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Detecting heterozygosity — growth relationships: Howshould growth be computed?Walter J. Diehl a & Michele C. Audo aa Department of Biological Sciences, PO Drawer GY, Mississippi State University, Mississippi,39762, USAPublished online: 20 Feb 2012.

To cite this article: Walter J. Diehl & Michele C. Audo (1995): Detecting heterozygosity — growth relationships: How shouldgrowth be computed?, Ophelia, 43:1, 1-13

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OPHELIA 43 (1): 1-13 (September 1995)

DETECTING HETEROZYGOSITY ­GROWTH RELATIONSHIPS:

HOW SHOULD GROWTH BE COMPUTED?

J11alterJ Diehfl & MicheIe C. AudoDepartment of Biologieal Seiences, PO Drawer GY,Mississippi State University, Mississippi 39762, USA

Ito whom correspondenee should be addressed

ABSTRACT

Individual multiloeus heterozygosity (MLH) for eight polymorphie allozyme loei and weekly freshweight (FW) over four weeks were measured in juvenile earthworrns (Eiseniafetida, n = 85) raisedin a moderately stressful environment (25°C, 3 ml HzO/g peat moss). Initial FW of earthwormswas 6.6±0.4 mg. The growth eurve of heterozygotes (MLH ~ 4) diverged from that ofhomozygotes (MLH :5 3) throughout the experiment after whieh weight of heterozygotes andhomozygotes was 106.1±6.0 and 71.1±4.6 mg, respectively. MLH-growth eurves were cornpared forseveral cornputations of growth. MLH-FW eurves were signifieantiy positive four of the five timesweight was measured. MLH-~ FW/week curves were signifieantiy positive in three offour weeklyintervals. MLH-standardized ~ FW/week eurves (i.e. adjusted for initial FW) were signifieantiypositive in two offour weekly intervals. MLH-instantaneous growth rate eurves were signifieantiypositive in only one of four intervals because of eontrasting autocorrelations between FW andMLH ( +) vs. FW and instantaneous growth (-). The best eomputations of growth for deteetingrelationships with MLH in populations with divergent sizes are size adjusted for differenees in ageand change in size per unit time.

INTRODUCTION

Relationships between multilocus heterozygosity (MLH) and individual fitnessor some surrogate thereof have been sought in numerous species of plants andanimals (reviewed by Mitton & Grant 1984, Zouros & Foltz 1987). Positive corre­lations have been established between MLH and survivorship, fecundity orgrowth in large, panmictic populations of many, but not all, species examined.Growth is the most commonly examined variable for correlation with MLH.

Interpreting the relationship between MLH and growth may depend on themethod chosen to estimate growth in a particular data set. This choice is not trivi­al forthree reasons. First, some (perhaps much) ofthe variance in growth may beattributed to size prior to the time growth is measured. Second, growth may bea positive or negative function ofsize depending on how and when growth is com-

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2 WAr;fER J. DlEHL & MICHELE C. AUDO

puted. Third, size does not usually increase linearly with time. Differences in in­terpretation also derive from the fact that terms such as size (length or mass),growth, and growth rate, are often used interchangeably, even though strictlyspeaking, they refer to different aspects of a common concept.

The most frequently used indicator of growth to be correlated with MLH in aspecies is size of an individual (length, mass, etc.) at the time of collection. Oftensize is adjusted for differences in age (e.g. Singh & Zouros 1978, Koehn & Gaffney1984), and sometimes it is not (e.g. Teska et al. 1990, Diehl & Biesiot 1994). Theformer is desirable, but not always necessary, to distinguish the effects of growthon size from the effects of age on size and thereby improve the chances of detect­ing MLH-size relationships. The frequent use of size as an indicator of growth isusually a matter of expediency since it may be quite difficult to obtain measure­ments of growth directly in many species.

In some cases, direct measurements of growth are available from field orlaboratory studies, and thus different computations of growth rates are possible,Estimates of growth rate fall into three broad categories: (1) change in size of anorganisrn per unit time (e.g. Diehl et al. 1986, Bush et al. 1987, Diehl 1988), (2)change in size per unit time adjusted for initial size (e.g. Green et al. 1983, Koehnet al. 1988, Scott & Koehn 1990), and (3) instantaneous change in size (k =

(dW/dt) (l/W), e.g. JI2Jrgensen 1992). Deterrnining wh ich ofthese computationsis most appropriate for detecting and evaluating relationships between multilo­cus heterozygosity and growth rate has not been done. Nevertheless, conclusionsof some experiments (e.g. Diehl et al. 1986) have been questioned (jargensen1992) based solelyon differences in the method used to compute growth rate.Thus, it is appropriate to evaluate the consequences ofcomputing growth by vari­ous formulae as they apply to the MLH-growth phenomenon.

We have generated a data set in which multilocus heterozygosity data havebeen collected in concert with multiple individual size measurements over a fourweek period early in ontogeny ofthe earthworm EiseniaJetida. We compared thelikelihood of detecting MLH-growth relationships, and the patterns thereof, us­ing four different methods for computing growth: (1) fresh weight at time of sam­pling, (2) change in fresh weight per unit time, (3) change in fresh weight per unittime standardized by initial weight, and (4) instantaneous change in fresh weight.Although E.Jetida is not a marine species, we expect that any conclusions drawnfrom this study can be generalized to other species which show exponentialgrowth early in ontogeny. In comparing these methods, we have limited the dis­cussion to their effects on MLH-growth correlations among individuals, not oncorrelations between average growth and heterozygosity classes.

We thank P. M. Gaffney for useful comments on this manuscript. This work was supported by NSFgrant DEB-9221094 to WJD and by Sigma Xi Grant-in-Aid of Research to MCA.

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HETEROZYGOSITY-GROWTH RELATIONSHIPS

METHODS AND MATERIALS

3

Earthworms were obtained from a population of E. Jetida that has been main­tained in the greenhouse of the Department of Biological Seiences at MississippiState University, USA, since 1987 as described by Diehl (1988) and Diehl andWilliams (1992). The population is estimated to contain about 50,000 earth­worms (5,000 adults) at present (Spring 1994). Juvenile earthworms (n = 85)were obtained about 2 weeks after hatching(mean fresh weight = 6.60±0.37 mg)and were raised at room temperature (25 DC) in individual plastic cups (75 ml)containing peat moss whose moisture content constituted a moderately stressfulenvironment (3 ml H 20/g dry neutral peat moss). Fresh weight (FW) was rneas­ured weekly for four weeks; earthworms were fed a mixture of commercial earth­worm food and soy-protein baby formula ad libitum (Diehl & Williams 1992).The plastic containers were covered with foil to prevent evaporation and the peatmoss mixture was changed weekly when FW was measured. The final FW ofearthworms raised under moderate stress was about 50 % of that ofcontrol earth­worms raised in 4 ml H 20/g dry neutral peat moss. Comparisons of MLH­growth relationships among control and stressful treatments are discussed byAudo and Diehl (in press).

After final fresh weights were measured, the portion ofthe earthworm posteri­or to the clitellum was removed and stored at -80 DC until electrophoresis couldbe performed. The genotypes of 8 polymorphie loci were resolved by horizontalstarch-gel electrophoresis. The following enzymes (with locus abbreviation andE. C. number) were run on a Tris-maleate buffer system, pH 7.4 (Selander et al.1971): phosphoglucomutase (Pgm, EC 5.4.2.2), 6-phosphogluconate de­hydrogenase (Pgd, EC 1.1.1.44), hydroxybutyrate dehydrogenase (Hbd, EC1.1.1.30). The following enzymes were run on a Tris-borate-EDTA buffer system,pH 8.7 (Pasteur et al. 1988): malate dehydrogenase (Mdh, EC 1.1.1.37), glycer­ol-3-phosphate dehydrogenase (Gpd2, EC 1.1.1.8),hexokinase (Hk2, EC 2.7.1.1),mannose-6-phophate isomerase (Mpi, EC 5.3.1.8), alanyl amino peptidase (Aap,EC 3.4.1.-). Staining recipes for allloci except Aap and Hbd are given in Diehland Williams (1992). Aap was stained according to Garton et al. (1984); Hbd wasstained according to Pasteur et al. (1988).

For each locus, earthworms were scored 0 ifhomozygous and 1 ifheterozygous.Multilocus heterozygosity (MLH) was computed as the sum ofthe individual 10­cus scores for eight loci. Growth was computed four ways and for all possible in­tervals oftime: (1) fresh weight at time ofsampling, (2) change in fresh weight perunit time, (3) change in weight standardized by initial weight (residuals from aregression of change in weight on initial weight = standardized change inweight), (4) instantaneous change in weight (100*[ln(wtt+ 1) -In (wtt)]/unit time;Weatherly & Gill1987). In all computations, initial weight refers to the weight ofindividuals at the beginning of astated time interval for estimating growth. Time

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4 WALTER J. DIEHL & MICHELE C. AUDO

•

-ß'MLH ~ 3

.MLH ~ 4

200, •

150.-rnE--.-~

rn'ä) 100$:~cnQl.....L.L

431o 2

Time (weeks)Fig. 1. Fresh weight as a function oftime in young Eiseniafetida sorted by degree ofheterozygosity.Heterozygous earthworms (MLH 2: 4) are represented by circles and solid line; homozygousearthworms (MLH S 3) are represented by triangles and dashed line. The lines were fit according

to the formula: ln(y) = a+b(x), using Harvard Graphicsf 3.0.

was measured in weeks. Associations between various computations of growthand between growth and MLH were determined by product-moment correla­tions. Predictive relationships were determined by linear regressions using theBIOM package of statistical programs (Sokal & Rohlf 1981). The figure wasgenerated using Harvard Graphics (R) 3.0. All data are reported as means (± SE)unless otherwise noted.

The large number ofcorrelations computed in this study may lead to Type I er­rors in reporting significant relationships if the results are considered as simul­taneous events. It is the intention ofthis paper to evaluate the chance ofdetectingan MLH-growth relationship as if one chose a single computation of growth thatwas measured over a single time interval and applied to a single size-range of in­dividuals. For this reason, results are presented and discussed as if Type I errorsattributable to multiple statistical tests would not occur. Nevertheless for con­venience, the results of sequential Bonferroni tests (o = 0.05; Rice 1989) thatcontrol Type I errors in simultaneous determinations within each set of correla­tions are also given.

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HETEROZYGOSITY-GROWTH RELATIONSHIPS 5

Table 1. Matrix of correlation coefficients between computations ofgrowth (FW, fresh weight at be­ginning ofinterval; Ä FW, change in weight; Std. Ä FW, change in weight standardized for initialweight; Instan. Ä FW, instantaneous change in weight; see text) for each weekly interval. All signifi­cant correlations were retained after sequential Bonferroni tests (01 = 0.05, k = 4; Rice 1989) were

applied to each set of correlations. N = 85.

FW

ÄFW

Std. Ä FW

Interval ÄFW Std. Ä FW Instan. Ä FW(weeks)

1 0.596"· < 0.001 NS 0.004 NS2 0.735·" < 0.001 NS -0.446···3 0.410··· < 0.001 NS -0.319 ••

4 0.671··· < 0.001 NS -0.462·"

1 - 0.803' ,. 0.728" ,

2 - 0.678'" 0.178 NS3 - 0.912"· 0.657'"4 - 0.741·" 0.250 •

1 - 0.904" ,

2 - 0.747·"3 - 0.863·'·4 - 0.757'·'

NS, not significant; , P < 0.05; ., P < 0.01; '" P < 0.001.

RESULTS

Whole-animal fresh weight appeared to increase exponentially with time inyoung Eiseniafetida (Fig. 1). At each point, more heterozygous earthworms (MLH~ 4, N = 40) had a significantly greater fresh weight (P < 0.05) than less heter­ozygous earthworms (MLH ~ 3, N = 45). The difference in fresh weight be­tween the two groups continued to diverge throughout the experiment. By theend offourweeks, the fresh weight ofheterozygous earthworms (106.1 ± 6.0 mg)was 50% greater than that ofhomozygous earthworms (71.1 ± 4.6 mg).

A matrix of correlation coefficients between computations of growth is shownin Table 1. As expected, change in fresh weight was correlated positively (P <0.001) with fresh weight in all weekly intervals. Standardized change in weightwas not correlated (P > 0.05) with fresh weight in any interval; these correlationcoefficients were the lowest in the matrix. Instantaneous change in fresh weightwas not correlated (P > 0.05) with fresh weight in the first weekly interval, butwas correlated negatively (P < 0.01) with fresh weight in subsequent intervals.For the most part, the remaining correlations among change in fresh weight,standardized change in fresh weight, and instantaneous change in fresh weightwere positive and significant (P < 0.05).

Where significant MLH-growth relationships occurred in the sample popula­tion, MLH was always correlated positively with individual growth regardless ofthe way growth was computed (Tables 2-6). Growth measured as fresh weight at

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6 WALTER J. DIEHL & MICHELE C. AUDO

Table 2. Equations from linear regressions where x = MLH and y = growth computed as freshweight (mg) at the time of sampling, correlation coefficients, and significance for these relation­

ships without (P) and with the sequential Bonferroni test (P', a = 0.05, k = 5; Rice 1989).

Sarnple Time Equation r P P'

Week 0 y = 3.99 + 0.758 (x) 0.305 < 0.01 < 0.05

Week 1

Week2

Week3

Week4

y = 9.82 + 1.04 (x)

Y = 19.4 + 2.66 (x)

Y = 27.1 + 7.61 (x)

7 = 45.8 + 12.2 (x)

0.179

0.250

0.391

0.429

NS

< 0.05

< 0.001

< 0.001

NS

< 0.05

< 0.05

< 0.05

the time of sampling was correlated positively (P < 0.05) with MLH at four offive possible sampie dates (Table 2). MLH explained an average 12 % ofthe vari­ation in fresh weight. Growth measured as change in fresh weight per unit timewas correlated positively (P < 0.05) with MLH in three offour weekly intervals(Table 3) and was correlated positively with MLH in all possible 2-, 3-, and4-week intervals. Thus among all possible time fntervals, there was a 90 %chance of detecting an MLH-growth relationship if growth was computed aschange in weight. MLH explained an average 13 % ofthe variation in change infresh weight. Growth measured as change in fresh weight per unit time stan­dardized by initial fresh weight was correlated positively (P < 0.05) with MLHin two offour weekly intervals (Table 4) and was correlated positively with MLHin five ofsix possible 2-, 3-, and 4-week intervals. There was a 70% chance of de­tecting an MLH-growth relationship if growth was computed as standardizedchange in weight. MLH explained an average 8 % of the variation in stan­dardized change in fresh weight. Growth measured as instantaneous change infresh weight per unit time was correlated positively (P < 0.05) with MLH in oneoffourweekly intervals (Table 5) and was correlated positively with MLH inthree ofsix possible 2-,3-, and 4-week intervals. There was only a 40% chanceofdetecting an MLH-growth relationship if growth was computed as instantane-

Table 3. Equations from linear regressions where x = MLH and y = growth computed as changein fresh weight per unittime (mg/week), correlation coefficients, and significance for these relation­

ships without (P) and with the sequential Bonferroni test (P', a = 0.05, k = 4; Rice 1989).

Time Interval Equation r P P'

Week 1 - Week 0

Week 2 - Week 1

Week 3 - Week 2

Week 4 - Week 3

y = 5.83 + 0.282 (x)

y = 9.58 + 1.62 (x)

y = 7.68 + 4.95 (x)

7 = 18.7 + 4.57 (x)

0.071 NS NS

0.289 < 0.01 < 0.05

0.396 < 0.001 < 0.05

0.402 < 0.001 < 0.05

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HETEROZYGOSITY-GROWTH RELATIONSHIPS 7

Table 4. Equations from linear regressions where x = MLH and y = standardized change inweight computed as the residuals from a linear regression of change in weight on initial weight perunit time (residual mg/week), correlation coefficients, and significance for these relationships with-

out (P) and with the sequential Bonferroni test (P', a = 0.05, k = 4; Rice 1989).

Time Interval Equation r P P'

Week1-WeekO y=1.52-0.443(x) -0.138 NS NS

Week 2 - Week 1

Week 3 - Week 2

Week 4 - Week 3

y = -3.04 + 0.885 (x)

Y = -12.6 + 3.67 (x)

7 = -5.46 + 1.59 (x)

0.232 < 0.05 NS

0.321 < 0.01 < 0.05

0.189 NS NS

ous change in weight. MLH explained an average 6 % of the variation in instan­taneous change in fresh weight. The chances of detecting an MLH-growth rela­tionship depended greatly on the method used to compute growth. For eachmethod, computing growth over a time period greater than one week improvedthe chances of detecting these relationships.

Sampling a limited size range of earthworms (simulated by sorting earth­worms into quartiles based on weight at the beginning ofthe experiment) affect­ed the ability to detect MLH-growth relationships differently depending on themethod used to compute growth. There were no significant MLH-growth rela­tionships (P > 0.05) within any size quartile in the first l-week interval (data notshown). Over a 4-week interval, a positive MLH-growthrelationship was detect­ed within only two of four size quartiles for growth computed as either change inweight or standardized change in weight, although this could likely be improvedwith greater sarnple sizes (Table 6). However, for growth computed as instan­taneous change in weight over a 4-week interval, a positive MLH-growth rela­tionship was detected within three of four size quartiles. If the size range of in­dividuals is limited, extending the period for computing growth may improve thechances of detecting positive MLH-growth relationships, as it did when sizeranges were not limited.

Table 5. Equations from linear regressions where x = MLH and y = instantaneous growth com­puted as 100*[ln(wtt+1) -ln(wtt)] per unit time (week), correlation coefficients, and significancefor these relationships without (P) and with the sequential Bonferroni test (P', a = 0.05, k = 4; Rice

1989).

Time Interval Equation r P P'

Week 1 - week 0 y = 80.6 - 4.20 (x) -0.180 NS NS

Week 2 - Week 1 y = 69.7 + 2.88 (x) 0.167 NS NS

Week 3 - Week 2 y = 44.6 + 5.31 (x) 0.250 < 0.05 NS

Week 4 - Week 3 y = 52.9 - 0.247 (x) -0.024 NS NS

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8 WALTER J. DIEHL & MICHELE C. AUDO

Examining group variables for the 4-week growth interval among quartilesproduced apparently conflicting patterns among different computations ofgrowth (Table 6). Patterns of some group variables (e.g. mean MLH, meanchange in weight) were consistent with the positive MLH-growth relationshipsexisting among individuals. Both mean MLH and mean growth computed aschange in weight increased with successive size quartiles. Mean MLH ofthe topsize quartile was significantly greaterthan that ofthe bottom quartile (t = 2.845,df = 40, P < 0.01)and mean change in weight of the top quartile was significant­ly greater than that ofthe bottom quartile (t = 8.673, df = 40, P < 0.001). Pat­terns of other group variables (e.g. mean standardized change in weight, meaninstantaneous change in weight) were superficially inconsistent with such posi­tive relationships (Table 6). Meanstandardized change in weight did not changemonotonically with successive size quartiles and mean instantaneous change inweight decreased with successive size quartiles. The mean instantaneous growthrate of the top size quartile was significantly less than that of the bottom quartile(t = -4.116, df = 40, P < 0.001). The differences in patterns for variable meansamong quartiles derive from predicted differences in relationships betweengrowth as computed and fresh weight, not from relationships between growth andMLH. This is especially true for computations of mean instantaneous growth.

DISCUSSION

This population of earthworms shows a very robust positive relationship betweenMLH and growth early in ontogeny. The ability to detect this relationship de­pends in part on the method chosen to compute growth. Each method has advan­tages and disadvantages.

Computing growth as size at time of sampling has the advantage of requiringonly one measurement to estimate growth and this may be all that is available. Itcan be an effective way to detect MLH-growth relationships. Also physiologicalprocesses usually vary with individual size, and ecological interactions may be af­fected by size. Thus, size is more likely to be important evolutionarily thangrowth rate per se. However, size is only an indirect estimate of growth and it mayinclude potential confounding effects of multiple age classes and numerous en­vironmental factors which should be taken into account if possible.

Computing growth as change in fresh weight over aperiod oftime has the ad­vantage of being the most effective way to detect MLH-growth relationships inthis and other experiments (Bush et al. 1987, Koehn et al. 1988). This occurs be­cause change in weight is usually a positive function of size during both exponen­tial and early non-exponential growth. IfMLH is correlated positively with bothinitial size and 'true growth' during a succeeding interval of time, then the corre­lation between MLH and change in weight incorporates both of these relation­ships. Computing growth in this way also eliminates some (but not all) of the mul-

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HETEROZYGOSITY-GROWTH RELATIONSHIPS 9

Table 6. MLH, initial weight (mg), 4-week growth rates (computed as in Tables 3-5) and correla-tions between MLH and individual growth rates for Eiseniafetida sorted into initial size quartiles.Bottom initial size quartile = 1; top initial size quartile = 4. N = 21in each quartile except 2 where

N = 22. Means (SE).

Change in Wt Standardized InstantaneousChange in Wt Change in Wt

Initial MLH Initial Growth r Growth r Growth rSize WeightQuartile

2.95 3.18 47.6 0.46 .~ -5.4 0.51 • 68.3 0.47 .~

(0.26) (0.14) (3.7) (3.3) (1.7)

2 3.29 4.87 70.6 0.04 NS 4.1 0.01 NS 67.2 0.07 NS(0.33) (0.09) (5.7) (5.6) (1.9)

3 3.50 6.94 88.8 0.29 NS 5.5 0.37 NS 65.2 0.4-3 .~

(0.29) (0.20) (5.5) (4.8) (1.2)

4 4.00 11.48 116.6 0.73 •• -4.5 0.58 •• 59.9 0.57 ••(0.26) (0.52) (7.0) (5.6) (1.2)

• P < 0.05; •• P < 0.01; ~ Not significant after sequential Bonferroni test (O! = 0.05, k = 4; Rice1989) was applied within each growth rate category.

tiple age or environmental effects usually by limiting the temporal component ofvariation in growth. However, it does require at least two measurements to esti­mate growth and these may not be available. Also change in size is not exclusivelyameasure ofgrowth rate since alarge component ofthe variance is still attributa­ble to initial size. Whether this is a problem depends on whether the primary goalis to detect relationships ofany sort with MLH or to test specific hypotheses con­cerning MLH and growth rate.

Computing growth as the standardized change in fresh weight over aperiod oftime is the only measure of growth rate that is usually independent of initial sizeregardless of when it is measured in ontogeny. Virtually all of the variance ingrowth is attributable to the change in size that occurs during the time intervalmeasured. It may be the most useful estimate of growth if understanding thecause and effect relationship between MLH and growth rate per se is a primarygoal. It also eliminates most potential confounding effects ofmultiple age classesand environmental factors ifthis cannot be done otherwise. However, it still re­quires at least two measurements to estimate growth and it is only moderatelyef­fective in detecting MLH-growth relationships because the 'benefits' ofpositiveMLH-size relationships are eliminated.

Instantaneous growth is usually correlated negatively with initial size duringexponential growth (Table 1, Weatherly & Gill 1987, J0rgensen 1990). Thenegative relationship is also seen as greater mean instantaneous growth rates ofbottom size quartiles (Tables 6, 7). Thus use ofinstantaneous growth may be in-

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10 WALTER J. DIEHL & MICHELE C. AUDO

effective in detecting MLH-growth relationships in samples with divergent ini­tial sizes because ofthe contrasting relationships between size and MLH (positiverelationship) and size and instantaneous growth rate (negative relationship). In­terpreting differences in instantaneous growth among individuals that have beeneffectively sorted into different size categories by time, selection, or experimentaldesign must be done cautiously. Since a positive MLH-size relationship accorn­plishes a similar degree ofsorting by MLH, this also limits the use of instantane­ous growth rate for evaluating MLH-growth relationships in whole populations.However, instantaneous growth may be useful in detecting MLH-growth rela­tionships in groups ofindividuals that sarnple a limited range of sizes comparedto that which exists in the entire cohort or population. Velocity of growth (dW/dt;Brody 1945, Warren 1971) may be a useful computation of growth that preservesthe exponential nature of early growth. During this time, velocity of growth in­creases with initial size and thus provides similar attributes and results as changein weight.

The contrasting relationships among MLH and size, MLH and change inweight, MLH and instantaneous change in weight, and the effects of sorting in­dividuals into size categories are at the heart of a dispute concerning whetherMLH is associated positively with growth in young Mytilus edulis G0rgensen1992). Table 7 shows data reported by Diehl et al. (1986) and re-computed byJ0r­gensen (1992) for at cohort of mussels that had been sorted into top and bottomsize quartiles to amplify and show indirectly the effects of MLH on oxygen con­sumption in starved and fed mussels. The patterns of mean MLH, change inweight and instantaneous change in weight in top and bottom size quartiles ofM.edulis are nearly identical to patterns for the same variables in E. fetida over a4-week interval reported here (Table 6). In both cases mean MLH and meanchange in weight is greater in the top quartile, whereas mean instantaneouschange in weight is greater in the bottom quartile. Also after the growth periodin both experiments, the percent differences in weight between individuals in thebottom and top quartiles were less than initial percent differences. J0rgensen(1992) suggested that the greater instantaneous growth in the bottom quartile ofM. edulis represented a burst ofcatch-up growth as individuals reached their biot­ic potential when they were placed in a more benign environment. From this, heconcluded that the homozygous mussels showed greater growth than the heter­ozygous mussels G0rgensen 1992). The same argument could be made for E. feti­da which were removed from a stock population where densities exceeded 10,000earthworms per m 2 and were allowed to grow in individual containers withoutcompetition. But since MLH was always associated positively with growth in E.fetida (including within quartiles), a greater instantaneous growth rate in a bot­tom size quartile must be consistent with positive MLH-growth relationships ingeneral, contrary to the conclusions ofjergensen (1992). This occurs because alower instantaneous growth rate is expected to occur in larger (i.e. more heterozy-

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HETEROZYGOSITY-GROWTH RELATIONSHIPS 11

Table 7. MLH, 72-day growth rates computed as change in dry weight (from Diehl et al. 1986) andinstantaneous change in dry weight (from]0rgensen 1992) for Mytilus edulis sorted into top and bot­tom size quartiles. N = 140in the bottom size quartile and N = 143 in the top size quartile. Means

(SE).

Initial Initial Change in InstantaneousSize Dry Weight DryWeight Change inQuartile MLH (mg) (mg/day) DryWeight

Bottom 25% 2.33- 0.22 0.84 7.8(0.22) (0.02)

Top 25% 2.58 b 3.30 1.30 4.7(0.20) (0.18)

"N = 95 (A subset ofindividuals was used to compute MLH); bN = 96.

gous) individuals once sufficient time has elapsed for sizes to diverge. Thushomozygous groups of earthworms, mussels, and presumably other organismsas well, remain the slower growing groups during early ontogeny, regardless ofthe potential for catch-up growth. The consequences ofMLH-growth relation­ships early in ontogeny on any such relationships later in ontogeny as individualsapproach asymptotic size are not yet known.

In conclusion, the method used to compute growtli affects the likelihood ofde­tecting MLH-growth relationships to some extent and should be chosen on thebasis of specific hypotheses that an experiment is designed to test. Without thiscontext, the concept of 'true' growth does not exist, and even in proper context,the concept of growth may remain ambiguous. However the choice of computa­tional method is not likely to explain the majority of cases in the literature whereMLH-growth relationships have been sought but not found. Most of thesestudies (e. g. Bricelj & Krause 1992, Hutchings & Ferguson 1992) have used sizeat the time ofsampling adjusted for age differences as estimators ofgrowth. Theyshould have shown positive relationships if computational methods alone affect­ed detection. Thus explanations for most non-significant MLH-growth relation­ships must be sought elsewhere. This work shows that due care must be used inevaluating growth of individuals for correlation with MLH particularly if (1)only a limited range ofsize classes is available by choice or default or (2) the sizesof individuals of similar age have diverged sufficiently that they effectively oc­cupy different stages in the ontogeny of a species. It also points out the difficultyin extrapolating a relationship among individuals from a relationship amonggroup means when it is the former information that is necessary to make a point.

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