1
Supplementary Information:
2
Migratory diversity predicts population declines in birds
3
List of supplements:
4
1. Methods supplement
5
2. Figure S1 – Examples of varying migratory connectivity and dispersion scenarios
6
3. Figure S2 – Plot of migratory strategy against arrival advancement
7
4. Figure S3 – Plot of migratory dispersion against arrival advancement
8
5. Table S1 – Species included in analyses (separate file)
9
6. Table S2 – List of climate bioclim variables used in climate niche modelling
10
7. Table S3 – Correlations between predictor variables
11
8. Table S4 – Variance explained by models
12
9. Table S5 – Table of top-ranked models for whole study period
13
10. Table S6 – Table of top-ranked models for 1990-2000
14
11. Table S7 – Table of top-ranked models for 2001-2012
15
16
1
17
Appendix S1 – Methods supplement
18
19
Network models of migratory dispersion and partial migration
20
Graph theory offers a powerful approach to derive hypotheses about the resilience of
21
migratory populations to environmental change (Taylor & Norris 2010; Betini et al. 2015). In
22
these models, populations are viewed as interconnected networks of seasonally-occupied
23
‘nodes’ (i.e. sites) connected by ‘edges’ (i.e. migration routes). To generate hypotheses
24
concerning links between population resilience and migratory diversity, we extended the
25
migratory network model of Taylor & Norris (2010) to examine scenarios of varying
26
migratory dispersion and partial migration within a connected migratory population network.
27
The model structure follows Taylor & Norris (2010) and assumes that a population is
28
composed of individuals with fixed migratory strategies, such that each individual uses one
29
non-breeding node (W) and one breeding node (B). Individuals interact with each other
30
through density dependence at both the W and B nodes. At time t, the total number of
31
individuals (Aij) that use the strategy of breeding at node j and migrating to node i is given by:
32
Aij (t +1) = (cij)2 Fij Sij Aij(t)
33
where cij is the survival rate during migration for an individual moving between nodes i
34
and j (assumed to be the same in both directions), Fij is the breeding success and Sij is the non-
35
breeding survival rate for individuals that migrate from breeding node j to non-breeding node
36
i.
37
38
39
The migration survival rate cij is assumed to be proportional to Dij, the Euclidian distance
between nodes i and j, and is calculated thus:
cij = exp (-0.06 Dij)
2
40
Both breeding success and survival are density dependent. Breeding success for
41
individuals breeding at node j is dependent on the abundance of individuals breeding at that
42
node, summed across all migration routes, given by:
43
44
45
𝑤
∑𝑁
ℎ=1 𝐴ℎ𝑗
𝐹𝑖𝑗 = 𝑏𝑗 exp (−
)
𝑘𝑗
where kj is the carrying capacity of the breeding node (fixed at 20,000 in all scenarios)
46
and bj is a constant (fixed at 1.4 in all scenarios). Similarly, non-breeding survival for
47
individuals migrating to node i depends on the total number of individuals migrating to that
48
node, across all migration routes, given by:
49
𝐵
∑𝑁
ℎ=1 𝐴𝑖ℎ
𝑆𝑖𝑗 = exp (−
)
𝑘𝑖
50
where ki is the carrying capacity of the non-breeding node. To ensure that carrying
51
capacity remains fixed across all migratory dispersion scenarios (see below), ki is set as the
52
summed carrying capacity of all breeding nodes, divided by the number of non-breeding
53
nodes in the scenario. We solve model numerically for each scenario by selecting a nonzero
54
random starting number of individuals in each strategy Aij , and iterating until a stable
55
equilibrium is reached. We tested for stability by repeating each scenario with multiple
56
random start points to ensure convergence at the same equilibrium.
57
To compare different migratory dispersion scenarios, we varied the number of non-
58
breeding nodes occupied by the population (see Figure 2A-D, main article), keeping the
59
breeding nodes constant. Because the carrying capacity of non-breeding nodes is a function
60
of both the total breeding carrying capacity and the number of non-breeding nodes, the
61
equilibrium population size is approximately equal in each scenario despite variation in the
62
number of non-breeding nodes (see Fig. 2, main article). Hence, the model assumes that
3
63
populations with lower migratory dispersion occupy nodes with higher carrying capacity than
64
populations with higher migratory dispersion.
65
To incorporate partial migration (Fig. 2E & F, main article), we allowed a proportion of
66
the breeding population at one breeding node to remain there for the non-breeding period.
67
These individuals avoid the cost of migration (cij2), but incur an additional survival cost pj
68
(fixed at 0.8) which reflects the potentially more challenging environmental conditions
69
encountered by residents than migrants in seasonal environments (Taylor & Norris 2007).
70
Therefore, density-dependent survival during the non-breeding period for resident individuals
71
at breeding node j is given by:
𝑆𝑗 = 𝑝𝑗 exp (−
72
73
𝐴𝑗𝑗
)
𝑘𝑤𝑗
where pj is the additional cost of residence, Ajj is the number of individuals remaining
74
resident at the node, and kwj is the carrying capacity of node j in the non-breeding period
75
(fixed at 20,000).
76
To examine how migratory dispersion and partial migration influence the resilience of
77
populations to environmental perturbation in the non-breeding season, we subjected each
78
equilibrium population to an 80% loss of carrying capacity at a single non-breeding node (see
79
Fig. 2, main article) and again iterated until a new equilibrium population size was reached.
80
We then calculated the proportionate change in total population size resulting from the
81
habitat loss.
82
Comparing relative effects of migratory dispersion and migratory connectivity
83
Connectivity arises in the network model when individuals from different breeding nodes
84
migrate to the same non-breeding nodes, such that there is mixing of breeding populations in
85
the non-breeding season (Taylor & Norris 2010). In the model, the level of connectivity
4
86
depends on the relative costs of migrating to different non-breeding nodes for individuals
87
from a given breeding node – if costs are similar across multiple migration routes,
88
connectivity will be high. As the cost of migration in the model depends on the distance
89
between nodes, connectivity levels therefore depend on the relative proximity of non-
90
breeding nodes to each other (Fig. S1). A population inhabiting nonbreeding nodes that are
91
relatively close together (Fig. S1A) shows greater connectivity than a population inhabiting
92
an equivalent number of nodes that are spaced further apart (Fig. S1B).
93
To examine the relative impact of connectivity and dispersion on the resilience of populations
94
to non-breeding habitat loss, we compared scenarios spanning a range of variation in each
95
characteristic, assuming a population has 12 breeding nodes in each scenario (with all other
96
parameters as described above). We varied migratory dispersion by varying the number of
97
non-breeding nodes from 6 to 24, quantifying dispersion as the dispersion index described in
98
the main article. To vary connectivity, we changed the horizontal spacing of nodes from 0.1
99
to 1.1 in increments of 0.1, and quantified the realized level of connectivity in each case by
100
calculating the proportion of available migration routes (i.e. available non-breeding nodes)
101
that were used by individuals at each breeding node, averaged across all breeding nodes. We
102
ran each combination of both variables, giving a total of 110 scenarios. For each scenario, we
103
ran 100 replicates where carrying capacity declined by 80% at a single randomly-chosen non-
104
breeding node, took the mean decline in equilibrium population size across all replicates as
105
the average impact in a given scenario. Results are shown in Fig. S1E.
106
References
107
Taylor, C.M. & Norris, D.R. (2007) Predicting conditions for migration: effects of
108
density dependence and habitat quality. Biol. Lett. 3, 280–283. doi:10.1098/rsbl.2007.0053
109
5
110
111
Figure S1 Examples of varying migratory connectivity and dispersion scenarios. In the
112
network model, connectivity increases when nodes are close together in latitudinal space,
113
such that migration costs for individuals at a given breeding node (green) are similar across a
114
range of non-breeding nodes (blue). Thus, a population where nodes are close together (A)
115
has higher connectivity than an otherwise identical population with nodes further apart (B).
116
We quantify connectivity as the mean proportion of available migration routes that are used
117
by individuals from a breeding node, averaged across all breeding nodes. We compared a
118
range of scenarios in which we varied both connectivity and migratory dispersion (measured
119
as the dispersion index, described in main article), with cases A-D being extremes of
120
variation in each case. For each scenario, we calculated the proportionate population decline
6
121
following 80% habitat loss at a single non-breeding node, and show the results as a heat plot
122
(E). Levels of population decline show greater variation in response to varying migratory
123
dispersion (i.e. difference along y axis) than varying connectivity (i.e. difference along x
124
axis).
7
125
126
127
128
Figure S2 Across 89 species for which data were available, rates of advance in Europe-wide
129
mean spring arrival date differed significantly between partial migrants (A) and full migrants
130
(B, F = 13.96, P<0.001). Negative changes in mean spring arrival date (x axis) indicate
131
advancing arrival times. Orange = declining species, blue = stable or increasing species.
132
8
133
134
Fig S3 Across 89 species for which data were available, rates of advance in mean spring
135
arrival date did not show any correlation with migratory dispersion. Orange = declining
136
species, blue = stable or increasing species.
137
138
9
139
140
Table S1 Dataset used in the analysis
141
<see separate file attached>
142
10
143
144
Table S2 Climate variables from the ‘bioclim’ database (www.worldclim.org/bioclim) that
were used in the seasonal climate niche breadth and overlap analysis.
145
Variable name
Description
BIO1
Annual Mean Temperature
BIO4
Temperature Seasonality (standard deviation *100)
BIO5
Max Temperature of Warmest Month
BIO6
Min Temperature of Coldest Month
BIO12
Annual Precipitation
BIO13
Precipitation of Wettest Month
BIO14
Precipitation of Driest Month
BIO15
Precipitation Seasonality (Coefficient of Variation)
146
11
147
148
149
Table S3 Correlations between continuous predictor variables. We excluded variables from analysis if they showed high correlation
150
(Pearson R > 0.5, < -0.5), retaining whichever variable of the correlated pair was deemed to have more explanatory relevance to population
151
trends. Breeding and non-breeding range size were excluded due to close correlation with climate niche overlap (R = 0.55) and climate niche
152
breadth (R = -0.54) respectively. Non-breeding range latitude was also excluded due to a correlation with migration distance (R = -0.83).
Migratory dispersion
Migratory
Migration
dispersion
distance
Non-breeding
Breeding range
range
Breeding latitude
Non-breeding
Climate niche
Climate niche
latitude
overlap
breadth
1
Migration distance
0.04
1
Breeding range
-0.31
0.43
1
Non-breeding range
-0.23
0.07
0.63
1
-0.2
0.09
0.2
0.15
1
Non-breeding latitude
-0.12
-0.83
0.03
0.28
0.28
1
Climate niche overlap
-0.06
-0.02
0.55
-0.15
-0.15
0.67
1
Climate niche breadth
0.14
0.33
0.19
-0.54
0.12
-0.33
-0.05
1
Body mass
0.09
0.03
-0.17
-0.11
0.06
0.11
-0.01
0.02
Breeding latitude
12
153
154
155
156
Table S4 Model results substituting correlated variable pairs. We repeated each analysis substituting the three variables that were eliminated
due to correlation with other variables of interest (breeding range size for climate niche overlap, winter range size for climate niche breadth, nonbreeding latitude for migration distance). Effect sizes reflect model-averaged parameter estimates 𝛽̂ and bootstrap 95% confidence intervals.
Model averaged parameter estimates with confidence intervals that do not overlap zero are shown in bold.
Dataset:
Whole period
Early period
1990-2000
̂ (LCI, UCI)
𝜷
AICc
̂ (LCI, UCI)
𝜷
AICc
̂ (LCI, UCI)
𝜷
AICc
Spring arrival
dataset (n = 89)
1990-2012
̂ (LCI, UCI)
𝜷
Partial migration
-0.44 (-0.84, -0.03)
0.92
-0.78 (-1.41, -0.15)
0.99
-0.02 (-0.56, 0.52)
0.28
-0.15 (-1.33, 1.04)
0.31
Migratory dispersion
-0.24 (-0.48, -0.02)
0.94
-0.30 (-0.67, -0.01)
0.87
-0.19 (-0.48, -0.01)
0.80
-0.39 (-0.94, 0.01)
0.75
Non-breeding latitude
-0.13 (-0.37, 0.10)
0.57
-0.41 (-0.77, -0.06)
0.88
0.16 (-0.12, 0.45)
0.60
-0.27 (-1.13, 0.56)
0.33
Breeding range size
0.21 (-0.10, 0.57)
0.42
0.38 (-0.57, 0.15)
0.56
0.06 (-0.26, 0.36)
0.27
0.34 (-0.34, 1.02)
0.42
Non-breeding range size
-0.13 (-0.47, 0.20)
0.55
-0.26 (-0.02, 0.60)
0.48
-0.03 (-0.13, 0.29)
0.27
-0.01 (-0.68, 0.68)
0.31
Breeding latitude
-0.07 (-0.32, 0.17)
0.32
-0.21 (-0.57, 0.14)
0.44
0.19 (-0.09, 0.48)
0.55
0.45 (-0.08, 1.02)
0.70
Body mass
-0.34 (-0.61, -0.06)
0.99
-0.47 (-0.96, -0.02)
0.98
-0.23 (-0.58, 0.10)
0.50
-0.52 (-1.59, 0.56)
0.61
1990-2012
Variable:
Habitat *:
1.00
Farmland
2.18 (1.28, 3.08)
Forest
0.55 (-0.10, 0.88)
Shrubland
1.23 (-0.05, 2.06)
Rocky
1.09 (-0.08, 1.52)
Wetland
1.41 (0.30, 2.20)
Guild *:
0.51 ( -0.18, 1.01)
Insectivore
0.09 (-0.52, 0.35)
Granivore
0.28 (-0.38, 1.34)
Herbivore
0.15 (-0.91, 1.21)
Spring arrival trend
0.98
-
1.97 (0.69, 3.24)
-
0.17 (-1.07, 1.39)
-
0.77 (-0.61, 2.16)
-
0.63 (-0.79, 2.03)
-
1.11 (-0.09, 2.48)
0.12
Omnivore
n/a
Late period
2001-2012
1.00
-
-0.36 (-1.30, 0.56)
-
-0.13 (-1.32, 1.03)
-
0.33 (-1.17, 1.86)
n/a
n/a
1.00
-
2.38 (1.13, 3.64)
-
0.81 (-0.43, 2.05)
-
2.12 (-0.33, 4.60)
-
1.56 (0.24, 2.90)
-
1.45 (-1.07, 4.01)
-
-
1.62 (0.24, 2.99)
-
2.35 (-0.37, 5.11)
-
-
1.69 (0.46, 2.92)
-
3.29 (0.91, 5.64)
-
0.02
0.08 (-0.86, 1.02)
AICc
-
5.88 (2.88, 8.86)
-
0.30
-
0.92 (0.02, 1.81)
-
0.39 (-0.47, 1.24)
-
0.98 (-0.06, 2.03)
-
-0.18 (-1.54, 1.16)
n/a
n/a
0.01
-
-1.28 (-3.35, 0.80)
-
-
-0.62 (-3.25, 1.12)
-
-
-0.34 (-2.70, 1.98)
-
-
-1.06 (-3.27, 1.12)
-
n/a
0.84 (0.21, 1.48)
0.98
157
13
161
Guild
Clim. niche overlap
Breeding latitude
Migration distance
Clim. niche breadth
Partial migration
Migratory dispersion
Body mass
Table S5 Details of the 40 highest-ranked models explaining variation in decline probability
across the whole survey period. Grey boxes indicate that a given term is included in the
model.
Habitat
158
159
160
df
12
11
13
13
11
12
12
12
14
12
10
13
13
10
16
11
10
10
11
11
11
15
12
10
17
11
17
9
15
11
12
12
11
10
11
11
12
12
13
9
logLik
AICc
delta
weight
-314.77
654.49
0.00
0.10
-315.86
654.52
0.03
0.10
-314.09
655.30
0.82
0.07
-314.20
655.51
1.03
0.06
-316.36
655.52
1.03
0.06
-315.42
655.79
1.30
0.05
-315.52
655.98
1.50
0.05
-315.77
656.49
2.00
0.04
-313.60
656.49
2.00
0.04
-316.07
657.09
2.60
0.03
-318.28
657.22
2.73
0.03
-315.13
657.38
2.89
0.02
-315.53
658.17
3.68
0.02
-318.78
658.22
3.73
0.02
-312.35
658.38
3.89
0.01
-317.83
658.47
3.98
0.01
-319.03
658.72
4.23
0.01
-319.11
658.89
4.40
0.01
-318.05
658.91
4.42
0.01
-318.14
659.08
4.59
0.01
-318.14
659.09
4.60
0.01
-313.87
659.23
4.74
0.01
-317.22
659.39
4.90
0.01
-319.42
659.50
5.01
0.01
-311.80
659.51
5.02
0.01
-318.44
659.68
5.19
0.01
-311.93
659.76
5.27
0.01
-320.65
659.84
5.36
0.01
-314.20
659.88
5.39
0.01
-318.55
659.91
5.42
0.01
-317.49
659.93
5.44
0.01
-317.53
660.02
5.53
0.01
-318.62
660.04
5.55
0.01
-319.75
660.16
5.67
0.01
-318.69
660.18
5.69
0.01
-318.69
660.19
5.70
0.01
-317.71
660.37
5.88
0.01
-317.74
660.43
5.94
0.01
-316.71
660.54
6.05
0.00
-321.04
660.63
6.14
0.00
162
14
166
Guild
Clim. niche overlap
Breeding latitude
Clim. niche breadth
Migration distance
Migratory dispersion
Body mass
Habitat
Table S6 Details of the 40 top models explaining variation in decline probability across the
early census period (1990-2000). Grey boxes indicate that a given term is included in the
model.
Partial migration
163
164
165
df
13
12
14
12
12
13
13
11
11
13
12
12
12
11
12
10
11
13
12
8
13
7
11
10
12
11
11
10
9
11
12
11
11
11
12
8
17
12
12
10
logLik
AICc
delta
weight
-174.77
376.78
0.00
0.15
-176.34
377.72
0.94
0.09
-174.19
377.80
1.02
0.09
-176.82
378.70
1.92
0.06
-176.98
379.02
2.24
0.05
-176.03
379.29
2.51
0.04
-176.07
379.38
2.60
0.04
-178.29
379.46
2.69
0.04
-178.36
379.60
2.82
0.04
-176.54
380.30
3.52
0.03
-177.71
380.46
3.69
0.02
-177.90
380.86
4.08
0.02
-177.95
380.95
4.17
0.02
-179.06
381.01
4.23
0.02
-177.99
381.03
4.25
0.02
-180.18
381.09
4.31
0.02
-179.12
381.12
4.34
0.02
-177.05
381.34
4.56
0.02
-178.20
381.45
4.68
0.01
-182.57
381.62
4.85
0.01
-177.28
381.79
5.02
0.01
-183.80
381.96
5.18
0.01
-179.71
382.30
5.52
0.01
-180.86
382.45
5.67
0.01
-178.75
382.54
5.77
0.01
-179.84
382.56
5.79
0.01
-179.90
382.69
5.91
0.01
-181.02
382.77
5.99
0.01
-182.26
383.12
6.34
0.01
-180.16
383.20
6.42
0.01
-179.10
383.26
6.48
0.01
-180.23
383.34
6.57
0.01
-180.27
383.43
6.65
0.01
-180.38
383.65
6.87
0.00
-179.38
383.80
7.02
0.00
-183.69
383.85
7.08
0.00
-174.13
384.36
7.58
0.00
-179.66
384.38
7.60
0.00
-179.68
384.41
7.63
0.00
-181.91
384.55
7.77
0.00
167
15
171
Partial migration
Clim. niche overlap
Migration distance
Clim. niche breadth
Guild
Breeding latitude
Body mass
Migratory dispersion
Table S7 Details of the 40 top models explaining variation in decline probability across the
late census period (2001-2012). Grey boxes indicate that a given term is included in the
model.
Habitat
168
169
170
df
8
9
9
8
8
7
13
12
10
9
9
12
10
13
9
10
8
14
9
13
13
14
10
13
9
9
10
9
10
9
10
9
14
10
10
9
9
8
10
11
logLik
AICc
delta
weight
-184.38
385.25
0.00
0.03
-183.32
385.25
0.00
0.02
-183.39
385.41
0.16
0.02
-184.47
385.43
0.18
0.02
-184.54
385.57
0.32
0.02
-185.60
385.58
0.33
0.02
-179.37
386.01
0.77
0.02
-180.47
386.02
0.78
0.02
-182.74
386.25
1.00
0.02
-183.88
386.38
1.13
0.01
-183.90
386.42
1.17
0.01
-180.67
386.43
1.18
0.01
-182.93
386.61
1.37
0.01
-179.68
386.63
1.39
0.01
-184.08
386.78
1.53
0.01
-183.08
386.92
1.67
0.01
-185.21
386.92
1.67
0.01
-178.77
387.01
1.76
0.01
-184.21
387.04
1.80
0.01
-179.98
387.24
1.99
0.01
-179.99
387.25
2.00
0.01
-178.89
387.26
2.01
0.01
-183.26
387.29
2.04
0.01
-180.02
387.30
2.06
0.01
-184.35
387.31
2.07
0.01
-184.37
387.35
2.11
0.01
-183.30
387.36
2.12
0.01
-184.38
387.37
2.13
0.01
-183.32
387.39
2.14
0.01
-184.39
387.40
2.15
0.01
-183.35
387.47
2.22
0.01
-184.45
387.52
2.27
0.01
-179.02
387.52
2.28
0.01
-183.38
387.53
2.28
0.01
-183.39
387.53
2.29
0.01
-184.46
387.54
2.29
0.01
-184.47
387.56
2.31
0.01
-185.53
387.56
2.31
0.01
-183.40
387.56
2.32
0.01
-182.33
387.57
2.33
0.01
172
16
173
174
175
Table S8 Variance explained by global models fitted to each dataset. The conditional
variance is that which is explained by fixed effects in the model, whereas marginal variance
is the total explained by both fixed and random effects (in this case family-level phylogeny).
R2 metric:
Dataset:
Conditional
Marginal
Whole period (1990-2012)
0.227
0.230
Early census (1990-2000)
0.294
0.334
Late census (2001-2012)
0.187
0.188
Arrival date trend subset (1990-2012)
0.716
0.717
176
177
17