Supplementary Information for “Life-history traits of voles in a fluctuating population
respond to the immediate environment”
Nature 411, 1043
Torbjørn Ergon, Xavier Lambin & Nils Chr. Stenseth
Density (voles ha-1)
400
300
200
100
A B
C D
0
400
300
200
100
0
'97
'98
'99
'00
'97
'98
'99
'00
Year
Supplementary figure 1. Density trajectories at the four sites. Open circles are
based on vole sign indices (see ref. 21 in paper). Estimates plotted as filled circles
are obtained by the ‘robust design model’ (see ref. 27 in paper) of capture-markrecapture data. Triangles show density estimates (vole sign indices) of voles in a
neighbouring control site. Vertical lines show the time of transplant.
Males:
30
25
time ***
site ***
time × site ***
C to D
time ***
site ***
time ***
site ***
D to A
B to A
time *
site (*)
time ***
D to B
site NS
time × site **
B to C
Body mass (g)
mean ± SE
20
D to C
A to D
A to B
B to D
C to A
15
Females:
30
time **
time (*)
site **
no change
25
D to C
D to A
site (*)
time **
B to C
D to B
B to A
20
C to D
15
1/12 1/1 1/2 1/3
C to B
A to D
1/12 1/1 1/2 1/3
1/12 1/1 1/2 1/3
1/12 1/1 1/2 1/3
B to D
1/12 1/1 1/2 1/3
Date
Supplementary figure 2. Change in body mass of transplanted voles that were
recaptured during the first session after transplanting. Lines connect means (±SE) of
the same individuals before and after transplant. Changes in individual body mass
were analysed with a repeated-measures cross-over analysis (individuals as random
subjects and an unstructured covariance matrix for repeated measurements fitted in
SAS Proc MIXED28). Significant effects from separate analysis of each pair of
transplants for each sex are given in each sub-plot (***: p<0.001, **: 0.001<p<0.01, *:
0.01<p<0.05, (*): 0.05<p<0.1, NS: not selected by the lowest AIC). A ‘time’ effect
indicates a change in body mass over time, whereas a ‘site’ effect indicates a change
in body mass due to the transplantation between sites. The interaction effect
(‘time*site’) implies carry-over effects or effects caused by the fact that the sites were
not trapped on the same days.
Analysis of transplant success
Only 266 of the 761 transplanted voles were ever recaptured after transplant. A potential bias
of the differences between transplant groups could arise from differential selection (i.e.,
transplant success) in the transplant groups. To statistically test whether transplant success
was differently related to body mass and reproductive history in the different transplant
groups we employed logistic regression models. This analysis show that there is no reason to
believe that differential selection among the transplant groups invalidates our interpretation
that direct environmental effects are the main source of variation in spring growth and
maturation.
When considering transplant group (10 groups, see figure 1 in paper), sex, body mass,
reproductive history (previously reproduced or not) and all possible interactions, the best
model selected by a step-wise AIC-based procedure (the stepAIC function in the S-Plus
library MASS (Venables, W. N., and B. D. Ripley. 1997. Modern Applied Statistics with SPlus, Springer)) includes the following effects:
Terms added sequentially (first to last)
Df
Deviance
NULL
Resid. Df
Resid. Dev
758
980.7
Pr(Chi)
Group
9
62.64
749
918.1
<0.0001
Sex
1
0.16
748
917.9
0.68
Rep
1
4.84
747
913.1
0.028
Group:Sex
9
32.69
738
880.4
<0.0001
Forcing the Group×Mass effect to stay in the model during the selection procedure gives:
Group:Mass
Df
Deviance
9
5.52
Resid. Df
713
Resid. Dev
848.3
Pr(Chi)
0.79
Forcing the Group×Reproductive history effect to stay in the model during the selection
procedure result in:
Df
Deviance
Resid. Df
Resid. Dev
Pr(Chi)
Group:Rep
9
9.98
729
870.4
0.35
Because the tests of the above interaction terms suffer from low statistical power, we also
tested the interactions of ‘Site’ and ‘Source’ with ‘Body mass’ and ‘Reproductive history’.
The selected model (by the lowest AIC – see above) when considering ‘Site’ and ‘Source’ as
predictors includes the following effects:
Terms added sequentially (first to last)
Df
Deviance
NULL
Resid. Df
Resid. Dev
760
985.0
Pr(Chi)
Site
3
0.81
757
984.2
0.85
Source
3
46.13
754
938.0
<0.0001
Sex
1
0.09
753
938.0
0.76
Rep
1
4.33
752
933.6
0.037
Site:Source
5
20.46
747
913.1
0.0010
Site:Sex
3
2.92
744
910.2
0.40
Source:Sex
3
20.43
741
889.8
0.0001
Site:Source:Sex
3
9.36
738
880.4
0.025
The ‘site’ and ‘source’ interactions with body mass and reproductive history when these
effects are forced to stay in the model during the selection procedure (one by one) results in
the following tests:
Df Deviance Resid. Df Resid. Dev Pr(Chi)
Site:Mass
3
0.494
722
861.5
0.92
Source:Mass
3
1.476
722
860.5
0.69
Site:Rep
3
6.106
737
883.5
0.11
Source:Rep
3
4.338
738
885.4
0.23
In conclusion, there is no significant ‘body mass × transplant group’ or ‘reproductive state ×
transplant group’ effect on the probability of recapture after transplant. There is a significant
effect of reproductive history on transplant success, although there is no significant difference
in the relations between the sites. Post-reproductive voles have a lower transplant success than
pre-reproductive ones (odds-ratio = 0.7). This probably reflects variation in the “background”
mortality rather than responses to the transplant per se because the frequency of post-
reproductive voles always decline over the winter (in this and other unpublished datasets from
the study system).
Although we found no support for differential effects of body mass and reproductive state on
the success of transplant, there may still have been differential selection with respect to other
unmeasured traits. Nevertheless, two facts point to the importance of individual level
responses to changes in the environment even if differential selection has influenced the
results:
1. The results presented in figure 2 in the paper clearly show change in individual body mass.
2. The magnitude of the differences in growth and maturation that we observed suggest that
selection cannot alone be responsible for the site effects. For example, among the males that
originated from site A, even the slowest growing among those moved away from the site grew
larger than the fastest growing of the ones that stayed behind in site A. The figure below
shows body mass of males that originated from site A. The letter denotes the site the voles
lived in (note that most A voles are immigrants, but immigrants were not statistically different
from other voles in the same site – see figure 3 in the paper).
50
B
B
B
B
B
D
BB
D
B
30
Body Mass
40
DD
B
20
DD
B
DD
DBB
B
C
C
B
BB
B
B
A
A D
DD
D
DD
A
A AAAD
D
A DD
A
A
A
A
13 Jan 99
03 Feb 99
24 Feb 99
D
DD
B
D B
D
D
A DD
A
A
A
AA
CC
A AA
A
AAA
AAA
A
A
C
D
D
DDD
D
AD
A
AA
AA
AA
A
A
17 Mar 99
B
DD
DD
A DD
C
AA
A
AAA
AA
AA
AA
A
07 Apr 99
B
DD
A
A
AAA
A
AA
AAA
A
AA
AAAAA
AAA
AAA
AA
AA
A
A
28 Apr 99
A
A
A
A
AA
AAA
A
A
19 May 99
Date
We conclude that the interpretation that direct environmental effects are the main source of
variation in spring growth and maturation is robust.