for a sibship of
four are presented in Table 3. No significant differences exist between classes
and no trend of any kind is evident.
DISCUSSION
Turning first to the single locus, incomplete dominance model, the results of
our analyses are in complete agreement with those of Cooke & Cooch (1968).
Not only is incomplete dominance sufficient to explain the observed trend in the
Table 3. Offspring colour ratios by colour
phase, for ‘heterozygotes’ in White
(Wh) x Blue (Bl) matings
Mating
No. of crosses
I x2
0
I x3
45
97
1 x4
1x5
1x6
40
19
Offspring colour
ratio (Bl : W h ) *
1 : I .22
1 : 1.20
1 : 1.28
I : 1.17
*As heterozygote crosses producing ‘zero’ white offspring
are not includrd in this analysis, the expected ratio of white
t o bluc goslings is more than one ( I j .
B. RATTRAY AND F. COOKE
444
offspring colour ratio (Table l ) , it also successfully predicts an invariant
offspring colour ratio with respect to the colour class of mated pairs when using
White x “heterozygote” matings (Table 3).
The multiple allelic hypothesis does not fare as well. In general, regardless of
the number of alleles or their dominance relations, a multiple allelic model
produces a pattern of inheritance which conflicts with at least one of the
following observations: the frequency of white goslings decreases in crosses 2 x 2
through to 6 x 6 (Table 1); no heritable relationship exists between the colour
class of blue offspring and that of their parents (Fig. 2); and crosses of light
bellied x light bellied, light bellied x dark bellied and dark bellied x dark bellied
birds can produce both light bellied and dark bellied offspring (Table 4). this
necessitates rejection of this model.
Table 4. Mating combinations with the blue phase-light bellied (LB) colour
classes 2-4, and dark bellied (DB), colour classes 5 and 6
~~
~
Offspring
Cross
No. of crosses
LB
DB
LBxLB
LBxDB
DB x DB
4
31
26
61
1
10
3
21
22
4
Two testable predictions may be made from the threshold polygenic model:
first, a relationship should be found when regressing offspring colour scores on
parental values, second, a positive correlation should exist between the offspring
colour ratio and the colour class of the parents.
As noted earlier, the regression of offspring colour scores on parental scores is
not significant (Fig. 2). This is inconsistent with a model of polygenic
inheritance. This model does nevertheless, successfully account for the observed
trend in offspring colour ratios in Table 1. However, if we examine a set of
White x Blue matings (Table 3), this model’s prediction of a correlation
between the offspring colour ratio and the Blue parental colour class fails to
materialize. As a consequence, the threshold polygenic model must be
considered incorrect and be rejected.
We may now conclude that the single locus, incomplete dominance model is
both adequate and unique in its ability to explain the plumage dimorphism and
its variation in the Snow Goose. However, some mention should be made of
what we have called “the dangers of failing to consider alternatives to the first
acceptable hypothesis”. What could we have concluded if, in addition to the
single locus model, one of the alternate hypotheses had proven to be an adequate
explanation of the dimorphism? This would place us in the uncomfortable
position of having too many ‘right’ answers. Most researchers invoke Occam’s
Razor and select the simplest alternative (Dunbar, 1980; Ruse, 1979).
Unfortunately, some vagueness exists as to the definition of ‘simplest’. Although
it is frequently implied, Occam’s Razor is not intended to select the correct or
most likely hypothesis. Instead, given models of equal explanatory power, it
chooses whichever model is more readily tested and hence, if incorrect, most
COLOUR POLYMORPHISM IN SNOW GEESE
445
quickly eliminated (Kneale, 1949; Popper, 1968). I n this manner Occam’s
Razor provides the most expedient null hypothesis.
Finally, our corroboration of the single locus model should be seen as
especially strong support when it is recognized that the two studies described
were performed on different populations. In addition, and of equal importance,
we have considered and rejected the alternative hypotheses which previously
had remained untested.
ACKNOWLEDGEMENTS
Both authors are grateful for comments received from members of the Queen’s
University Ecology and Evolutionary Biology Group. Special thanks must go to
J. C. Davies, J. Eadie and C. S. Findlay for criticisms of an earlier version of the
manuscript.
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caerulescens) . Evolution, 22: 289-300.
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EDWARDS, J. H., 1960. The simulation of mendelism. Acta Gmetica, 10: 63-70.
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Ph.D. thesis, Queens University, Kingston, Ontario, Canada.
FOX, D. L. 1976 Animal Biochroms and Structural Colours. California: University of California Press.
GRANT, P. R. & PRICE, T. D., 1981. Populational variation in continuously varying traits as an ecological
genetics problem. American < o o l o , ~ ,21: 795-81 1.
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KNEALE, W. E., 1949. Probability and Induction. New York: Macmillan and Co.
MEDAWAR, P. B., 1969. Induction and Intuition in Scientijc Thought. Philadelphia: American Philosophical
Society.
MIRSKY, P. J., 1972. Colour dimorphism in the Lesser Snow Goose, Anser caerulescens caerulescens. Unpubl.
M.Sc. thesis, Queens University, Kingston, Ontario, Canada.
POPPER, K. R., 1972. The Logic of SCientiJic Discovery. New York: Harper and Row.
RUSE, M., 1979. Falsifiability, consilience and systematics. Systematic < o o l o ~ , 29: 530-536.
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