Basic and Applied Ecology 12 (2011) 107–115
Variation in age-structured vital rates of a long-lived raptor: Implications
for population growth
Fabrizio Sergioa,∗ , Giacomo Tavecchiab , Julio Blasa , Lidia Lópeza , Alessandro Tanfernaa,c ,
Fernando Hiraldoa
a
Department of Conservation Biology, Estación Biológica de Doñana, CSIC, 41092 Seville, Spain
Department of Population Ecology, Institute for Mediterranean Studies (IMEDEA), CSIC-UIB, 07190 Esporles, Spain
c
DISUAN, Department of Human, Environmental and Natural Sciences, University of Urbino, 61029 Urbino, Italy
b
Received 28 April 2010; accepted 16 November 2010
Abstract
Age-structured variation in multiple vital-rates is a fundamental determinant of population growth, with important implications for conservation management. However, for many long-lived vertebrates such as birds of prey, such variation has been
usually examined in shorter-lived species. Here, we investigate the pattern of age-related variation in fitness components and
its repercussions on population growth for a migratory raptorial bird, the black kite (Milvus migrans), with a longer lifespan
than most other previous model species. Both survival and offspring production varied along the lifespan in conjunction with
the sequence of major life history stages: they were lowest during the initial years of life, increased steeply during the period
of progressive incorporation of floaters in the breeding sector of the population (age 2–6), levelled off between 7 and 11 years
of life, declined with senescence after age 12, and increased again for the few high-quality individuals capable of reaching age
18–25. This pattern was more gradual, asymmetrical and protracted than in shorter-lived species. Matrix modelling estimated a
stationary growth rate, which was more sensitive to changes in survival in early life rather than to survival in adult life, contrary
to expectations for long-lived species. Our results highlight: (1) a growing appreciation of the importance of juvenile survival
for population dynamics, (2) the need for caution on the generalization that population-trends of long-lived species are primarily
determined by adult survival, and (3) that the trajectory of the breeding populations of migratory species may be determined by
environmental variation experienced in early life in staging areas located far away from breeding areas.
Zusammenfassung
Die altersbedingte Variation bei vielen Vitalparametern ist ein fundamentaler Faktor bei der Bestimmung des
Populationswachstums mit wichtigen Auswirkungen auf das Naturschutzmanagement. Dennoch wurde bei langlebigen
Wirbeltieren, wie z. B. Greifvögeln, diese Variation gewöhnlich nur bei kurzlebigeren Arten untersucht. Hier untersuchten
wir die Muster der altersbedingten Variation der Fitness-Komponenten und ihre Rückwirkungen auf das Populationswachstum
bei einem ziehenden Greifvogel mit einer längeren Lebenserwartung als die bisher untersuchten Modellarten, dem Schwarzmilan
∗ Corresponding author at: Department of Conservation Biology, Estación Biológica de Doñana, CSIC, c/Americo Vespucio s/n, 41092 Seville, Spain.
Tel.: +34 959232340.
E-mail address: [email protected] (F. Sergio).
1439-1791/$ – see front matter © 2010 Gesellschaft für Ökologie. Published by Elsevier GmbH. All rights reserved.
doi:10.1016/j.baae.2010.11.004
108
F. Sergio et al. / Basic and Applied Ecology 12 (2011) 107–115
(Milvus migrans). Sowohl die Überlebensraten als auch die Nachwuchsproduktion variierten im Laufe der Lebenszeit im Zusammenhang mit der Abfolge der wichtigeren Stadien der Entwicklung. Sie waren am geringsten während der ersten Lebensjahre,
stiegen steil während der Periode an, in der die umherstreifenden Tiere in den brütenden Anteil der Population integriert wurden (im Alter von 2–6), blieben zwischen dem 7. und 11 Jahr des Lebens auf der gleichen Höhe und nahmen schließlich in
der Seneszenz ab dem Alter von 12 wieder ab, nahmen dann aber für die wenigen hochqualitativen Individuen, die ein Alter
von 18–25 Jahren erreichen konnten, wieder zu. Dieses Muster war gradueller, asymmetrischer und langgezogener als bei
kurzlebigeren Arten. Matrixmodelle kamen im Gegensatz zu den Erwartungen für langlebige Arten zur Einschätzung einer
stationären Wachstumsrate, die empfindlicher gegenüber Veränderungen in den Überlebensraten in den früheren Stadien war
als gegenüber Überlebensraten im Erwachsenenstadium. Unsere Ergebnisse betonen (1) eine zunehmende Wahrnehmung der
Wichtigkeit der Überlebensraten im Jugendstadium für das Populationswachstum, (2) eine notwendige Vorsicht gegenüber der
Generalisierung, dass die Populationstrends langlebiger Arten primär durch das Überleben der Adulten bestimmt wird und (3)
dass der Kurvenverlauf der Brutpopulation ziehender Arten durch eine Veränderung der Umwelt bestimmt werden kann, die in
den Gebieten der frühen Lebensstadien erfahren wird, die in einiger Entfernung zu den Brutgebieten liegen können.
© 2010 Gesellschaft für Ökologie. Published by Elsevier GmbH. All rights reserved.
Keywords: Capture–recapture; Demography; Elasticity; Matrix population models; Milvus migrans; Population dynamics; Sensitivity;
Survival
Introduction
Obtaining robust estimates of age- or stage-dependent
vital rates and population structure is essential for the study
of population functioning (Caswell 2001; Sibly, Hone, &
Clutton-Brock 2003). For example, individuals of different
age and experience may survive at different rates in response
to the same environmental stressors, so that population variation can only be explained by taking into account the effect
of an age-by-time interaction on vital rates (e.g. Saether et al.
2000). As a consequence, detailed knowledge of age-related
variation in vital rates is a fundamental pre-requisite for
effective population management and conservation (Wisdom,
Mills, & Doak 2000; Sibly & Hone 2002).
Advances in demography in the last decades have recurrently highlighted two novel aspects. First, there is a growing
appreciation of the differential contribution of different vital
rates and their variability to population growth (Saether &
Bakke 2000; Wisdom et al. 2000; Caswell 2001). Such contribution varies along a continuum ranging from short-lived
species, for which fecundity is a major determinant of population dynamics, to long-lived species, whose population
growth is usually thought to be most dependent on adult survival (Heppell, Caswell, & Crowder 2000; Saether & Bakke
2000). Second, a growing emphasis on long-term studies
facilitates increasing access to datasets on individual life histories long enough to cover the variation in vital rates along
the whole lifespan of the target species. In turn, this allows
to capture a more realistic picture of population dynamics
even for longer-lived species, whose demography has been
traditionally elusive to model.
Despite the above, and with the exception of some
mammalian herbivores and seabird species (e.g. Gaillard,
Festa-Bianchet, & Yoccoz 1998; Schreiber & Burger 2002),
comprehensive analyses of age-related variation in multiple
vital rates are still rare for many long-lived animal groups,
largely because of the enormous amount of field effort nec-
essary to describe the fates of large numbers of individuals
composing the population. One such group includes birds
of prey, despite the importance of such species in terms of
ecological role and threatened status, and despite the great
attention and funding traditionally devoted to these charismatic taxa. With few exceptions (e.g. Green, Pienkowski,
& Love 1996; Kenward, Marcström, & Karlbom 1999;
Ferrer, Otalora, & García-Ruiz 2004; Whitfield, Fielding,
Mcleod, & Haworth 2004; Anthony et al. 2006), comprehensive demographic analyses on these species have mainly
focused on smaller-sized, shorter-lived species (e.g. Newton
& Rothery 1997; Hakkarainen, Korpimaki, Koivunen, &
Ydenberg 2002; Altwegg, Roulin, Kestenholz, & Jenni 2003;
Karell, Ahola, Karstinen, Zolei, & Brommer 2009). Even
among these, we are aware of only one study which has
provided a comprehensive picture of variation in multiple
vital rates along the whole lifespan of the study species
(Newton & Rothery 1997). More commonly, fitness components are reported for the first years of life, but pooled
altogether for all the older age-classes. This is mostly done
because the exact age of older birds is unknown (e.g. individuals were marked when adult) or is available for only a
small fraction of individuals. All the above leaves open the
question of whether the patterns observed so far on shorterlived species also apply to larger, longer-lived ones. For the
latter, existing information reflects the daunting task of collecting data over several decades, and is mainly obtained
from introduced or artificially maintained populations (Green
et al. 1996; Sarrazin & Legendre 2000), it typically concerns
only one fitness component (e.g. Oro, Margalida, Carrete,
Heredia, & Donázar 2008; Grande et al. 2009), is based on
one or two coarse age classes (e.g. comparison of immatures
vs. adults; Kenward et al. 1999; Ferrer et al. 2004; Sulawa,
Robert, Köppen, Hauff, & Krone 2010), or is indirectly or
partially estimated thorough various assumptions or modelling simulations (e.g. Wootton & Bell 1992; Kenward et al.
1999; Whitfield et al. 2004; Krüger, Grünkorn, & Struwe-Juhl
F. Sergio et al. / Basic and Applied Ecology 12 (2011) 107–115
2010). Such lack of comprehensive information is particularly important because longer-lived species are frequently
threatened and population management is increasingly based
on population viability analyses that use educated guesses
or parameters borrowed from other populations (Wootton &
Bell 1992; Katzner, Bragin, & Milner-Gulland 2006; Krüger
et al. 2010).
Here, we use a data-rich sample to provide a comprehensive account of age-structured variation in multiple vital
rates and of its repercussions on population dynamics for a
long-lived raptorial species, the black kite (Milvus migrans,
maximum observed lifespan of 25 years). In particular, we
(1) examine age-related variation in offspring production and
survival, (2) estimate the population growth of the population
through deterministic matrix modelling, and (3) assess the
contribution of different age-dependent vital rates to population growth. We show that larger species may be characterized
by more complex variation in fitness components across
age-classes than previously appreciated and that assumptions on age-dependent parameters might lead to incorrect
or oversimplified management guidelines. For example, current generalizations about the importance of adult survival
for population growth may not hold systematically across
all long-lived species, and the pre-breeding stage of the lifecycle, i.e. before the age of full recruitment, might play a more
important role than generally assumed (see also Whitfield
et al. 2004; Katzner et al. 2006).
Materials and methods
Study species and data collection
We studied the black kite, a medium-sized, migratory raptor (adult body mass in our population ∼700–1200 g; Sergio,
Blas, Forero, Donazar, & Hiraldo 2007) in a 430 km2 plot
located in Doñana National Park (south-western Spain). In
this population, the age of first territorial establishment ranges
between 1 and 7 years and the maximum recorded lifespan is
25 years (Blas, Sergio, & Hiraldo 2009; unpublished data).
Observed breeding and natal dispersal distances are short
(median 302 m and 4800 m, respectively) and intensive, spatially extensive multi-year surveys suggest an extremely low
rate of emigration to other populations (Forero, Donázar, &
Hiraldo 2002). This ensures that modelled survival should
not be confounded or biased by emigration.
In all analyses, we employ data collected between 1986
and 2009. Since 1986, the nestlings were marked with a
white Darvic ring with a black three-character alphanumeric
code, which can be read by telescope from a distance. Even
if ringing activities started earlier (since 1964), it was only
after 1989 that a standard protocol for systematic resighting
was established (Sergio, Blas, & Hiraldo 2009). We analysed 6543 reencounters of 4581 kites born in Doñana Nation
Park and marked as nestlings at the time of fledgling. As
a consequence, we know the exact chronological age of all
109
birds in the dataset. Encounters included birds resighted on
their territories, on carrion-baits or at communal roosting
sites. Birds of different age or breeding status may be differentially detected by each of these methods: readings at
territories mostly recorded breeders, readings at roost-sites
mainly included non-breeding, younger individuals, while
ring-readings at carrion-baits included birds of all ages and
status (Sergio et al. 2009). Because the type of resighting (on
territory, at carrion-baits or at roost-sites) was recorded only
since 1996, all three encounter types were pooled in a single
dataset and analysed together. This probably increased the
level of recapture heterogeneity (see section ‘Results’), but
allowed us to include in the analysis data collected before
1996, thus increasing the number of old birds in the analysis.
When a marked bird was detected on a territory, the area was
visited weekly to locate its nest and to record clutch size and
the number of chicks raised to fledging age (40–45 days old,
Blas et al. 2009). No further ring-readings were conducted
during such nest checks (i.e. such territories did not receive
a subsequent higher ring-reading effort).
Modelling survival and encounter probabilities
Survival and reencounter probabilities were modelled
simultaneously as a function of age, year of observation, and
their statistical interactions, and estimated by maximum likelihood methods (Lebreton, Burnham, Clobert, & Anderson
1992). Hereafter, the effect of the year of observation is
defined as “time” and noted ‘t’ to conform to classical terminology in survival analyses (Lebreton et al. 1992). Following
Catchpole, Morgan, Coulson, Freeman, and Albon (2000),
we first considered the effect of age alone to detect the best
age structure. In doing so, we modelled one parameter at
a time while keeping the others as general as possible (e.g.
Grosbois & Tavecchia 2003). Once the best age structure was
detected, we considered the effect of the year of observation
within each age class. Finally, we built additive models to
verify whether year-to-year variation had a similar effect in
all age classes (parallel variation of survival across ages).
Model notation was complex because a given effect can be
important for one age class or parameter, but not for others. We choose a model notation similar to the one used
in Catchpole et al. (2000), in which each modelled parameter was separated by a “/” symbol. The model assuming
a full age effect (22 age classes) for the survival probability, φ, and for the reencounter probability, p, was then
denoted φ0/. . ./φ22/p0 /. . ./p22. The subscript indicates the
age of the bird and the symbol “/. . ./” indicates that all ages in
between were modelled separately. To simplify model structure, we grouped in a single class the age parameters with
similar values. In model notation, such age-classes will be
denoted by the first and the last age of the class joined by
the under score symbol “ ”. For example, a model assuming only two age classes for survival, the first including ages
from 0 to 10 and the second from 11 to 24, will be denoted as
110
F. Sergio et al. / Basic and Applied Ecology 12 (2011) 107–115
φ0 10/φ11 24. The effect of year of observation was denoted
in parentheses after the parameter as φ0 10(t)/φ11 24(t).
When the two parameters were assumed to vary in parallel over time (i.e. no interaction effect), the notation was
φ0 10(t)//φ11 20(t). We began the analysis of encounter histories by a goodness of fit test (Choquet, Reboulet, Lebreton,
Gimenez, & Pradel 2003) of a general model including
the effects of age, year of observation and their statistical
interaction on survival and recapture probabilities, noted as
φ0(t)/. . ./φ22(t)/p0(t)/. . ./p22(t).
Model selection was based on the Akaike’s Information
Criterion (AIC, Burnham & Anderson 2002) calculated as
the model deviance plus twice the number of estimable
parameters in the model. The AIC value for each model
was calculated using the program M SURGE (Choquet,
Reboulet, Pradel, Gimenez, & Lebreton 2003). In addition,
we calculated the AIC weight of each model as a measure
of its relative ‘plausibility’ (Burnham & Anderson 2002).
Models with similar AIC values should be considered equivalent. During the early stages of the analysis, when our
interest was mainly in detecting the correct age-structure, we
simply retained the model with the highest AIC weight. However, when estimates were used to parameterise the transition
matrix (see below), their values were derived as a weighted
mean using the weight of each model (i.e. model averaging,
Burnham & Anderson 2002).
Modelling breeding performance
We employed the number of fledged young per breeding
attempt, denoted F, as a measure of reproductive performance
and investigated its age-structure through multiple regression
(GLM with Poisson errors and a log-link structure). Model
notation and selection were the same as detailed above for
the survival analyses. Data were available for 1380 nesting
attempts by known-age individuals.
Matrix population model and perturbation
analyses
The age-dependent values of survival and fertility were
included into an age-structured demographic matrix, M
(Caswell 2001; Appendix A). The matrix M describes the
transition of the population between two consecutive years,
t and t + 1. The matrix is of dimension n × n where n corresponds to the number of age classes detected. The asymptotic
population growth, λ, is calculated as the dominant eigenvalue of M (Caswell 2001). In a stable population, λ is equal
to 1, while lower values indicate a declining trend. To account
for the stochastic variation of parameters, the value, αj, of
each vital rate for the age class j, was randomly drawn from
a truncated normal distribution, tN(πj, σj), with probability
mean π and variance σ 2 (πj and its variance were derived
by the analysis of individual based information; Appendix
A). We also included demographic stochasticity, the varia-
tion due to the random process of mortality and reproductive
success within the population by using a value, θj, drawn from
a binomial distribution B(Pj,α j), with probability α and population size P for each class j, following Katzner et al. (2006).
Because the Doñana population is around 1500 individuals,
P was assumed to be 100 individuals for each age class. The
population growth rate including stochasticity, noted λs, and
its variance were calculated as the average values from 1000
simulations. We compared these values with the deterministic population growth rate (λd), which was estimated using
the average values πj and σ 2 j. The 95% confidence interval
of λd can be calculated combining parameter variances with
their respective sensitivity (Lande 1988). The difference of
the two population growth rates, as the parameter notation
suggests, is that λd was calculated using the average values of the parameters while λs was calculated by randomly
drawing each parameter value from its estimated distribution.
Finally, we used perturbation analyses to calculate the sensitivity, Sθ, and elasticity, Eθ, of the population growth rate to
a given parameter θ (Caswell 2001). Sensitivity is the change
in population growth rate in response to an absolute change
of a given parameter θ, while elasticity is the change in the
population growth rate in response to a proportional change
of a given parameter θ. All analyses were implemented with
program R (R Development Core Team 2009).
Results
Age-structured survival
The goodness-of-fit test of the general model
φ0(t)/. . ./φ22(t)/p0(t)/. . ./p22(t) indicated a large resid2 = 261.60, p < 0.0001). This lack of fit
ual deviance (χ183
was probably due to the inclusion of different types of
resighting, which might have increased the heterogeneity in
encounter probability across individuals. As a consequence,
deviances were typically inflated and were scaled using a
variance inflator factor (ĉ = χ2 /d.f. = 261.60/183 = 1.42).
Note that recapture heterogeneity can be partially accommodated in capture–recapture models by modifying the
encounter histories (Pradel 1993; Tavecchia, Minguez,
De León, Louzao, & Oro 2008). However, by doing this,
recapture and survival cannot be fully age-dependent
simultaneously as the model including trap-dependence and
transient-effects becomes parameter redundant (Tavecchia,
Pradel, Genovart, & Oro 2007). Because recapture and
survival are expected to change with age, we preferred to
correct model deviances by a scale parameter.
The retained model-structures for encounter probabilities
and for survival were not the same (Table 1). Encounter
probabilities and survival increased constantly with age, but
recapture had a more complex age-structure than survival.
The effect of time was retained in all age-classes (Table 2).
For survival, virtually all the top models gave indication of
a complex age-structure incorporating a survival-decline in
F. Sergio et al. / Basic and Applied Ecology 12 (2011) 107–115
111
Table 1. Models of encounter probability (A), age-structured survival (B) and offspring production (C) (number of nestlings raised to fledging
age, see text). (A) and (B) are based on capture–recapture data for 4581 black kites marked as fledglings, and (C) is based on 1380 nesting
attempts by individuals of known age sampled in Doñana National Park (Spain). Notation: np, number of parameters in the model; AIC,
Akaike’s Information Criterion; AIC, difference in AIC-value between the target model and the model with the lowest AIC; AICw , Akaike
weights; φ, survival probability; p, reencounter probability; F, number of fledged young. The best model (highest AIC weight) is highlighted
in bold. See section ‘Materials and methods’ for details. For conciseness of presentation, we report only the 10 best competing models. The
complete list of models is available on request from the authors.
Model
(A) Reencounter probability
p1/p2 3/p4 6/p7 16/p17 20/p21 22
p1/p2/p3 6/p7 16/p17 20/p21 22
p1/p2/p3 6/p7 13/p14 16/p17 20/p21 22
p1/p2/p6/p7 16/p17 20/p21 22
p1/p2/p3 6/p7 20/p21 22
p1/p2/p3/p4/p5/p6/p7 20/p21 22
p1/p2 5/p6/p7 20/p21 22
p1/. . ./p15/p16/p17 20/p21 22
p1/. . ./p22
p1/. . ./p15 22
(B) Survival probability
φ1/φ2 6/φ7 10/φ11 17/φ18 22
φ1/φ2 22
φ1/φ2 6/φ7 10/φ11 14/φ15 22
φ1/φ2 6/φ7 11/φ12 14/φ15 22
φ1/φ2/φ3 6/φ7 10/φ11 14/φ15 22
φ1/φ2 6/φ7 10/φ11 17/φ18 22
φ1/φ2 5/φ6 10/φ11 22
φloge (Age) + loge (Age)2 a
φ1/φ2/φ3/φ4/φ5/φ6/φ7 10/φ11 14/φ15 22
φ1/φ2/φ3 6/φ7 11/φ12 22
(C) Offspring production
F1 2/F3 6/F7 11/F12 25
F1 2/F3 6/F7 25
F1/F2/F3/F4/F5/F6/F7/F8 25
F1/F2/F3/F4/F5/F6/F7/F8/F9 25
F1/F2/F3/F4/F5/F6/F7/F8/F9/F10 25
F1/F2/F3/F4/F5/F6/F7/F8/F9/F10/F11 25
F1/F2/F3/F4/F5/F6/F7/F8/F9/F10/F11/F12 25
F1/F2/F3/F4/F5/F6 25
F1 6/F7 25
F1/F2/F3/F4/F5/F6/F7/F8/F9/F10/F11/F12/F13 25
a Age
Classes
np
AIC
AIC
AICw
6
6
7
5
5
7
4
18
21
15
219
219
220
218
218
221
217
231
232
229
8868.00
8870.41
8872.15
8873.50
8878.09
8880.63
8881.18
8888.60
8890.20
8890.78
0
2.41
4.15
5.49
10.08
12.62
13.18
20.60
22.20
22.78
0.4726
0.1416
0.0802
0.0410
0.0041
0.0012
0.0009
2.2E−05
9.7E−06
7.2E−06
5
2
5
5
6
5
4
–a
9
5
233
230
233
233
234
233
232
231
237
233
8184.40
8185.33
8185.48
8187.33
8187.44
8187.52
8187.78
8188.53
8190.67
8190.83
0
0.93
1.08
2.93
3.05
3.12
3.39
4.14
6.28
6.43
0.3025
0.1896
0.1757
0.0698
0.0659
0.0634
0.0556
0.0381
0.0130
0.0121
4
3
8
9
10
11
12
6
2
13
4
3
8
9
10
11
12
6
2
13
3367.32
3368.16
3368.29
3369.29
3370.88
3372.83
3372.90
3374.62
3374.83
3374.90
0
0.84
0.97
1.97
3.56
5.51
5.59
7.30
7.51
7.58
0.328
0.215
0.201
0.122
0.055
0.021
0.020
0.009
0.008
0.007
modelled as a continuous variable.
Table 2. Model structure and percentage of explained variance. Variations in survival among-years were more pronounced for younger birds
than for adults. The percentage of variance explained by variations among-years (%) decreased with age. Notation: DEV, model deviance;
AIC, Akaike’s Information Criterion.
Model
DEV
%
AIC
φ1(t)/φ2 6(t)/φ7 10(t)/φ11 17(t)/φ18 22(t)
φ1/φ2 6(t)/φ7 10(t)/φ11 17(t)/φ18 22(t)
φ1(t)/φ2 6/φ7 10(t)/φ11 17(t)/φ18 22(t)
φ1(t)/φ2 6(t)/φ7 10/φ11 17(t)/φ18 22(t)
φ1(t)/φ2 6(t)/φ7 10(t)/φ11 17/φ18 22(t)
φ1(t)/φ2 6(t)/φ7 10(t)/φ11 17(t)/␾18 22
φ1/φ2 6/φ7 10/φ11 17/φ18 22
7643.04
7682.68
7658.96
7657.17
7646.38
7643.44
7718.46
100
0.52
0.21
0.19
0.04
0.01
0
8184.39
8210.61
8186.89
8195.09
8192.30
8201.36
8200.96
112
1.0
0.16
0.9
0.14
0.8
0.12
Elasticity value
Survival
A
F. Sergio et al. / Basic and Applied Ecology 12 (2011) 107–115
0.7
0.6
0.5
0.4
Elasticity - survival
Elasticity - offspring production
0.10
0.08
0.06
0.04
0.3
0.02
1
2-6
7 - 11
12 - 17
18 - 25
Age
B
0.00
1
Number of young fledged
0.90
2
3
4
5
6
7
8
9
10
11
12
Age
0.80
Fig. 2. Elasticity of population growth rates to age-structured variation in survival and offspring production (number of nestlings raised
to fledging age) in a black kite population in Doñana National Park
(Spain). Elasticity is the change in population growth rate due to
proportional changes in a given parameter.
0.70
0.60
0.50
0.40
0.30
3–6 years of age, it peaked at ages 7–11 and declined slightly
after age 12 (Fig. 1B, Appendix A).
0.20
0.10
Population model and perturbation analyses
0.00
1-2
3-6
7 - 11
12 - 25
Age
Fig. 1. Variation in (A) survival and (B) offspring production (number of nestlings raised to fledging age) across age-classes of black
kites in Doñana National Park (Spain). Survival estimates are based
on 6543 reencounters of 4581 kites marked as fledglings. Estimates
of offspring production are based on 1380 nesting attempts by kites
of known age. All estimates are means ± 1 SE.
older ages (Table 1). According to the best model, survival
was minimal in the first year of life, it increased steeply after
age 2, it levelled-off for ages 7–11, it declined after age 12 and
increased again for the few individuals capable of reaching
ages older than 18 (Fig. 1A). For the oldest age class, survival
and encounter probabilities were estimated to be 1.00. While
this is an unrealistic value for survival probably exaggerated
by the small sample size (only 18 individuals belonged to this
group), it does suggest that survival may be high for this tail
of the population. Accumulation of larger samples in future
years will allow more realistic estimates of survival rates of
very old birds. We did not consider this issue further in our
population model.
Age-structured breeding performance
In the best model (Table 1C), breeding output was minimal
for first and second year birds, intermediate for individuals of
The stochastic population growth rate λs was 0.991
(se = 0.024; 95% CI: 0.941–1.037), which suggested a stable
population. A regression of nest counts on year also yielded a
stable trend in numbers (slope = 0.009 ± 0.003). The value of
λd, calculated using a deterministic model, indicated a similar result (λd = 0.991, se = 0.015; 95% CI: 0.961–1.021). As
expected, the variation associated with the stochastic value
was larger than the one calculated through the deterministic model. Both elasticity and sensitivity analyses gave the
same indications with values decreasing with age (Fig. 2).
The population growth rate was least sensitive to changes
in the average value of fledglings production (E(F) = 0.143;
S(F) = 0.224) and most sensitive to variations in average survival probability (E(φ) = 0.857; S(φ) = 1.08; Fig. 2). However,
when considering survival during different stages of the life
cycle, the population growth rate was more affected by an
overall change in survival parameters up to age 7 (the maximum age of first breeding) than by changes in survival
during the later years of life (all parameters considered:
E(φ0 6) = 0.61; E(φ7 22) = 0.37, respectively).
Discussion
We showed a detailed, comprehensive pattern of agestructured variation in multiple vital rates for a raptorial
species with a maximum lifespan of 25 years. Both reproduction and survival rates varied in a more complex manner
F. Sergio et al. / Basic and Applied Ecology 12 (2011) 107–115
along the lifespan of the population than previously reported
for shorter-lived raptors (e.g. Korpimäki 1992; Newton &
Rothery 1997; Karell et al. 2009). Survival showed a very
abrupt increase from the first to the second year of life, suggesting a very strong mortality-peak and selection-episode
during the first migration and wintering stages. Later variations in survival were never as abrupt, but fitted well the
sequence of major life-history stages of the species: (1)
survival was rather stable between ages 2 and 6, which is
the period of progressive incorporation of floating individuals into the breeding population (Sergio et al. 2009); (2) it
increased and reached a plateau at age 7–11, when virtually
all individuals have recruited into the breeding population
and breeding performance is highest (Blas et al. 2009); (3) it
declined to lower senescent levels between ages 12 and 17;
and (4) it increased again to very high levels after 18 years
of life. The survival of this last age-class was not considered
in population modelling as it refers to only few individuals.
Mortality plateaus like this are increasingly found in datarich samples, for example in human demography (Pletcher
& Curtsainger 1998). Although this has important implications for the evolution of senescence (Weitz & Faser 2001), it
has little influence on population dynamics and will be examined in more detail after the accumulation of larger samples
in the future. Fledglings production followed a pattern rather
similar to the one depicted for survival: (1) it was extremely
low during the initial breeding attempts in the first 2 years
of life; (2) it increased to higher levels for ages 3–6 when
many birds in the population were still breeding for the first
time(s) and accumulating experience (Blas et al. 2009); and
(3) it levelled-off at maximum levels after age 7.
Compared to previous studies on similar taxa, the abovedescribed pattern highlights two important points. First,
previous studies have usually pooled all adult-individuals
(aged > 1–2 years old) in a single age-class. This may obscure
much variation in age-structured vital rates as well as the
relative importance of different phases of the life-cycle in
determining population growth rates, potentially leading to
oversimplified views of population functioning (e.g. Zabel &
Levin 2002) and, ultimately, to incorrect management guidelines (see below).
Second, previous analyses on shorter-lived species have
reported steep improvement and deterioration of fitness components with age (e.g. Newton & Rothery 1997). Such
dynamic, rapid changes may not apply to longer-lived
species, which may be characterized by more gradual, complex and protracted variations in vital rates, as seen in various
seabirds (e.g. Newton 1989; Nisbet 2001). For example,
restraint strategies, by which individuals refrain from costly
activities, may be more viable for longer-lived animals and
dilute the costs of reproduction through optimal allocation of
age at first breeding (e.g. Weimerskirch 1992). In agreement
with this idea, similarly complex variations in survival along
multiple age-stages has been reported by the only other study
which examined detailed, age-related variation in survival
for a long-lived raptor, the Egyptian vulture (Neophron perc-
113
nopterus, Grande et al. 2009). This is even more remarkable
given that the study did not cover the whole lifespan of the
species (Grande et al. 2009). All the above suggests that our
current picture of raptor demography may be over-simplified
and biased towards the life-history strategies of shorter-lived
species. Longer-lived eagles and vultures, which are more frequently imperilled and in need of robust management plans,
may need modelling exercises based on more complex and
realistic demographic estimates (see Kelly & Durant 2000
for similar reasoning).
Results of the elasticity analyses suggested that the stationary growth rate of the population was most dependent on
survival in the first few years of life. Although our results
are consistent with those reported in two previous studies
on raptors (e.g. Whitfield et al. 2004: golden eagles Aquila
chrysaetos, Katzner et al. 2006: imperial eagles Aquila heliaca), they were rather surprising given that long-lived species
are usually expected to show higher elasticities for adult than
for juvenile (i.e. before full recruitment) survival (Saether &
Bakke 2000; Stahl & Oli 2006), as also observed in many previous studies on birds of prey (Wootton & Bell 1992; Hiraldo,
Negro, Donázar, & Gaona 1996; Seamans & Gutiérrez 2007;
Karell et al. 2009). We showed that changes in survival probability in the first 7 years of life (i.e. up until all birds are
recruited in the breeding population; Sergio et al. 2009),
affected the population growth rate more than changes in
subsequent survival. The discrepancy of these results with
previous studies could be caused by different reasons. The
large sample used here, nearly unique in a study on longlived raptors, allowed us to describe fine-scale variations in
vital rates, otherwise frequently masked by a lack of statistical power. In this sense, we believe that our conclusions
could apply to many other raptor species. However, we cannot
exclude that the differences found are the results of specific
biological processes acting in our population. For example,
the marked mortality-peak in early life of this population may
have accentuated the importance of survival in such early life
stages. Also, the fact that improvements in performance in
this population are promoted by positive selection for highquality phenotypes in early life (Blas et al. 2009; Sergio et al.
2009) may contribute to exaggerate the importance of early
processes of recruitment and survival at the population level.
Finally, it should be noted that sensitivity and elasticity analyses are based on the analytical properties of the matrix model,
among these the convergence to a stationary age distribution
(Caswell 2001). In highly dynamic systems, this might lead
to minor differences with other studies, such as those based
on simulations (e.g. Katzner et al. 2006). However, given the
small year-to-year variation in most parameters considered,
we believe that in our case these differences were negligible.
Whatever the mechanism causing the discrepancy with earlier studies, such results have three major implications: (1)
they contribute to a growing awareness of the importance of
survival in early life on population persistence and variation
(e.g. Gaillard et al. 1998; Whitfield et al. 2004; Penteriani,
Otalora, Sergio, & Ferrer 2005; Katzner et al. 2006); (2) they
114
F. Sergio et al. / Basic and Applied Ecology 12 (2011) 107–115
stress how generalizations about the importance of different
vital rates for population management should be taken with
caution and, whenever possible, examined in detail for the
species in question; and (3) they show that migratory populations like ours, where the initial years of life may be spent on
another continent, may be regulated by factors operating far
from the breeding quarters (e.g. Greenberg & Marra 2005).
This may make their conservation management extremely
challenging.
In conclusion, our population was characterized by a
pronounced mortality-bottleneck in early life, followed by
gradual improvements in performance, a mid-life plateau,
and a less abrupt progression of senescence than observed in
shorter-lived raptors. Unexpectedly, the population trajectory
was found to be largely determined by survival before the age
of full recruitment, which, in turn, may be affected by factors
operating far from the breeding quarters. The appreciation of
such complexity may be a key progress for conservation,
given that management of vulnerable species is increasingly based on viability modelling (e.g. Kauffman, Frick, &
Linthicum 2003; Schaub, Pradel, & Lebreton 2004; Katzner
et al. 2006), which is often based on educated guesses or
on parameters taken from other populations (Kelly & Durant
2000).
Acknowledgements
We thank F.G. Vilches, R. Baos, S. Cabezas, J.A. Donázar,
J.M. Giralt, F. Gómez, M.G. Forero, E. García, G. García, L.
García, M. Guerrero, and A. Sánchez for help in the field,
and K. Hövemeyer, T.E. Katzner, D. Oro and an anonymous reviewer for comments and discussion on a previous
draft of the manuscript. Part of this study was funded by
the research projects PB96-0834 of the Dirección General de
Investigación Científica y Tecnológica, CGL2008-01781 and
200930I172 and BFU2009-09359 of the Ministerio de Ciencia e Innovación, JA-58 of the Consejería de Medio Ambiente
de la Junta de Andalucía and by the Excellence Project RNM
1790 and RNM 03822 of the Junta de Andalucía.
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in the online version, at
doi:10.1016/j.baae.2010.11.004.
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