1
Electronic Appendix S1: Estimates of model parameters used in stochastic population model
2
From 1983-2007, each breeding season (May-August) population numbers were counted and we recorded which
3
individuals were alive and what their stage-class and reproductive output was (~300 marked individuals; ~100
4
breeding territories annually [1,2].
5
6
General statistical modeling approach of field data
7
The full details and results of the data-analyses are described in [3]. By assuming that the fecundity in state k of
8
individual i in year j is Fkij ~ Poisson ( f k ij ) and survival is Skij ~ Binomial (sk ij ) , the temporal variation in
9
individual’s realized fecundity and survival was decomposed into components due to demographic variation,
10
climatic and other environmental variables, density effects and residual unexplained environmental (co)variation
11
using the following statistical model:
  fLN 
  f L ZN 
 log f L ij    f L 0    f L Z 
u fL 0 j 
 


 log f       
u

H ij 
 fH N 
 f H ZN 

 fH 0   fH Z 
 fH 0 j 
  s0 N 
  s0 ZN 
 logit so ij    s0 0    s0 Z 
 u s0 0 j 





 
  




 logit s1ij     s1 0    s1Z  Z   s1N  N   s1ZN  Z N   us N 0 j  ,
 logit s2 ij    s2 0    s2 Z  j   s2 N  j   s2 ZN  j j  us N 0 j 






 
 


  sN N 
  s N ZN 
logit s N ij    sN 0    s N Z 
 usN 0 j 
 s N 
  s ZN 
 logit s L ij    s 0    sL Z 
 us 0 j 

 L 
 L 

  L  
 L 



logit
s

 sH N 
 sH ZN 
 usH 0 j 
H ij 

  sH 0   sH Z 
12
13
where Z j is a column vector of climatic and other environmental variables (e.g., winter temperature, food) and
14
N j is a column vector of conspecifics densities (e.g., npop, nL) observed during the study period. The beta’s
15
(  fk 0 ,
16
specifically considered interactions between climate and density effects ( Z j N j ). In addition, we estimated the
17
residual environmental process variance and covariance in demographic rates that was not explained by Z j or
18
N j , by including random intercepts ( u 0 j ) that vary between years.
 s 0 , and row vectors  f Z ,  s N , etc.) are parameters estimated by the statistical model. We
k
k
k
19
Due to data limitations we were forced to constrain u s1 0 j  u s2 0 j  u sN 0 j . Based on preliminary data
20
exploration it seemed reasonable to assume that u fk 0 j and u sk 0 j can be approximated by a multivariate normal
21
(MVN) distribution with mean zero and a between-year variance-covariance matrix Ωu:
1
  u2f 0
 u fL 0 j 
L

u


 u fL 0 fH 0
 fH 0 j 

 u s0 0 j 
u f 0s 0

 ~ MVN (0,  u ) :  u   L 0
 u f L 0 sN 0
 u sN 0 j 

 us 0 j 
  u f L 0 sL 0
 L 
 u
u sH 0 j 
 f L 0 sH 0
22
 u2
u
u
u
u
fH 0
f H 0 s0 0
f H 0 sN 0
f H 0 sL 0
f H 0 sH 0
 u2
u
u
u
s0 0
s0 0 s N 0
s0 0 s L 0
s0 0 s H 0
 u2
u
u
sN 0
s N 0 sL 0
s N 0 sH 0
 u2
u
sN 0
sL 0 sH 0








2
 usH 0 
23
Note that we assume a multivariate normal distribution of (co)variances of vital rates on the transformed log and
24
logit scale (with base e). Between-year covariances between fecundity and survival were based on fecundity in
25
the breeding season and survival during the preceding period (and not survival during the following period).
26
27
Final model with climatic, density and other environmental covariates
28
Below we give the final model that included three environmental variables explaining between 32% and 71% of
29
the temporal variation in each of the vital rates (see [3] for details). Models that included various density and
30
other environmental variables were not better supported by the data as determined by model selection procedures
31
based on information theoretic criteria (all ΔDIC>1). The model can be described by the following multivariate
32
regression equation:
33
 log f L ij    1.821(0.156)  
u f L 0 j 
0

0.0142(0.0044)
  1.318(0.388) 
 log f
 
u

 

0.0132(0.0028) 
 1.229(0.404)

2
.
712
(
0
.
146
)
0
H ij 

 fH 0 j 

 





 logit s o ij   0.126(0.153)   0.190(0.081) 
 u s0 0 j 




0
0

 


 





0
0
 logit s1 ij    1.203(0.136)   0.182(0.067) ( w  w*)  
 (r  r*)  
 (q  q * )  u s N 0 j 
 logit s 2 ij   3.358(0.165)  0.200(0.095) 
u s 0 j 




0
0

 
 N 
 





logit
s
0
0

N ij 
u s N 0 j 
 2.830(0.099)   0.195(0.053) 




 logit s   3.057(0.116)   0.235(0.061) 
u





0
0
L ij

 
 sL 0 j 
 





0
0
logit s H ij   3.213(0.175)  0.344(0.093) 
u s H 0 j 




34
with three environmental variables winter temperature w (°C), food abundance r (ragworms/m2) and flooding
35
event q (0 or 1) included. These variables were standardized to mean 0 by subtracting the normalization
36
constants w*=3.67, r*=107.2 and q*=0.375 as determined over the study period 1983-2007. Food abundance
37
was subsequently modelled as a function of the variable winter temperature: r  153.04(15.0)  12.8(3.6)w  er .
j
38
In this paper we focus on temperature effects and therefore residual food abundance process variance
39
( er ) and flooding events were modelled as white noise random variables part of the residual environmental
40
stochasticity:
j
2
41
 log f L ij    1.821(0.156)   0.182(0.076)
u fL 0 j 
0.0142(0.0044)
  1.318(0.388) 
 log f  
u

  0.169(0.060)
0.0132(0.0028) 
 1.229(0.404)

2
.
712
(
0
.
146
)
H ij 

 fH 0 j 

 





 logit so ij   0.126(0.153)   0.190(0.081) 
 u s0 0 j 




0
0

 


 





logit
s
0
0
1 ij 

 1.203(0.136)    0.182(0.067)   ( w  w*)  
e  
e  u sN 0 j 

 logit s 2 ij   3.358(0.165)   0.200(0.095) 

 rj 
 q j u sN 0 j 
0
0

 


 





0
0
logit s N ij   2.830(0.099)   0.195(0.053) 
u sN 0 j 




 logit s   3.057(0.116)   0.235(0.061) 
u





0
0
L ij

 
 sL 0 j 
 





0
0
u sH 0 j 




logit s H ij   3.213(0.175)   0.344(0.093) 
erj ~ Normal(0,  er ) :  er  31.5(9.1) ,
42
with
43
eq j ~ Bin ( )    :   0.375(0.049) and residual environmental (co)variances:
44
food
abundance
process
variance
u fL 0 j 
 0.617(0.178)
u

 0.021(0.088)
 fH 0 j 

 u s0 0 j 
 0.114(0.117)
~
MVN
(
0
,

)
:





u
u
u
 sN 0 j 
 0.078(0.076)
us 0 j 
 0.010(0.0087)
 L 

 0.030(0.132)
u sH 0 j 
0.300(0.087)
 0.114(0.083)
 0.116(0.057)
 0.163(0.069)
 0.119(0.095)
flooding
variance




0.513(0.148)

0.143(0.074) 0.216(0.062)


0.221(0.091) 0.147(0.060) 0.295(0.085)

0.239(0.130) 0.124(0.082) 0.108(0.094) 0.674(0.195)
45
46
Density-dependent recruitment and breeder movement
47
The density dependent movement probabilities between stages (recruitment MNL, MNH and breeder dispersal MLH)
48
was modelled differently. Breeder-removal experiments have shown that the amount of high- and low-quality
49
habitat is limited in this population, consequently surplus adult nonbreeders are despotically excluded from
50
breeding [4]. We therefore included a ceiling for the number of high- and low quality territories to account for
51
the fact that breeding habitat is a limiting resource ([3,5], the ceiling was set to the maximum number of high-
52
and low-quality territories from 1983 to 2007; max(nH)=60 and max(nL)=150). A fixed ceiling is based on the
53
idea that at high density the breeding habitat become saturated and cannot be subdivided into smaller parts
54
without their quality becoming below the territory acceptance threshold for nonbreeders [6]. Movement
55
probabilities from the nonbreeder stage to the high- or low-quality breeding stages are thus expected to be a
56
function of both the number of vacant territories (due to deaths of breeders; (1-SH)nH or (1-SL)nL) and the number
57
of surviving nonbreeders that compete for these vacancies (SNnN). In addition, vacancies in high-quality habitat
58
are more likely to be occupied by nearby breeders from low-quality habitat than by non-breeders [7]. Therefore,
59
we expected the number of vacancies for nonbreeders to be also a function of the number of breeders moving
60
from the low to high-quality habitat breeding stage (SLMLHnL). More specifically, we modelled:
61
M NL ~
(1  S L )nL  S L M LH nL
,
S N nN
3
62
M NH ~
(1  S H )n H  S L M LH n L
,
S N nN
M LH ~
63
(1  S H )nH
,
S L nL
64
which ensures that recruitment MNL & MNH and breeder dispersal MLH are density dependent in a similar fashion
65
as observed in the field (see Fig. 3E,F in [3]). Although oystercatchers sometimes lose their territory ([MHN,
66
MHL, MLN]>0), we did not model this explicitly, as these vacancies were typically reoccupied immediately and
67
consequently this mainly concerns individuals swapping stages and thus does not affect the stage distribution of
68
the model.
69
70
References Appendix S1
71
1.
72
73
Ens, B.J., Kersten, M., Brenninkmeijer, A. & Hulscher, J.B. 1992 Territory quality, parental effort
and
reproductive success of oystercatchers (Haematopus ostralegus). J. Anim. Ecol. 61, 703–715.
2.
van de Pol, M., Bruinzeel, L.W., Heg, D., van der Jeugd, H.P. & Verhulst, S. 2006 A silver spoon for a
74
golden future: long-term effects of natal origin on fitness prospects of oystercatchers. J. Anim. Ecol. 75,
75
616–626.
76
3.
van de Pol, M., Vindenes, Y., Sæther, B.-E. Engen, S., Ens, B.J., Oosterbeek, K. & Tinbergen, J.M. 2010
77
Effects of climate change and variability on population dynamics in a long-lived shorebird. Ecology 91,
78
1192-1204.
79
4.
80
81
Behavioural Ecology 50: 290–266.
5.
82
83
86
van de Pol, M., Pen, I., Heg, D. & Weissing, F.J. 2007 Variation in habitat choice and delayed reproduction:
Adaptive queuing strategies or individual quality differences? Am. Nat. 170, 530–541.
6.
84
85
Bruinzeel, L. W. & M. van de Pol. 2004. Site attachment of floaters predicts success in territory acquisition.
Kokko, H., Sutherland, W. J. & Johnstone, R. A. 2001 The logic of territory choice: implications for
conservation and source–sink dynamics. American Naturalist 157, 459–463.
7.
Heg, D., Ens, B. J., van der Jeugd, H. P. & Bruinzeel, L. W. 2000 Local dominance and territorial settlement
of nonbreeding oystercatchers. Behaviour 137, 473–530.
4