vol. 172, no. 4
the american naturalist

october 2008
Conspecific Brood Parasitism and Population Dynamics
Perry de Valpine1,* and John M. Eadie2,†
1. Department of Environmental Science, Policy and Management,
University of California, Berkeley, California 94720;
2. Department of Wildlife, Fish and Conservation Biology,
University of California, Davis, California 95616
Submitted August 21, 2007; Accepted April 1, 2008
Electronically published August 26, 2008
Online enhancements: appendixes.
abstract: Conspecific brood parasitism (CBP), defined as parasitic
laying of eggs in a conspecific nest without providing parental care,
occurs in insects, fishes, amphibians, and many birds. Numerous
factors have been proposed to influence the evolution of CBP, including nest site limitation; effects of brood size, laying order, or
parasitic status on offspring survival; randomness of parasitic egg
distribution; adult life-history trade-offs; and variation in parental
female quality or risk of nest predation. However, few theoretical
studies consider multiple possible types of parasitism or the interplay
between evolution of parasitism and population dynamics. We review
existing theory of CBP and develop a synthetic modeling approach
to ask how best-of-a-bad job parasitism, separate-strategies parasitism (in which females either nest or parasitize), and joint-strategies
parasitism (in which females can both nest and parasitize) differ in
their evolutionary conditions and impacts on population dynamics
using an adaptive dynamics framework including multivariate traits.
CBP can either stabilize or destabilize population dynamics in different scenarios, and the role of comparable parameters on evolutionarily stable strategy parasitism rate, equilibrium population size,
and population stability can differ for the different modes of
parasitism.
Keywords: intraspecific brood parasitism, conspecific brood parasitism, adaptive dynamics, evolutionary dynamics, evolutionarily stable
strategy (ESS), bird population dynamics.
Conspecific brood parasitism (CBP) occurs in diverse taxa,
including insects (Tallamy 2005), fishes (Wisenden 1999),
amphibians (Summers and Amos 1997), and most prom* E-mail: pdevalpine@nature.berkeley.edu.
†
E-mail: jmeadie@ucdavis.edu.
Am. Nat. 2008. Vol. 172, pp. 547–562. 䉷 2008 by The University of Chicago.
0003-0147/2008/17204-42817$15.00. All rights reserved.
DOI: 10.1086/590956
inently, birds (Yom-Tov 1980, 2001; Davies 2000). For example, more than 230 species of birds are known to lay
eggs in the nests of conspecifics (Eadie et al. 1998; YomTov 2001). Increasing interest in this phenomenon over
the past two decades has led to a plethora of studies examining the fitness consequences to parasites and their
hosts and the ecological factors influencing the frequency
of CBP within and among populations (Petrie and Møller
1991; Davies 2000). Because conspecifics provide the only
hosts for brood parasites, obligate parasitism cannot become fixed in a population. Further, the advantages of
parasitic laying are likely to be greatest when the frequency
of parasitism is low and many host nests are available
containing few parasitic eggs; the advantages will decrease
as frequency of parasitism increases and more host nests
contain many parasitic eggs. Accordingly, fitnesses are
likely to be frequency dependent, and several game theory
models have been proposed under which CPB could persist
in an evolutionarily stable strategy (ESS; May et al. 1991;
Eadie and Fryxell 1992; Nee and May 1993; Maruyama
and Seno 1999a; Robert and Sorci 2001; Broom and Ruxton 2002, 2004; Ruxton and Broom 2002).
Less well appreciated are the possible roles of CBP in
population dynamics and vice versa. In several species,
parasitic egg laying appears to be strongly influenced by
the availability of resources essential for breeding. For example, in many hole-nesting birds, parasitism is more frequent when population density is high, nest sites are limited, and many host nests are available (Haramis and
Thompson 1985; Eadie 1991). Similar relationships with
density occur for colonial-nesting species and for species
concentrated on islands (Lank et al. 1990; Lokemoen 1991;
Lyon and Everding 1996; Waldeck et al. 2004). High levels
of CPB in turn may lead to increased levels of nest desertion and reduced hatching success of eggs or fledging
success of young (Haramis and Thompson 1985; Semel
and Sherman 1986, 2001; Semel et al. 1988; Eadie 1991;
Eadie et al. 1998). Few models have considered CBP and
population dynamics together, but those that did suggested
that CBP could lead to fluctuating or unstable population
dynamics (May et al. 1991; Eadie and Fryxell 1992; Nee
and May 1993). Indeed, Semel et al. (1988) suggested that
high levels of CBP, exacerbated by high densities of nest
548 The American Naturalist
boxes placed in close proximity, could result in population
crashes in the cavity-nesting wood duck (Aix sponsa). Theoretical and empirical work in other systems highlights the
fact that evolution shapes the traits affecting population
dynamics, and population dynamics define the relative fitnesses on which evolution acts, so neither process can be
fully understood without the other (Kokko and LopezSepulcre 2007).
In this article, we show that the impact of CBP on
population dynamics, in terms of population equilibrium
and stability, depends on why and how parasitism occurs.
In particular, scenarios with higher parasitism can give
either more stable or less stable dynamics, depending on
the model, and a factor such as value of a parasitic egg
may affect dynamics differently in different models. Investigating the role of CBP on population dynamics leads
to several modeling challenges. First, we want to build on
existing theory about evolution of CBP, but that theory
involves diverse models with different biological considerations and modes of parasitism. Therefore we begin by
reviewing the theoretical literature with the aim of developing as a starting point a general model based on existing models of the three major types of parasitism that
have been proposed, defined below as best-of-a-bad-job,
separate-strategies, and joint-strategies parasitism.
We then incorporate population dynamics and density
dependence into the general model and develop four specific cases. For each case, we examine the interactions between parasitism, equilibrium population size, and stability. For continuous strategy variables, we use the
adaptive dynamics framework, which generalizes evolutionarily stable strategies to evolutionarily singular strategies that may be dynamical attractors (convergence stable) or branching points for simple evolutionary models
(Eshel 1983; Christiansen 1991; Waxman and Gavrilets
2005). Most adaptive dynamics research considers only
univariate traits, with exceptions such as work by Abrams
et al. (1993), Dieckmann and Law (1996), Leimar (2005),
and Brown et al. (2007). For model 4 below, we show that
when total reproductive effort can evolve (constrained by
adult costs of reproduction) in addition to parasitism strategy, the population dynamics consequences of CBP are
qualitatively different than when only parasitism strategy
evolves. Thus, while this article’s primary focus is on the
role of CBP in population dynamics, it also extends theories of evolution of CBP. While our models do not cover
all potentially important aspects of parasitism, they represent a synthesis and generalization of many ideas in the
literature.
Biology and Models of CBP
At least 17 studies have developed models to examine the
evolutionary dynamics of conspecific brood parasitism
from an ESS perspective. Table 1 summarizes some of the
major features included in these models, while key results
of each model are described in table A1 in the online
edition of the American Naturalist. Three major types of
brood parasitism have been considered. In best-of-a-badjob (BOBJ) parasitism, a parasitism strategy has lower fitness than nesting but is used by females who cannot breed
otherwise, typically due to nest site limitation. In separatestrategy models, females either nest or parasitize but not
both, and the strategies may have equal fitness under ESS
conditions so that parasites are not just females who cannot obtain a nest site. An ESS of separate-strategy parasitism (separate ESS) can occur if, when parasitism frequency is low (or zero), an individual could obtain higher
fitness by parasitizing than by nesting (Eadie and Fryxell
1992). Here the term “separate strategy” is the same as
the “mixed strategy” of Eadie and Fryxell (1992; there
distinguished from BOBJ parasitism) and the “professional” parasitism of Nee and May (1993). In joint-strategy
models, the same individuals may nest and also parasitize
other nests. In an ESS of joint-strategy parasitism (joint
ESS), an individual must find it advantageous to trade
some of its potential nest eggs for parasitic eggs it could
lay in other nests, which may also increase the survival of
its remaining nest eggs. Most of the studies summarized
in table 1 consider only a single type of parasitism.
Biology Included in Existing Models on Evolution of CBP
The possibility of CBP increases not only the range of
conceivable reproductive strategies but also the range of
factors that may influence relative fitness between strategies, as reflected in various models (see table 1 for citations). Without CBP, evolution of reproductive effort involves trade-offs between quality and quantity of offspring
as well as costs of reproduction. With CBP involved, there
may also be trade-offs between laying one’s eggs parasitically or in one’s own nest and between nesting at all or
reproducing completely parasitically. Each of these could
potentially have different quantity versus quality trade-offs
and costs of reproduction, although a full combination of
possibilities would make a quite complicated model and
has not been treated. Most models either assume fixed
clutch sizes for each strategy or include one trade-off such
as a cost of reproduction or a trade-off between own-nest
and parasitic eggs.
For birds, offspring value typically depends on brood
size, an effect included in most models. Parasitic eggs may
be inherently less valuable (i.e., have lower fitness) than
host eggs, a parameter that has been included in many
models, but a dependence of laying order on offspring
value has been included in only two models. The relative
fitness of nesting versus parasitism may depend on the
Y
Y
Y
§
Zink
2000
Y
Y
Y
Y
Y
Y
Y
Y
Eadie and
Fryxell 1992
Y
Y
Y
Y
Y
Y
Y
Nee and
May 1993;
model A
Y
Y
Y
Nee and
May 1993;
model B
§
Y
Y
Y
Yamauchi
1993
Y
Y
Y
§
§
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
§
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Andersson Robert and Lopez-Sepulcre Ruxton and Broom and
Broom and
2001
Sorci 2001 and Kokko 2002 Broom 2002 Ruxton 2002 Ruxton 2004
Y
Y
Y
Y
Y
Y
Y
Y
May et al.
1991
§
Y
Y
Y
Takasu
2004
Y
Y
Y
Y
Y
Y
Y
Pöysä and
Pesonen 2007
Y
Y
Y
Y
§
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Our
models
Y
Y
§
Y
Yamauchi Maruyama and Maruyama and
1995
Seno 1999a
Seno 1999b
Note: “Y” means an issue was included in the models of a paper; a blank cell means it was not; § indicates that an explanation is given in table A1 in the online edition of the American Naturalist.
BOBJ p best of a bad job; ESS p evolutionarily stable strategy.
BOBJ parasitism
Separate-ESS parasitism
Joint-ESS parasitism
Total brood size affects fledge success
Parasite displaces/removes host eggs
Inherent lower value of parasite eggs
Rejection of parasite eggs/females by host
Variation in maternal quality
Randomness of parasite distribution
Nest site limitation
Adult cost of reproductive effort
Laying order affects fledge success
Inclusive fitness considered
Variation in nest susceptibility to predation
Population dynamics considered
Offspring survival depends on adult density
BOBJ parasitism
Separate-ESS parasitism
Joint-ESS parasitism
Total brood size affects fledge success
Parasite displaces/removes host eggs
Inherent lower value of parasite eggs
Rejection of parasite eggs/females by host
Variation in maternal quality
Randomness of parasite distribution
Nest site limitation
Adult cost of reproductive effort
Laying order affects fledge success
Inclusive fitness considered
Variation in nest susceptibility to predation
Population dynamics considered
Offspring survival depends on adult density
Features included in model
Andersson
1984
Table 1: Comparison of existing models of conspecific brood parasitism
550 The American Naturalist
randomness of parasitic egg distributions, included in several models, or on the randomness of host clutch sizes,
considered in only one model. Hosts may reject parasitic
eggs, and parasites may eject one or more host eggs when
visiting a host nest, but the former has been included more
often than the latter, perhaps because it is mathematically
simpler. The tendencies to eject host eggs or reject parasitic
eggs may themselves evolve, along with evolution of recognition of one’s own eggs, and these tendencies have been
considered in a few models. Between some models, the
same biological considerations are treated differently. For
example, several models include a factor by which parasitic
eggs have lower value than host eggs and describe it
broadly as encompassing egg rejection by hosts without
specifically including egg rejection in calculations of brood
size that affect offspring survival.
A somewhat distinct group of models (Zink 2000; Andersson 2001; Lopez-Sepulcre and Kokko 2002) considers
CPB as an alternative to cooperative breeding or solitary
nesting. These models are distinguished by their focus on
the influence of relatedness among hosts and parasites and
hence inclusive fitness (see also Andersson 1984). Most
recently, Pöysä and Pesonen (2007) considered variation
in predation risk among nest sites and the potential influence of spatial bet hedging (cf. Rubenstein 1982; Bulmer
1984). These studies provide important directions for adding further complexity and realism to models of CBP, but
they are outside the scope of our model. In summary,
existing models are diverse and not easy to synthesize.
Results of Existing Models on Evolution of CBP
and Population Dynamics
A common result of most of the models summarized in
tables 1 and A1 is that under specific sets of conditions,
CBP can invade a nonparasitic population and be evolutionarily stable. Hence, the original suggestion of Andersson and Eriksson (1982) that CBP could exist as an
ESS has now been validated using several different modeling approaches. However, of all the models summarized
in table 1, only three explicitly consider the population
dynamic implications of CBP.
May et al. (1991) modeled populations comprising three
types of strategies: vigilant hosts (that reject parasitism),
naive hosts (that accept parasitism), and parasites. Population dynamics depended on the cost of vigilance and
egg laying activity of parasites. Cyclic oscillations of the
three strategies were possible, leading in turn to unstable
and cyclic total population size. Nee and May (1993) also
focused on the interplay between population dynamics and
evolutionary stability. They give scenarios in which it is
impossible to have both population dynamical stability
and evolutionary stability. Finally, Eadie and Fryxell (1992)
explored the interaction of frequency dependence and density dependence in maintaining CBP as a mixed (i.e., separate) ESS. With nest limitation and random nest choice
by parasites, high levels of CBP could destabilize population dynamics.
These three studies provide interesting early results
about CBP and population dynamics, but they are limited
in several ways. They consider much less general models
than the one developed here and give less general analysis.
For example, model A of Nee and May (1993) assumes
fixed clutch sizes and ejection of one host egg per parasite
egg (so that brood size effects are not important), omits
considerations such as joint strategies (their model B includes joint strategies but is limited to an informal graphical analysis) and costs of reproduction, and is formulated
in specific rather than general terms. Here we ask the
question of how different types of CBP can affect population dynamics stability. For simplicity, we incorporate
density dependence such that its interaction with ESS parasitism levels is small.
Our Models
We examine the evolutionary stability of parasitism and
its effect on population dynamics for several specific cases
of a general model that includes many biological aspects
of the separate models listed in table 1. First we introduce
the general model and its assumptions, with parameters
summarized in table 2. Then we give additional assumptions for the specific cases. The general model can lead to
BOBJ, separate-ESS, and/or joint-ESS parasitism, although
in the results presented here only one type of parasitism
is considered in each specific case.
The general model allows two types of strategy, nesting
and non-nesting. The nesting strategy allows eggs to be laid
both in one’s own nest (nest eggs) and in other nests (parasitic eggs), while the non-nesting strategy allows only parasitic eggs. The nesting strategy involves total reproductive
effort of T, split between Cn nest eggs and Cp/t non-nest
eggs. Therefore each nest egg can be traded for t parasitic
eggs, and C p p t(T ⫺ C n), with 0 ≤ C n ≤ T. The trade-off
parameter t may be greater or less than 1 depending, for
example, on how much effort is required to find nests to
parasitize and whether production of nest eggs is limited
by ability to feed them versus physiological limits in producing them. The fraction of parasitic eggs that are not
rejected (killed) by the host is h. The value of a parasitic
egg relative to a nest egg, given that each survives the nest,
is g, and in the specific cases we assume 0 ≤ g ≤ 1.
The population fraction of non-nesters is p, each of
which produces Cp parasitic eggs. If non-nesters have
equivalent physical state to nesters, then it is reasonable
to assume Cp p tT, the maximum parasitic eggs that even
Brood Parasitism and Population Dynamics 551
Table 2: Model parameters and notation
Parameter
N
Cn
Cp
Cp
T
t
Xi
Xr
Y
W
Sn, Sp
S0
mn, mp
B
D(N)
An, Ap
Q
K
H
p
g
h
Fn
Fp
G(N)
Interpretation
Adult population size
Eggs laid by a nester in her own nest (equal to T for models 1, 2)
Eggs laid by a nester in other nests
Eggs laid by a non-nester (equal to tT)
Reproductive effort (maximum number of own nest eggs, equal to 8 for models 1–3)
Number of parasitic eggs a female can produce instead of 1 nest egg
Strategy variable X (with X p T or Cn) for an invading strategy
Strategy variable X (with X p T or Cn) for a resident strategy
Number of parasite eggs in a nest
Abstract vector of nest laying orders or other random quality variable
Offspring survival of host eggs and parasitic eggs, respectively
Intercept of offspring survival as a function of total eggs in nest (equal to 1 in all models)
Negative exponential slope for offspring survival of host and parasitic eggs, respectively, as a function
of brood size (mn p .125; mp p mn in models 1 and 3; mp p .15 in models 2 and 4)
Negative slope of offspring survival as a function of N (.005 in models 2–4; 0 in model 1).
Density-dependent factor in offspring survival, equal to 1⫺bN or 0
Adult survival for nesters and non-nesters, respectively
Maximum adult survival for model with adult cost of reproduction (.8 in model 4)
Negative slope of adult survival as a function of T for adult cost of reproduction (.05 in model 4)
Number of nest sites available (100 for model 1)
Fraction of adults using a parasitic strategy (derived for each model)
Offspring value of a parasitic egg relative to a nester egg from same nest, 0 ! g ≤ 1
Probability that a parasitic egg is not rejected by host (1 in all models)
Fitness of nesters
Fitness of non-nesters
Population dynamics function: N(t ⫹ 1) p G(N(t))
a nester could produce. Alternatively, Cp could be greater
or less than tT depending on the costs and benefits of
building and using a nest. Non-nesting may occur either
as a separate strategy ESS or as a BOBJ strategy if there
is nest limitation.
Parasitic eggs may be distributed either evenly or randomly among nests. It is assumed that parasitic eggs from
nesters and non-nesters follow the same distribution and
that the parasitic eggs of one parent are not aggregated in
one or more nests. Survival rates of nest eggs and parasitic
eggs are Sn(Cn, y, w, N) and Sp(Cn, y, w, N), respectively.
These each depend on the numbers of nest eggs (Cn) and
parasitic eggs (y), the vector of laying orders or other
random factors for each egg (w), and total adult population size (N). The random variables for parasitic eggs
per nest that are not rejected by the host and for laying
order are Y and W, respectively, with realized values denoted y and w, respectively. In the specific models below,
we use Poisson distributions for Y and do not include W.
To implement a particular model for W, the general equations (1) and (2) below are still valid, but one would need
to consider specific models for laying orders in more detail
(Broom and Ruxton 2002).
Finally, adult survival may either be constant or depend
on reproductive strategy (costs of reproduction) and/or N
(density dependence). For a non-nester, dependence on
reproductive strategy is via Cp, while for a nester it is via
T and/or Cn. It would also be possible for adult survival
for a nester to depend on the number of parasitic or total
eggs it has raised.
For nesters, a strategy is defined by either Cn, if there
is no adult cost of reproduction and hence T can be assumed fixed at a physiological maximum, or by (Cn, T),
if adult cost of reproduction creates a trade-off between
total reproductive output and adult survival. To formulate
fitness in an adaptive dynamics framework, define
(C nr , T r) as the resident strategy of an entire population
and (C ni , T i) as an invading strategy of a mutant individual.
The fitness of an invading nester strategy in a population
playing a resident strategy is
Fn(C ni , T i ; C nr , T r) p C ni EY, W[Sn(C ni , Y, W, N )]
⫹ ghC pi (C ni , T i)
EY, W[YS p(C nr , Y, W, N )]
⫹ A n(C ni , T i, N ).
EY[Y ]
(1)
The three terms in this equation correspond to offspring
from a nester’s own nest, offspring from parasitically laid
552 The American Naturalist
eggs, and adult survival, respectively. The expected value in
the own-nest term is the average survival (per nest) of the
nest eggs across all random values of parasitic eggs per nest
and laying orders. The average survival of parasitic eggs (per
egg) that are not rejected is calculated as the average number
of parasitic eggs that survive per nest divided by the average
number of parasitic eggs per nest. (This is the average survival of a randomly chosen parasitic egg in the population
rather than the average survival of parasitic eggs in a randomly chosen nest.) In all expectations, the distribution of
Y incorporates parasitic eggs from both non-nesters and
nesters (using the resident strategy) that are not rejected at
laying. The benefit to the invading strategy of parasitic eggs
is multiplied by their relative value (g) and the probability
that they are not rejected (h). Finally, adult survival of a
nester, An, may depend on reproductive effort and/or adult
population size.
For non-nesters, fitness is given by
Fp(Cp) p ghCp
EY, W[YS p(C nr , Y, W, N )]
⫹ A p(Cp, N ),
EY[Y ]
(2)
where Ap is adult survival for non-nesters. The average
fitness in the population is
F p pFp ⫹ (1 ⫺ p)Fn.
(3)
The population dynamics are given by
N(t ⫹ 1) p N(t)F(N(t)) { G(N(t)).
(4)
In equation (4), F has been rewritten F(N(t)) to emphasize
that average fitness depends on population size via equations (1) and (2).
Several aspects of model formulation (1)-(2) deserve
comment. The model is closely related to the general model
of Broom and Ruxton (2004), which was formulated to
understand the evolution of CBP rather than its effects on
population dynamics. The model here includes rejection of
parasite eggs by hosts, density dependence, and non-nesters,
which are all omitted by Broom and Ruxton (2004). Their
model includes random numbers of nester eggs in their
own nest, which is omitted here simply to avoid extraneous
notation. Including that feature in our model would be
straightforward, accomplished by redefining Cn as reproductive effort for a nester’s own nest, which determines the
distribution of nest eggs laid, and by adjusting the expectations accordingly. Both models are formulated with general notation for laying-order effects that are not used in
specific cases. We included general notation (W) for laying
order effects to highlight its potential role in frequency dependence (Broom and Ruxton 2002).
The model of Robert and Sorci (2001) is a subset of
our model, with t p 1, no density dependence, no adult
cost of reproduction or random laying order, and a nonrandom distribution of parasite eggs. The model of Eadie
and Fryxell (1992) formulates the expected value of parasitic egg survival in a different but equivalent way than
(1)-(2). They formulate it as the expected per-nest survival
for all eggs in the population except one parasite’s eggs,
with that parasite’s eggs added for each term in the expectation. This gives the same result as (1)-(2) but would
be slightly trickier to implement numerically if the distribution of eggs involves over- or underdispersion, such
as a negative binomial.
Perhaps the most important biological considerations
omitted from our model are ejection of host eggs by parasites as they deposit their eggs and trade-offs between egg
quality and quantity. It would be straightforward to include ejection of host eggs abstractly in (1)-(2), but that
could lead to a complicated stochastic process for a specific
case. Including trade-offs between egg quality and quantity
would also be straightforward to formulate, but that would
lead to additional strategy variables that are beyond the
scope of this article.
Analysis
Analysis of model (1)-(2) involves up to three types
of stability: evolutionary stability of the fraction of nonnesters, for which nester or non-nester are discrete strategies; evolutionary stability of the continuous strategy variables Cn and/or T among nesters; and population
dynamics stability. These could be intertwined in general,
for example, with the evolutionary equilibria and stability
of nesting strategies affected by population dynamics parameters and vice versa. In the specific cases here, such
dependencies are minor, so analysis of each type of stability
is presented separately. Although Cn, Cp, and Cp in reality
must be integers, we allow them to be real (continuous)
numbers for mathematical convenience.
Stability of Non-Nesting Fraction
An equilibrium of the fraction of non-nesters, p∗, is defined as the value of p such that Fn p Fp (noting that Fn
and Fp are both functions of p and assuming Cn, T, and
N fixed). It is a stable equilibrium if
F
⭸
(F ⫺ Fp)
⭸p n
ppp∗
1 0.
This condition states that if an infinitesimally larger fraction of the population than p∗ adopts the non-nesting
Brood Parasitism and Population Dynamics 553
strategy, the fitness of nesters would be greater than that
of non-nesters, so some of the non-nesters would have
higher fitness if they nested, decreasing the non-nesting
fraction back to p∗.
Stability of Joint Nesting–Parasitism Strategy Variables
Next we introduce evolutionarily singular strategies and
stability for the nester strategy variables, Cn and/or T. Conditions are given here for Cn when T is fixed, and the
multivariate conditions for (Cn, T) are given in appendix
B in the online edition of the American Naturalist. If there
is no adult cost of reproduction, then T will be fixed at a
maximum effort; even if there is no benefit to laying additional nest eggs, laying any possible parasitic eggs will
always be favored if there is no cost. Then
Fn(C ni , T i; C nr , T r) p Fn(C ni ; C nr). An evolutionarily singular strategy C ∗ is defined by
dFn
dC ni
F
C ni pC nr pC∗
p 0.
This means that individual fitness is at an optimum at
C ni p C ∗ when the resident strategy is also at C ∗. The
optimum is a local maximum and therefore is stable to
invasion of nearly similar strategies, if
d 2Fn
(dC ni )2
F
C nipC nrpC∗
! 0.
The final condition involves the direction of the selection
gradient if the resident strategy deviates from C ∗. The
singular strategy has convergence stability if
[ F
d dFn
dC dC ni
C ni pC nr pC
]F
CpC∗
!0
(Eshel 1983; Christiansen 1991). This states that if the resident strategy increased infinitesimally from C ∗, then the
slope of fitness with respect to an invading strategy, evaluated at the resident strategy, would be back toward C ∗.
⫺1 !
F
⭸
G(N )
⭸N
NpN∗
! 1.
This condition states that if a deviation from equilibrium leads to a larger deviation at the next time step, either
in the same direction or by overcompensation in the opposite direction, then the equilibrium is not stable. The
⫺1 boundary is of interest here because values of
(⭸/⭸N )G(N )FNpN∗ less than ⫺1 can give oscillatory dynamics. In interpreting results about population dynamics stability, it is important to interpret all values of the stability
condition, (⭸/⭸N )G(N )FNpN∗, rather than focusing solely
on the boundary values (⫺1 and 1) and the bifurcation
from stable equilibrium to cycles at ⫺1. Values of
(⭸/⭸N )G(N )FNpN∗ that are closer to 0 will give quicker returns to equilibrium, that is, greater resiliency, than values
farther from 0. In the specific cases below, parameters have
been chosen to be biologically reasonable and to highlight
changes in the stability condition by including a bifurcation (crossing ⫺1). However, other parameters in each
model give similar results for the stability condition even
if it does not cross ⫺1. In addition, effects of CBP on
equilibrium population density are potentially as biologically important as effects on stability.
Interactions among Stability Conditions
In general, one could consider the evolutionary and population dynamics stability conditions all together. For example, if a model admits both separate strategies and joint
strategies, then are the joint, variable singular strategies
stable to perturbations in the fraction of non-nesters? Interactions with population dynamics could also require
some assumptions about trait inheritance and plasticity.
For example, in a joint-strategies model, if a stable ESS
solution is a function of population density N, then one
could consider different assumptions about how the strategies track population size. In the specific cases analyzed
here, such complications are minimal. Only one type of
strategy is considered for each model. For models 1–3, the
strategy results are independent of N. For model 4, the
strategy results depend on N, but the results about CBP
and dynamics are unaffected by this dependence, so we
assume the strategy variables are optimized for equilibrium
population size.
Population Dynamics Stability
Finally, a population dynamics equilibrium, N ∗, is defined
by F(N ∗) p 1 or G(N ∗) p N ∗. The equilibrium is stable
if
Assumptions Used for Specific Cases
Next we give assumptions and specific functions used in
the following cases.
554 The American Naturalist
1. A parasitic egg has the same effect on brood survival
as a host egg. This is reasonable because once a parasitic
egg has been adopted in a nest, its impact on factors such
as food per nestling and attraction of predators could be
similar to host eggs.
2. Laying order does not affect offspring survival.
3. In the BOBJ and separate-strategies model, given reproductive effort T, nesters lay C n p T eggs and parasites
lay Cp p tT eggs.
4. The effects of density dependence and brood size on
offspring survival occur independently on a log scale. This
means that each effect contributes a factor to the offspring
survival function, and those factors are multiplied. For
models 1–3 below (with no cost of reproduction), this
assumption decouples strategy optimization from population size. In general, optimal clutch size could depend
on population size, and our simpler assumption represents
a step toward more complex modeling in the future.
5. Brood survival is a negative exponential function of
brood size, which may differ for nest eggs and parasitic
eggs:
SL(C, y, N ) p S 0e⫺mL(C⫹y)D(N ),
where L is either n or p; S0 is a constant maximum survival,
set to 1 in all cases; mn and mp are coefficients for the
effect of brood size on survival for nest eggs and parasitic
eggs, respectively, with m n p 0.125 in all cases and
mp p 0.125 or 0.15; and D(N ) is the density-dependent
effect of adults on offspring survival, with 0 ≤ D(N ) ≤ 1.
6. Nester clutch size in the absence of parasitism is at
its optimal value, 1/m n p 8. An important consequence
of assumption 5 is that this optimal clutch size does not
depend on the number of parasitic eggs in the nest. If
optimal own-nest clutch size depended on the number of
parasitic eggs, then own-nest clutch size might evolve
downward if parasitism is established in the population,
and we do not consider such cases here.
7. D(N) is either constant at 1 or a linear function of
N down to a minimum of 0:
D(N ) p max {1 ⫺ bN, 0}.
8. Adult survival is either constant (no cost of reproduction) or a linear function of total reproductive effort,
T, down to a minimum of 0:
A n(T) p max {Q ⫺ kT, 0}.
9. Parasitic eggs are Poisson distributed among nests.
The mean number of parasitic eggs per nest is
EY[Y ] p
h[pCp ⫹ (1 ⫺ p)C pr ]
.
1⫺p
For a large number of nests, the Poisson distribution is
essentially identical to the binomial distribution. This assumption makes parasitism less favorable because parasitic
eggs are disproportionately in large broods, which have
lower survival.
Specific Cases and Simulations
Each model was implemented numerically, and the equations were solved for equilibrium population size, parasitism rate, and stability conditions. All evolutionary equilibria were stable, with one subtlety for model 4 described
below, so they are evolutionarily plausible. Parameters for
each model, including ranges of g and t values, were chosen to make the models comparable while elucidating differences between models in the role of parasitism on population dynamics. The results are interpreted comparatively rather than as specific numerical predictions because
the models do not incorporate all aspects of bird ecology.
Model 1: Nest Limitation and BOBJ Parasitism
The BOBJ parasitism model by definition requires nest site
limitation. This model makes sense only if parasitism is
inferior to nesting for at least some individuals. For BOBJ
parasitism, every non-nester favors some reproduction
over none and so will parasitize if possible. We consider
a BOBJ model with (in addition to the parameters specified
above) no joint strategies allowed (C n p T); constant
adult survival that is lower for non-nesters than for nesters
(such as if non-nesters are inferior competitors), A n p
0.4, A p p 0.2; no effect of adult density on offspring survival (b p 0); and equal brood survival for nest and parasitic eggs, mp p m n. In comparison to models 2–4, the
assumption of no adult density effect amplifies the role of
nest limitation in regulating density. The maximum number of nest sites is H p 100, and the fraction of nonnesters is
p p max
{
}
N⫺H
,0.
N
The range of g and t values for model 1 was such that
parasitism is never favored over nesting at equilibrium
population density.
Brood Parasitism and Population Dynamics 555
Model 2: Separate-Strategies Model
Model 4: Joint-Strategies Model with Evolution of
Total Reproductive Effort
For separate-ESS parasitism to occur, non-nester fitness
must be greater than nester fitness at low frequency and
also must be frequency dependent such that at low frequencies non-nesting is favored and vice versa. For the
separate strategies model, we assume that adult density
affects brood survival (b p 1/200), there is no nest site
limitation (no BOBJ parasitism), and we do not allow joint
strategies (C n p T). Then the frequency dependence must
affect the difference between the expected survival of nest
eggs in equation (1) and the expected survival of parasitic
eggs in equation (2). This could occur if for any reason
the difference between Sn and Sp depends on the fraction
of non-nesters, p. For example, if later laying order decreases survival and parasitic eggs are disproportionately
laid later, and if this effect is stronger when there are more
parasites, frequency dependence would result. In the
model of Eadie and Fryxell (1992), frequency dependence
arose from the randomness of the parasitic egg distribution. Parasitic eggs are disproportionately in large broods
to an extent that depends on p. This effect occurs in the
model here, but here the frequency dependence it generates is weak; if we replace the exponential brood survival
model with a linear model, then variance in parasitic eggs
per nest generates stronger frequency dependence (results
not presented).
For a generic model of frequency dependence, model 2
here assumes that parasitic eggs are slightly more sensitive
to brood size than are nest eggs, mp p 0.15 1 m n (a very
small difference), which could arise as a type of quality or
laying order effect. Adult survival is the same for nesters
and non-nesters, A n p A p p 0.5.
Model 4 includes an adult cost of total reproductive effort,
with an intercept of Q p 0.8 and slope of k p 0.05 so
that Cn and T must be jointly optimized. Preliminary results with other parameters that were the same as for model
3 gave a sharp transition from low parasitism to complete
parasitism. When parasite egg value g and the trade-off
between nest eggs and parasitic eggs t are both low, no
parasitism occurs, and T is essentially the only strategy
variable to maximize fitness. When g and t are large
enough, parasitism is favored, T increases to its maximum
possible value (such that adult survival is 0), and nearly
all reproductive effort is parasitic. Based on these preliminary results, we added more frequency dependence to
model 4 in the same manner as in model 2, mp p
0.15 1 m n, to generate a larger range of stable parasitism
levels.
Model 3: Joint-Strategies Model with
No Adult Cost of Reproduction
Like the separate ESS, a joint ESS requires frequency dependence in the fitness difference between laying nest eggs
and parasitic eggs. However, in the joint-strategies model,
the same individuals can lay nest and parasitic eggs, so
frequency dependence arises automatically and does not
require the mechanisms described for model 2. Model 3
is identical to model 2 except that joint strategies are allowed; brood survival is the same for all eggs, mp p m n;
and adult survival is A n p A p p 0.4. For this model,
smaller values of t and g (than in model 2) allow evolution
of parasitism. No parameters were considered for which
a separate strategy would be favored (assuming it has the
same adult survival and other parameters).
Results
In the BOBJ model (model 1; fig. 1), as parasite fecundity
Cp p tT increases, the equilibrium population size decreases because the reproductive success of all eggs is decreased by the large brood sizes due to parasite eggs. Lower
equilibrium population size implies lower parasitism rate,
so higher t leads to lower parasitism. Higher parasite offspring value g increases the fitness of parasites without
affecting offspring survival, so it increases equilibrium
population size and parasitism rate, but only slightly. Although higher t leads to a lower equilibrium population
size and parasitism rate, it destabilizes dynamics, as shown
by the bifurcation diagram. Meanwhile, parasite offspring
value g has negligible effect on stability. These results are
explained by the population dynamics map of N(t ⫹ 1)
versus N(t) (fig. 2). Parasitism does not affect the population dynamics when N ! H, but for N 1 H, higher t leads
to a steeper negative slope in the population dynamics
map around equilibrium, which is destabilizing.
For the separate-ESS model (model 2; fig. 3), parasitism
increases as either t or g increases because these represent
greater parasitism fitness. This leads to lower ESS fitness
for both nesters and parasites and hence lower equilibrium
population size. The impact of parasite offspring value g
on parasitism rate is much stronger than in the BOBJ
model, and its impact on equilibrium population size and
stability are opposite to the BOBJ model. Also, unlike the
BOBJ model, parasitism in the separate-ESS model affects
the entire population dynamics map (fig. 2), with higher
parasitism causing lower N(t ⫹ 1) for any given N(t). This
flattens the slope of the population dynamics map at equilibrium and hence stabilizes dynamics.
556 The American Naturalist
Figure 1: Best-of-a-bad-job model. Top left, equilibrium population size (contours) as a function of t and g. Top right, same for parasitism rate
(contours). Bottom left, same for stability condition (contours). When the stability condition is below ⫺1, the model is unstable. Bottom right, for
fixed g and different values of t, the model was run for many time steps, and the last 50 population sizes were plotted for that t. When the model
has a stable equilibrium, the last 50 population sizes fall on the same point and appear as one point. When the model has an unstable equilibrium,
the last 50 population sizes oscillate between two values, which appear as two points.
The joint-ESS model without costs of reproduction
(model 3; fig. 4) has a stability picture that is more similar
to the separate-ESS model than to the BOBJ model, but
it allows parasitism for lower values of g and t than does
the separate-ESS model. In model 3, if the entire population uses a strategy that is entirely nesting (C n p D),
then a single individual that shifts some reproduction toward parasitism experiences three effects on its fitness. The
offspring survival of all of its remaining nest eggs is increased by having a smaller total number of eggs in the
nest, it gains the reproductive output from its parasitic
eggs, and it loses the output of the eggs not included in
its own nest. Since T has been set at the optimal value for
nesting alone, the loss of an egg from its own nest is worse
than the gain of increased survival for the remaining eggs.
However, the gain from parasitic eggs—even if each is
worth less than nesting eggs—can make parasitism ad-
vantageous. As t increases, making parasitic eggs easier to
produce, the ESS rate of parasitism increases, net fitness
decreases, and hence equilibrium population size
decreases.
Like the separate-ESS model, the entire population dynamics map (fig. 2) is less steep, so the population dynamics are stabilized. Although the flattening of the population dynamics map is similar between models 2 and 3
with regard to t, the role of parasite offspring value g on
population dynamics stability differs between these models. For both models, higher g favors higher parasitism,
but for model 3, this actually increases average fitness and
thus destabilizes the population dynamics.
The joint-ESS model with costs of reproduction (model
4; fig. 5) gives yet different results. Qualitatively, the results
are more similar to model 2 than model 3, but with different parameters values and for different reasons. For
Brood Parasitism and Population Dynamics 557
Figure 2: Population dynamics surfaces. For each model, two relationships between N(t ⫹ 1) and N(t) are shown for two evolutionarily stable
strategy values of conspecific brood parasitism. For each model, the parameters are the same as in the bifurcation diagrams from figures 1 (best of
a bad job), 3 (separate strategies), 4 (joint strategies without cost of reproduction), and 5 (joint strategies with cost of reproduction). The two values
of parasitism are labeled and can be located on the abscissas from figures 1, 3–5. The dotted line shows the identity line (N[t ⫹1] p N(t)), which
crosses each population dynamics map at its equilibrium population size. When the slope of the population map crosses the identity line with slope
steeper (less) than ⫺1, the equilibrium is unstable.
model 4 there is a relatively narrow range of g and t over
which sharp changes in strategy are predicted. For larger
values of g and t, total reproductive effort increases to its
maximum value of 16 (giving zero adult survival), and the
fraction of reproduction invested in parasitic eggs increases. In all cases, higher parasitism gives lower fitness
and hence lower equilibrium population size and higher
stability. The lower elbow in the bifurcation (stability)
subfigure arises when the T reaches its maximum value as
t is increased. The sensitivity of results to g and t, which
are not subject to evolution in the model here, suggests
that the evolutionary trade-offs shaping them, in terms of
quality versus quantity and reproductive effort, could play
an important role in CBP evolution and population
dynamics.
A subtlety in stability of the evolutionary dynamics
arises for model 4 (app. B). For parameters where the ESS
solution involves intermediate levels of reproductive effort
and parasitic effort, the convergence stability conditions
are satisfied, but the invasion stability condition is neutral
in the T direction, suggesting that some distribution of
strategies centered at the ESS may be supported. This result
is not troubling for the overall analysis (one could assume
slight curvature in An to achieve complete stability), but
it points to the potential for further interesting results if
heritability of strategies is modeled explicitly.
Discussion
Our results show that one cannot easily or simply predict
the effect of CBP on population dynamic stability without
knowing more about how parasitism actually occurs. Nev-
558 The American Naturalist
Figure 3: Separate evolutionarily stable strategy model. Top left, equilibrium population size (contours) as a function of t and g. Top right, same
for parasitism rate (contours). Bottom left, same for stability condition (contours). When the stability condition is below ⫺1, the model is unstable.
Bottom right, for fixed g and different values of t, the model was run for many time steps, and the last 50 population sizes were plotted for that
t. When the model has a stable equilibrium, the last 50 population sizes fall on the same point and appear as one point. When the model has an
unstable equilibrium, the last 50 population sizes oscillate between two values, which appear as two points.
ertheless, some general predictions do emerge from the
models here. When CBP is caused by nest limitation, parasitism increases the strength of density dependence
caused by nest limitation, decreasing equilibrium population size and destabilizing dynamics. When CBP is not
caused by nest limitation, it may increase or decrease average fitness. If parasitism increases average fitness, it also
increases population density and decreases stability. If parasitism decreases average fitness, it also decreases population density and increases stability.
While our model includes many biological considerations, the evolution and consequences of CBP are likely
to be even more complex. For example, several models
have included egg rejection behavior in relation to the
degree of relatedness between hosts or parasites and to
the ability to recognize kin (Zink 2000; Andersson 2001;
Lopez-Sepulcre and Kokko 2002). Empirical studies of
such inclusive fitness benefits are mixed in their support
(Andersson and Ahlund 2000, 2001; Pöysä 2003a, 2004;
Nielsen et al. 2006; Waldeck and Andersson 2006), but
evidence is increasing that host-parasite interactions
among conspecifics may be more complex than considered
in many existing models of CBP. Recent work by Pöysä
and colleagues demonstrates that, in at least some species,
parasites are able to assess the relative safety of nests with
respect to the risk of nest predation and differentially parasitize safe nest sites (Pöysä 1999, 2003b, 2006; Pöysä et
al. 2001; Pöysä and Pesonen 2007). Pöysä and Pesonen
(2007) included this factor and showed that selection for
laying eggs in safe sites could have a strong influence on
the occurrence and persistence of CBP. In addition to this
spatial aspect of CBP, one could consider the temporal
dynamics of reproductive seasons in more detail, including
timing of nesting and egg laying.
Brood Parasitism and Population Dynamics 559
Figure 4: Joint evolutionarily stable strategy model without adult cost of reproduction. Top left, equilibrium population size (contours) as a function
of t and g. Top right, equilibrium fraction of reproductive effort invested in parasitism, (T⫺Cn∗)/T, as a function of parasite eggs per nest t and
g. Bottom left, same for stability condition (contours). When the stability condition is below ⫺1, the model is unstable. Bottom right, for fixed g
and different values of t, the model was run for many time steps, and the last 50 population sizes were plotted for that t. When the model has a
stable equilibrium, the last 50 population sizes fall on the same point and appear as one point. When the model has an unstable equilibrium, the
last 50 population sizes oscillate between two values, which appear as two points.
We suggest several questions for future empirical work,
which can be biologically important in their own right.
First, estimates of parameters in the model and differences
between nesters and non-nesters or nest eggs and parasitic
eggs would be fundamental for improved understanding.
For example, do nest eggs and parasitic eggs differ in brood
survival or in fitness if they do fledge? Are there different
adult costs to laying nest eggs or parasitic eggs? Under
separate parasitism, do nesters and non-nesters differ in
reproductive effort and/or survival? Do parasitic versus
nonparasitic species adopt different strategies of egg quantity and/or quality?
Second, from a behavioral ecological perspective, when
and where is each type of parasitism (BOBJ, separate ESS,
or joint ESS) most prevalent? To date, most studies on
birds suggest a mix of BOBJ or joint-strategy parasitism
(Brown and Brown 1989, 1998; Eadie 1989, 1991; Pinxten
et al. 1991; Lyon 1993a, 1993b, 2003; Sorenson 1993;
McRae and Burke 1996; McRae 1998; Ahlund and Andersson 2001; Ahlund 2005). This is consistent with our
model result that the separate ESS arises only if the joint
strategy is assumed to be impossible in the specific cases
considered.
Third, from a population ecological perspective, there
is a remarkable paucity of studies examining the relationship between CBP and population density and dynamics.
While a test of the full interplay between CBP evolution
and population dynamics would be daunting (Kokko and
Lopez-Sepulcre 2007), narrower aspects of their relationship can be tested. For example, a handful of studies on
a small number of species (mostly hole-nesting ducks)
have reported significant impacts of CBP on nesting suc-
560 The American Naturalist
Figure 5: Joint evolutionarily stable strategy model with adult cost of reproduction. Top left, equilibrium reproductive effort (contours) as a function
of t and g. Top right, same for equilibrium fraction of reproductive effort invested in parasitism, (T∗⫺Cn∗)/T∗. Bottom left, same for stability condition
(contours). When the stability condition is below ⫺1, the model is unstable. Bottom right, for fixed g and different values of t, the model was run
for many time steps, and the last 50 population sizes were plotted for that t. When the model has a stable equilibrium, the last 50 population sizes
fall on the same point and appear as one point. When the model has an unstable equilibrium, the last 50 population sizes oscillate between two
values, which appear as two points.
cess (Jones and Leopold 1967; Heusmann 1972; Heusmann et al. 1980; Haramis and Thompson 1985; Semel
and Sherman 1986, 2001; Semel et al. 1988; Eadie 1991;
Eadie et al. 1998).
Finally, we emphasize that the role of CBP on population dynamics may have practical, as well as theoretical,
implications. If CBP does influence population stability,
as our models suggest, and if the management of critical
resources such as nest sites influences the frequency and
intensity of CBP, as a number of empirical studies suggest
(Semel and Sherman 1986, 1995, 2001; Semel et al. 1988;
Eadie 1991), then a deeper understanding of the linkage
between CBP and population dynamics will be essential
to develop effective conservation and management strategies for the growing list of species in which this intriguing
behavior occurs (Eadie et al. 1998).
Acknowledgments
J.M.E. thanks the Dennis G. Raveling Endowment and the
University of California Agricultural Experiment Station
Cooperative State Research, Extension, and Education Service (grant CADXXX6342-H) for support of this research.
We thank two anonymous reviewers for suggestions that
improved the article.
Literature Cited
Abrams, P. A., H. Matsuda, and Y. Harada. 1993. Evolutionarily
unstable fitness maxima and stable fitness minima of continuous
traits. Evolutionary Ecology 7:465–487.
Ahlund, M. 2005. Behavioural tactics at nest visits differ between
parasites and hosts in a brood-parasitic duck. Animal Behaviour
70:433–440.
Brood Parasitism and Population Dynamics 561
Ahlund, M., and M. Andersson. 2001. Brood parasitism: female ducks
can double their reproduction. Nature 414:600–601.
Andersson, M. 1984. Brood parasitism within species. Pages 195–
228 in C. J. Barnard, ed. Producers and scroungers: strategies of
exploitation and parasitism. Croom Helm, London.
————. 2001. Relatedness and the evolution of conspecific brood
parasitism. American Naturalist 158:599–614.
Andersson, M., and M. Ahlund. 2000. Host-parasite relatedness
shown by protein fingerprinting in a brood parasitic bird. Proceedings of the National Academy of Sciences of the USA 97:
13188–13193.
———. 2001. Protein fingerprinting: a new technique reveals extensive conspecific brood parasitism. Ecology 82:1433–1442.
Andersson, M., and M. O. G. Eriksson. 1982. Nest parasitism in
goldeneye Bucephala clangula: some evolutionary aspects. American Naturalist 120:1–16.
Broom, M., and G. D. Ruxton. 2002. A game theoretical approach
to conspecific brood parasitism. Behavioral Ecology 13:321–327.
———. 2004. A framework for modelling and analysing conspecific
brood parasitism. Journal of Mathematical Biology 48:529–544.
Brown, C. R., and M. B. Brown. 1989. Behavioral dynamics of intraspecific brood parasitism in colonial cliff swallows. Animal Behaviour 37:777–796.
———. 1998. Fitness components associated with alternative reproductive tactics in cliff swallows. Behavioral Ecology 9:158–171.
Brown, J. S., Y. Cohen, and T. L. Vincent. 2007. Adaptive dynamics
with vector-valued strategies. Evolutionary Ecology Research 9:
719–756.
Bulmer, M. G. 1984. Risk avoidance and nesting strategies. Journal
of Theoretical Biology 106:529–535.
Christiansen, F. B. 1991. On conditions for evolutionary stability for
a continuously varying character. American Naturalist 138:37–50.
Davies, N. B. 2000. Cuckoos, cowbirds and other cheats. Poyser,
London.
Dieckmann, U., and R. Law. 1996. The dynamical theory of coevolution: a derivation from stochastic ecological processes. Journal
of Mathematical Biology 34:579–612.
Eadie, J. M. 1989. Alternative female reproductive tactics in a precocial bird: the ecology and evolution of brood parasitism in
goldeneyes. PhD thesis. University of British Columbia,
Vancouver.
———. 1991. Constraint and opportunity in the evolution of brood
parasitism in waterfowl. International Ornithological Congress 20:
1031–1040.
Eadie, J. M., and J. M. Fryxell. 1992. Density dependence, frequency
dependence, and alternative nesting strategies in goldeneyes.
American Naturalist 140:621–641.
Eadie, J. M., B. Semel, and P. W. Sherman. 1998. Conspecific brood
parasitism, population dynamics, and the conservation of cavitynesting birds. Pages 306–340 in T. Caro, ed. Behavioral ecology
and conservation biology. Oxford University Press, New York.
Eshel, I. 1983. Evolutionary and continuous stability. Journal of Theoretical Biology 103:99–111.
Haramis, G. M., and D. Q. Thompson. 1985. Density-production
characteristics of box-nesting wood ducks in a northern greentree
impoundment. Journal of Wildlife Management 49:429–436.
Heusmann, H. W. 1972. Survival of wood duck broods from dump
nests. Journal of Wildlife Management 36:620–624.
Heusmann, H. W., R. H. Bellville, and R. G. Burrell. 1980. Further
observations on dump nesting by wood ducks. Journal of Wildlife
Management 44:908–915.
Jones, R. E., and A. S. Leopold. 1967. Nesting interference in a dense
population of wood ducks. Journal of Wildlife Management 31:
221–228.
Kokko, H., and A. Lopez-Sepulcre. 2007. The ecogenetic link between
demography and evolution: can we bridge the gap between theory
and data? Ecology Letters 10:773–782.
Lank, D. B., R. F. Rockwell, and F. Cooke. 1990. Frequency-dependent
fitness consequences of intraspecific nest parasitism in snow geese.
Evolution 44:1436–1453.
Leimar, O. 2005. The evolution of phenotypic polymorphism: randomized strategies versus evolutionary branching. American Naturalist 165:669–681.
Lokemoen, J. T. 1991. Brood parasitism among waterfowl nesting
on islands and peninsulas in North Dakota. Condor 93:340–345.
Lopez-Sepulcre, A., and H. Kokko. 2002. The role of kin recognition
in the evolution of conspecific brood parasitism. Animal Behaviour
64:215–222.
Lyon, B. E. 1993a. Conspecific brood parasitism as a flexible female
reproductive tactic in American coots. Animal Behaviour 46:911–
928.
———. 1993b. Tactics of parasitic American coots host choice and
the pattern of egg dispersion among host nests. Behavioral Ecology
and Sociobiology 33:87–100.
———. 2003. Ecological and social constraints on conspecific brood
parasitism by nesting female American coots (Fulica americana).
Journal of Animal Ecology 72:47–60.
Lyon, B. E., and S. Everding. 1996. High frequency of conspecific
brood parasitism in a colonial waterbird, the eared grebe Podiceps
nigricollis. Journal of Avian Biology 27:238–244.
Maruyama, J., and H. Seno. 1999a. Mathematical modelling for intraspecific brood-parasitism: coexistence between parasite and nonparasite. Mathematical Biosciences 156:315–338.
———. 1999b. The optimal strategy for brood-parasitism: how many
eggs should be laid in the host’s nest? Mathematical Biosciences
161:43–63.
May, R. M., S. Nee, and C. Watts. 1991. Could intraspecific brood
parasitism cause population cycles? Proceedings of the International Ornithological Congress 20:1012–1022.
McRae, S. B. 1998. Relative reproductive success of female moorhens
using conditional strategies of brood parasitism and parental care.
Behavioral Ecology 9:93–100.
McRae, S. B., and T. Burke. 1996. Intraspecific brood parasitism in
the moorhen: parentage and parasite-host relationships determined by DNA fingerprinting. Behavioral Ecology and Sociobiology 38:115–129.
Nee, S., and R. M. May. 1993. Population-level consequences of
conspecific brood parasitism in birds and insects. Journal of Theoretical Biology 161:95–109.
Nielsen, C. R., B. Semel, P. W. Sherman, D. F. Westneat, and P. G.
Parker. 2006. Host-parasite relatedness in wood ducks: patterns of
kinship and parasite success. Behavioral Ecology 17:491–496.
Petrie, M., and A. P. Møller. 1991. Laying eggs in others’ nests: intraspecific brood parasitism in birds. Trends in Ecology & Evolution 6:315–320.
Pinxten, R., M. Eens, and R. F. Verheyen. 1991. Conspecific nest
parasitism in the European starling. Ardea 79:15–30.
Pöysä, H. 1999. Conspecific nest parasitism is associated with in-
562 The American Naturalist
equality in nest predation risk in the common goldeneye (Bucephala clangula). Behavioral Ecology 10:533–540.
———. 2003a. Low host recognition tendency revealed by experimentally induced parasitic egg laying in the common goldeneye
(Bucephala clangula). Canadian Journal of Zoology 81:1561–1565.
———. 2003b. Parasitic common goldeneye (Bucephala clangula)
females lay preferentially in safe neighbourhoods. Behavioral Ecology and Sociobiology 54:30–35.
———. 2004. Relatedness and the evolution of conspecific brood
parasitism: parameterizing a model with data for a precocial species. Animal Behaviour 67:673–679.
———. 2006. Public information and conspecific nest parasitism in
goldeneyes: targeting safe nests by parasites. Behavioral Ecology
17:459–465.
Pöysä, H., and M. Pesonen. 2007. Nest predation and the evolution
of conspecific brood parasitism: from risk spreading to risk assessment. American Naturalist 169:94–104.
Pöysä, H., V. Ruusila, M. Milonoff, and J. Virtanen. 2001. Ability to
assess nest predation risk in secondary hole-nesting birds: an experimental study. Oecologia (Berlin) 126:201–207.
Robert, M., and G. Sorci. 2001. The evolution of obligate interspecific
brood parasitism in birds. Behavioral Ecology 12:128–133.
Rubenstein, D. I. 1982. Risk, uncertainty and evolutionary strategies.
Pages 91–112 in King’s College Sociobiology Group, eds. Current
problems in sociobiology. Cambridge University Press, Cambridge.
Ruxton, G. D., and M. Broom. 2002. Intraspecific brood parasitism
can increase the number of eggs that an individual lays in its own
nest. Proceedings of the Royal Society B: Biological Sciences 269:
1989–1992.
Semel, B., and P. W. Sherman. 1986. Dynamics of nest parasitism in
wood ducks. Auk 103:813–816.
———. 1995. Alternative placement strategies for wood duck nest
boxes. Wildlife Society Bulletin 23:463–471.
———. 2001. Intraspecific parasitism and nest-site competition in
wood ducks. Animal Behaviour 61:787–803.
Semel, B., P. W. Sherman, and S. M. Byers. 1988. Effects of brood
parasitism and nest-box placement on wood duck breeding ecology. Condor 90:920–930.
Sorenson, M. D. 1993. Parasitic egg-laying in canvasbacks: frequency,
success, and individual behavior. Auk 110:57–69.
Summers, K., and W. Amos. 1997. Behavioral, ecological, and molecular genetic analyses of reproductive strategies in the Amazonian
dart-poison frog, Dendrobates ventrimaculatus. Behavioral Ecology
8:260–267.
Takasu, F. 2004. How many eggs should be laid in one’s own nest
and others’ in intra-specific brood parasitism? Population Ecology
46:221–229.
Tallamy, D. W. 2005. Egg dumping in insects. Annual Review of
Entomology 50:347–370.
Waldeck, P., and M. Andersson. 2006. Host-parasite relatedness in a
brood-parasitic colonial bird. Journal of Ornithology 147:269.
Waldeck, P., M. Kilpi, M. Ost, and M. Andersson. 2004. Brood parasitism in a population of common eider (Somateria mollissima).
Behaviour 141:725–739.
Waxman, D., and S. Gavrilets. 2005. 20 questions on adaptive dynamics. Journal of Evolutionary Biology 18:1139–1154.
Wisenden, B. D. 1999. Alloparental care in fishes. Reviews in Fish
Biology and Fisheries 9:45–70.
Yamauchi, A. 1993. Theory of intraspecific nest parasitism in birds.
Animal Behaviour 46:335–345.
———. 1995. Theory of evolution of nest parasitism in birds. American Naturalist 145:434–456.
Yom-Tov, Y. 1980. Intraspecific nest parasitism in birds. Biological
Reviews of the Cambridge Philosophical Society 55:93–108.
———. 2001. An updated list and some comments on the occurrence
of intraspecific nest parasitism in birds. Ibis 143:133–143.
Zink, A. G. 2000. The evolution of intraspecific brood parasitism in
birds and insects. American Naturalist 155:395–405.
Associate Editor: Marc Mangel
Editor: Michael C. Whitlock