Behavioral Ecology Vol. 10 No. 1: 30-40
© 1999 International Society for Behavioral Ecology
Redhead reproductive strategy choices: a dynamic state variable model
Department of Zoology, University of Manitoba, Winnipeg, MB R3T 2N2, Canada
Address correspondence to T. Yerkes, Department of Wildlife, Humboldt State University, Arcata, CA 95521-8299, USA.
Received 21 August 1997; accepted 4 June 1998.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONREDHEAD NATURAL HISTORYMODEL DESCRIPTIONMODEL PREDICTIONSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Female redhead ducks (Aythya americana) exhibit one of the highest frequencies of facultative parasitic egg laying, extending reproductive choices within a season beyond nesting only. The occurrence of alternative strategies on a population level within and among years and the factors that influence choices are not well documented or understood. We developed a dynamic state variable model to predict reproductive strategy choice and the influence of female age, body mass, food availability, and host availability on strategy choice. The model predicts a general distribution of strategy choice by body mass and a strong influence of both age and host availability on strategy choice. As body mass increases, females choose more costly reproductive strategies from nonbreeding to parasitizing to nesting to a dual strategy, which is defined as a parasitically laid clutch of eggs followed by another clutch laid in the females' own nest. Comparatively, food availability only influenced strategy choice by slightly increasing the use of more costly strategies. Predictions of strategy choice by body mass reflect relationships similar to those proposed by others. Previous studies of the influence of food availability on observed parasitic frequencies produced mixed and often conflicting results. We propose that female redheads are assessing the host environment before making reproductive choices and food availability functions to fine tune this assessment by encouraging or discouraging more costly strategies at a lower body mass.
Key words: Aythya americana, brood parasitism, dynamic state variable model, redhead, reproductive strategy choices.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONREDHEAD NATURAL HISTORYMODEL DESCRIPTIONMODEL PREDICTIONSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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The life history of an organism is the result of differential allocation of limited resources between the often conflicting demands of reproduction and survival. In all animal populations studied thus far, individuals vary greatly in the lifetime number of offspring produced (Clutton-Brock, 1988)
. Some have the
option of choosing among alternative reproductive strategies that may result
in varying numbers of offspring produced. Reproductive strategies chosen are
assumed to have been selected to maximize fitness by maximizing lifetime
reproductive success. Variation in behavior may be contingent upon the
environment or upon phenotypic characters, with reproductive effort increasing
when environmental conditions are favorable (James
and Stugart, 1974; Morton et al.,
1972; Nolan and Thompson,
1975), increasing with age (Trivers,
1972, 1974), and increasing
with body mass or size assuming a physiological cost to reproduction
(Askenmo, 1982;
Chastel et al., 1995;
Erikstad et al., 1993;
Moss and Watson, 1984;
Winkler and Allen, 1995).
One of the most commonly studied forms of female alternative reproductive
strategies is brood parasitism or facultative parasitic egg-laying
(Rohwer and Freeman, 1989;
Yom-Tov, 1980). Among North American
waterfowl, redheads (Aythya americana) exhibit one of the highest
frequencies of facultative parasitic egg-laying in which eggs are laid in
conspecific as well as heterospecific nests (Dugger,
1996; Eadie et al.,
1988; Sayler,
1992; Sorenson, 1997).
Redheads may adopt this behavior as an additional strategy to increase
reproductive success; however, the occurrence of alternative strategies
on a population level within and among years and the possible factors that
influence reproductive choices are not well understood.
Sayler (1985) hypothesized that under
restricted environmental conditions, female redheads employed a bet-hedging
strategy and increased reproductive success by laying only parasitic eggs. He
attributed low nesting frequency and increased costs in drought years to lower
water levels, which may have caused reduced food abundance. Increased
parasitism in drought years represented lower reproductive effort by avoiding
reproductive costs of incubation and brood rearing. Thus, under restricted
environmental conditions, some females may lack sufficient endogenous reserves
and foraging time to both lay and incubate. Sayler
(1985) concluded that redhead females
were employing a bet-hedging strategy by increasing production of parasitic
eggs under environmental conditions less favorable to reproductive
success.
Sorenson (1990) attributed within-year
variation among redhead females to a conditional strategy where reproductive
choices were influenced by female age and physical condition. Age appeared to
affect individual choices with adults most often employing a dual strategy,
which is defined as a "strategy which entails the separate and
sequential utilization of two different reproductive strategies in which
females first lay a parasitic clutch and then lay their own clutch"
(Sorenson, 1990: 82). Yearlings, in
contrast, either parasitized or nested only. Alternatively, yearling females
may be less proficient at acquiring resources, resulting in higher costs of
reproduction, lower probability of success, or greater likelihood of
constraints (constraint hypothesis; Rohwer,
1992). Or, yearling females may invest less in reproduction
because they have higher future reproductive value
(Pianka and Parker, 1975). In waterfowl,
young females lay fewer eggs, nest later in the season, and experience
increased rates of nonbreeding as well as decreased rates of renesting
(Afton, 1984;
Krapu and Doty, 1979) compared to older
females.
Variation in reproductive strategy choice among individual female redheads
has been documented both within and among years. Previous research
(Sayler, 1985;
Sorenson, 1990;
Weller, 1959) alludes to the importance
of environmental conditions within and among years and the influence of
individual female age and body condition on variation in reproductive strategy
choice. Long-term studies, however, have not been conducted to determine the
influence of these different factors on variation in strategy choice. Further,
the variation of observed strategies within a year, on a population level, is
not well documented because obtaining this information in the wild is
difficult. To predict strategy choice on a population level and the influence
of female age, female body mass, and environmental variability on strategy
choice, we developed a dynamic state variable model
(Mangel and Clark, 1988).
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REDHEAD NATURAL HISTORY |
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TOPABSTRACTINTRODUCTIONREDHEAD NATURAL HISTORYMODEL DESCRIPTIONMODEL PREDICTIONSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Redheads spend winters in southern locales, primarily along the Gulf coast of the United States and the Chesapeake Bay, and breed on northern prairies of the United States and Canada and on mountain marshes of the west (Bellrose, 1980)
. Redheads arrive at
northern latitudes in mid- to late April along with canvasbacks (Aythya
valisineria), the primary recipient of redhead parasitic eggs.
Canvasbacks begin nesting in late April and early May, while redheads begin in
mid- to late May and continue into late June. Individual female redheads are
faced with four possible reproductive strategy choices: forego breeding
in that year, lay only parasitic eggs, lay eggs in their own nest and invest
to raise those young to fledging, or employ a dual strategy. Most other duck
species either lay their own nest of eggs or do not breed. Redhead parasitic
egg-laying peaks during canvasback nesting and early redhead nesting
(Erickson, 1948;
Giroux, 1981;
Johnson, 1978;
Low, 1945;
Sayler, 1985;
Wingfield, 1951). Recorded parasitic
frequencies vary from as low as 27% (Sayler,
1985) to as high as 98% (Bouffard,
1983), and an average parasitic clutch laid by a single female
contains 10 eggs (Lokemoen, 1966;
Weller, 1959;
Wingfield, 1951). Parasitic egg-laying
after nesting is rare and has only been documented once when a female's nest
of six eggs was destroyed and she subsequently laid the seventh egg in the
nest of another female (Sorenson,
1990).
Nesting females typically lay a clutch of 7-10 eggs, which hatch after 24
days of female-only incubation. Nest success, defined as at least one egg
hatching in a clutch (Klett et al.,
1986), varies greatly and has been documented from a low of
16% to a high of 80% (Sayler,
1985; Sorenson, 1990).
Predators such as skunks (Mephitis mephitis) and raccoons
(Procyon lotor) destroy many nests. Having a nest destroyed and
subsequently nesting again by the same redhead female has not been documented,
though this strategy, known as renesting, is common in most prairie-nesting
ducks.
Employing a dual strategy requires laying a parasitic clutch of eggs
followed by a nested clutch of eggs. Sorenson
(1990) determined that females generally
laid a 10-egg parasitic clutch followed by approximately 10 days of inactivity
before laying their own clutch of eggs.
After eggs hatch, females leave the nest with their brood. Ducklings are
fairly independent, but females lead and protect the brood for as long as 60
days. Posthatch care is most critical during the first 1-2 weeks, when
mortality is highest (Ball et al.,
1975; Mauser et al.,
1994; Savard et al.,
1991).
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MODEL DESCRIPTION |
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TOPABSTRACTINTRODUCTIONREDHEAD NATURAL HISTORYMODEL DESCRIPTIONMODEL PREDICTIONSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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To model the reproductive strategy decisions of female redheads, a dynamic state variable model was constructed (see Tables 1 and 2 for a list of the model parameters and values). Environmental variability was divided into the probability of finding food and the probability of finding a host. Age of the female was included as the probability of surviving to the next breeding season; body mass ranges were obtained from a wild population of female redheads. This model runs over one breeding season split into seven time steps (T = 7), representing approximately 10 days each. The behavioral decisions available to a female include (1) sit out or abandon (S), (2) parasitize (P), (3) nest (N), (4) incubate time one (I1), (5) incubate time two (I2), (6) incubate time three (I3), (7) rear (R), and (8) finish the season (F). Finishing the season represents a time when brood rearing is complete and the female can molt and forage in preparation for the fall migration. All these options are not available to a female in every time period. In each time period, the options available to a female (Table 3) depend on both the option chosen in the previous time period (it-1) and the value of the current time period (t). This constrains females to choosing reproductive strategies during the first three time periods and forces any female that chooses to nest to follow the pattern of incubating eggs for three time periods, then rearing ducklings for one time period, or she loses all nested offspring. A female always has the option to abandon a nest.
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Parasitic eggs only require the energetic investment associated with
formation of the eggs. If a female decides to parasitize early in the season
(the first time period), there is the possibility for a second parasitic
clutch to be laid or for the female to subsequently nest. The female must take
one time period off, however, between her initial decision to parasitize and
her subsequent decision to parasitize or nest. This time period represents the
hypothetical time required to regain an appropriate amount of nutrient
reserves to lay another clutch of eggs (Sorenson,
1990).
Decisions made in each time period are based on three state variables: body mass of the female (xt), the number of nested eggs (nt), and the number of eggs laid parasitically (pt). Body mass and the number of nested eggs are influenced by the decisions made by the female at each time step and by the current environmental conditions. The number of parasitic eggs is determined when the female chooses brood parasitism and is unaffected by any of her future decisions. The options available to a female are constrained by her previous decision, the fourth state variable, it-1 (Table 3). Fitness is calculated at the end of the season based on the final values of the first three state variables: xT, nT, and pT.
Body mass is affected by the probability of finding food (
), the
benefit of finding food (Y) expressed as body mass gained, and the
cost of each decision (
i) expressed as body mass
lost. Costs (Table 2), in terms of body
mass lost, for parasitizing, nesting, and incubating were determined from a
captive study of breeding redheads (Yerkes,
1998). Although captive females do not face the same pressures of
wild hens (i.e., finding and obtaining food and avoiding depredation), mass
loss patterns over the reproductive season are similar between wild and
captive females (Yerkes, 1998). The value
of Y was chosen so that Y and i
together roughly conform to the data obtained in captivity. The cost of
rearing a brood is arbitrary, but is assumed to be small. There are no body
mass costs associated with sitting out, abandoning, or finishing the
season.
During each time step, body mass changes depend on the female's behavioral
choice. If the individual chooses option i and finds food, body mass
in the next time step will be:
 | (1) |
If no food is found, however, body mass at time t + 1 will
be:
 | (2) |
To be consistent with wild populations, body mass ranges are bound by an upper maximum, xm, and a minimum critical level, xc. Body mass increases in discrete steps of 10 g. At any time, if female body mass falls below the minimum level, xc, the female dies and all nested eggs are lost.
The number of nested eggs is affected by the rate of offspring mortality
(ßi). Offspring mortality
(Table 2) was subdivided into the nesting
phase (one time period), the incubation phase (three time periods), and the
brood-rearing phase (one time period). Most waterfowl studies do not
differentiate between mortality experienced during nesting and incubation, but
lump the two events into a single measure of nest success. Generally, survival
probability of nested eggs during incubation decreases over time by virtue of
the accumulation of exposure days (Mayfield,
1961). In our model, we emulate this decrease by decreasing
survival among incubation phases 1, 2, and 3. For redheads, average nest
success is approximately 60% (Joyner,
1983; Sayler,
1985; Sorenson,
1990; Weller,
1959; Yerkes, 1998).
Although we chose an average mortality value (0.34) for all runs of the model,
we tested extreme values of 0.8, 0.6, and 0.0 and found that a wide range of
mortality rates resulted in practically no difference in reproductive strategy
choice predictions. Only at extremely low values of offspring mortality (0),
values that are not biologically realistic, were predictions drastically
altered.
Brood mortality during rearing is based on the body mass of the female at
the time of hatch and was derived from a study on wild brood-rearing females.
A significant relationship was found between female body mass at hatch and the
number of ducklings that survived to 30 days posthatch (R2
=.19, df = 35, p =.007; Yerkes,
1998).
The nested-eggs state variable is affected by choice,
it, so the number of nested eggs at time t + 1
will be:
 | (3) |
where en is defined as the number of eggs laid by a female in her own nest, which is compared to parasitic eggs laid in conspecific or heterospecific nests.
The number of parasitic eggs is affected by the probability of finding a
host nest in which to lay a parasitic egg (
) and the survival rate of
eggs laid in a host nest (
t). The survival
probability of parasitic eggs varies in the wild, averaging 0.20, but
generally decreases with time (Sayler,
1985; Sorenson, 1990).
Therefore, in our model we used the average survival of parasitic eggs (0.20),
but reflected decreasing survival with time so that parasitic eggs laid
earlier experienced higher survival (0.25) compared to parasitic eggs laid
later (0.15). Offspring mortality in heterospecific nests is not explicitly
included in the model. Instead, mortality of parasitic eggs is assumed to be
equal for conspecific and heterospecific nests
(Sorenson, 1990). At time t + 1,
the number of parasitic eggs will be:
 | (4) |
where ep is the number of eggs laid by a female in a host nest.
The form of offspring mortality depends on the manner in which the eggs are laid. Nested eggs suffer mortality in every time step, so the optimal policy is derived based on the expectation of some egg loss from the nest (Equation 3). The mortality rate of nested eggs depends on both their developmental stage and the behavioral decision of the female redhead (Table 2). Parasitic eggs, however, experience a single survival probability (Equation 4) that includes mortality due to host rejection of parasitic eggs, mortality due to laying asynchronously with the host, and host nest depredation. We assume that once a female redhead has laid a parasitic egg, she has no further interaction with that offspring, so the survival rate of parasitic eggs is applied at the time of laying, and any influence the parasitic-egg state variable may have on future decisions will be through the expected number of offspring obtained from brood parasitism.
A female redhead's expected fitness from time t to the horizon,
T, given xt energy reserves,
nt nested eggs, pt parasitically laid
eggs, and previous choice it-1 is defined
by:
 | (5) |
where x't+1,
x''t+1, nt+1,
and pt+1 are defined by Equations 1, 2, 3, and 4,
respectively. The female redhead chooses the option
it to maximize F(xt,
nt, pt,
it-1, t, T). At the horizon, T,
individual fitness is based on the number of surviving nested and parasitic
offspring, as well as a future reproductive component defined as a function of
body mass at the end of the breeding season and overwinter survival (
).
Thus, the terminal fitness function (TFF) is defined as:
 | (6) |
where a (=5) is a scalar constant used to produce a TFF with a
logistic form that ranges from 0 to 5. Body mass at the end of the breeding
season has been positively correlated with reproductive success in the
following season (Dubovsky and Kaminski,
1994; Jeske et al.,
1994; Lessels,
1986; Porter et al.,
1993).
The optimal policy was derived through backward iteration, producing
optimal decisions for all possible values of each state variable in each time
period. A new optimal policy was derived for each run of the model. Monte
Carlo simulations were run to generate population-level predictions about the
reproductive behavior of redheads through forward iteration of the model
(Mangel and Clark, 1988). During the
forward iterations, all events occurred with the probability used to derive
the optimal policy, with the only difference occurring in the form of nest
depredation. In the backward iterations, nests experienced partial
depredation; however, in the forward iterations, nests only experienced
complete depredation, though partial depredation of duck nests can occur in
the wild (Hall, 1987). Complete nest
depredation was used in the forward iterations because it is more reasonable
to assume that a nest predator will completely exploit a nest than to take one
egg and never return. Partial depredation was used in the backward iterations
to achieve a complete decision matrix, including nest abandonment. In cases
where multiple options were optimal, the modeled females chose randomly from
the options with the highest expected fitness. Forward iterations were run
with a population of 40,981 female redheads normally distributed across all
mass categories (Figure 1; based on
data obtained from a wild population: mean = 1051 g, SD = 77.23,
n = 25) to determine the proportion of strategies that may be
observed on a population level. Because the values of en,
ep, i,
ßi, and t were obtained from
experimental work on redheads, we do not present any sensitivity analyses on
these parameter values. Instead, we present the results from forward
iterations and the influence of changes in the probability of overwinter
survival (), the probability of finding food (), and the
probability of finding a host nest () on the reproductive strategy
choices of redhead females.
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MODEL PREDICTIONS |
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TOPABSTRACTINTRODUCTIONREDHEAD NATURAL HISTORYMODEL DESCRIPTIONMODEL PREDICTIONSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Optimal policy
Reproductive strategy choices are limited to the first three time periods, and a female can only choose to parasitize or nest during the current time period if she sat out during the previous time period (Table 3). Thus, to look at the optimal policy related to reproductive strategy choices, we limited the policy to when a female sat out at t - 1 (it-1 = S). The number of parasitic eggs a female has is not influenced by and has no influence on the current decision, therefore, we limited the policy to when a female has no parasitic eggs (pt = 0) because the optimal policy is the same regardless of the number of parasitic eggs. Furthermore, if a female sat out during the previous time step, she will have no nested eggs (nt = 0). This allows us to present an optimal policy for the first three time steps as a function of body mass (xt) with nt = 0, pt = 0, and it-1 = S (Figure 2). For all t > 3, the optimal policy is too large to be presented in three dimensions.
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The optimal policy for the base model (Figure
2b; parameter values as in Tables
1 and 2) involves mostly
parasitizing during the first time period. During the second time period, any
females that did not parasitize during the first time period should parasitize
if the female is small, then the optimal decision oscillates between sitting
out and nesting as body mass increases. During the third time period, all
large females should nest, and all small females should sit out. This pattern
is largely insensitive to manipulation of overwinter survival, with thresholds
for nesting shifting to lower body masses as overwinter survival decreases
(not shown). There is little influence of the probability of finding food on
either the pattern or threshold values (not shown). The probability of finding
a host has the strongest influence on the optimal policy
(Figure 2), almost entirely on the choice
to parasitize. When the probability of finding a host is low ( = 0.25),
parasitism drops out of the optimal policy completely, mostly replaced by
sitting out and some nesting at higher body masses
(Figure 2a). When the probability of
finding a host is high ( = 0.75), the occurrence of parasitism in the
optimal policy is increased through the replacement of sitting out with
parasitism in the third time period and increased incidence of parasitism in
the first time period (Figure 2c). Nesting
in the optimal policy is relatively unaffected by the probability of finding a
host.
If a female redhead chose to nest in the previous time period (it-1 = N), the options available to her (Table 3) are to incubate the nested eggs (it-1 = 11) or to abandon the nest (it-1 = S). The optimal policy (Figure 3) as a function of nt, xt, and t for time periods 2, 3, and 4 when it-1 = N and pt = 0 (again, the optimal policy is unaffected by the number of parasitic eggs) is relatively insensitive to changes in overwinter survival, the probability of finding food, and the probability of finding a host. At low body masses for all three time periods, the optimal policy is to abandon the nest regardless of the number of nested eggs (Figure 3), which is consistent with the lack of nesting in the optimal policy for these body masses (Figure 2). During time periods three and four, the minimum number of nested eggs for a female to incubate decreases as body mass increases, but levels out at four eggs. The threshold body mass at which the minimum number of nested eggs drops from 10 is slightly influenced by other parameters, but a minimum of four eggs is insensitive to most of our parameter manipulations. The only condition under which the minimum number of eggs drops below four is when the probability of overwinter survival is zero, and then it is never optimal to abandon a nest. A minimum of four eggs is consistent with observations that female redheads do not start incubating a nest with fewer than four eggs (Yerkes T, personal observation).
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Body mass
The model predicts a general distribution of strategy choice by initial
body mass (see Figures 4, 6, and
8). Females in lower mass categories are restricted to no breeding
and parasitizing either once or twice depending on specific situations
reported below. Females in higher mass categories choose more costly
strategies, nesting and dual strategy, while incurring a higher payoff. In
most situations, threshold levels of current body mass at which switches occur
from low- to high-cost strategies exist between approximately 900 g and 1100
g.
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Overwinter survival
The probability of survival to the next breeding season has a strong effect
on strategy choice by initial body mass and on a population level. As the
probability of survival decreases, females at the lower end of the current
mass threshold choose more costly strategies at lower mass categories
(Figure 4). Threshold mass levels decrease
as overwinter survival decreases; thus, the proportion of dual
strategists observed in a population increases among the females at lower mass
categories. Choosing more costly strategies, in this situation, results in
more deaths due to the gamble of investing heavily. As overwinter survival
decreases, the proportion of costly strategies observed on a population level
increases (Figure 5).
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Food availability
The general mass distribution described above is slightly influenced by the
probability of finding food. As the probability of finding food increases, the
current mass threshold decreases slightly, and females choose more costly
strategies at a lower body mass (Figure
6). On a population level, dual strategists increase as food
availability increases, whereas single parasitism decreases slightly as food
availability increases (Figure 7).
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Host availability
The probability of finding a host nest has a strong effect on the
reproductive strategies chosen within a population, whereas the current mass
threshold levels are only slightly altered among host levels. The threshold
mass levels at which strategies change are similar between levels of host
availability (low to high), resulting in major strategy switches between
approximately 1000 and 1100 g (Figure 8).
Host availability exerts a strong influence on strategy choice and
distribution at the population level (Figure
9) through the probability of a fitness gain from a parasitic egg
( from Equation 4). When the probability of finding a host is low
( = 0.25), the average probability of a fitness gain from a parasitic
egg is only 0.05, and pure nesting and nonbreeding are the only viable
alternatives. At intermediate host availability levels ( = 0.5), the
average probability of a fitness gain from a parasitic egg is 0.10, and single
parasitic events and dual strategists are common, whereas pure nesting
accounts for a very small proportion of the population. At high levels of host
availability ( = 0.75), the average probability of a fitness gain from
a parasitic egg is 0.15, and double parasites and dual strategists account for
the majority of the population. Again, pure nesting is relatively
insignificant. In all cases, the current mass threshold at which females
switch from lower to higher cost strategies is similar (1000-1100 g).
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Environmental variability: food and host availability
Although female redheads make choices based both on food and host
availability, the model predicts that food availability has little influence
on strategy choice compared to host availability, which has a strong
influence. Together, as environmental variability, this trend continues, but
each parameter has a distinct effect (Table
4). By increasing host availability, we find that the predicted
proportion of redhead females in a population investing in parasitic behavior
increases, and the proportion exhibiting nesting behavior decreases. However,
these dynamics do not offset one another, with a greater increase in
reproductive effort in parasitic strategies, resulting in an overall increase
in reproductive effort as host availability increases. Food availability still
has a weaker influence than host availability. Instead, food availability
seems to impact the decision to nest, with more females investing in nesting
as food availability increases.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONREDHEAD NATURAL HISTORYMODEL DESCRIPTIONMODEL PREDICTIONSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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When environmental conditions vary among years, we expect an animal to adjust reproductive behavior each breeding season to maximize within-season and lifetime reproductive success. Our model predicts that variation of within-season reproductive strategy choice is influenced by environmental variability, female age, and both initial and current body mass.
Optimal policy
The current model has a coarse grain of analysis about the timing of
nesting during the early breeding season because it uses 10-day time periods.
From the optimal policy (Figure 2), this
model predicts that nesting should rarely occur immediately upon arrival on
the breeding grounds, and most nesting should start later (t = 3).
This is consistent with the biology of redheads, which arrive on the breeding
grounds slightly after canvasbacks, but delay nesting for a few weeks.
Interestingly, this is only slightly influenced by the ability to brood
parasitize (Figure 2a), suggesting that
under conditions of low host availability, the mean timing of nesting should
only be slightly earlier for larger females. Note that
Figure 2 shows the optimal policy for
females that sat out the previous time step (it-1
= S), so few if any of the females in Figure 2b and
c will nest at t = 2. However, when host availability
() is low, females with the specified body masses could nest in either
the first or second time periods, resulting in earlier mean nesting times for
the population. Due to computer memory limitations, however, we do not know if
this prediction would hold true under a finer-grain analysis with 1-day time
periods.
Body mass
Female body mass had a significant influence on reproductive strategy
choice. This relationship agrees with the conditional strategy proposed by
Sorenson (1990). Evidence provided from
his work demonstrated that nesters were heavier than females that did not
nest. He further suggested the existence of a threshold level of phenotype and
environmental condition where females switched from one strategy to another.
This is also predicted by the model, and, with the parameter values we used,
this threshold occurs between 900 g and 1060 g. The relationship between mass
and strategy choice is further supported by a captive study of female redheads
(Yerkes, 1998), where mass at the
beginning of the reproductive cycle was significantly correlated with
reproductive strategy choice (rs =.46, p =.04,
n = 21; Figure 10).
Threshold mass levels found in captivity, however, cannot be compared directly
to those of wild females given differential constraints faced by wild females.
Wild females face food limitations, depredation pressure, higher mortality
rates, and often competition both among and within species.
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Overwinter survival
Several studies on birds have demonstrated a relationship between
reproductive effort and age, with reproductive effort generally increasing
with age (Bryant, 1988;
Newton, 1988;
Scott, 1988). This relationship has also
been shown for several duck species (Afton,
1984; Cowardin et al.,
1985; Heusmann,
1975; Krapu and Doty,
1979; Ratcliffe et al.,
1988). In our model, age was not explicitly included;
rather, we used the probability of survival to obtain future reproduction.
This could represent age, assuming that overwinter survival decreases as age
increases, suggesting that female redheads are increasing reproductive effort
with age. Sorenson (1990) and Sayler
(1985) both suggested that older females
tend to exhibit nesting and dual strategies, whereas young females were
restricted to parasitic events. Our model does not support the qualitative
difference in strategy choice by age predicted by Sorenson
(1990). Instead, our model predicts that
females of all ages choose a variety of strategies. Older females are not
restricted to nesting or dual strategies, nor are younger females limited to
parasitism, but instead survival probabilities exert an influence on the mass
category at which a female switches from low- to high-cost strategies. At low
survival probabilities, females at lower mass categories invest more heavily
in the current season by choosing more costly strategies.
Our model does not directly address the cost of reproduction on future
survival or fecundity. We attempted to control for this through the use of a
future reproduction component in the calculation of fitness. Each female
receives a value of future expected eggs based on her body mass at the end of
the current season, with lower masses resulting in fewer eggs in the future.
Cost of reproduction is controversial. Several studies have correlated various
aspects of reproductive performance in the current season with future survival
and fecundity (Dijkstra et al.,
1990; Nur, 1984,
1988;
Reid, 1987).
Host availability
Parasitism is a strategy uncommon among birds, yet prevalent among
waterfowl species. Several ecological factors and lifehistory correlates have
been proposed to account for the high frequency of parasitism among waterfowl.
Life-history correlates associated with an increased incidence of parasitism
in waterfowl include precocial young, large clutch sizes and thus longer
laying periods, longer incubation periods, lack of territorial defense
behaviors, lack of defense weaponry, and large body size
(Eadie, 1991;
Rohwer and Freeman, 1989;
Sayler, 1985;
Sorenson, 1990). Furthermore, within
waterfowl species, those with strong philopatric tendencies exhibit higher
parasitic frequencies. Ecological factors associated with parasitic events
among waterfowl species include nest location, nest density, and nest
chronology (Beauchamp, 1997;
Sayler, 1992). Nests that are easily
located (cavity and emergent nests) or densely spaced (islands and colonies)
experience higher rates of parasitism. Host nest chronologies that are similar
to parasitic species receive more parasitic eggs. These factors, however, do
not satisfactorily explain the difference in parasitic frequencies between two
ecologically similar species, such as the redhead and the canvasback.
Beauchamp (1998) focused his
comparative analysis on the incidence of interspecific parasitism in lineages
that expressed intraspecific parasitism and found no effect of ecological or
life-history correlates on the transition of intra- to interspecific
parasitism when the influence of intraspecific parasitism was accounted for.
This analysis suggested the expression of interspecific parasitism is not
related to nest dispersion, nest substrate, type of brood care, or level of
reproductive effort. Hence, the opportunity to lay parasitic eggs in
heterospecific nests was not facilitated or inhibited by variation found
across large ecological or life history factors. Beauchamp
(1998) suggested three potential factors
that may prevent the expression of interspecific parasitism: (1) the
sparsity of heterospecific hosts, (2) aggressive behavior by the host, and (3)
lack of suitable hosts due to different breeding chronology or food and
habitat requirements. As our model suggests, the expression of interspecific
parasitism by redheads, and its lack in canvasbacks, may be highly influenced
by the overall availability of host species.
Environmental variability: food and host availability
The probability of finding food had a smaller influence on strategy choice
than expected. Previous field studies of reproductive strategies observed in
the wild under varying environmental conditions have provided mixed results.
Most studies of environmental variability examined water fluctuations during
the nesting season and assumed low water levels were correlated with low food
availability. Weller (1959) stated that
the parasitic behavior of redheads was inherent and not subject to
modification by the physical environment. In contrast, Low
(1945) and Erickson
(1948) attributed parasitic laying to
fluctuating water levels. Giroux (1981)
attributed low parasitism in a dry year to low population levels of redheads.
Olson (1964), Michot
(1976), Joyner
(1983), and Sorenson
(1990) found no association between water
levels and frequency of parasitism. They proposed that (1) parasitism was a
low-cost alternative to nesting under poor environmental conditions, a
best-of-a-bad job strategy, and (2) parasitism functioned to increase
fecundity when environmental conditions were good. None of these studies,
however, examined the occurrence of pure nesting and dual strategy.
Sayler (1985) found great differences
in parasitic frequencies between "good" and "bad"
years. During drought or "bad" years, parasitic frequency was
51-61%, as opposed to wet or "good" years, when parasitism
was only 27%. Although our predicted proportions of different strategies
on a population level cannot compare directly to parasitic frequency, the
overall proportion of individuals laying parasitic eggs should reflect the
number of parasitic eggs found in other species' nests, which is defined as
parasitic frequency. Our model predictions support Sayler's
(1985) trends of lower parasitic
frequency in good years. At extremes, when the probability of finding food is
low (0.3), the total proportion of individuals laying parasitic eggs is 0.94
(parasites = 0.57 added to dual strategist = 0.37). When compared to a
situation where the probability of finding food is high (1.0), 0.79 of the
population is laying parasitic eggs (parasites = 0.28 added to dual
strategists = 0.51). This suggests that food availability does have some
influence on strategy choice, but it does not produce as large a disparity in
the proportions of different strategies observed on a population level as one
might expect.
Our model predicts that redhead females vary reproductive effort by availability of food resources and that parasitism is a viable reproductive strategy option in all situations except when host availability is very low. Based on the model's predictions, we propose an alternative explanation for the previously conflicting results and nonconsistent relationships observed between parasitic frequency and fluctuating water levels. We propose that female redheads assess the host environment before making choices regarding strategy choice. Host availability, and not food variability per se, is driving the occurrence of parasitism and other strategies on a population level. This is particularly true with a pure nesting strategy, which is relatively unpopular except when the probability of fitness gains from parasitic eggs are very low (0.05) or the probability of finding food is very high (1.0). From Table 4 we see that when host availability is low, the model predicts no parasitism, regardless of the availability of food. When host availability is at intermediate or high levels, a high frequency of parasitism should be observed; however, the specific reproductive strategy chosen will depend on food availability. Under low food availability, high parasitism occurs through cheaper strategies, either single or double parasitism. When food availability increases, an increase in the occurrence of the dual strategy is predicted, resulting in little change in the level of parasitism.
Data from Sayler (1985) and Sorenson
(1990) support our model's predictions
from Table 4, upon which the above
proposal is based. We grouped 7 years of data into categories of low and high
host availability and low and high food availability
(Table 5). For each year, the numbers of
parasitized and nested eggs are presented, along with the model's predictions.
We predicted that investment in parasitism would be low, compared to nesting,
when host availability is low, resulting in fewer parasitic than nested eggs.
This trend would be reversed when host availability is high. Our prediction
was supported in all 7 years (binomial test, p =.0078). Because the
total number of females on the study areas was not known, it was not possible
to test the following predictions: (1) parasitic clutches per female
redhead should increase and nested clutches per female should decrease as host
availability increased, (2) nested clutches per female should increase as food
availability increased, and (3) total reproductive effort per female should
increase as host availability increased. These predictions require data that
are currently uncollected.
|
Conclusions
We propose, based on model predictions, that female redheads arriving on
the breeding ground assess three factors before making reproductive strategy
choices. First, they use their own body mass and age to decide how much
effort, if any, to invest in reproduction. This investment is a trade-off
between the number of young produced within a season and the potential for
survival and future reproduction. Once a female has chosen to reproduce, she
must then decide among parasitism, nesting, or both. Her assessment of the
host environment will determine which tactic to take. The inclusion of brood
parasitism depends on the availability of hosts, with more parasitism
occurring at higher levels of host availability. The availability of food will
determine whether females choose to nest. As more food is available, more
females will choose to invest in nesting, either alone under low host
conditions, or as the dual strategy.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONREDHEAD NATURAL HISTORYMODEL DESCRIPTIONMODEL PREDICTIONSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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We thank Glen McMaster, Darren Gillis, and Mark Abrahams for discussion and comments on the manuscript and two anonymous referees for their suggestions for improving this paper. Field research conducted by T.Y. was supported by the Delta Waterfowl Foundation, and captive studies were supported by the Conservation Research Center of the Smithsonian Institute. M.A.K. was supported by a Natural Sciences and Engineering Research Council (NSERC) Postgraduate Study B, a University of Manitoba Graduate Fellowship, and an NSERC Research Grant to Mark Abrahams.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONREDHEAD NATURAL HISTORYMODEL DESCRIPTIONMODEL PREDICTIONSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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