Redhead reproductive strategy choices: a dynamic state variable model

Behavioral Ecology Vol. 10 No. 1: 30–40

Redhead reproductive strategy choices: a dynamic state variable model Tina Yerkes and Marten A. Koops Department of Zoology, University of Manitoba, Winnipeg, MB R3T 2N2, Canada 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. [Behav Ecol 10:30–40 (1999)]

T

he 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 parAddress correspondence to T. Yerkes, Department of Wildlife, Humboldt State University, Arcata, CA 95521-8299, USA. Received 21 August 1997; accepted 4 June 1998. q 1999 International Society for Behavioral Ecology

asitic 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

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Table 1 Description of the model parameters and values used in the basic model

a

Parameter

Values

Description

T t xt xc xm nt pt it21 en ep l Y ai bi ft e g

7 — — 800 g 1200 g — — — 10 10 0.8 10 g —a —a 0.25, 0.2, 0.15 1.0 0.5

The final time step (time horizon) The current time step for all t , T The current body condition (a state variable) Critical (minimum) body mass Maximum body mass Current number of nested eggs (a state variable) Current number of eggs laid parasitically (a state variable) Option chosen at t 2 1 (a state variable) Expected number of nested eggs Expected number of parasitically laid eggs Probability of finding food per t Benefit to body mass of finding food Cost to body mass of option i Offspring mortality associated with decision i Survival rate of parasitic eggs laid at t 5 1, 2, or 3 Overwinter survival Probability of finding a host nest

See Table 2 for specific values.

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). REDHEAD NATURAL HISTORY 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 Table 2 Parameter values specific to each reproductive strategy Strategy (i)

Energetic cost (ai)

Nested offspring mortality (bi)

S, sit out/abandon P, parasitize N, nest I1, incubate 1 I2, incubate 2 I3, incubate 3 R, rear F, finish the season

0 20 40 40 40 40 20 0

1 1 0.1 0.075 0.1 0.125 2.2–0.0018xt 0

Energetic costs are expressed as grams of body mass lost; xt is the female’s body condition at the start of rearing (R).

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). MODEL DESCRIPTION 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 5 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

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Table 3 Options available to a female in a given time step (t) as a function of the option chosen in the previous time step (it21)

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: xt911 5 xt 2 ai 1 Y.

it21 t

S

P

N

I1

I2

I3

R

F

1 2 3 4 5 6 7

S, P, N S, P, N S, P, N S S S S

— S S S — — —

— S, I1 S, I1 S, I1 — — —

— — S, I2 S, I2 S, I2 — —

— — — S, I3 S, I3 S, I3 —

— — — — S, R S, R S, R

— — — — — S, F S, F

— — — — — — S, F

All females start the season with i0 5 S. Options are: —, no options available; S, sit out or abandon; P, parasitize; N, nest; I1, incubate time one; I2, incubate time two; I3, incubate time three; R, rear; and F, finish the season.

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 (it21) 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. 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, it21 (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 (l), the benefit of finding food (Y ) expressed as body mass gained, and the cost of each decision (ai) 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 ai 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.

(1)

If no food is found, however, body mass at time t 1 1 will be: xt011 5 xt 2 ai.

(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 (bi). 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 5 .19, df 5 35, p 5 .007; Yerkes, 1998). The nested-eggs state variable is affected by choice, it, so the number of nested eggs at time t 1 1 will be: nt11 5

5

(1 2 bi )nt 1 en if it 5 nest (1 2 bi )nt

otherwise

(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 (g) and the survival rate of eggs laid in a host nest (ft). 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 1, the number of parasitic eggs will be: pt11 5

5

pt 1 gftep if it 5 parasitize pt

otherwise

(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

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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 it21 is defined by: Figure 1 The normal distribution of mass categories used in the forward iterations of the model (mean 5 1051g, SD 5 77.23). Total population size is 40,981 females.

F(xt , nt , pt , it21 , t, T) 5 lF(x9t11 , nt11 , pt11 , it , t 1 1, T) 1 (1 2 l)F(x0t11 , nt11 , pt11 , it , t 1 1, T)

(5)

where x9t11, xt011, nt11, and pt11 are defined by Equations 1, 2, 3, and 4, respectively. The female redhead chooses the option it to maximize F(xt, nt, pt, it21, 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 (e). Thus, the terminal fitness function (TFF) is defined as: F(xT , nT , pT , iT21 , T, T) 5

5

ues of en, ep, ai, bi, and ft 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 (e), the probability of finding food (l), and the probability of finding a host nest (g) on the reproductive strategy choices of redhead females. MODEL PREDICTIONS

if xT , xc

0 nT 1 pT 1 ea(1 2 e

20.0001(x T2x c) 2

)

if xT $ xc

(6)

where a (55) 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 5 1051 g, SD 5 77.23, n 5 25) to determine the proportion of strategies that may be observed on a population level. Because the val-

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 2 1 (it21 5 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 5 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 5 0). This allows us to present an optimal policy for the first three time steps as a function of body mass (xt) with nt 5 0, pt 5 0, and it21 5 S (Figure 2). For all t . 3, the optimal policy is too large to be presented in three dimensions. 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 (g 5 0.25), parasitism drops out of the optimal policy completely, mostly replaced by sitting out and some nesting at higher body masses (Figure

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Figure 3 The minimum number of nested eggs necessary to incubate in the time period immediately following nesting (t 5 2, 3, or 4) as a function of body mass with pt 5 0 and it21 5 N. For females with fewer nested eggs than shown by the surface, the optimal policy is to abandon the nest. If the number of nested eggs surpasses the minimum, the optimal policy is to incubate. The maximum number of nested eggs a female can have is 10. All parameter values as per Tables 1 and 2.

Figure 2 The optimal policy derived from backward iterations for the first three time periods for females which chose to sit out (it21 5 S) during the previous time period and nt 5 0, pt 5 0. (a) g 5 0.25; (b) g 5 0.50, the base model; and (c) g 5 0.75. All other parameter values as per Tables 1 and 2. White area 5 sit out (S), stippled area 5 parasitize (P), diagonal hatching 5 tie between sit out and parasitize (SP), gray area 5 nest (N), and vertical hatching 5 tie between sit out and nest (SN).

2a). When the probability of finding a host is high (g 5 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 (it21 5 N), the options available to her (Table 3) are to incubate the nested eggs (it21 5 I1) or to abandon the nest (it21 5 S). The optimal policy (Figure 3) as a function of nt, xt, and t for time periods 2, 3, and 4 when it21 5 N and pt 5 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). 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. 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). Food availability The general mass distribution described above is slightly influenced by the probability of finding food. As the probability

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Figure 5 The influence of the probability of surviving to the next breeding season (e) on strategy choices at the population level.

Figure 4 The range and 25th and 75th quartiles of body masses which chose each reproductive strategy during the forward iterations when the probability of overwinter survival is (a) e 5 0.0, (b) e 5 0.5, and (c) e 5 1.0, the base model. All other parameter values as per Tables 1 and 2. NB, no breed; P, parasitize once; PP, parasitize twice; N, nest; and PN, dual strategy.

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). 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 approx-

imately 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 (gf from Equation 4). When the probability of finding a host is low (g 5 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 (g 5 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 (g 5 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). 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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Figure 7 The influence of the probability of finding food (l) on strategy choices at the population level.

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 (it21 5 S), so few if any of the females in Figure 2b and c will nest at t 5 2. However, when host availability (g) 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. Figure 6 The range and 25th and 75th quartiles of body masses which chose each reproductive strategy during the forward iterations when the probability of finding food is (a) l 5 0.3, (b) l 5 0.5, and (c) l 5 0.8, the base model. All other parameter values as per Tables 1 and 2. NB, no breed; P, parasitize once; PP, parasitize twice; N, nest; and PN, dual strategy.

DISCUSSION 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 5 3). This is consistent with the biology

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 5 .46, p 5 .04, n 5 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. Overwinter survival Several studies on birds have demonstrated a relationship between reproductive effort and age, with reproductive effort

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Figure 9 The influence of the probability of finding a host (g) on strategy choices at the population level.

Figure 8 The range and 25th and 75th quartiles of body masses which chose each reproductive strategy during the forward iterations when the probability of finding a host is (a) g 5 0.25, (b) g 5 0.5, the base model, and (c) g 5 0.75. All other parameter values as per Tables 1 and 2. NB, no breed; P, parasitize once; PP, parasitize twice; N, nest; and PN, dual strategy.

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

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Table 4 Predicted proportions of redhead reproductive strategies given different levels of food availability and host availability

Host availability (g)

Food availability (l)

Low (0.25) Low (0.25) Intermediate (0.50) Intermediate (0.50) High (0.75) High (0.75)

Low (0.30) High (0.80) Low (0.30) High (0.80) Low (0.30) High (0.80)

NB

P

PP

N

PN

Parasitic clutches per redhead

0.45 0.30 0 0 0 0

0 0 0.57 0.39 0.01 0

0 0 0 0 0.65 0.50

0.55 0.70 0.07 0.04 0 0

0 0 0.37 0.57 0.34 0.5

0 0 0.94 0.96 1.65 1.50

Strategy

Nested clutches per redhead

Total clutches per redhead

0.55 0.70 0.44 0.61 0.34 0.50

0.55 0.70 1.38 1.57 1.99 2.00

NB, no breeding; P, single parasitism; PP, double parasitism; N, nest; PN, dual strategy.

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.

Figure 10 The relationship between initial body mass of captive female redheads and subsequent reproductive strategy choice (rs 5 .46, p 5 0.04, n 5 21). NB, no breed; P, parasitize once; PP, parasitize twice; N, nest; and PN, dual strategy. A semi-dual strategy category was created for females in captivity that laid three or fewer parasitic eggs and then nested. The occurrence of this activity in wild populations is unknown.

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 5 0.57 added to dual strategist 5 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 5 0.28 added to dual strategists 5 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

Yerkes and Koops • Redhead reproductive strategy choice

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Table 5 Redhead nesting and parasitic egg laying in canvasback nests Host availability

Food availability

Low Low High

Low High Low

High

High

Year

No. of parasitized eggs founda

No. of nested eggs foundb

Model predicts

1980 1979 1977 1978 1986 1988 1987

99 33 116 194 255 205 191

140 350 30 130 200 40 90

P P P P P P P

, , . . . . .

N N N N N N N

Data obtained from Sayler (1985) for 1977–1980 and from Sorenson (1990) for 1986–1988. Host availability was classified as low if the number of canvasback nests found in a given year was significantly lower than the number found across all 7 years (mean 5 33.4, SD 5 24.9). Food availability was classified based on wet (high) and dry (low) years. Model predictions are based on the results reported in Table 4. P, parasitized eggs; N, nested eggs. a The number of parasitized eggs found was calculated as the product of the number of canvasback nests found and the average number of redhead eggs per canvasback nest. b The number of nested eggs found was calculated as the number of redhead nests found multiplied by an assumed 10 eggs per nest.

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 5 .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. 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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