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Summary. The effect is modeled of a positive relationship between clutch size and offspring fitness on the optimal investment in offspring. In species which meet ...
Evolutionary Ecology, 1989, 3, 150-156

The influence of a positive correlation between clutch size and offspring fitness on the optimal offspring size M A R K A. McGINLEY Department of Ecology and Behavioral Biology, University of Minnesota, Mineapolis, Minnesota 55455 U.S.A.

Summary The effect is modeled of a positive relationship between clutch size and offspring fitness on the optimal investment in offspring. In species which meet the assumptions of the model, the model predicts a positive correlation between maternal resource level and offspring size. If larger mothers are able to allocate more resources to offspring, then the model would also predict a positive correlation between maternal size and offspring size when the assumptions of the model are met. Thus, this model may help explain both among and within individual variation in offspring size. When offspring are produced in groups and the number of offspring killed per clutch is limited by predator satiation, offspring in larger clutches may experience a higher probability of survival. Such a life style may be found'in animals such as sea turtles. Offspring size is positively correlated with maternal size in some members of this group. Keywords: Optimal investment in offspring; optimal offspring size; offspring size variation.

Introduction The resolution of the life history trade-off between the size and number of offspring is important because it influences the two important components of parental fitness: offspring number and offspring fitness. In a seminal paper, Smith and Fretwell (1974) concluded that the optimal investment in offspring depends on the relationship between offspring size and offspring fitness and that the optimal offspring size should not vary if the size-fitness relationship remains unchanged. In a recent paper, Parker and Begon (1986) suggested that the size-fitness relationship of offspring produced by different mothers could vary because of the influence of clutch size on offspring fitness. They argued that if sibling competition was an important factor in determining offspring survival rates, then larger mothers, those with higher maternal resource levels, should produce larger eggs than smaller mothers. If this is true, then larger mothers may be selected to produce larger offspring when larger clutch sizes decrease the probability of survival. Here I present a model showing that differences in the size-fitness relationship of offspring produced by mothers with different maternal resource levels may also arise when offspring from larger clutches experience higher survival due, for example, to predator satiation. This model predicts that mothers with larger maternal resource levels should also produce larger offspring when larger clutches increase the probability of offspring survival. Because the conditions which increase the fitness of offspring in larger clutches may not be general, I will also discuss the types of organism in which this may select for variable investment in offspring.

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The model The model assumes a prereproductive life history with two stages. The offspring experience an initial stage where the probability of survival is dependent on clutch size, followed by a period where offspring fitness is determined by offspring size (independent of clutch size). The clutch size influences offspring fitness in two ways, first because it influences survival in the initial period of the life history and second because it influences offspring size. Such a life history could be observed in species which produce offspring in groups and experience a period of vulnerability to predators followed by dispersal into an environment where fitness is determined solely by offspring size. Sea turtles are a possible example of such a life history. If predators can kill only a limited number of young during the scramble of newly hatched turtles down to the sea, then the proportion of each clutch that survives predation increases with clutch size 1 will first assume that the probability of survival during the first stage of the life history depends only upon clutch size and then relax this assumption and allow the probability of survival during this period to depend upon both clutch size and egg or seed size (which may have either a positive or negative effect on the probability of survival during this stage). In both models I will assume that offspring fitness is an increasing convex function of egg or seed size (Smith and Fretwell, 1974) once the offspring have survived the initial period where the probability of survival is dependent on clutch size. No relationship between probability of surviving the initial period of predation and offspring size

Initially, I will assume that the number of young killed by predators during the initial period of predation (k) is independent of egg or seed size. Therefore, the number of young which survive predation (/V) is the number of young produced (Y) minus the number of young killed by predators (k). I will also assume that k is independent of the number bf young in a clutch. This could occur, for example, if the rate at which predators could capture the prey is limited and the prey are vulnerable for only a short period of time. The probability of any individual offspring surviving this initial period is N/Y, which is positively related to clutch size (Y) and negatively related to the number of young taken by predators (k). Parental fitness (Wp) is the product of the fitness of each offspring once they have survived the initial period of mortality and the number of young that survive this period. This can be written as follows: wp

=

[1 -

(m/x)a] [(I/x)

-

k]

where m is the minimum viable egg, x is egg size, a is a constant which controls the rate of approach of the offspring fitness curve to its asymptote, and I is the parental resource level. The egg size which maximizes parental fitness can be determined by setting d(Wp)/dx equal to zero. 0 = Ix a + akxm a - lma(a

+

1)

I have determined the optimal egg size (x) for various values of parental investment (/) and number of young killed by predators (k) (Fig. 1A). The model predicts that the optimal egg size should depend on both I and k. As maternal resource level increases, the optimal egg size increases until it reaches an asymptotic value (Fig. 1A). The rate at which egg size reaches the asymptote decreases as the number of young taken by predators (k) increases. Therefore, when the benefit of being in a large clutch is high (when k is large), mothers with low resource levels may be selected to produce larger clutches of smaller offspring because this results in a net gain in maternal fitness. The lower mortality rate associated

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2.o A k=5

1.5

I 1.o

m=l a=l

m

i

I

| o

B 2.0

I

I

o-o

| C 01 - ~ "

I 1.0 1

I

---.-.--------

a=l I 50

I 100

I 150

I 200

Maternal resource level Figure 1. (A) The predicted relationship between maternal resource level and the optimal egg size for two different values of the importance of predator satiation (k) when the probability of escaping early predation is independent of egg size (c = 0). (B) The predicted relationship between maternal resource level and the optimal egg size for different values of the effect of egg size on the number of young killed by predators (c). When c is positive, young from smaller eggs experience less predation and when c is negative young from larger eggs experience less predation. with larger clutches during the initial stage where the offspring experience predation outweighs the lower fitness smaller offspring achieve once they survive the initial predation.

Probability of surviving the initial period of predation is influenced by offspring size The number of young killed by predators may be influenced by offspring size. Predators may kill a smaller number of large young if larger offspring are able to escape predation more often (e.g. if larger turtles run to the ocean faster than smaller turtles). Therefore, the benefit gained by smaller mothers who produce smaller offspring could decrease because smaller offspring experience higher predation rates. Conversely, predators may kill fewer small offspring if small offspring are harder to catch than larger offspring. In this case, mothers who decrease egg size

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will gain the benefit of the production of larger clutches as well as producing young that experience lower predation levels. As before, maternal fitness is the product of the fitness of each offspring and the number of offspring that reach the ocean. The number of offspring reaching the ocean is the number of eggs produced (I/x) minus the number of young killed by predators, which is now a function of both the environment (k) and the size of the offspring (x). Maternal fitness can be written as follows: Wp = [1 - (m/x) a] [I/x

--

k

(1 + cx)]

where c is a constant which controls how strongly size influences the number of offspring killed by predators. When c is positive, large egg size increases the number of offspring killed by predators and when c is negative large egg size decreases the number of offspring killed by predators. I determined the egg size which maximizes maternal fitness by setting d(Wp)/dx = 0 and solving for the optimal egg size for various values of I, k, and c (Fig. 1B). Again, mothers with smaller resource levels are predicted to lay smaller eggs. Egg size reaches an asymptotic value as the maternal resource level increases. The rate at which the optimal egg size reaches its asymptote increases as the benefit of large body size for escaping predation (negative values of c) increases. The first model presented here represents the case where c = 0. Any advantage of young from large eggs in surviving predation decreases the range of maternal resource level over which females should be selected to decrease egg size (Figs 1A and B). When larger eggs experience higher predation rates (positive values of c) mothers with smaller resource pools should be selected to produce smaller eggs. Increasing the predation rate on large eggs increases the range of maternal resource levels where mothers should be selected to produce smaller offspring. The benefit of a large clutch in decreasing predation should depend on the synchrony of egg hatching. If many clutches hatch at the same time, then the offspring of all mothers can benefit from the large number of hatchlings attempting to cross the beach. In this case, smaller mothers decreasing egg size may not represent an evolutionarily stable strategy because it could be invaded by a mother who produced larger young and relied on the offspring of other mothers to protect her offspring from predation. Thus, these models would not predict a decrease in egg size with smaller body sizes in species which lay egg clusters at high density and whose eggs hatch synchronously. Positive correlations between maternal size and egg size would only be predicted to occur in species where clutches hatch asynchronously because the offspring of only a single female benefit from predator satiation. Discussion

When offspring from large clutches have a greater probability of survival, these models suggest that smaller mothers should be selected to produce smaller offspring. Similar patterns have been predicted when larger clutches experience lower survival (Parker and Begon, 1986), when larger mothers provide better parental care (Sargent et al., 1987), or when females accumulate resources prior to switching to reproductive mode where they face a decreased probability of survival (Begon and Parker, 1986). Because similar patterns can be caused by many different factors, it will be necessary to measure carefully the relationship between maternal size, clutch size, offspring size, and offspring fitness and to determine whether parental fitness is maximized in order to understand the cause of these patterns in any circumstance. What sorts of organisms might fit the assumptions of the model presented here? The model assumes that offspring mortality is influenced by clutch size during the initial period of the life cycle. Species which produce eggs or seeds in groups and provide little or no parental care may

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experience such a life history if predators capture a constant number of offspring regardless of clutch size before the offspring disperse. As examples of the types of organism to which these models might apply, I will now discuss two groups (sea turtles and frogs) which may match the assumptions of the models and show a positive correlation between either maternal size or maternal resource level and offspring size in some species. I will also discuss the alternative hypothesis that morphological or developmental constraints may cause the positive correlation between maternal size and offspring size.

Sea turtles Some sea turtles may show the life history assumed by these models. Eggs are laid in large clutches on the beach and then abandoned by the mother. The hatchlings experience high predation risk during their scramble across the beach to the ocean. Turtles from larger clutches may have a higher probability of reaching the ocean than turtles from small clutches: (i) because of predator satiation, and (ii) because social facilitation appears to increase the speed at which the turtles make their way down the beach thereby decreasing the period of time they are exposed to terrestrial predators (H. F. Hirth, unpublished data). Thus, if the probability that a clutch is discovered by egg predators is independent of clutch size, the probability of survival of offspring from larger clutches may be higher than the survival of offspring from smaller clutches. Larger females lay larger clutches of larger eggs than smaller females in the leatherback turtle (Dermochelys coriacea; Hirth and Ogren, 1987).

Frogs Many anurans lay their eggs in large clusters and tadpoles disperse after hatching. The probability of survival in egg clusters may increase with increasing clutch size. Egg mortality may be due to predation by leeches (Licht, 1969, 1974; Howard, 1978) and diving beetle larvae (Herried and Kinney, 1966), desiccation (Licht, 1974), and algal and fungal attack (Licht, 1974). For example, if the number of leeches attracted to an egg cluster is independent of clutch size, then eggs in larger clutches would experience a lower probability of predation. However, if more leeches were attracted to larger egg clusters then the possible benefit of large clutches could be negated. Clutch size may affect the probability of offspring survival for reasons other than predator satiation. For example, eggs in larger clutches may experience greater survival because larger clutches provide more favorable conditions for development. There is a lower chance of desiccation due to lower surface/volume ratios or a more stable thermal environment (Ryan, 1978). Therefore, it is possible that larger clutch sizes increase the probability of survival to the larval stage for some anurans for a variety of reasons. The predicted correlation between maternal size and egg size has been observed in some species of frogs (McAllister, 1962; Honig, 1966; Crump and Kaplan, 1979; Travis, 1983) although information about the effect of clutch size on offspring survival is not available in these studies. If these relationships are the result of a benefit of larger egg clusters in protection from predation, then the relationship between female size and egg size might be expected to differ between frogs and toads because toad eggs are inedible to most organisms and thus experience low predation rates (Licht, 1968).

Morphological and developmental constraints Alternatively, positive correlations between maternal size and offspring size may arise as the result of developmental or morphological constraints (Maynard Smith et al., 1985). Egg size may be limited by the size of the oviduct or cloaca so that these correlations may be simple scaling

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phenomena. The size of the pelvic girdle has been shown to limit the maximum egg size that can be produced in some freshwater turtles (Congdon et al., 1983; Congdon and Gibbons, 1987).

Conclusion In order for selection to favor variable investment in offspring, the relationship between offspring fitness and egg size must vary (Smith and Fretwell, 1974). The models presented here and in Parker and Begon (1986) have suggested that the size-fitness relationship may vary within or between individuals because of effects of clutch size on offspring fitness. Of the two groups that I have discussed here, sea turtles might be the group most likely to match the assumptions of the model because the time that their offspring are vulnerable to predators may be limited to the period that they travel to the ocean so they are more likely to satiate their predators. Offspring may be vulnerable to predispersal predation for a longer period of time in other groups and are thus less likely to satiate their predators. However, because it is possible that clutch size can influence fitness in positive ways other than predator satiation (e.g. decreasing desiccation), it may be useful to consider this hypothesis when investigating offspring size variation in other groups (including plants). Several hypotheses predict a positive relationship between maternal size and egg size (discussed above), and alternative hypotheses explaining seasonal changes in offspring size have also been developed (Begon and Parker, 1986; McGinley et al., 1987; McGinley and Charnov, 1988). Because many models of selectively favored variation and the constraint hypotheses make the same qualitative predictions, it is necessary: (i) to determine precisely the relationship between clutch size, offspring size, and offspring fitness, and (ii) to test whether parental fitness is maximized before we can determine the causes of offspring size variation.

Acknowledgments I thank Jon Seger for suggestions about the models, Harry Hirth for informative discussions about sea turtles, and Liz Queathem, Jess Zimmerman, Dave Temme, Jon Seger, Ric Charnov, Chris Smith, Peter Taylor, and two anonymous reviewers for helpful comments on earlier drafts of the manuscript. I have benefited from discussions with Joe Travis, Sharon Emerson, Dennis Bramble, Monica Geber, and members of the Ecology and Evolution Journal Club at the University of Utah.

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