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Estimates of Genetic Correlations Among Clinical Measures of the Eye
ESTIMATES O F G E N E T I C CORRELATIONS AMONG CLINICAL MEASURES O F T H E EYE B R U C E E. SPIVEY, M.D.,
A N D A. J A N E M A S H
San Francisco, California AND J O S E P H P. H E G M A N N , P H . D . Iowa City, Iowa
Correlations between measures of the eye and eye function can result from genetic or nongenetic (environmental) in fluences, or b o t h . 1 3 The finding that two measures are asso ciated permits only a limited amount of interpretation until one can distinguish between those that are purely environ mental in origin and those that are partly gene imposed. Determining the extent to which associated measures are genetical ly correlated can allow fuller interpreta tion and lead to specific hypotheses of what and how underlying processes me diate these associations. We report herein our first efforts to determine if genetic factors do contribute to the associations observed between cer tain ophthalmic clinical measures. S U B J E C T S AND M E T H O D S
Clinical procedures—We examined 163 families (parents and siblings) of children randomly selected from the local elemen tary school population; we include herein data for 118 family units, all those con-
From the Department of Ophthalmology, Pacific Medical Center (Dr. Spivey), the Smith-Kettlewell Institute of Visual Sciences, Institutes of. Medical Sciences (Ms. Mash), San Francisco; and the De partment of Zoology, University of Iowa (Dr. Heg mann), Iowa City. This study was supported in part by grants EY-00117 and 5P30-EY-01186 from the National Institutes of Health; by Research to Pre vent Blindness, Inc.: and by the Smith-Kettlewell Eye Research Foundation. Reprint requests to Bruce E. Spivey, M.D., Pacific Medical Center, P.O. Box 7999, San Francisco, CA 94120. 502
sisting of two or more offspring and both biological parents. All individuals were examined in a uni versity hospital eye clinic; a standard battery of ophthalmic and orthoptic tests was administered in accordance with an established protocol. We analyzed seven of these clinical measures as previously described 4 - 7 : spherical refractive error, corneal power, cover test, divergence break point (loss of fusion), divergence recovery point (recovery of fusion), con vergence break point, and convergence recovery point. Vergences were measured on an amblyoscope. 'Analytic procedures—Observed corre lations among the seven clinical test measures were calculated by the Pearson product-moment correlation. The calcula tion of genetic correlations among the clinical measures involved parent-off spring cross-covariance methods. 8 Where as covariance between two character istics is calculated by using measures of both characteristics from all individuals in a group (for example, height and weight of parents), cross-covariance is calculated by using measures of one char acteristic from individuals in one group and measures of the second characteristic from individuals in another group (for example, height of parents and weight of offspring, or weight of parents and height of offspring). The calculation of genetic correlation 9 involves a ratio of (1) the degree of association between two char acteristics (XandY) when one is measured on parents and the other on their off-
AMERICAN JOURNAL O F OPHTHALMOLOGY 88:502-505, 1979
VOL. 88, NO. 3, PART I
503
GENETIC CORRELATIONS
spring (the cross-covariance or CovXY), and (2) the degree to which offspring resemble parents (parent-offspring covariance) for each trait (Cov XX and CovYY). The formula for a genetic corre lation is: Cov X Y / V [ ( C o v XX) (Cov YY)]. For the numerator, there are two ways to estimate the cross-covariance: (1) trait X for parents with trait Y for off spring, and (2) trait Y for parents with trait X for offspring. In most cases, the value used is the geometric mean of the two estimates (that is, the square root of the product of the two estimates); if the estimates differ in sign, the arithmetic mean is used. RESULTS
Significant (P<.05) observed correla tions were indicated between spherical refractive error and corneal power (nega tive), between spherical refractive error and cover test measure (positive), between corneal power and cover test measure (positive), between cover test
measure and divergence recovery point (positive), and between divergence and convergence recovery point (positive) (Table). Significant (P<.05) genetic associations were indicated between corneal power and cover test measure (negative), be tween corneal power and divergence re covery point (negative), between diver gence and convergence recovery points (positive), between divergence break and recovery points (positive), and between convergence break and recovery points (positive). DISCUSSION
Corneal power and cover test mea sure—The heritability of corneal power in this population was previously re ported 7 to be 0.86 ± 0.08, indicating that differences among individuals for measures of corneal power are caused largely by gene differences. Many of those gene differences have a simultane ous influence on cover test measure. Be-
TABLE M E A N S ± STANDARD ERRORS OF OBSERVED CORRELATIONS AND GENETIC CORRELATIONS
Correlations Clinical Variables Sphere and Corneal power Cover test measure Divergence recovery point Convergence recovery point Corneal power and Cover test measure Divergence recovery point Convergence recovery point Cover test measure and Divergence recovery point Convergence recovery point Divergence recovery point and convergence recovery point Divergence break point and divergence recovery point Convergence break point and convergence recovery point *P < .05. f P < .01.
Observed
Genetic
-0.14d:0.07* 0.21dt0.07* -0.07:!t0.07 -0.09d;0.07
0.22±0.13 0.21±0.26 -0.16±0.22 0.17±0.12
-O.Md:0.07* 0.09dt0.07 -0.12:!:0.07
-0.95±0.36* -0.21±0.10* -0.08±0.06
0.59:!t0.06* -0.09d:0.07
0.23±0.20 -0.12±0.12
0.20d:0.07*
0.20±0.09*
0.80d:0.05f
0.43±0.15t
0.93 d:0.03f
0.97±0.01f
504
AMERICAN JOURNAL OF OPHTHALMOLOGY
cause a relatively small proportion of the observed variability for cover test mea sures is caused by genetic variability (heritability is 0.27 ± 0.10 5 ), genes in common for the two may account almost entirely for gene influence on cover test measures. Specifically, the genetic correlation be tween corneal power and cover test mea sures (-0.95) indicates that 9 5 % of gene differences resulting in individual (ob served) differences for the cover test mea sure also result in individual differences for corneal power. This genetic correlation predicts that parents who are above the population mean for corneal power will have off spring who will be below the mean for cover test measure, that is, have a more lateral deviation tendency (since an exodeviation was assigned a negative value and esodeviation a positive value in this study). Indeed, in clinical experience, individ uals with a higher corneal curvature tend to be more myopic, and to have an exodeviation rather than esodeviation. Also, because an undercorrected myopic indi vidual requires less accommodation to focus at near than do hyperopic persons, the myopic individual should display less associated accommodative convergence. When excessive amounts of accommoda tive convergence are elicited, an esodevi ation can result. Corneal power and divergence recovery point—Gene differences which increase corneal power also tend to decrease diver gence recovery point. We adjusted the observed amplitudes of all the vergence points for the dissociated position, thus, a vergence measure reflects the amount of rotation beyond the basic (dissociated) deviation. Gene differences which in crease corneal power and impose a ten dency for an esodeviation should also decrease divergence recovery point if in dividuals are less able to control eye movement in the direction of their usual dissociated position. Genes which influ
SEPTEMBER, 1979
ence cover test measure should also influ ence divergence recovery point in the same direction, unless those genes com mon to both these measures as well as corneal power are a trivial fraction of the total. In our study, the genetic correlation between these two variables was directionally consistent with this expectation (that is, a positive correlation), but the degree of association was not statistically significant." Recovery points—The genetic associa tion between the divergence and conver gence recovery point may reflect the in volvement of the same mechanism of sen sory response to retinal fusional stimuli, and a common motor mechanism. Break and recovery points—The ob served correlations between the clinical measures of the amplitude at the break point (loss of fusion) and the amplitude at the recovery point for the two vergences were 0.80 for divergence and 0.93 for convergence. The genetic correlations are 0.43 and 0.97 for divergence and conver gence, respectively. Break point and re covery point amplitudes for convergence are dependent on virtually the same gene differences and should be reasonably equivalent indices of fusional conver gence ability. With divergence, however, the two measures appear to reflect only partly a common function and may be indexing somewhat different underlying physiologic mechanisms. The magnitude and even the sign of a genetic correlation cannot be determined from the observed correlation of mea sured values. Genetic and nongenetic sources of association can influence char acteristics through either the same or dif ferent mechanisms. A genetic correlation between characteristics but no significant observed correlation indicates that nongenetic sources obscure the genetic cor relation and influence the two charac teristics through a different underlying mechanism. 8 Investigation of genetic correlations can lead to a better under-
V O L . 88, N O . 3 , P A R T I
GENETIC CORRELATIONS
standing of physiologic organization and development. SUMMARY
In a quantitative genetic investigation of seven clinical tests, five pairs were significantly correlated: (1) cover test measures and corneal power, (2) corneal power and divergence recovery points, (3) convergence and divergence recovery points, (4) divergence break and recovery points, and (5) convergence break and recovery points. Common genes may ac count entirely for the gene influence on cover test measure; thus, parents who are above the population mean for corneal power will have offspring with a tenden cy toward an exodeviation (phoria). The two convergence amplitudes may depend on the same gene differences, whereas the two divergence amplitudes only partly reflect a common function, suggesting that they may be indexing somewhat different underlying physio logic mechanisms.
505
REFERENCES 1. Nakajima, A.: Quantitative genetics in ophthal mology. In Proceedings of the XX International Congress of Ophthalmology, Munich, 14-19 August 1966, International Congress series 146. Amster dam, Excerpta Medica, 1966, p. 1111. 2. Sorsby, A., Leary, G. A., and Fraser, G. R.: Family studies on ocular refraction and its compo nents. J. Med. Genet. 3:269, 1966. 3. Young, F. A.: An estimate of the hereditary component of myopia. Am. J. Optom. Physiol. Opt. 35:337, 1958. 4. Hegmann, J. P., Mash, A. J., and Spivey, B. E.: Genetic analysis of human visual parameters in populations with varying incidences of strabismus. Am. J. Hum. Genet. 26:549, 1974. 5. Mash, A. J., Hegmann, J. P., and Spivey, B. E.: Genetic analysis of cover test measures and AC/A ratio in populations with varying incidences of strabismus. Br. J. Ophthalmol. 59:23, 1975. 6. : Genetic analysis of vergence measures in populations with varying incidences of strabis mus. Am. J. Ophthalmol. 79:978, 1975. 7. : Genetic analysis of indices of corneal power and corneal astigmatism in human popula tions with varying incidences of strabismus. Invest. Ophthalmol. 14:826, 1975. 8. Falconer, D. S.: An Introduction to Quantita tive Genetics. Edinburgh, Oliver and Boyd, 1960, pp. 104-185. 9. Spivey, B. E.: Quantitative genetics and clini cal medicine. Trans. Am. Ophthalmol. Soc. 74:661, 1976.
A N D A. J A N E M A S H
San Francisco, California AND J O S E P H P. H E G M A N N , P H . D . Iowa City, Iowa
Correlations between measures of the eye and eye function can result from genetic or nongenetic (environmental) in fluences, or b o t h . 1 3 The finding that two measures are asso ciated permits only a limited amount of interpretation until one can distinguish between those that are purely environ mental in origin and those that are partly gene imposed. Determining the extent to which associated measures are genetical ly correlated can allow fuller interpreta tion and lead to specific hypotheses of what and how underlying processes me diate these associations. We report herein our first efforts to determine if genetic factors do contribute to the associations observed between cer tain ophthalmic clinical measures. S U B J E C T S AND M E T H O D S
Clinical procedures—We examined 163 families (parents and siblings) of children randomly selected from the local elemen tary school population; we include herein data for 118 family units, all those con-
From the Department of Ophthalmology, Pacific Medical Center (Dr. Spivey), the Smith-Kettlewell Institute of Visual Sciences, Institutes of. Medical Sciences (Ms. Mash), San Francisco; and the De partment of Zoology, University of Iowa (Dr. Heg mann), Iowa City. This study was supported in part by grants EY-00117 and 5P30-EY-01186 from the National Institutes of Health; by Research to Pre vent Blindness, Inc.: and by the Smith-Kettlewell Eye Research Foundation. Reprint requests to Bruce E. Spivey, M.D., Pacific Medical Center, P.O. Box 7999, San Francisco, CA 94120. 502
sisting of two or more offspring and both biological parents. All individuals were examined in a uni versity hospital eye clinic; a standard battery of ophthalmic and orthoptic tests was administered in accordance with an established protocol. We analyzed seven of these clinical measures as previously described 4 - 7 : spherical refractive error, corneal power, cover test, divergence break point (loss of fusion), divergence recovery point (recovery of fusion), con vergence break point, and convergence recovery point. Vergences were measured on an amblyoscope. 'Analytic procedures—Observed corre lations among the seven clinical test measures were calculated by the Pearson product-moment correlation. The calcula tion of genetic correlations among the clinical measures involved parent-off spring cross-covariance methods. 8 Where as covariance between two character istics is calculated by using measures of both characteristics from all individuals in a group (for example, height and weight of parents), cross-covariance is calculated by using measures of one char acteristic from individuals in one group and measures of the second characteristic from individuals in another group (for example, height of parents and weight of offspring, or weight of parents and height of offspring). The calculation of genetic correlation 9 involves a ratio of (1) the degree of association between two char acteristics (XandY) when one is measured on parents and the other on their off-
AMERICAN JOURNAL O F OPHTHALMOLOGY 88:502-505, 1979
VOL. 88, NO. 3, PART I
503
GENETIC CORRELATIONS
spring (the cross-covariance or CovXY), and (2) the degree to which offspring resemble parents (parent-offspring covariance) for each trait (Cov XX and CovYY). The formula for a genetic corre lation is: Cov X Y / V [ ( C o v XX) (Cov YY)]. For the numerator, there are two ways to estimate the cross-covariance: (1) trait X for parents with trait Y for off spring, and (2) trait Y for parents with trait X for offspring. In most cases, the value used is the geometric mean of the two estimates (that is, the square root of the product of the two estimates); if the estimates differ in sign, the arithmetic mean is used. RESULTS
Significant (P<.05) observed correla tions were indicated between spherical refractive error and corneal power (nega tive), between spherical refractive error and cover test measure (positive), between corneal power and cover test measure (positive), between cover test
measure and divergence recovery point (positive), and between divergence and convergence recovery point (positive) (Table). Significant (P<.05) genetic associations were indicated between corneal power and cover test measure (negative), be tween corneal power and divergence re covery point (negative), between diver gence and convergence recovery points (positive), between divergence break and recovery points (positive), and between convergence break and recovery points (positive). DISCUSSION
Corneal power and cover test mea sure—The heritability of corneal power in this population was previously re ported 7 to be 0.86 ± 0.08, indicating that differences among individuals for measures of corneal power are caused largely by gene differences. Many of those gene differences have a simultane ous influence on cover test measure. Be-
TABLE M E A N S ± STANDARD ERRORS OF OBSERVED CORRELATIONS AND GENETIC CORRELATIONS
Correlations Clinical Variables Sphere and Corneal power Cover test measure Divergence recovery point Convergence recovery point Corneal power and Cover test measure Divergence recovery point Convergence recovery point Cover test measure and Divergence recovery point Convergence recovery point Divergence recovery point and convergence recovery point Divergence break point and divergence recovery point Convergence break point and convergence recovery point *P < .05. f P < .01.
Observed
Genetic
-0.14d:0.07* 0.21dt0.07* -0.07:!t0.07 -0.09d;0.07
0.22±0.13 0.21±0.26 -0.16±0.22 0.17±0.12
-O.Md:0.07* 0.09dt0.07 -0.12:!:0.07
-0.95±0.36* -0.21±0.10* -0.08±0.06
0.59:!t0.06* -0.09d:0.07
0.23±0.20 -0.12±0.12
0.20d:0.07*
0.20±0.09*
0.80d:0.05f
0.43±0.15t
0.93 d:0.03f
0.97±0.01f
504
AMERICAN JOURNAL OF OPHTHALMOLOGY
cause a relatively small proportion of the observed variability for cover test mea sures is caused by genetic variability (heritability is 0.27 ± 0.10 5 ), genes in common for the two may account almost entirely for gene influence on cover test measures. Specifically, the genetic correlation be tween corneal power and cover test mea sures (-0.95) indicates that 9 5 % of gene differences resulting in individual (ob served) differences for the cover test mea sure also result in individual differences for corneal power. This genetic correlation predicts that parents who are above the population mean for corneal power will have off spring who will be below the mean for cover test measure, that is, have a more lateral deviation tendency (since an exodeviation was assigned a negative value and esodeviation a positive value in this study). Indeed, in clinical experience, individ uals with a higher corneal curvature tend to be more myopic, and to have an exodeviation rather than esodeviation. Also, because an undercorrected myopic indi vidual requires less accommodation to focus at near than do hyperopic persons, the myopic individual should display less associated accommodative convergence. When excessive amounts of accommoda tive convergence are elicited, an esodevi ation can result. Corneal power and divergence recovery point—Gene differences which increase corneal power also tend to decrease diver gence recovery point. We adjusted the observed amplitudes of all the vergence points for the dissociated position, thus, a vergence measure reflects the amount of rotation beyond the basic (dissociated) deviation. Gene differences which in crease corneal power and impose a ten dency for an esodeviation should also decrease divergence recovery point if in dividuals are less able to control eye movement in the direction of their usual dissociated position. Genes which influ
SEPTEMBER, 1979
ence cover test measure should also influ ence divergence recovery point in the same direction, unless those genes com mon to both these measures as well as corneal power are a trivial fraction of the total. In our study, the genetic correlation between these two variables was directionally consistent with this expectation (that is, a positive correlation), but the degree of association was not statistically significant." Recovery points—The genetic associa tion between the divergence and conver gence recovery point may reflect the in volvement of the same mechanism of sen sory response to retinal fusional stimuli, and a common motor mechanism. Break and recovery points—The ob served correlations between the clinical measures of the amplitude at the break point (loss of fusion) and the amplitude at the recovery point for the two vergences were 0.80 for divergence and 0.93 for convergence. The genetic correlations are 0.43 and 0.97 for divergence and conver gence, respectively. Break point and re covery point amplitudes for convergence are dependent on virtually the same gene differences and should be reasonably equivalent indices of fusional conver gence ability. With divergence, however, the two measures appear to reflect only partly a common function and may be indexing somewhat different underlying physiologic mechanisms. The magnitude and even the sign of a genetic correlation cannot be determined from the observed correlation of mea sured values. Genetic and nongenetic sources of association can influence char acteristics through either the same or dif ferent mechanisms. A genetic correlation between characteristics but no significant observed correlation indicates that nongenetic sources obscure the genetic cor relation and influence the two charac teristics through a different underlying mechanism. 8 Investigation of genetic correlations can lead to a better under-
V O L . 88, N O . 3 , P A R T I
GENETIC CORRELATIONS
standing of physiologic organization and development. SUMMARY
In a quantitative genetic investigation of seven clinical tests, five pairs were significantly correlated: (1) cover test measures and corneal power, (2) corneal power and divergence recovery points, (3) convergence and divergence recovery points, (4) divergence break and recovery points, and (5) convergence break and recovery points. Common genes may ac count entirely for the gene influence on cover test measure; thus, parents who are above the population mean for corneal power will have offspring with a tenden cy toward an exodeviation (phoria). The two convergence amplitudes may depend on the same gene differences, whereas the two divergence amplitudes only partly reflect a common function, suggesting that they may be indexing somewhat different underlying physio logic mechanisms.
505
REFERENCES 1. Nakajima, A.: Quantitative genetics in ophthal mology. In Proceedings of the XX International Congress of Ophthalmology, Munich, 14-19 August 1966, International Congress series 146. Amster dam, Excerpta Medica, 1966, p. 1111. 2. Sorsby, A., Leary, G. A., and Fraser, G. R.: Family studies on ocular refraction and its compo nents. J. Med. Genet. 3:269, 1966. 3. Young, F. A.: An estimate of the hereditary component of myopia. Am. J. Optom. Physiol. Opt. 35:337, 1958. 4. Hegmann, J. P., Mash, A. J., and Spivey, B. E.: Genetic analysis of human visual parameters in populations with varying incidences of strabismus. Am. J. Hum. Genet. 26:549, 1974. 5. Mash, A. J., Hegmann, J. P., and Spivey, B. E.: Genetic analysis of cover test measures and AC/A ratio in populations with varying incidences of strabismus. Br. J. Ophthalmol. 59:23, 1975. 6. : Genetic analysis of vergence measures in populations with varying incidences of strabis mus. Am. J. Ophthalmol. 79:978, 1975. 7. : Genetic analysis of indices of corneal power and corneal astigmatism in human popula tions with varying incidences of strabismus. Invest. Ophthalmol. 14:826, 1975. 8. Falconer, D. S.: An Introduction to Quantita tive Genetics. Edinburgh, Oliver and Boyd, 1960, pp. 104-185. 9. Spivey, B. E.: Quantitative genetics and clini cal medicine. Trans. Am. Ophthalmol. Soc. 74:661, 1976.