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Natural selection on genetically correlated phenological characters in Lythrum salicaria L. (Lythraceae).

The seasonal timing of life-history events such as flowering can be critical to plant reproductive success (Rathcke and Lacey 1985). There is considerable evidence for a relationship between the timing of flowering and fecundity (Schemske 1977; Augspurger 1981; Roach 1986; Mazer 1987), and for selection on timing of initial flowering (Schemske 1984; Stewart and Schoen 1987; Campbell 1989, 1991; Kelly 1992a). However, the prevalence of phenotypic (Mazer 1987; Dorn and Mitchell-Olds 1991; Kelly 1992a,b) and genetic correlations (Dorn and Mitchell-Olds 1991; but see Kelly 1993) between the timing of flowering and other life-history events or other quantitative traits makes it difficult to predict how populations might respond to selection acting on flowering time. Many of the traits that can be correlated with the timing of flowering such as plant size, duration of flowering, and the number of flowers produced, are traits that could be subject to selection themselves. A high degree of intercorrelation among characters can make it difficult to disentangle the effects of direct selection from the effects of selection on correlated traits, especially if correlated traits are not included in the selection analysis.

Many of the potential problems associated with the interpretation of selection on correlated characters can be ameliorated if the genetic variance-covariance structure of the traits in the population subject to selection is known. Unfortunately, few studies have simultaneously assayed selection gradients, heritabilities, and genetic correlations (but see Kelly 1992a, 1993; Campbell et al. 1994). Knowledge of heritabilities allows a prediction of whether the population will respond to selection. Moreover, low additive genetic coefficients of variation (Houle 1992) for characters that are subject to strong phenotypic selection can be interpreted as evidence that selection has eroded genetic variation. The existence of genetic correlations can explain the presence of significant additive genetic variance in the face of strong selection if they act as evolutionary constraints. Knowing both the pattern of phenotypic selection and genetic correlations can allow a much more insightful interpretation of the potential for an evolutionary response to indirect selection via selection on a genetically correlated trait (see Campbell et al. 1994).

The study of life-history characters such as flowering time provides an ideal system to understand how selection acts on phenotypically and genetically correlated characters. The degree of flowering synchrony among individuals within a plant population could influence reproductive success by enhancing the ability of individual plants to attract pollinators if attraction is density dependent (Augspurger 1980, 1981; Thomson 1980; but see Schemske 1980; Zimmerman 1980; Melampy 1987; Rodriguez-Robles et al. 1992). Plants flowering in synchrony will also have a greater number of potential mates. Thus, stabilizing selection should favor individuals exhibiting flowering phenologies that are similar to the mean phenology of the population (Thomson 1980).

The duration of flowering for individual plants could also significantly influence reproductive success. Flowering duration could determine the total number of flowers produced and thus set an upper limit on the number of ovules and pollen grains produced. A protracted flowering period could reduce the uncertainty of pollination (Wilson and Rathcke 1974; Ackerman 1989; Preston 1991) and act as a means of reproductive assurance which could be critical in pollen-limited obligately outcrossing species (Pojar 1974; Bawa 1983). Thus, selection on flowering duration and number of flowers produced should be directional.

The purpose of this study was to quantify natural selection on phenological traits in Lythrum salicaria and estimate heritabilities and genetic correlations to determine the genetic potential for a selection response. Specifically, the following questions were addressed: (1) Does stabilizing selection act on initiation of flowering to promote synchronous flowering within a population? (2) Does directional selection act to increase the duration of flowering or flower production? (3) Is there heritable variation for phenological characters or genetic correlations between characters that could act as evolutionary constraints? (4) How do additive genetic coefficients of variation (C[V.sub.A]) and evolvabilities compare for traits subject to differing levels of selection?


Study Species

Lythrum salicaria L. (Lythraceae), purple loosestrife, is a common, introduced, tristylous plant found in marshes and along riverbanks. Tristylous plants are characterized by the presence of three morphologically distinct mating types that can be easily distinguished on the basis of their floral morphology. A genetic incompatibility system in this species enforces phenotypic disassortative mating among types (Darwin, 1877; O'Neil 1994). Therefore, the number of potential mates in a population is restricted and dependent on mating-type frequencies in the population. Lythrum salicaria is a perennial with multiple shoots arising from as single tap root. Clonal growth results in a tightly packed clump of stems that is easily recognized as a unique genotype in the field.

Lythrum salicaria is pollinated by a variety of bees and lepidopteran pollinators (O'Neil 1992). A large inflorescence of over 850 flowers is produced and flowers are retained on the inflorescence long after the period of stigma receptivity and pollen dehissence, presumably as a means of enhancing pollinator attraction (see Wilson and Price 1977; Schemske 1980). Flower maturation is acropetal (base to tip) and the inflorescence increases in size throughout the flowering period.

Field Study

A large population of L. salicaria located on the shore of the Kennebec River in Lincoln County, Maine was used for the selection study. All plants within the population (585 plants) were followed throughout the flowering period during the summer of 1992. The morph type (long, mid, or short), and Julian dates of initiation and completion of flowering were recorded for all individuals within the population. Morph type was not included in any of the analyses described below because preliminary analyses demonstrated that there was not a morph effect on any of the phenological characters measured. A 15-[m.sup.2] area that was away from a nearby road was chosen for the selection study and all plants (65) within this area were measured for additional characters. Plant height was measured at the onset of flowering as an estimate of plant size, and final inflorescence height was measured at the completion of flowering as an estimate of the number of flowers produced. Previous measurements of inflorescence size and number of flowers per inflorescence have indicated that inflorescence height explains 87% of the variation in flower number (b = 5.22, df = 1,60, P [less than] 0.0001). Seeds were collected when they matured and the total number of seeds produced per plant was calculated as an estimate of fitness. I counted the total number of capsules produced and the number of seeds per capsule for a subsample of 10 capsules per plant. The total number of seeds produced was then calculated as the product of the number of capsules and the mean number of seeds per capsule. Relative fitness was calculated by dividing the estimate of number of seeds by the population mean (Endler 1986, p. 168).

Statistical Analysis of Selection

To estimate the magnitude and direction of selection acting on the traits measured, a multiple regression analysis (Lande and Arnold 1983; Arnold and Wade 1984a,b) was performed. The directional selection gradient, [Beta], was estimated as the vector of partial regression coefficients from the regression of relative fitness on the set of character measures (PROC REG, SAS Institute 1990). The selection differential, S, was estimated as the covariance between relative fitness and each quantitative character using PROC CORR (SAS Institute 1990). The stabilizing-disruptive selection gradient, [Gamma], was calculated as the vector of partial quadratic regression coefficients of relative fitness on each character deviation from the mean PROC GLM (SAS Institute 1990) using the following model:

[Mathematical Expression Omitted] (1)

where w is relative fitness, [Alpha] is a constant, [X.sub.i] are the trait means, [Delta] is = 1 if i = j and 0 when i [not equal] j, [Epsilon] is the error term, P is the number of traits included in the analysis, and [Beta][prime] and [Gamma] are the first- and second-order regression coefficients. Selection differentials were standardized by dividing by the standard deviation (Falconer 1989). Selection gradients were standardized by multiplying by the standard deviation or appropriate product of standard deviations for the quadratic terms (Endler 1986). Characters included in the analysis were the Julian date of initiation of flowering, duration of flowering (number of days in flower), plant height, and inflorescence height. Inflorescence height was log transformed to improve normality for this analysis. Correlations among characters were calculated using PROC CORR (SAS Institute 1990).

Quantitative Genetic Analysis

Crosses were performed to generate 60 full-sib families for the quantitative genetic analysis. Dams were randomly assigned to compatible sires, and both dams and sires were bagged for more than 24 hours prior to pollination. This insured the availability of pollen from sires and prevented contamination of the stigmas of newly opened flowers on dams. The inflorescence of dams were rebagged after pollination for a period of 48 hours. Lythrum salicaria is very amenable to controlled crosses because it is self-incompatible and sets 60 to 100 seeds per capsule following hand pollinations (O'Neil and Schmitt 1993; O'Neil 1994). I grew 10 progeny from each cross in a tilled experimental garden located in a wet meadow at the Darling Marine Center in Walpole, Maine. All progeny were censused for the Julian dates of initiation and completion of flowering, plant height at the onset of flowering, and final inflorescence height.

Narrow-sense heritabilities were estimated using parent-offspring regression. I regressed the average offspring value on the parent value and calculated heritability estimates as twice the slope of the regression line (Falconer 1989) for single parent regressions (dam-offspring and sire-offspring) for all traits where the dam and sire traits were uncorrelated. There were significant correlations between dam and sire values for the date of initial flowering and the date of last flowering. This is an unavoidable consequence of the fact that performing a cross requires that the randomly chosen dam and sire flower simultaneously. For these traits, heritabilities were calculated as twice the slope of the regression line divided by 1 + r, where r equals the correlation coefficient (Falconer 1989). I conducted power tests using JMP (SAS Institute 1994) to determine whether the sample sizes were adequate to detect significant heritabilities.

I calculated coefficients of genetic variation and evolvabilities as described by Houle (1992) for traits with heritabilities that were significantly greater than zero. The additive genetic coefficient of variation, C[V.sub.A], and the residual coefficient of variation, C[V.sub.R], were calculated as follows:

C[V.sub.A] = 100[square root of[V.sub.A]/X] (2)


C[V.sub.R] = 100[square root of([V.sub.A] - [V.sub.P])/X], (3)

where [V.sub.A] = additive genetic variance, X = the trait mean, and [V.sub.p] = phenotypic variance. Evolvabilities were calculated for truncation selection: [V.sub.A]/(X[square root of[V.sub.P]]); directional selection: [V.sub.A]/([X.sup.2])100; and weak stabilizing selection: [V.sub.A]/X. To avoid problems of scale, the Julian date of initial flower production was converted to a sequential number by subtracting the Julian date that the population began flowering.

I calculate genetic correlations as the cross-covariance divided by the square root of the product of the offspring-parent covariances of each character (Falconer 1989) using PROC REG and PROC CORR (SAS Institute 1990). The cross-covariance used in this analysis was the mean of Cov (trait 1 in offspring, trait 2 in parents) and Cov (trait 2 in offspring, trait 1 in parents). Significance levels for heritability estimates and phenotypic correlations were calculated using PROC REG (SAS Institute 1990) and PROC CORR (SAS Institute 1990). I calculated standard errors for genetic correlations ([r.sub.A]) as [Mathematical Expression Omitted], where [Mathematical Expression Omitted] = the heritability of trait x, and [Mathematical Expression Omitted] = the standard error of the heritability of trait x (Falconer 1989). Tablewide significance levels for heritabilities and genetic correlations were calculated using the sequential Bonferroni technique (Rice 1989).

Because L. salicaria is auto-tetraploid and inheritance in polysomic (Fisher and Mather 1943), the parent-offspring covariance = 1/2 [V.sub.A] + 1/6 [V.sub.d] (Kempthorne 1955b) where [V.sub.A] = additive genetic variance, and [V.sub.d] = variance due to digenic interaction (analogous to dominance deviation in the diploid case). This could lead to a slight overestimate of heritability. However, Kempthorne (1955a) indicates that heritability estimates for tetraploids should be only mildly sensitive to the nonadditive effects of genes because the digenic interaction is proportionally small. The bias due to narrow-sense heritability estimates containing a small fraction of nonadditive genetic variance is considerably less serious than biases in other experiments due to the use of field collected half-sibships that could be inbred or maternal effects (see Mitchell-Olds and Rutledge 1986).


Phenotypic Variation among Individuals

There was considerable variation in the timing of flowering among individuals in the entire population [ILLUSTRATION FOR FIGURE 1A OMITTED] and among individuals within the subset of plants used for the selection study [ILLUSTRATION FOR FIGURE 1B OMITTED]. Flowering duration in the full population ranged from three days to 38 days, and there was a significant negative correlation between date of first flowering and flowering duration (R = -0.88, df = 1,324, P [less than] 0.0001). The subsample of plants used for the selection study was representative of the full population and displayed many significant correlations among traits (Table 1). There were [TABULAR DATA FOR TABLE 1 OMITTED] significant negative correlations between initiation of flowering and both flowering duration and inflorescence height. Plants that flowered early also flowered long [ILLUSTRATION FOR FIGURE 1B OMITTED] and produced more flowers than late-flowering individuals. Correlations among plant height, inflorescence height, and flowering duration were positive (Table 1). There were significant correlations between relative fitness and all of the traits measured (Table 1).

Selection Analysis

Standardized selection differentials (S) for all traits included in the analysis were significant and large in magnitude, suggesting the potential for phenotypic selection to result in appreciable change in these characters (Table 2). Standardized directional selection gradients ([Beta]) were significant, for initiation of flowering, flowering duration, and inflorescence height, indicating that selection is acting on these traits directly. The selection gradient for plant height was not significant. Thus, the large selection differential for plant height is probably the result of selection on correlated traits such as inflorescence height and flowering duration. There were significant quadratic selection gradients ([Gamma]) for both initiation of flowering and inflorescence height. However, caution should be used in interpreting the nonlinear selection gradients because of the high degree of correlation among the predictor variables. The selection gradient ([Gamma]) for initiation of flowering was negative, indicating that there is a convex component to the fitness function. The shape of the fitness function estimated by this multiple regression model is plotted as a fitness surface with flowering duration for plants of average height with average size inflorescences in Figure 2A. The shape of the fitness surface did not change when I used large or small values for plant height and inflorescence height, but the magnitude of relative fitness varied with inflorescence size. The shape of the fitness surface suggests [TABULAR DATA FOR TABLE 2 OMITTED] that the timing of flowering is subject to a combination of stabilizing and directional selection. Note that much of the fitness surface depicted in Figure 2A, including the fitness maximum represents a portion of the phenotype space where data do not occur (compare with [ILLUSTRATION FOR FIGURE 2B OMITTED]).

The stabilizing-disruptive selection gradient ([Gamma]) for inflorescence height was positive, indicating a possible concave component to the fitness function for this trait. However, the fitness surface estimated by this gradient predicts that only plants with very small inflorescences ([less than] 3 cm) should have higher fitness than plants with slightly larger inflorescences. There are only two data points that exist in this range and neither have higher fitness than any other plants in the population. Thus, selection on inflorescence height is linear throughout the major portion of the range of inflorescence heights and the quadratic selection gradient might not provide an accurate representation of the shape of the selection surface where data points do not occur.

Quantitative Genetic Variation

There was significant heritable variation for several of the traits included in the selection analysis (Table 3). Narrow-sense heritabilities were significant for the date of initial flowering, the date of last flowering, and the number of seeds per capsule. However, I failed to detect significant heritable variation for flowering duration, plant height, inflorescence height, number of capsules, and number of seeds per plant. There was a high degree of consistency between heritabilities estimated from dam-offspring and sire-offspring, and mid-parent-offspring regression. Heritabilities estimated from dam-offspring regressions contain maternal effects. The small magnitude of the difference between dam and sire heritability estimates suggests that maternal effects are minimal for these traits.

Additive genetic coefficients of genetic variation were higher for number of seeds per capsule and date of flowering initiation than for date of last flowering (Table 4). This suggests that high levels of genetic variation for these traits are maintained in this population. The coefficient of residual variation for date of flowering initiation was extremely high, suggesting that the low but significant heritability for this trait could be attributed to high nonadditive genetic or environmental variance. Predictors of evolvability under directional selection were higher than those for truncation or stabilizing selection. Evolvability estimates were considerably higher for date of flowering initiation and number of seeds per capsule than for date of last flowering. The evolvability for date of flowering initiation under directional selection was considerably higher than the evolvability under stabilizing selection. This suggests that there is a greater potential for response to the linear component of selection on this trait than the stabilizing component.
TABLE 3. Heritabilities from dam, sire, and midparent offspring

Trait                        Dam         Sire        Midparent

Initiation of flowering    0.100(***)   0.093(**)   0.093(**)
Date of last flowering     0.594(*)     0.526(**)   0.415(***)
Flowering duration         0.022        0.030       0.027
Plant height               0.024        0.015       0.022
Inflorescence height       1.039        0.174       0.240
Seeds per capsule          0.443(***)   0.436(*)    0.440(****)
Number of capsules         0.007        0.034       0.199
Number of seeds/plant     -0.052        0.242       0.233

* = P [less than] 0.05, ** = P [less than] 0.02,
*** = P [less than] 0.008, **** = P [less than] 0.0001.

Genetic correlations were calculated for the three traits that displayed significant narrow-sense heritabilities. There was a significant genetic correlation between the date of initial flowering and the date of last flowering ([r.sub.A] = 1.08 [+ or -] 0.03). This supports the hypothesis that there is one pleiotropic system controlling flowering time. There was also a significant genetic correlation between the date of initial flowering and number of seeds per capsule ([r.sub.A] = 1.77 [+ or -] 0.10). However, there was no evidence for a genetic correlation between date of last flowering and number of seeds per capsule ([r.sub.A] = 0.18 [+ or -] 0.34).


The results support the hypothesis that directional selection acts to increase both the duration of flowering and flower production estimated as inflorescence height. The significant negative stabilizing-disruptive and directional selection gradients for initiation of flowering suggests that a combination of directional and stabilizing selection are acting on this trait. This supports the hypothesis that stabilizing selection acts to promote synchronous flowering within this population. The magnitude of the directional selection gradients for duration of flowering and inflorescence height are both higher than the stabilizing selection gradient for initiation of flowering. Therefore, directional selection for long flowering duration and large inflorescence height is probably stronger than stabilizing [TABULAR DATA FOR TABLE 4 OMITTED] selection for initiation of flowering. The sign of the directional selection gradient for flowering initiation is positive, indicating that selection favors later flowering individuals. Both the positive linear and negative quadratic selection gradients can be interpreted in terms of selection for flowering synchrony. In this population later flowering individuals (i.e., between Julian dates 215 and 225) are more in synchrony with other individuals flowering in the population [ILLUSTRATION FOR FIGURE 1 OMITTED].

The high degree of interdependence among the predictor variables included in the selection analysis (see Neter et al. 1985; Mitchell-Olds and Shaw 1987) could lead to ambiguity in interpretation of the selection gradients. With multicollinearity, all different combinations of trait values do not exist. In the present data set, for example, there are no phenotypes that simultaneously flower late and have a long flowering duration, or phenotypes that have a long duration of flowering but produce few flowers [ILLUSTRATION FOR FIGURE 2B OMITTED]. If such phenotypes did exist, the phenotypic covariation structure would be altered, and the results of the selection analysis could change dramatically. For this reason the selection gradients from the multiple regression analysis should be considered conditional in the sense that they are only valid for the current covariance structure.

Where there is severe multicollinearity, it is impossible to distinguish between the direct effects of selection on individual characters and the effects of selection on correlated characters with the use of multiple regression alone (Mitchell-Olds and Shaw 1987). The significant stabilizing selection gradient for date of flowering initiation could be suspect due to the high degree of correlation between flowering date and flowering duration, particularly in light of the absence of an intermediate fitness maximum when flowering duration, plant height and inflorescence height are not held constant. However, there is independent evidence to confirm that when flowering duration is held constant selection will favor synchrony. I have measured seed production, on a per day basis, by tagging over 3500 individual flowers and estimating number of seeds per capsule at different times throughout the flowering season (O'Neil unpubl.). When seed set is dissected into the day by day contribution to total seed set so that the correlation with flowering duration is not a factor, there is clear evidence for an intermediate fitness maximum. There is a significant quadratic relationship between flowering date and number of seeds per capsule. Flowers open in midseason set a greater number of seeds per capsule then flowers open early or late in the season. Thus, if flowering duration were held constant, selection must favor plants flowering in mid-season. The quadratic selection gradient for date of flowering initiation is probably accurately portraying the existence of stabilizing selection for the portion of the phenotype space where there are data [ILLUSTRATION FOR FIGURES 2A, B OMITTED]. However, because some phenotype combinations are not present in this natural population (i.e., phenotypes that flower early for short duration or late for a long duration), the selection analysis cannot possibly accurately predict how selection would act on the total range of variation. The experimental creation of nonexistent phenotypes (such as late flowering individuals with long flowering duration) might provide insight that would not be otherwise possible. These experiments are currently in progress.

There was no evidence for selection on plant size. Other selection studies have found substantial selection on size related characters (Roach 1986; Stewart and Schoen 1987; Kelly 1992a). Plant height had a large and significant selection differential, but a small and nonsignificant selection gradient. This suggests that although taller plants have higher fitness, selection is not acting directly on plant height. Instead, tall plants are favored due to selection on correlated traits. Tall plants probably have a selective advantage because they flower longer and produce more flowers than short plants. Date of first flower and number of flowers have been found to be size dependent in other species (Dorn and Mitchell-Olds 1991; Kelly 1992b; but see Schmitt 1983).

The response to selection will depend on the presence of genetic variation in the population and the covariance structure of the traits subject to selection. Previous studies have found evidence for genetic variation in the timing of flowering in other plant species (Lawrence 1963, 1965; Paterniani 1969; Carey 1983). However, Kelly (1993) found no evidence of additive genetic variance for phenological traits in Chamaecrista fasciculata or evidence of either additive genetic correlations among phenological characters or phenotypic and genetic correlations between date of flowering and number of flowers produced. There is evidence of a genetic correlation between plant height and flowering date in Brassica campestris (Dorn and Mitchell-Olds 1991) that could act as an evolutionary constraint.

In this natural population of purple loosestrife there is significant narrow-sense heritability for both the timing of initial flowering and the completion of flowering. Evolvabilities under directional selection are much higher for initiation of flowering and seeds per capsule than for date of last flowering. The evolvability under weak stabilizing selection for initiation of flowering is also high, but not as high as the evolvability under directional selection. Thus, there is the genetic potential for a selection response in these traits in the absence of other genetic constraints. The positive genetic correlation between date of flowering initiation and number of seeds per capsule, which is a component of fitness, could result in a more intense selection response to the linear component of selection favoring later flowering initiation. In artificial selection experiments, Dorn and Mitchell-Olds (1991) found that the response to selection on flowering date and height was greatest along the axis of positive genetic covariation. However, the negative selection differential for flowering initiation suggests that indirect selection on correlated characters such as flowering duration could preclude a direct response to selection on initiation of flowering.

The genetic correlation between the two timing traits is approximately one. This suggests that the genetic system controlling the timing of flowering initiation also determines the timing of the cessation of flowering. In the absence of environmental variation the date of last flowering would be determined by the date of first flowering and there would be no variation in flowering duration. Thus, the genetic correlation between date of initial flowering and the date of last flowering is consistent with the absence of heritable variation for flowering duration. The lack of significant heritable variation for flowering duration, plant height, or inflorescence height suggests that selection may have reduced the additive genetic variation for these traits to undetectable levels.

Significant heritable variation and large additive genetic coefficients of variation for traits that are highly correlated with fitness such as the date of flowering initiation and the number of seeds per capsule is inconsistent with the prediction that selection should erode genetic variation (see Falconer 1989). Genetic variation for number of seeds per capsule is probably the result of variation in ovule number. There is a significant relationship between ovule number and seeds per capsule (O'Neil unpubl.) and a family effect for ovule number (unpubl. data) in this species. One possible explanation for the presence of additive genetic variance for the initiation of flowering that is supported by the selection study is that selection acting on the trait directly is in an opposing direction from indirect selection on correlated characters. In this case, directional selection favoring long flowering duration could result in a selection response for early flowering, whereas direct selection favors individuals flowering in synchrony. Alternatively, it is possible that substantial heritable variation for a trait could persist at evolutionary equilibrium if a nonheritable trait such as nutritional state affects the trait and fitness through different pathways (see Price et al. 1988). Although this hypothesis was originally suggested (Darwin 1871; Fisher 1958; Price et al. 1988) to explain why heritable variation for breeding date in birds persists in the face of strong directional selection, it is completely analogous to the situation in plants. If there is both a genetic component and a nutritional component determining the date of flowering, and the same nutritional component affects seed set, there could be an environmentally induced covariance between flowering date and fitness. It is probable that the availability of water, light, or nutrients could affect both flowering date and seed set. This problem can be alleviated by measuring selection on breeding values directly as has been suggested by Rausher (1992; see also Rausher and Simms 1989; Simms and Rausher 1993). I am currently measuring selection in an experimental population of plants from controlled crosses to estimate selection gradients using breeding values. Hopefully, the combined information from the measurement of selection in a natural population presented here, and the measurement of selection on breeding values in an experimental population will strengthen our understanding of how selection acts on the timing of reproduction in plants.


I would like to thank G. Fox, J. Howard, T. Mitchell-Olds, J. Schmitt, S. Rogers, and P. Yund, for useful comments on an earlier version of the manuscript. S. Rogers provided valuable statistical advice. K. Cray and M. M. Cray allowed me the use of their property in Dresden, Maine. S. Atkinson assisted in the field. I would also like to thank K. Eckelbarger, T. Miller, and the staff of the Darling Marine Center for providing lab space and facilitating work in Maine. Support for this research came from the UNO Faculty Development Fund, and the National Science Foundation (DEB 9419467 to PO), and (OCE-92-02805 to E Yund).


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Author:O'Neil, Pamela
Date:Feb 1, 1997
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