SUPPLEMENT 2 – ACCOUNTING FOR THE USE OF HETEROTHERMY
Use and duration of torpor has long been proposed as one explanation for the inordinately
high longevity quotient of bats relative to other mammals [1], and it has also been linked to
reduced extinction risk for non-chiropteran mammals [2,3]. For this reason we had expected
that it could perhaps have an impact on annual survival, and explored three possible means of
accounting for it in our survival model.
Latitude
There is some disagreement in the literature about whether use of temporal heterothermy can
be defined in a categorical fashion or occurs as a continuum [4,5], but we felt that a
continuous measure was more likely to be ecologically realistic. Therefore, as a first attempt,
we followed Wilkinson and South [6] and tested absolute latitude of each study as a proxy for
a species’ proclivity to use- or duration of- torpor and hibernation. However, early in the data
visualisation and exploration process, it became clear that latitude had far less of an influence
on bat annual survival estimates than the other variables presented in the body of this paper,
so it was discarded as a potential explanatory variable.
Daily heterotherms versus hibernators
We then explored whether categorisation of heterothermic behaviour might act as a better
indicator of annual survival. We had assumed in our initial analysis that latitude was acting as
a suitable proxy for heterothermy, so we first confirmed this by taking the 38 bat species
which Ruf and Geiser [5] had included in their categorisation study (made up of 28
“hibernators”, and 10 species which use “daily torpor”) and compared the absolute latitudes
of each (Fig. S1). An unequal variance t-test revealed that there were clear differences in the
absolute latitudes at which the two groups occur (p < 0.00001, t = -7.36, df = 35.9, daily
heterotherm mean absolute latitude = 4.75, hibernator mean absolute latitude = 27.8).
Figure S1 – Absolute latitudes of 10 species of bats classified as daily heterotherms (DH) and
28 species of hibernators (HIB).
We also took 37 species from our data set which we were confident in classifying as
hibernators or daily heterotherms, based on Ruf and Geiser [5] and Stawski et al. [7]. We ran
the best model as presented in the main body of this study (Table 1) with just those 37
species, and then another model which included a categorical “hibernator” covariate to
indicate whether each species was a daily heterotherm or hibernator:
Model1: logit(ϕ) ~ α + β1(number of young - µnumber of young) + βguild + βsex + βage + βmethod + βseason + εspecies
Model 2: logit(ϕ) ~ α + β1(number of young - µnumber of young) + βguild + βsex + βage + βmethod + βseason + βhibernator +
εspecies
Following this process we found that the inclusion of the “hibernator” term resulted in a
worse DIC value, and the 95% credible interval for the coefficient was very wide and
included 0 ([-0.401, 1.096], i.e. it was not statistically significant). We therefore concluded
that compared with the strong influence of other factors such as the number of young, age,
and feeding guild, use of heterothermy was having either zero or a very weak effect on the
annual survival rates of the bats in our study.
Heterothermy index
Detailed information about the heterothermic behaviour of most bat species is scant,
nonetheless as a final step we tested including the heterothermy index (HI) detailed by Boyles
et al. [4] in to the analyses. This was problematic, as winter HI's were available for only
seven of our study species (Chalinolobus morio, Eptesicus fuscus, Myotis lucifugus, Myotis
nattereri, Nyctophilus geoffroyi, Perimyotis subflavus, Rhinolophus ferrumequinum). We first
attempted to incorporate the HI of these species using the same approach as detailed above
for categories of heterothermy (see above): by running the best model with and without the
variable. However, there were too few data for this and our models would not converge.
Hence, we chose to run a model with just HI and the two most important variables from our
best model, which were age and number of young. The model was therefore:
logit(ϕ) ~ α + β1(number of young - µnumber of young) + βage + βHI + εspecies
This model converged, but because of the low number of data points (58) only age emerged
as having any effect on annual survival:
Posterior mean
95% credible
interval
Intercept (Age - Juvenile)
0.664
[-0.352, 1.858]
Number of young
Hibernator Index
Age - Adult
Age - Pooled
-0.275
-0.089
0.964
0.064
[-2.773, 2.004]
[-0.421, 0.254]
[0.552, 1.373]
[-0.563, 0.673]
Parameter
The estimate for HI was negative (though the credible intervals were wide), which is the
opposite of what one would expect if extensive use of heterothermy was the cause of the
increased longevity quotients in bats, so this result appears to be suspect.
In conclusion, in spite of our best attempts to account for heterothermy in various ways, we
found that other factors such as age, number of young, sex and guild are having a stronger
effect on annual survival of microbats. However, advances in technologies such as thermal
telemetry and loggers which allow for cheaper and easier estimation of heterothermy indices
may mean that there will be a greater number of reliable measures of this in future. We have
provided all the code, data, and detail necessary for other users to take model and refine it to
fit their needs or accommodate new data such as this.
Reference
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