Results
We had 651 photographs where shedding fraction could be well-estimated.
Photographs provided good spatial coverage as they spanned latitudes
37.6°N to 61.1°N and elevations between 0 at Glacier Bay, Alaska and
4333m in the southern Rocky Mountains of Colorado, USA. However, these
two environmental variables (latitude and elevation) were negatively
correlated (Figure 2). Community-submitted photographs were taken
between 1948 and 2018; but, as expected, dates were heavily biased
towards the latter few years (Figure 3). Sex and status with/without kid
could only be attributed to 55% of the photographs, and most
photographs were of females with kids (sample sizes: FN = 94, FY = 202,
FX = 61, MN = 104, XN = 2, XX = 188).
Animals predominantly shed over a 3-month period between day of year
(DOY) 150 (May 29) and DOY 250 (September 6) (Figure 3). We noted that
shedding estimates for 16 animals were unusually low and late in the
season (i.e., after DOY 220, see Supplementary Materials). These
photographs may be associated with incorrect dates and were removed from
the statistical analysis, as they will likely result in biased parameter
estimates; our final sample size was 635.
The photographs indicate that, on average, males shed earlier than
females and females with kids tend to shed later than females without
kids (Figure 3). There was no clear pattern of long-term trends in
shedding (Figure 3). Our statistical model was able to reproduce the
observed patterns of shedding (Figure 4) and supported these conclusions
(Table 1). The model estimated that about two-thirds of animals
photographed were female and half of those had a kid. There was strong
evidence that males shed before females by about 6.4 days, and that
females shed later when with kid by about 5.5 days.
The model did not find evidence of a long-term trend in either the date
or rate of shedding; 80% credible intervals (CIs) forτ Y and α Y contained zero
(Table 1). There was also not strong evidence that the rate of shedding
varied stochastically between years (Figure 5). However, there was some
evidence that in recent years (2015-2018) the date of shedding may have
been begun earlier by up to a week, relative to the long-term average
(Figure 5A). Note that the model also predicts earlier shedding for 1999
and 2004, however these estimates should be treated with caution as in
these years sample size was low and animal state was always unknown
(i.e., sex, female status with/without kid).
Shedding date was positively associated with elevation and latitude
(i.e., delayed), and shedding rate was greater at higher latitudes
(Table 1). The negative correlation between elevation and latitude
resulted in positive correlations between model parameters associated
with elevation and latitude (Supplementary Materials). Nonetheless,
posterior parameter estimates resulted in the model predicting slightly
later but shorter shedding periods at higher latitudes (Figure 6).
Although the number of animals observed during the study at YWP was very
low (animal numbers: FN = 9, FY = 3, MN = 2), the 58 photographs suggest
that males shed before females and females with kids had delayed
shedding (Figure 7). The model fit strongly supported animal state as
being an important determinant of the timing of shedding (Table 2). In
this case, on average, males were estimated to shed 23.7 days earlier
than females and the presence of a kid delayed female shedding date by
17.9 days. These offsets are greater than those predicted by the
community science analysis and may be the result of biases due to low
sample sizes for the YWP study, or uncertainty in animal state inherent
with the community data. Interestingly, the shedding date estimate of
alone females, τ 0, for the YWP study, is later
than the population-wide estimate associated with the community study,
however these two estimates are consistent because YWP is at the extreme
northerly latitude, and latitude is predicted to be associated with
delayed shedding date.