Integrative and Comparative Biology Advance Access originally published online on March 29, 2006
Integrative and Comparative Biology 2006 46(3):224-232; doi:10.1093/icb/icj026
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Estimation and interpretation of egg provisioning in marine invertebrates
* Department of Zoology, University of Florida Gainesville, FL 32611-8525, USA
Bodega Marine Laboratory, University of California Davis, Bodega Bay, CA 94923-0247, USA
Correspondence: 1E-mail: bgminer{at}ucdavis.edu
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 Synopsis IntroductionVance's definition of "s"Values of s and...Emprical estimates of sCalculations of s for...Evaluation and comparison of...ConclusionsReferences |
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Per-offspring maternal investment is an integral part of life-history theory. To understand the evolution of per-offspring maternal investment in marine invertebrates, a number of mathematical models have been developed. These models examine how selection affects the proportion of maternally derived egg energy used to produce a newly metamorphosed juvenile (s) and make predictions about the distribution of s in nature. However, there are very few published values of s and therefore it is difficult to evaluate how well these models match nature. We present several equations to empirically estimate values of s for any group of marine invertebrate, and use data from echinoderms to compare the different equations. The calculations that directly estimate s require information on the amount of egg energy, juvenile energy, and energy metabolized during development. Currently, there are few data available for directly estimating s, and thus generating distributions of s derived from direct estimates is not possible. Furthermore, the direct estimations of s are informative for planktotrophy but not for lecithotrophy. We have developed an equation that can be used to directly estimate s for lecithotrophs. The calculations to indirectly estimate s only require egg energy or egg size for the species in question and the value of s and egg energy or size for a reference species. This reference species replaces the need to measure juvenile energy and energy metabolized during larval development. Because egg energy or size is currently available for many species, the indirect estimates will be useful for generating distributions of s, and will allow comparisons with models. Although these indirect methods are good for generating distributions of s, they do not provide reliable estimates of s for any particular species. Estimating values of s to compare models is a critical gap in our current evaluations of marine invertebrate life-history models.
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Introduction |
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SynopsisIntroductionVance's definition of "s"Values of s and...Emprical estimates of sCalculations of s for...Evaluation and comparison of...ConclusionsReferences |
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The amount of resources that parents invest in an offspring can influence the evolution of life histories by affecting both the fitness of parents and offspring (Roff 1992
; Stearns 1992; Havenhand 1995). Among animals that free-spawn, such as many species of marine invertebrates, the amount of resources a mother provisions an egg represents the entire parental investment (Levin and Bridges 1995). This is because offspring develop independently in the water column without any parental care. Thus, changes in parental investment per offspring can only occur by changing the amount or type of material placed in an egg. As a result, per-offspring maternal investment is often measured as egg size (diameter or volume) or egg energy for marine invertebrates.
A number of theoretical models have been developed to understand the selective forces that shape the patterns of per-offspring maternal investment in marine invertebrates (Vance 1973; Christiansen and Fenchel 1979; Perron and Carrier 1981; Grant 1983; Roughgarden 1989; McEdward 1997; Levitan 2000; McEdward and Miner 2003), and these have provided important insights into the evolution of life histories (Havenhand 1995). Unfortunately, empirical tests of these models are hampered by the fact that the parameter these models use to represent per-offspring maternal investment, referred to as s, is rarely empirically measured. Although egg size has often been assumed to represent s, McEdward and Janies (1997) demonstrated that this assumption is incorrect and that past attempts to test these models by comparing the predictions of a model with distributions of egg sizes are misleading.
In order to ameliorate this situation it is necessary to develop and evaluate ways for empirically estimating s. Here, we review the definition of s and how to interpret values of s in the light of marine invertebrate developmental modes. We then review equations investigators have used to calculate s. To evaluate these equations, we estimate values of s for echinoderms and discuss advantages and disadvantages of each equation. The purpose of this review is to provide a conceptual framework for measuring s in nature for any group of marine invertebrates, so that theory can be empirically tested. A better integration of theoretical and empirical studies is essential to better understand the evolution of life histories in marine invertebrates.
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Vance's definition of "s" |
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SynopsisIntroductionVance's definition of "s"Values of s and...Emprical estimates of sCalculations of s for...Evaluation and comparison of...ConclusionsReferences |
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Vance (1973)
developed the first theoretical model to explain the evolution of maternal investment per offspring for free-spawning benthic marine invertebrates. This model has been extremely influential and has provided the theoretical framework for much of larval ecology (Strathmann 1985; Havenhand 1995). Most subsequent models of life-history evolution in marine invertebrates have been developed as modifications or extensions of the Vance model (Christian and Fenchel 1979; Perron and Carrier 1981; Grant 1983; Roughgarden 1989; McEdward 1997; Levitan 2000; McEdward and Miner 2003). All these models use the same parameter, s, developed by Vance (1973) to represent maternal investment per offspring and treat s as the quantity that natural selection acts on to maximize fitness.
Vance (1973) defined s, as the "egg energy content measured not in calories per se but in units of energy sufficient for a lecithotrophic egg" (eqn. 1).
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In other words, s represents the amount of energy in an egg scaled to the minimum amount of egg energy needed to produce a newly metamorphosed juvenile without any exogenous food.
Because egg energy only represents the numerator of this equation, it is clear that simply measuring egg energy or estimating egg energy from egg size is insufficient for calculating s. Both egg energy (the numerator) and the energy required for metamorphosis without food (the denominator) must be measured to calculate s.
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Values of s and developmental mode |
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SynopsisIntroductionVance's definition of "s"Values of s and...Emprical estimates of sCalculations of s for...Evaluation and comparison of...ConclusionsReferences |
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Despite the huge influence of Vance's model and its predictions about per-offspring maternal investment in terms of s, only recently has the translation between s and two common modes of development in marine invertebrates, planktotrophy and lecithotrophy, been explicitly discussed (Herrera and others 1996; McEdward and Janies 1997
; Levitan 2000). Planktotrophy is characterized by insufficient egg energy to complete larval development, requiring feeding during the larval stage, whereas lecithotrophy is defined as an adequate amount of egg energy to complete larval development without feeding (McEdward and Janies 1993). From Vance's definition of s, these two developmental modes are easily interpreted in terms of s (Herrera and others 1996). Planktotrophy is defined as values of s > 0 and <1 because there is insufficient egg energy to complete larval development without feeding. Thus larval feeding is necessary, and the lower the value of s, the more energy that must be acquired during the larval phase in order to complete larval development and metamorphose. In principle if s = 0.999, then larval feeding is still necessary because there is insufficient energy in the egg to complete larval development, though 99.9% of development can be fueled by egg energy.
Although Vance (1973) only considered one value of s that corresponded to lecithotrophy, s = 1 (see McEdward and Janies 1997), values of s 
1 indicate that eggs have enough energy to complete larval development without exogenous food and are therefore lecithotrophic. Furthermore, values of s > 1 signify that egg energy remains after metamorphosis and the larger the value of s the greater the amount of remaining egg energy. For example, a lecithotroph with a value of s = 100 requires only 1% of its egg energy for larval development and has 99% of its egg energy available for growth and development after metamorphosis.
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Emprical estimates of s |
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SynopsisIntroductionVance's definition of "s"Values of s and...Emprical estimates of sCalculations of s for...Evaluation and comparison of...ConclusionsReferences |
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Larval energy budget
Hoegh-Guldberg and Emlet (1997)
presented the first direct estimation of s for the sea urchins Heliocidaris erythrogramma and Heliocidaris tuberculata, although they did no put their finding in these terms. They estimated the numerator in equation 1 by measuring the energy of an egg, and the denominator by measuring (1) the energy used in basic metabolic functions and developmental processes and (2) the energy content of the metamorph. With these three measurements, s can be calculated using the following equation.
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Proportional egg energy
If we assume that larval metabolism is a small fraction of the denominator in equation 2, which maybe the case for some species, like H. erythrogramma (Hoegh-Guldberg and Emlet 1997), then we can simplify equation 2, and s can be estimated by measuring only the egg energy and the energy in the newly metamorphosed juvenile (eqn. 3). This equation may be preferred because it eliminates the labor and time-consuming measurements of larval metabolisms.
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Relative egg energy or volume
The "larval energy budget" (eqn. 2) and "proportional energy" (eqn. 3) equations both require time-consuming methods (for example, larval rearing and measurements of larval metabolic rates) to estimate s. As a result, there are only a few species for which we can currently estimate s with these methods. However, because one goal is to compare the predictions of theoretical models with distributions of s values, it is necessary to empirically estimate s for many species.
Levitan (2000) presented a method to easily estimate values of s for many species. His method uses a reference species, for which egg energy and the value of s are known, to estimate the minimum energy needed for a lecithotrophic egg (that is, the denominator of eqn. 1). The only additional information that is needed to calculate s is the egg energy (that is, the numerator) for a number of species of a particular group. This eliminates the difficult task of estimating the denominator in the above equations (eqns. 2 and 3). Of course the assumption is that the reference species is an accurate estimate of the denominator for each species for which s is calculated. With this method, values of s can be calculated for a species if three measures are known: (1) the egg energy of the species in question, (2) the egg energy of a reference species, and (3) the value of s for that reference species.
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For many species of marine invertebrates, only egg sizes are known, and therefore all of the above calculations (eqns. 2–4) are not an option. If we are willing to assume that egg size is a reasonable index of egg energy, egg size can be substituted for egg energy in equation 4. Studies have shown that indeed there is a good relationship between egg energy and size among species (for example, Jaeckle 1995; McEdward and Morgan 2001), but not within a species (McEdward and Coulter 1987). To estimate s with only egg size information, three values are needed: (1) the egg size of the species in question, (2) the egg size of a reference species, and (3) the value of s for that reference species. Volume is the most appropriate measure of egg size for estimating the level of provisioning, so s can be calculated as follows.
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Calculations of s for echinoderms |
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SynopsisIntroductionVance's definition of "s"Values of s and...Emprical estimates of sCalculations of s for...Evaluation and comparison of...ConclusionsReferences |
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To evaluate these different equations, we calculated s for species of echinoderm. We have used echinoderms because the needed information for these equations (for example, egg size and egg energy) is known (Emlet and others 1987; Jaeckle 1995
; Hoegh-Guldberg and Emlet 1997; McEdward and Morgan 2001). We were able to calculate s for 2 species with the "larval energy budget" equation (eqn. 2), for 4 species with the "proportional energy" equation (eqn. 3), and for 39 species with the "relative egg energy and volume" equation (eqns. 3 and 4).
With the larval energy budget equation and based on the data provided from Hoegh-Guldberg and Emlet (1997), we calculated s for two species of sea urchin. For H. tuberculata, which has a planktotrophic larva, s equaled 0.0168, and for H. erythrogramma, which has a lecithotrophic larva, s equaled 0.9480 (Table 1). With the proportional energy equation, we calculated s values for these two species and two additional species. For the two species with planktotrophic larvae (both sea urchins), the values were 0.073 for Paracentrotus lividus and 0.023 for H. tuberculata (Table 1), based on data from Fenaux and colleagues (1985) and Hoegh-Guldberg and Emlet (1997). For the two species with lecithotrophic larvae (a crinoid and a sea urchin), the values were 5.296 for Florometra serratissima and 1.000 for H. erythrogramma (Table 1), based on data from McEdward and colleagues (1988) and Hoegh-Guldberg and Emlet (1997).
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With the relative egg energy and volume equations (eqns. 4 and 5), we calculated s in three different ways: (1) with egg energy, (2) with egg energy predicted from egg volume, and (3) with egg volume. For each of these, we used Clypeaster rosaceus as our reference species. Egg energy has been measured for C. rosaceus (Miner and others 2002), and because it is near the border of lecithotrophy and planktotrophy (Emlet 1986
), s for C. rosaceus is assumed to be 
1 (see McEdward and Janies 1997; Levitan 2000). Because this is only a rough estimation of s for C. rosaceus, we also used H. tuberculata as a reference species for calculating s from egg energy. We chose H. tuberculata because we had a direct estimate of s from the "larval energy budget" calculation.
Based on the data from McEdward and Morgan (2001), values of s calculated from egg energy for planktotrophs ranged from 0.008 to 0.284, whereas for lecithotrophs the values ranged from 0.279 to 84.07 when C. rosaceus was used as the reference species (Table 2). We obtained similar values when H. tuberculata was used as the reference species; values of s for planktotrophs ranged from 0.006 to 0.239 and those of lecithotrophs ranged from 0.235 to 70.65 (Table 2). We calculated s from estimates of egg energy derived from egg volume using the allometric regression equation estimated for echinoderms by McEdward and Morgan (2001)—EggEnergy = –0.012 + 9.644 EggVolume0.868. Other allometric relationships between egg size and energy should be used for other taxa (see Pernet and Jaeckle 2004). Estimated values of s for planktotrophs with C. rosaceus as the reference species ranged from –0.031 to 0.489, and those for lecithotrophs ranged from 0.703 to 54.79 (Table 2). Using egg volumes and C. rosaceus as the reference species, values of s for planktotrophic species ranged from 0.021 to 0.472 and those for lecithotrophs ranged from 0.687 to 95.53 (Table 2).
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Evaluation and comparison of the different estimations of s |
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SynopsisIntroductionVance's definition of "s"Values of s and...Emprical estimates of sCalculations of s for...Evaluation and comparison of...ConclusionsReferences |
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We took several general approaches to evaluate the different equations. First, we checked whether the calculated values of s differed among the different calculations. Next, we checked whether the calculated values of s corresponded to the developmental mode for each species. In other words, were values of s <1 for species with planktotrophic larvae and
1 for lecithotrophic species? Lastly, for the relative egg energy and volume calculations, where we had values of s for a number of species, we also compared the distribution of s values derived from the different methods. This latter approach was intended to alleviate some of the problems associated with error in the data. Any comparison between species or methods for a species is influenced by error in the data used to calculate values of s. Looking at the distributions of s provided a way to see a pattern despite any underlying error (assuming the error is random). During our evaluations of the different equations, it became evident that there are problems with some of the equations. These problems are (1) the inability of the "larval energy budget" and "proportional energy" equations (eqns. 2 and 3) to accurately estimate s for lecithotrophs, (2) the inability of the "relative egg energy or volume" equation (eqn. 4) to accurately estimate s when the reference species does not accurately predict the minimum amount of energy for lecithotrophy in that species, and (3) the issue of scaling between egg energy and egg volume and its effects on the calculations of s when egg size is used.
The discrepancy between the direct calculations of s (eqns. 2 and 3) and the relative calculations (eqns. 4 and 5) and the lack of correspondence between the known developmental mode and the calculated values of s for two lecithotrophic species highlight the first two problems. For H. erythrogramma the direct calculations indicate that s is 
1, whereas the relative calculations indicate that s is 3 (Table 1). Clearly the value of s for H. erythogramma should be 1 because it has a lecithotrophic larva. In addition, a value of s = 3 seems much more reasonable than a value of 1, because this species has a nonfeeding larva (measurement error probably explains why the value derived from the "larval energy budget" of 0.948 was <1). Species that are lecithotrophic but close to the boundary between planktotrophy and lecithotrophy typically have facultative feeding larvae, for example C. rosaceus and Brisaster latifrons (Emlet 1986; Hart 1996). Thus, the direct equations (eqns. 2 and 3) appear to be inaccurate for lecithotrophic species.
This underestimation of s from the direct calculations for lecithotrophic species is caused by the value measured to represent the denominator (that is, the minimum amount of energy required to produce a lecithotrophic larva). With the direct calculations the denominator is estimated by measuring the energy of the juvenile. However, if a species provisions its eggs with more energy than the minimum needed to be lecithotrophic, then this energy will be present in the juvenile, and the denominator is overestimated. In other words, the more energy a lecithotrophic species provisions its egg, the larger the values of both the numerator and denominator, and therefore the value of s will remain approximately the same. Thus, with the direct equations (eqns. 2 and 3) it is likely that the value of s will be underestimated to some degree for all lecithotrophic species because all lecithotrophic species, even facultative planktotrophs, are provisioned with more energy than needed to just metamorphose.
This problem raises another potential problem when calculating s with the direct equations for species with feeding larvae (either planktotrophic or lecithotrophic). If larvae consume more food than the minimum amount necessary to metamorphose then the denominator will be overestimated and the value of s underestimated. Despite the potential for this problem, we have no evidence to suggest that it is a problem. For both species with feeding larvae in Table 1, the direct calculations of s were greater (not less than) than the indirect calculations.
Because the direct equations (eqns. 2 and 3) are uninformative for lecithotrophic species, we need an alternative way to directly calculate s for lecithotrophs. A possible solution is to calculate the energy needed to build the juvenile for lecithotrophs. By estimating how much energy is used after metamorphosis, we can subtract this amount from the egg energy and estimate the amount of energy required to just produce a juvenile. We might therefore consider using the following equation to estimate s for lecithotrophic species.
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So how do we measure the amount of energy used by the juvenile for metabolic processes? After larvae metamorphose, the juveniles can be held without food and the amount of energy in a juvenile can be quantified just before it starves. Either this value can be subtracted from the amount of energy in the newly metamorphosed juvenile to give the amount of energy used for juvenile metabolic processes, or it can represent the entire denominator of equation 6. Unfortunately this method is likely difficult and time consuming. In addition, this equation will overestimate values of s if a bigger juvenile skeleton or other energetic costs are required to incorporate extra energy for juvenile growth. Currently there are no data available to estimate s using this "juvenile energy budget" equation (eqn. 6).
Blastomere separation might provide an alternative way to estimate s for lecithotrophs. By halving or quartering embryos and rearing the reduced embryos to metamorphosis, the minimum size required to produce a juvenile could be estimated and used as the denominator in equation 2. However, this method is only viable for a few taxa (for example, echinoderms) and is also likely time consuming and labor intensive.
The species F. serratissima highlights the second problem. Although F. serratissima has a lecithotrophic larva, the values of s calculated with the relative equations were <1 and are clearly incorrect. These low s values of F. serratissima are because this species has a very small egg but also a very small juvenile, and as a result it can still be lecithotrophic despite the small egg size (McEdward and others 1988). Thus, the small value of egg energy or volume is divided by a reference species that requires more energy to produce a juvenile, and the value of s is underestimated. Although rather obvious, this highlights that a particular reference species is not suitable for all species. Investigators should acknowledge this potential problem when calculating s with the relative equations, and justify why a reference species is appropriate for that group. Alternatively, a number of appropriate reference species could be used, allowing the investigator to report a measure of error or confidence in the measurements.
The calculations from F. serratissima also indicate that for some species the "proportional energy" equation (eqn. 3) will greatly overestimate the value of s. As mentioned above, the problems with the direct calculations (eqns. 2 and 3) result in values of s that are 1 for lecithotrophs. However, the value of s calculated with the "proportional energy" equation for F. serratissima was 5 (Table 1). The reason for this discrepancy is that its larva uses a large amount of energy for metabolic processes. Thus the assumption that larval metabolic costs are negligible, which is necessary to use the "proportional energy" equation, is violated.
The distributions of s values for planktotrophic and lecithotrophic species show that values of s derived from egg volume and egg energy can differ. We observed rather different values of s calculated with the "relative egg energy" (eqn. 4) and "relative egg volume" (eqn. 5) (Fig. 1). This difference is expected whenever the relationship between egg energy and egg volume is nonlinear, and is likely the explanation for the differences we observed (McEdward and Morgan 2001). In addition, for five planktotrophic species, we obtained negative values of s with the "relative egg energy" equation (eqn. 4) when we estimated egg energy from egg size (see sb in Table 2). Negative values of s are not biologically possible and indicate that deriving egg energy from egg volume can produce inaccurate estimates. This is likely because the confidence intervals of regressions are poorest at the extremes. Lastly, values of s calculated with the "relative egg energy" equation (eqn. 4) were very similar even when we used different reference species (Fig. 1).
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Conclusions |
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SynopsisIntroductionVance's definition of "s"Values of s and...Emprical estimates of sCalculations of s for...Evaluation and comparison of...ConclusionsReferences |
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In this article, we have presented several equations to empirically estimate s for marine invertebrates and have discussed their advantages and limitations. The "relative egg energy" and "relative egg volume" equations (eqns. 4 and 5) allow researchers to estimate values of s for a number of species and are most appropriate for generating data to test theoretical models. However, because these equations require a reference species, they cannot take into account changes in the cost of development and production of the juvenile (that is, the denominator of equation 1). Therefore any estimate of s for a single species is probably not very reliable and should be considered with caution until further experimental work determines how different juvenile size and larval metabolic costs are among species. The "larval energy budget" and "proportional energy" calculations (eqns. 2 and 3) provide a more direct way of quantifying s and overcome the problems with the "relative egg energy" and "relative egg volume" equations. However, it unclear whether the "proportional energy" calculation can provide reliable estimates because it is currently unknown whether we can assume that energy spent on larval metabolism is sufficiently small and can therefore be ignored. The "larval energy budget" calculation should provide the most accurate and reliable values of s. However, it is very time consuming and likely unreliable for lecithotrophs. The "juvenile energy budget" equation (eqn. 6) is one solution for directly estimating s for lecithotrophs. Despite the time needed to obtain the data for these direct estimates (eqns. 2 and 6), they are important because they provide the most accurate estimates of s. Furthermore, they can provide data needed for the relative estimations (eqns. 4 and 5). The direct estimates (eqns. 2 and 6) can also be used to verify the relative estimates (eqns. 4 and 5), and if contradictions arise they provide information on the causes for different estimations—for example are costs of development and production of the juvenile different than the reference species (that is, the denominator of eqn. 1).
Empirical calculation and interpretation of s represents a gap in our understanding of the life histories of marine invertebrates, which is necessary to understand the evolution of reproductive strategies in marine invertebrates. Our critical evaluation of different ways to empirically estimate s should serve as a guide for future investigations and allow more accurate comparisons between models and nature.
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Acknowledgements |
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A. O. D. Willows, Director, provided space and facilities at the Friday Harbor Laboratories, University of Washington. We thank the following people for helpful discussions of the ideas presented in this article or for comments on the manuscript: J. Cowart, M. Hart, D. Levitan, A. Moran, D. Padilla, J. Pechenik, R. Strathmann, C. Osenberg, C. St Mary, and E. Werner. Support was provided by National Science Foundation grants OCE 9819593 to L.R.McE. and OCE 0385028 to S. Morgan and B.G.M. (Contribution 2295 Bodega Marine Laboratory, University of California, Davis).
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Footnotes |
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2Present address: Department of Biology, Western Washington University, Bellingham, WA 98225-9160, USA
From the symposium "Complex Life-Histories in Marine Benthic Invertebrates: A Symposium in Memory of Larry McEdward" presented at the annual meeting of the Society for Integrative and Comparative Biology, January 4–8, 2005, at San Diego, CA.
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