Marco Festa-Bianchet, Fanie Pelletier and David Coltman
A complement of information to Hedrick, P.W., Coltman, D.W.,
Festa-Bianchet, M. & Pelletier, F. 2014 Not surprisingly, no
inheritance of a trait results in no evolution. Proceedings of the
National Academy of Sciences 111, E4810.
In their reply to our criticism of their PNAS paper [1], Traill et al. [2] question our
good faith but ignore our principal challenge. In their demographic model, the only
link in phenotype across generations is the inheritance function, a statistical model
with lamb weaning mass as a function of maternal and paternal mass.
The inheritance function does not account for ram age, implying an expectation that
a ram will sire heavier lambs as it ages. Based on the weak relationship between
ram mass and lamb mass, interpreted as near-zero inheritance, [1] claims that an
imaginary hunt of heavy rams would have little evolutionary effect on adult ram
mass. Contrary to available knowledge on bighorn sheep [3], this analysis does not
allow large breeders to produce offspring that grow to become large adults. More
than a century of empirical data from animal breeding, laboratory models and
humans supports the contention that adult mass is heritable in mammals.
Traill et al. [1] then claim that their work is relevant to an understanding of the
selective effects of trophy hunting on ram horns. That is akin to taking the
correlation between mass of cocks and mass of eggs they sire to make inferences
about the efficiency of selective breeding for broiler chickens, then use the results to
discuss selection on spur length.
Animal scientists seeking to increase body weight of chickens through selective
breeding, or keen to reduce chicken-on-chicken aggression by blunting spurs may
be reluctant to adopt that approach. They may instead look at heritability of adult
mass. This is fairly high in bighorn sheep [3], while heritability of lamb mass is
nearly zero [4, 5]. We suggest that [1] cannot assess the evolutionary impacts of
selective hunting as it assumes no inheritance.
Models are a caricature of reality and cannot capture all the complexity of the real
world. Their worth depends on how well they incorporate known biological reality.
The functions used to build this bighorn IPM, however, are at times questionable, at
times not based on the data we provided.
Readers who accept that the inheritance function in [1] is relevant to understanding
the possible selective effects of trophy hunting on mass or horn size need not read
further. Once that function is set to an insignificant slope of 0.0195, details of ram
survival or mating success become irrelevant in the simulation. Readers interested
in ungulate biology, however, may find the following useful. We discovered these
characteristics of [1] after we had coauthored our comment.
0.6
0.4
0.0
0.2
Survival
0.8
1.0
Figure 2A in [1] shows a surprising strong negative relationship between mass and
survival of adult rams, and a positive relationship for senescent rams. Those
estimates include rams that were shot. When survival estimates based on the data
we provided to Traill et al. exclude harvested males in the year of death, a very
different picture emerges:
20
40
60
80
100
120
140
MassSept15
Fig. 1. Natural survival of bighorn rams at Ram Mountain. Black dashed: lambs;
solid black: yearlings; solid gray: adults (2-7 years), solid blue: senescent rams (8+
years). Rams shot by hunters were excluded in the year of death.
The effect of mass on survival estimates for adult rams remains slightly negative,
likely because rams aged 2 and 3 years are lighter and have higher survival than
those aged 6-7 [6], but the drastic drop reported by [1] disappears. The nonsignificant positive effect of mass on survival of senescent rams becomes steeper.
The impact of harvest mortality on survival is not trivial: Fig. 2A in [1] suggests a
decline of over 20% in annual survival within a biologically plausible mass range for
breeding adult rams (85-125 kg): from about 81% to about 59%. The actual decline
is about 4-5%, and almost entirely attributable to age. The survival function of Fig. 2
in [1] is used in the IPM, as confirmed by Table S1. The use of a separate intercept
for survival of harvested and not harvested rams is useful to explain the variability
in survival. It would be interesting to know how it is implemented in the IPM. We
have been told that the answer is in Table S1.
Next, look at figures 2B and 2D in [1]: small breeders (lighter than about 85 kg) are
shown in 2D but disappear in 2B. The reason for this difference is unclear. The
mating function in [1] is not based on Fig. 2B. The flat relationship in Fig. 2D means
that whether or not mass affects ram mating success is nearly irrelevant, as it does
not affect lamb mass or its subsequent development as modeled by the IPM. We are,
however, concerned about the misrepresentation of our data: Fig 2B in [1] implies
that even the heaviest rams have about a 20-25% chance of mating. That seems
pessimistic.
0.6
0.4
0.0
0.2
Bred or not?
0.8
1.0
The actual data look like this:
20
40
60
80
100
120
Ram mass in t
Fig. 2. Effect of body mass on Ram breeding success. Excludes rams in the year they
were shot because the hunt is before the rut. Dashed line is for rams aged between 2
and 7 years (adults). Solid line is for males aged 8 and older (senescent). Predicted
lines are from a linear mixed effect model including Id and year as random effects.
One model was fitted for each age class.
Here is the description of the IPM mating function from [1] (p. 13227):
“In our model we assume that male mating success increases linearly with male
body mass and intercept and slope of that function increases with male age, thus
achieving a size and age dependence of sexual selection. In reality, a few largebodied and dominant males sire most of the offspring (38), so we attempt to
simulate this by assigning 15% of successful male mating to the oldest age class and
50% to the heaviest quarter of reproducing rams. We included stochasticity as year
effects (based on the random effects intercept for the generalized models for
survival).”
That is interesting, but not based on data. Relative age-specific mass and horn
length indeed play a greater role in mating success of older rams, because a large 5year-old will not do much better than a small 5-year-old, while by about age 8
relative mass will be very important [7]. That is partly because mass increases until
about 7-8 years of age. Large 5-year-olds will be beaten by older rams that are
heavier. We have no evidence, however, of a positive interaction between age and
absolute mass affecting ram mating success. The IPM in [1] includes an interaction
of absolute mass and ram age. For example, it gives a 100-kg male a much higher
mating success when aged 10 than when aged 5. To achieve the same mating
probability of an 85-kg 8-year-old, a 6-year-old needs to weigh about 125 kg. The
attribution of 15% of paternities to 12-year-olds is interesting, given that only about
4-5% of yearling rams in unhunted populations survive to 12 years [6]. In the
modelled hunted population, there would be almost no 12-year-olds.
In a data-based scenario, a large ram would have a natural survival rate comparable
to that of lighter rams, and if it survived to about 7 years of age it would enjoy high
reproductive success because it would be dominant to lighter rams, including older
ones [7-10]. In [1], large rams aged 2-7 suffer higher mortality than light rams and
are outcompeted by lighter older rams, which should be numeorus because of the
negative mass-dependent survival at 2-7 years.
A paper on the selective effects of trophy hunting published in 2003 [11] used
quantitative genetic approaches and breeding values widely used in evolutionary
ecology at the time. The estimation and use of breeding values have since been
criticized for failing to adequately model correlated environmental effects and for
being intrinsically anti-conservative [12, 13]. We are analyzing a longer time series
taking into account those criticisms. Analyses of trait heritability accounting for
year effects have been published [3] but were ignored in [1]. Selective effects of
harvesting are undoubtedly real, but their genetic consequences are difficult to
accurately measure in wild populations. The IPM model in [1] claims to be an
alternative to [11]. It combines an unusual measure of inheritance with an
imaginary meat hunt and unrealistic survival and mating functions. We submit that
it is irrelevant to our understanding of the selective effects of selective hunting.
[1] Traill, L.W., Schindler, S. & Coulson, T. 2014 Demography, not inheritance, drives
phenotypic change in hunted bighorn sheep. Proceedings of the National Academy of
Sciences 111, 13223-13228.
[2] Traill, L.W., Schindler, S. & Coulson, T. 2014 Reply to Hedrick et al.: Trophy
hunting influences the distribution of trait values through demographic impacts.
Proceedings of the National Academy of Sciences 111, E4811.
[3] Poissant, J., Wilson, A.J., Festa-Bianchet, M., Hogg, J.T. & Coltman, D.W. 2008
Quantitative genetics and sex-specific selection on sexually dimorphic traits in
bighorn sheep. Proceedings of the Royal Society of London B 275, 623-628.
(doi:doi:10.1098/rspb.2007.1361).
[4] Réale, D., Festa-Bianchet, M. & Jorgenson, J.T. 1999 Heritability of body mass
varies with age and season in wild bighorn sheep. Heredity 83, 526-532.
[5] Wilson, A.J., Kruuk, L.E.B. & Coltman, D.W. 2005 Ontogenetic patterns in
heritable variation for body size: using random regression models in a wild ungulate
population. American Naturalist 166, E177-E192.
[6] Loison, A., Festa-Bianchet, M., Gaillard, J.-M., Jorgenson, J.T. & Jullien, J.-M. 1999
Age-specific survival in five populations of ungulates: evidence of senescence.
Ecology 80, 2539-2554.
[7] Coltman, D.W., Festa-Bianchet, M., Jorgenson, J.T. & Strobeck, C. 2002 Agedependent sexual selection in bighorn rams. Proc. R. Soc. London B 269, 165-172.
[8] Bonenfant, C., Pelletier, F., Garel, M. & Bergeron, P. 2009 Age-dependent
relationship between horn growth and survival in wild sheep. Journal of Animal
Ecology 78, 161-171.
[9] Festa-Bianchet, M., Jorgenson, J.T., Bérubé, C.H., Portier, C. & Wishart, W.D. 1997
Body mass and survival of bighorn sheep. Can. J. Zool. 75, 1372-1379.
[10] Pelletier, F. & Festa-Bianchet, M. 2006 Sexual selection and social rank in
bighorn rams. Animal Behaviour 71, 649-655.
[11] Coltman, D.W., O’Donoghue, P., Jorgenson, J.T., Hogg, J.T., Strobeck, C. & FestaBianchet, M. 2003 Undesirable evolutionary consequences of trophy hunting. Nature
426, 655-658.
[12] Hadfield, J.D., Wilson, A.J., Garant, D., Sheldon, B.C. & Kruuk, L.E.B. 2009 The
misuse of BLUP in ecology and evolution. American Naturalist 175, 116-125.
[13] Postma, E. 2006 Implications of the difference between true and predicted
breeding values for the study of natural selection and micro-evolution. Journal of
Evolutionary Biology 19, 309–320.