SUPPORTING INFORMATION
Section 1: Estimation of the core home range
The use of an individual’s home range does not tend to be uniform. As a result, the investigation of
the consequences of home range use should focus on the part of the home range that is frequently
used, known as the core home range. Random space use within a home range results in a positive
linear correlation between home range area and the number of observations/fixes used to estimate the
home range. However, if part of the home range is used to a greater degree, the relationship between
home range area and the number of observations results in a concave curve below that of random use
(see plot below). The core home range is then defined as the point where the probability density
results in the curves of observed and random home range area having the same gradient (Powell
2000). This is also the point at which the difference between these two curves is maximal (Powell
2000).
An example of an individual’s plot of kernel density against home range area, where the solid line represents the
actual use of the home range and the dashed line represents random/even use of the home range. The arrow shows
the point at which the distance between these two lines is greatest (in this case an isopleth of 66%), which represents
the kernel density that signifies the core home range.
We extracted all individuals, of both sexes, that were born in/after 1985, had birth date information
and a known death year, which had survived to at least one year of age and had been seen at least ten
times (868 females and 641 males). We then calculated each individual’s home range at density
isopleths ranging from 20% to 95%, extracting the home range area (hectares) at each step. We then
used these points to generate a home range area-kernel density contour curve which we could then
compare to a straight line representing random use of the home range (this line represents the case
where home range area is directly proportional to the kernel density). For each individual we then
extracted the kernel density percentage at which the difference between the predicted (random use)
home range area and observed home range area was greatest. Once this had been done for each
individual, we calculated the mean density isopleth representing the core home range for each sex.
Section 2: Incremental area analysis
So-called ‘incremental area analysis’ can be used to calculate the minimum number of observations
necessary to adequately describe home ranges. We took every individual that adhered to the criteria
used to estimate the kernel density and then, starting at 10 observations, adding one additional
observation each time until we reached the maximum number of observations available for each
individual, we used the package ‘adehabitatHR’ (Calenge 2006) to calculate the core home range
(70% isopleth). We then extracted the area in hectares of the home range estimated at each step and
calculated the percentage increase in home range area as each observation was added. We defined an
asymptote as the point on the observation-area curve at which home range area increased by no more
than 5 %. Once this had been done for each individual we extracted those for which an asymptote was
reached (798 females and 500 males), and calculated the mean number of observations needed to
reach an asymptote in home range area for each sex.
Section 3: Additional tables
Table S1 - Model selection tables for female LBS, LRS and components when considering
individuals with ≥ 49 observations. The top model set are shown in bold (models within ∆AIC <2 of
best model).
Model predictors
logLik
AICc/QAICc ∆AICc/QAICc ωi
2
Density + % H. lanatus
-1470.7
1293.8
0.00
0.547
1
Density + % H. lanatus + %
H. lanatus2
-1470.6
1295.7
1.93
0.208
4
% H. lanatus
-1476.9
1297.1
3.36
0.102
5
Density
-1477.4
1297.6
3.83
0.081
3
% H. lanatus + % H. lanatus2
-1476.5
1298.9
5.10
0.043
6
Intercept only
-1482.9
1300.4
6.65
0.020
2
Density + % H. lanatus
-1404.5
1193.9
0.00
0.510
1
Density + % H. lanatus + %
H. lanatus2
-1403.9
1195.5
1.58
0.232
5
Density
-1410.5
1197.0
3.07
0.110
4
% H. lanatus
-1411.2
1197.6
3.67
0.081
3
% H. lanatus + % H. lanatus2
-1410.3
1198.8
4.90
0.044
6
Intercept only
-1416.6
1200.1
6.22
0.023
Model
LBS
LRS
Fecundity
2
Density + % H. lanatus
-128.6
265.2
0.00
0.623
1
Density + % H. lanatus + %
H. lanatus2
-128.5
267.2
1.96
0.234
5
Density
-131.2
268.4
3.23
0.124
4
% H. lanatus
-133.6
273.2
7.98
0.012
3
% H. lanatus + % H. lanatus2
-133.6
275.2
10.01
0.004
6
Intercept only
-135.8
275.7
10.49
0.003
5
Density
-1281.4
1890.2
0.00
0.318
2
Density + % H. lanatus
-1280.3
1890.7
0.45
0.253
6
Intercept only
-1283.6
1891.5
1.28
0.167
4
% H. lanatus
-1282.7
1892.1
1.94
0.120
1
Density + % H. lanatus + %
H. lanatus2
-1280.2
1892.6
2.37
0.097
3
% H. lanatus + % H. lanatus2
-1282.7
1894.1
3.94
0.044
6
Intercept only
-685.8
1032.3
0.00
0.357
5
Density
-685.1
1033.1
0.87
0.232
4
% H. lanatus
-685.7
1034.1
1.86
0.141
3
% H. lanatus + % H. lanatus2
-684.7
1034.7
2.40
0.108
2
Density + % H. lanatus
-684.9
1034.9
2.63
0.096
1
Density + % H. lanatus + %
H. lanatus2
-684.0
1035.6
3.35
0.067
Longevity
Offspring
survival
Table S2 - Model selection tables for female LBS, LRS and components when considering
individuals with ≥ 100 observations. The top model set are shown in bold (models within ∆AIC <2 of
best model).
Model predictors
logLik
AICc/QAICc ∆AICc/QAICc ωi
1
Density + % H. lanatus + %
H. lanatus2
-962.0
1388.3
0.00
0.726
2
Density + % H. lanatus
-965.2
1390.8
2.59
0.199
5
Density
-968.5
1393.5
5.27
0.052
3
% H. lanatus + % H. lanatus2
-968.6
1395.7
7.45
0.017
4
% H. lanatus
-972.3
1399.0
10.74
0.003
6
Intercept only
-974.6
1400.2
11.98
0.002
1
Density + % H. lanatus + %
H. lanatus2
-938.9
1233.2
0.00
0.791
2
Density + % H. lanatus
-943.2
1236.7
3.47
0.139
5
Density
-946.3
1238.7
5.46
0.052
3
% H. lanatus + % H. lanatus2
-946.6
1241.1
7.93
0.015
4
% H. lanatus
-951.4
1245.4
12.18
0.002
6
Intercept only
-953.5
1246.0
12.81
0.001
2
Density + % H. lanatus
-33.4
74.9
0.00
0.319
1
Density + % H. lanatus + %
H. lanatus2
-32.5
75.1
0.21
0.286
3
% H. lanatus + % H.
lanatus2
-34.3
76.7
1.79
0.130
4
% H. lanatus
-35.3
76.7
1.84
0.127
5
Density
-35.7
77.5
2.65
0.085
6
Intercept only
-37.2
78.5
3.59
0.053
Model
LBS
LRS
Fecundity
Longevity
5
Density
-846.8
1697.7
0.00
0.507
1
Density + % H. lanatus + %
H. lanatus2
-845.6
1699.3
1.60
0.28
2
Density + % H. lanatus
-846.6
1699.3
1.60
0.228
6
Intercept only
-851.1
1704.1
6.46
0.020
3
% H. lanatus + % H. lanatus2
-849.8
1705.6
7.95
0.010
4
% H. lanatus
-851.0
1706.0
8.38
0.008
6
Intercept only
-550.5
892.6
0.00
0.315
5
Density
-549.4
892.9
0.28
0.274
4
% H. lanatus
-550.4
894.6
1.98
0.117
2
Density + % H. lanatus
-549.3
894.8
2.18
0.106
3
% H. lanatus + % H. lanatus2
-549.3
894.9
2.27
0.102
1
Density + % H. lanatus + %
H. lanatus2
-548.3
895.2
2.60
0.086
Offspring
survival
Table S3 – Parameter values for the best models (and model averaging) describing the relationships
between female reproductive performance and the mean proportion of H. lanatus grassland in the core
home range. This analysis includes those individuals with at least 100 observations for delimiting
their home range.
Term
Parameter estimate (SE)
t/z*
P
Female LBS
Best model
Percentage H. lanatus
2.9×103 (1.8×103)
1.57
0.117
Density
-9.9×10-4 (3.2×10-4)
-3.08
0.002
Percentage H. lanatus2
3.3×10-4 (1.5×10-4)
-2.14
0.032
2.9×103 (2.2×103)
1.36
0.174
Female LRS
Best model
Percentage H. lanatus
Density
-1.2×103 (3.8×10-4)
-3.15
0.002
Percentage H. lanatus2
-4.2×10-4 (1.8×10-4)
-2.33
0.020
Percentage H. lanatus
2.3×103 (1.1×103)
2.16
0.031
Density
-3.9×10-4 (2.0×10-4)
-1.97
0.050
Fecundity
Best model
Model averaged
Percentage H. lanatus
2.0×103 (1.1×103)
1.84
0.066
Density
-2.7×10-4 (2.4×10-4)
1.11
0.266
Percentage H. lanatus2
-6.1×10-5 (8.9×10-5`)
0.68
0.497
-7.3×10-4 (2.0×10-4)
-3.57
<0.001
Percentage H. lanatus
3.0×10-4 (8.5×10-4)
0.35
0.729
Density
-7.3×10-4 (2.0×10-4)
3.57
<0.001
Percentage H. lanatus2
-4.0×10-5 (8.5×10-5)
0.47
0.641
1.3 (0.05)
25.34
<0.001
Percentage H. lanatus
1.6×10-4 (1.7×10-3)
0.09
0.925
Density
-3.7×10-4 (6.5×10-4)
0.57
0.568
Longevity
Best model
Density
Model averaged
Offspring survival
Best model
Intercept
Model averaged
*z values were obtained from the model averaging procedure
Table S4 – Model selection tables for male LBS, LRS and components when considering individuals
with ≥ 39 observations. The top model set are shown in bold (models within ∆AIC <2 of best model).
Model predictors
logLik
AICc/QAICc ∆AICc/QAICc ωi
2
Density + % H. lanatus
-2108.6
195.8
0.00
0.360
5
Density
-2136.6
196.3
0.44
0.289
1
Density + % H. lanatus + %
H. lanatus2
-2105.1
197.6
1.75
0.150
4
% H. lanatus
-2159.8
198.3
2.51
0.103
3
% H. lanatus + % H. lanatus2
-2151.0
199.6
3.78
0.055
6
Intercept only
-2202.0
200.1
4.22
0.044
5
Density
-1609.7
204.4
0.00
0.443
2
Density + % H. lanatus
-1596.5
204.8
0.43
0.357
1
Density + % H. lanatus + %
H. lanatus2
-1593.9
206.6
2.17
0.150
4
% H. lanatus
-1658.1
210.4
5.96
0.022
6
Intercept only
-1682.4
211.3
6.92
0.014
3
% H. lanatus + % H. lanatus2
-1650.0
211.4
7.01
0.013
5
Density
-540.7
1087.4
0.00
0.420
2
Density + % H. lanatus
-539.7
1087.6
0.15
0.389
1
Density + % H. lanatus + %
H. lanatus2
-539.7
1089.5
2.07
0.149
4
% H. lanatus
-543.7
1093.4
5.95
0.021
3
% H. lanatus + % H. lanatus2
-543.4
1094.9
7.46
0.010
6
Intercept only
-545.4
1094.9
7.49
0.010
4
% H. lanatus
-620.4
1244.8
0.00
0.350
2
Density + % H. lanatus
-619.7
1245.4
0.64
0.254
Model
LBS
LRS
Fecundity
Longevity
3
% H. lanatus + % H.
lanatus2
-619.7
1245.5
0.73
0.242
1
Density + % H. lanatus + %
H. lanatus2
-619.2
1246.5
1.71
0.149
5
Density
-625.1
1254.2
9.42
0.003
6
Intercept only
-626.7
1255.3
10.55
0.002
Table S5 – Model selection tables for male LBS, LRS and components when considering individuals
with ≥ 100 observations. The top model set are shown in bold (models within ∆AIC <2 of best
model).
Model predictors
logLik
AICc/QAICc ∆AICc/QAICc ωi
5
Density
-940.0
94.2
0.00
0.535
2
Density + % H. lanatus
-936.7
95.9
1.69
0.230
6
Intercept only
-999.9
97.8
3.62
0.088
1
Density + % H. lanatus + %
H. lanatus2
-936.6
97.9
3.68
0.085
4
% H. lanatus
-993.1
99.2
4.98
0.044
3
% H. lanatus + % H. lanatus2
-991.8
101.0
6.85
0.017
5
Density
-697.7
100.9
0.00
0.650
2
Density + % H. lanatus
-697.2
103.0
2.10
0.228
1
Density + % H. lanatus + %
H. lanatus2
-696.6
105.1
4.23
0.078
6
Intercept only
-760.0
107.2
6.32
0.028
4
% H. lanatus
-757.5
109.0
8.11
0.011
3
% H. lanatus + % H. lanatus2
-754.5
110.8
9.87
0.005
Density
-212.6
431.5
0.00
0.614
Model
LBS
LRS
Fecundity
5
2
Density + % H. lanatus
-212.6
433.5
2.08
0.217
1
Density + % H. lanatus + %
H. lanatus2
-212.5
435.7
4.20
0.075
6
Intercept only
-216.0
436.1
4.64
0.060
4
% H. lanatus
-215.9
438.0
6.49
0.024
3
% H. lanatus + % H. lanatus2
-215.7
439.9
8.40
0.009
4
% H. lanatus
-204.5
413.2
0.00
0.269
2
Density + % H. lanatus
-203.5
413.3
0.11
0.254
5
Density
-205.0
414.2
0.99
0.164
6
Intercept only
-206.3
414.6
1.40
0.133
3
% H. lanatus + % H. lanatus2
-204.5
415.3
2.11
0.094
1
Density + % H. lanatus + %
H. lanatus2
-203.5
415.5
2.28
0.086
Longevity
Table S6 - Parameter values for the best models (and model averaging) describing the relationships
between male reproductive performance and the mean proportion of H. lanatus grassland in the core
home range. This analysis includes those individuals with at least 100 observations for delimiting
their home range.
Term
Parameter estimate (SE)
t/z*
P
-4.8×103 (2.0×103)
-2.38
0.019
Percentage H. lanatus
5.2×103 (0.02)
0.28
0.783
Density
-4.8×103 (2.0×103)
2.33
0.020
-5.8×103 (2.0×103)
-2.94
0.004
Male LBS
Best model
Density
Model averaged
Male LRS
Best model
Density
Fecundity
Best model
Density
-8.5×103 (3.2×103)
-2.62
0.010
Longevity
Best model
Percentage H. lanatus
0.02 (6.0×103)
2.71
0.008
Density
-8.9×10-4 (4.0×10-4)
-2.23
0.028
Percentage H. lanatus
0.01 (9.4×103)
1.13
0.257
Density
-4.7×10-4 (5.5×10-4)
0.86
0.389
Model averaged
*z values were obtained from the model averaging procedure
Section 4: Additional figures
Figure S1 – Female LBS (filled circles) and LRS (open circles) plotted against the mean percentage
cover of H. lanatus in an individual’s home range (for individuals with ≥100 census observations).
The regression lines come from the best fit generalised linear models (the solid line represents the
relationship for LBS whilst the dashed line represents the relationship for LRS).
Figure S2 – Female fecundity plotted against the mean percentage cover of H. lanatus in an
individual’s home range (for individuals with ≥49 census observations). The regression line comes
from the best fit generalised linear model.
Figure S3 – Female fecundity plotted against the mean percentage cover of H. lanatus in an
individual’s home range (for individuals with ≥100 census observations). The regression line comes
from the best fit generalised linear model.
Figure S4 – Male longevity plotted against the mean percentage cover of H. lanatus in an individual’s
home range (for individuals with ≥39 census observations). The regression line comes from the best
fit generalised linear model.
Figure S5 – Male longevity plotted against the mean percentage cover of H. lanatus in an individual’s
home range (for individuals with ≥100 census observations). The regression line comes from the best
fit generalised linear model.