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Note to the Reader This is a revised edition of a paper published in The Journal of Neuroscience. The data described in this unpublished manuscript were generated through 1995. More recent data and corrections are available from the Neurogenetics server. The number of cases considered in this web publication is much greater than the print publication.
Journal of Neuroscience 16: 719–7205

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Genetic and Environmental Control of Retinal Ganglion Cell Number in Mice

Robert W. Williams, Richelle C. Strom, Dennis S. Rice, and Dan Goldowitz
Center for Neuroscience, Department of Anatomy and Neurobiology, University of Tennessee, 855 Monroe Avenue, Memphis, Tennessee 38163

 

Contents

Material and Methods
Results
    Table 1: Individual counts with replication
    Fig. 1: Mouse lineage chart (74 KB; updated June 96)
    Correlations with age, sex, and brain weight
    Variation among species and subspecies of mice
    Standard inbred strains; Table 3
    Recombinant inbred strains; Table 4
    Extent of non-genetic variation
    Heritability, heterosis, etc.
    Estimates of factor number
Discussion




 

Abstract

How much of the often remarkable variation in neuron number within a species is generated by genetic differences, and how much is generated by environmental or developmental factors? We address this problem for a single population of neurons in the mouse central nervous system. Retinal ganglion cells of inbred, outbred, hybrid, and wild strains were studied using electron microscopic and quantitative genetic methods. Numbers of ganglion cells range from 32,000 to 87,000. The distribution of all cases (n = 451) is close to normal and has mean of 60,000 and a standard deviation of 8,000. Male and female averages are matched to within 1%. There is no loss of ganglion cells with age over a range from 21 to 765 days of age (r = - 0.031).

Genetic factors predominate in the control of ganglion cell number. Estimates of additive gene effects (narrow-sense heritability) range from 70% to 85%. Estimates of total genetic determination (broad-sense heritability) reach close to 90%. In contrast to individual counts, the averages of 40 homozygous strains have a striking bimodal distribution, with peaks at 55,000 and 63,000 cells. This suggests that single quantitative trait loci control much of the variation among mice.

The coefficient of variation within isogenic strains averages about 4.5%. Most of this non-genetic variation in neuron number within groups of isogenic mice appears to be produced by developmental noise rather than by conventional environmental factors.

 



 

Introduction

Thre is a great deal of variation in the size of neuron populations among individuals within a species. For example, the number of giant interneurons in the spinal cord of sea lampreys ranges from 12 to 22 (Selzer, 1979). At the other extreme, the number of neurons in the lateral geniculate nucleus of rhesus macaque monkeys ranges from 1.0 to 1.8 million (Williams and Rakic, 1988a; Ahmad and Spear, 1993). The adaptive significance of this wide variation has not yet been explored in detail (Williams and Herrup, 1988), but there is a rough relationship between neuron number and an animal's behavioral capacity (Wimer and Wimer, 1985; Purves, 1988; Lipp et al., 1989; Crusio et al., 1989a,b; Legendre et al., 1994; Stevens, 1994; Tejedor et al., 1995). Variation in the size of cell populations is therefore likely to be an important target of natural selection (Williams et al., 1993). But variation can be traced to many causes, and a key problem now is estimating their relative importance. How much of the variance in single neuron populations is due to heritable gene effects? How much is generated by the environment, and how much is generated by random fluctuations in cell cycle kinetics, cell commitment, and cell death? To rephrase this in a complementary way—how precisely does the genome, in concert with an intricate array of developmental processes, specify the size of cell populations?

To partition variation in neuron number we have used an efficient electron microscopic method to count retinal ganglion cells. These cells are the sole projection neurons of the vertebrate retina (Rodieck and Brening, 1983), and a census of the entire population can be obtained by counting axons in a single cross-section of the optic nerve (Chalupa et al., 1984; Williams et al., 1986; Lia et al., 1986; Rice et al., 1995a). Data were collected from a variety of mice, including:

 

  1. Several species and subspecies belonging to the genus Mus
  2. Fully inbred and isogenic strains of common laboratory mice
  3. Recombinant inbred strains generated from a cross between two common inbred strains—C57BL/6J and DBA/2J
  4. Isogenic but heterozygous F1 intercross progeny generated by crossing strains with high and low cell numbers
  5. Outbred mice that have a level of genetic variability similar to that of natural populations of mammals
  6. Mendelian test cross progeny generated between two strains that have a large difference in ganglion cell number

The results provide answers to several questions. We now have a good idea of how precisely a discrete population of neurons can be regulated when genetic differences are eliminated and when environmental perturbations are minimized. We know the relative importance of genes and the environment in controlling ganglion cell numbers. We have also generated estimates of heritability that can be used to predict the effects of selection for or against high or low cell number. Finally, this work sets the stage to explore the genetic and developmental mechanisms that control natural variation in neuron number in the vertebrate CNS.


 

Materials and Methods

Tissue was taken from 451 mice belonging to 59 different strains or types (Figure 1). Most animals were shipped directly from the Jackson Laboratory (Bar Harbor, Maine). The mix of sexes among strains varied, but the ratio across all strains was close to 1:1. The age of mice ranged from 21 to 765 days. No systematic attempt was made to ensure that the average age or sex ratio among strains was matched. While at the Jackson Laboratory most animals were fed a 6% fat NIH31 diet. With three exceptions, all BXD recombinant inbred strains were fed a high fish oil diet (Wayne Lab Tech). Strains BXD13, BXD20, and BXD31 were fed a 9% fat diet (modified NIH 911A). While housed at the University of Tennessee mice were fed a 5% fat Agway Prolab 3000 rat and mouse chow. Colonies were maintained at 20-24 °C on a 14/10 h light-dark cycle.

Figure 1: Mouse lineage chart (74 KB; updated June 96). Lineage chart of strains, species, and subspecies of mice in relation to variation in retinal ganglion cell number. Major categories of mice are indicated on the left and are described briefly in Materials and Methods. Numbers associated with each strain are the average, standard error of the mean, and number of cases. For other features refer to the Key.

Standard inbred strains. Standard inbred laboratory strains of mice (Fig. 1, middle group) are derived from domesticated hybrids generated from crosses between Mus musculus domesticus (also known as M. domesticus) and M. musculus molossinus (Silver, 1995). All of the standard strains that we studied have been inbred by successive sibling matings for more than 80 generations (Festing, 1993). Animals are therefore homozygous at essentially all loci. C57BL/6Ax1 is a non-standard nomenclature we have introduced (see Results) to designate animals obtained from the Jackson Laboratory Annex 1 colony. The particular strains that we studied were for the most part selected without regard to CNS or ocular characteristics. TgN(Hbb-b1)/LoGo (abbreviated TgHBB) is a transgenic strain derived from a cross between SJL/J and C57BL/6J. TgHBB was inbred for 10 to 15 generation (C. Lo, personal communication), but has been maintained for several years by quasi-random mating. We have not used this strain in calculating heritabilities. We have also not used a partially inbred strain, B6C3/FeJ, in these calculations.

Wild strains. We studied four species of mice: 1) M. musculus, the common house mouse, a wide-ranging and highly adaptable commensal species from which laboratory mice are derived (Bronson, 1984); 2) M. spretus (SPRET/Ei), a short-tailed field mouse distributed around the western Mediterranean; 3) M. spicilegus (PANCEVO/Ei), a colonial mound-building species from the Balkans and Ukraine; and 4) M. caroli (CARL/ChGo), a small tropical East Asian species (Fig. 1, bottom group, Table 2).

We also studied four subspecies of M. musculus: 1) M. m. castaneus (CAST/Ei and CASA/Rk), a South East Asian subspecies; 2) M. m. musculus (CZECHII/Ei), the commensal Eastern European and Asiatic mouse; 3) M. m. molossinus (MOLD/Rk), a Japanese hybrid subspecies; and 4) M. m. domesticus (WSB/Ei), the commensal and very widely dispersed subspecies of Western Europe and the Americas (Fig. 1, bottom group, Table 2). Seven of these wild strains have been inbred for more than 16 generations at the Jackson Laboratory. The exception is CARL/ChGo—an outbred wild sample of Mus caroli maintained since the middle 1970s as a colony of 5-10 breeding pairs with specific avoidance of sib mating (V. Chapman, personal communication). The evolutionary relations and ecological characteristics of these species are reviewed briefly in Bonhomme and Guénet (1989), Nowak (1991), and Bonhomme (1992).

Genetically heterogeneous mice. Several types of mice included in this study are genetically heterogeneous. The first is referred to as CD-1 or ICR (Hsp:ICR). This strain has been bred for high fecundity and fitness (Eaton, 1980), and is maintained by random non-sib matings at Harlan Sprague Dawley Inc. (Indianapolis, IN). The strain is derived from non-inbred Swiss albinos originally designated HaM/ICR (Hauschka and Mirand 1973). The second is CARL/ChGo, described above (Wild strains). The third and most heterogeneous group is made up of the F2 progeny of a cross between BALB/cJ and CAST/Ei. These progeny are referred to as BCF2 (Fig. 1, Test cross). BCBN2 and BCCN2 are the backcross progeny generated by crossing BCF1 females to BALB/cJ and CAST/Ei males, respectively.

Isogenic F1 hybrids. We studied five sets of isogenic F1 hybrids (Fig. 1). Four of these were hybrids between a BALB/cJ parent and either an A/J, C57BL/6J, C57BL/6JAx1, or CAST/Ei parent. They are referred to as CB6F1/J (a BALB/cJ female crossed to a C57BL/6J male), B6AxCF1 (the cross between a C57BL/6JAx1 mother and a BALB/c father), CAF1 (BALB/cJ female by A/J male), and BCF1 (BALB/c female by CAST/Ei male). We also examined the PLSJF1 progeny of a cross between PL/J and SJL/J. The CAF1, CB6F1, and PLSJF1 were obtained from Jackson Laboratory. The B6AxCF1 and BCF1 progeny were generated in our colony from animals obtained from the Jackson Laboratory. In this paper we treat both these F1 hybrids and the fully inbred strains as isogenic. Formally, only animals of the same type and sex are isogenic.

BXD recombinant inbred strains. We studied 26 of the BXD recombinant inbred strains (Fig. 1, top group). These strains were generated by inbreeding the hybrid progeny of matings between C57BL/6J and DBA/2J mice. The genome of each BXD strain is an isogenic mosaic of C57BL/6J and DBA/2J chromosomal segments (Bailey, 1981; Taylor, 1989).

Mutants. Several strains carry mutations that affect the retina. Five strains that we studied (C3H/HeJ, CD-1, PL/J, SJL/J, and MOLD/Rk) carry the retinal degeneration allele, rd, at the beta-phosphodiesterase locus. These strains lose virtually all photoreceptors by two months of age. With the exception of MOLD/Rk, all rd strains have normal nerves, and several have high ganglion cell populations. Eight of the strains we used are albinos and have a reduced proportion of retinal ganglion cells with uncrossed projections (A/J, AKR/J, BALB/cBy, BALB/cJ, CD-1, 129/J, NZW/LacJ, SJL/J, see Rice et al., 1995a). We have not noted any correlation between pigmentation and total ganglion cell number.

Fixation and processing of tissue. Mice were anesthetized with an injection of Avertin (0.5-0.8 ml ip) and were perfused transcardially with 0.9% saline followed by fixative using a peristaltic pump. Approximately 15 ml of 1.25% glutaraldehyde and 1.0% paraformaldehyde in 0.1 M phosphate buffer was injected for 2-4 min. An additional 10 ml of double-strength fixative (2.5% glutaraldehyde and 2.0% paraformaldehyde in the same buffer) was injected for 1-2 min at an increased flow rate. The head was removed and placed in fixative overnight at 4 °C and placed in 0.1 M phosphate buffer the next morning. Optic nerves were dissected and were subsequently osmicated and embedded in Spurr's resin. For most cases, the brains, including olfactory bulb, were dissected free, trimmed just behind the cerebellum, and weighed. Thin sections of either nerve were placed on Formvar-coated slot grids and were stained with uranyl acetate and lead citrate. The nerves were examined and photographed on a JEOL EX2000II microscope using a systematic unstratified sampling protocol (Fig. 2A, Deming, 1950).

An important variable determining count precision is the accuracy with which image magnification is measured (Fig. 2B,D). Magnification was calibrated by photographing a grid replica (EMS, Ft. Washington PA, # 80051, 2160 lines/mm) at the conclusion of every photography session. The procedure was performed in the following sequence:

 

  1. A set of 20 or more high magnification micrographs were usually taken at X12,000 (Fig. 2C), in a square lattice pattern. No adjustments in position were made with respect to blood vessels or glial cells.
  2. The calibration grid was photographed at the same high magnification(Fig. 2D).
  3. The calibration grid was rephotographed at a low magnification, usually X200 or X250 (Fig. 2B.
  4. The thin section of the entire nerve was then photographed at the same low power (Fig. 2A).

The overall image quality of each set of micrographs was scored using a four point scale. The correlation between these scores and the within-strain standardized z score of the count was used to assess the sensitivity of estimates to fixation and image quality. After discarding about 25 cases that scored in the worst image and fixation category, the correlation was close to zero (r= 0.07). The average z score for samples ranked adequate was -0.246 z, whereas that for samples ranked excellent was +0.034 z. Given the small size of the effect, no compensation was applied.

Counting rulesCounting. A counting frame (63 x 86 mm), was traced directly on the 3 by 4 inch negatives with a Sharpie ultra fine-point marker pen and all axons within the frame and intersecting the upper and right edges were marked and counted on the negative using stereological counting rules (Fig. 2C, Gundersen, 1977). The typical sample area gave a count of 25 axons, and the typical set of samples from one micrography session gave a total count of 500 axons. From 2% to 50% of axons in the adult mouse optic nerve are unmyelinated (higher percentages are only found in sections cut close to the lamina cribrosa). To ensure that the small unmyelinated fibers were recognized, negatives were counted on a light box while wearing magnifying glasses (X2.5 from Optivisor, Donegan Optical Co, $35.00). The effective magnification was therefore above X25,000. All counts were double-checked. The average density of axons was multiplied by the area of the nerve cross-section to estimate the total axon population. When two or more completely independent samples were obtained from one nerve, we computed a variance weighted average and standard deviation (Bevington and Robinson, 1992, p. 59). Strain averages are presented as unweighted means. The variance weighted strain averages typically differ from unweighted means by about 500 cells, with a peak difference of 1,200.

Legend to Figure 2. A set of four marked contract prints (1:1 reproduction) of negatives used to generate estimates of ganglion cell number. A and B are matched low power transmission electron micrographs of the ultrathin section (A) and the calibration grid (B). The series of white spots in A are regions bleached during the high magnification sampling. The outline of the nerve was traced on the negative under a dissecting microscope. The boundary was drawn across the outer rank of axons, even if that involved an occasional intrusion into the nerve. The area of the nerve was computed by tracing this boundary using a calibrated digitizing tablet two or more times (see faint numbers, upper left in A). The asterisk in A marks the site illustrated at higher magnification in C. Two sites marked by arrows on the calibration negative (B) have been measured. The upper site (inset) is illustrated at higher magnification. A series of 41 marks, spanning 80 grid units, were made with a microscalpel. The separation between endpoints was measured under a dissecting microscope with a digital caliber accurate to 10 µm. Distances on all calibration negatives were measured two or four times in the two orthogonal axes of the grid. C is one of the sample negatives that illustrates the counting frame and the axons that were counted. The three faintly circled axons are unmyelinated. D is the high magnification calibration grid used to compute the sample area. Grid dimensions are 0.463 x 0.463 µm. If one calculates the axon population just from these four micrographs, the estimate should be close to 81,500. However the average axon count for the 22 sample micrographs was 40.5 ± 9.07, giving an estimate of 68,669 ± 3,361. This case was replicated independently, and the other estimate from a different thin section was 68,154 ± 3,329. The final estimate was 68,409 ± 2,365 (variance weighted average).

The standard deviation and its derivates such as the standard error of the mean and the coefficient of variation are seriously biased for small sample size (Sokol and Rohlf, 1981). For example, a standard deviation estimated from a sample of two cases will on average underestimate the population standard deviation by 25%. Because the number of cases we studied per group varied from 4 to more than 20, we needed to correct for this bias. Gurland and Tripathi (1971) provide the corrections for this bias. The factors are reproduced below for sample sizes of between 2 and 39. Note that variance estimates are not subject to this bias.

 

Appendix Table 1: Gurland and Tripathi corrections for SD
n Correction* n Correction
2 1.25331 21 1.01257
3 1.12838 22 1.01197
4 1.08540 23 1.01142
5 1.06385 24 1.01093
6 1.05094 25 1.01047
7 1.04235 26 1.01005
8 1.03624 27 1.00966
9 1.03166 28 1.00930
10 1.02811 29 1.00897
11 1.02527 30 1.00866
12 1.02296 31 1.00833
13 1.02103 32 1.00806
14 1.01940 33 1.00781
15 1.01800 34 1.00758
16 1.01679 35 1.00735
17 1.01574 36 1.00714
18 1.01481 37 1.00694
19 1.03980 38 1.00676
20 1.01324 39 1.00658

*The standard deviation should be multiplied by the correction factor. Do not over-correct by subsequently using these factors on the standard error of the coefficient of variation.

Estimates of genetic determination. We used complementary methods to calculate heritability. The additive genetic component from inbred strain data was computed using the method of Hegmann and Possidente (1981). The confidence intervals of these estimates were computed using a jackknife procedure (Mosteller and Tukey, 1977, p. 135). The uncertainty of the strength of additive gene effects were assessed directly by counting independent sets of inbred strains. One set consisted of 17 standard strains (Fig. 1, middle panel); the other set consisted of 23 recombinant inbred strains (Fig. 1, upper panel). Gene dominance, heterosis, and inbreeding depression were estimated from 1) F1 heterozygotes, 2) Mendelian test cross progeny, and 3) by comparing inbred and outbred populations (Falconer, 1989). Estimates of broad-sense heritability, or total genetic determination, were computed by comparing levels of variance in outbred and isogenic groups (Vogel and Motulsky, 1986; Crusio, 1992; Wahlsten, 1992), both before and after correcting for technical variance. It is worth emphasizing that most quantitative genetic procedures and heritability estimates in particular, are not designed to address modes of gene action or specific developmental processes. These methods provide global insight on the mean effects of genes on phenotypes within specific populations and under specific environmental conditions (Cheverud, 1984, 1990).

Reliability and accuracy of estimates. To directly assess total technical variance, 116 nerves were counted two or more times. All of these replicate counts are listed in table 1 within parentheses. Usually an adjacent thin section was photographed and counted several months after the original sample. Interobserver sources of variance were assessed in a subset of 28 replicates in which photography, calibration, and counting were done by different individuals. The test-retest reliability coefficient r(TX) across all replicates was approximately 0.77 (Snedecor and Cochran, 1980; Wahlsten, 1992). The mean absolute difference between pairs of estimates was 2,415 and the standard deviation between these pairs averaged 3,435 (n = 129 paired comparisons). The technical coefficient of variation (CV) for individual samples of about 25 micrographs averaged 5.70 +/- 0.1% SE. The effective sampling error over all cases was 4.65%. For the interobserver replicates the CV was 6.6%. The cumulative average technical variance, including all replicates for all 451 cases, averaged 5.28%. The relationship
CV2(total within isogenic strains) = CV2(technical) + CV2(environmental within isogenic strain)

was used to obtain a more accurate estimate of the average environmental variation for groups of isogenic strains. We assume that there is no covariation between technical and strain variation. Replicated cases were not chosen randomly, but usually represented the highest and lowest cases in each strain (Table 1). This non-random selection could have inflated estimates of technical error. However, a comparison with cases that were selected randomly for replication demonstrate that this bias is negligible.

Confirmation of count accuracy. Counts of peroxidase-labeled ganglion cells in 17 cases (Rice et al. 1995a for methods) confirm the accuracy of the electron microscopic method used to estimate ganglion cell number. The average axon count for these cases was 57,474 ± 1,766 (standard error of the mean, SE), whereas the estimates based on counting peroxidase labeled ganglion cell bodies in these same cases averaged 55,850 ± 2,007; an insignificant difference.

Table 1: Individual Estimates with Replication

Type case 1 ± SE (first estimate for case 1 ± SE, second estimate for case 1 ± SE), case 2 ± SE, ... (all values in thousands)
Standard Inbred Strains
129/J 57.2 ± 1.8 (57.3 ± 2.1, 57.0 ± 3.2), 59.3 ± 2.8, 62.8 ± 3.1, 65.7 ± 5.9, 66.3 ± 2.5, 66.7 ± 4.7, 68.4 ± 2.4 (68.2 ± 3.3, 68.7 ± 3.4)
129/SvJ* 64.3 ± 3.6 , 65.1± 3.9, 77.9 ± 5.3
A/J 46.3 ± 2.1, 49.3 ± 2.8, 49.5 ± 2.6, 49.8 ± 3.1, 50.5 ± 2.8, 51.3 ± 2.3 (49.0 ± 2.6, 46.6 ± 5.7, 56.7 ± 3.3), 56.4 ± 4.9, 56.7 ± 2.0 (55.5 ± 2.8, 58.0 ± 2.9)
AKR/J 60.1 ± 1.9 (62.7 ± 4.6, 60.0 ± 2.1, 58.4 ± 3.5, 60.3 ± 3.2), 61.1 ± 2.3 (65.1 ± 4.4, 59.3 ± 2.8, 61.4 ± 4.3), 62.5 ± 4.7, 63.2 ± 2.3 (66.1 ± 4.2, 63.8 ± 2.8, 62.1 ± 2.3), 64.7 ± 4.5, 65.1 ± 2.8 (69.0 ± 4.5, 65.9 ± 3.5, 61.3 ± 3.9)
BALB/cBy 51.3 ± 2.0 (49.2 ± 3.4, 52.3 ± 2.4), 54.4 ± 2.4, 55.0 ± 3.0, 57.4 ± 7.0, 59.8 ± 4.0 (64.7 ± 6.8, 57.3 ± 4.9), 61.0 ± 2.2 (57.7 ± 5.0, 61.8 ± 2.5), 63.9 ± 3.8
BALB/cJ 53.3 ± 2.7 (53.8 ± 3.3, 54.9 ± 5.1, 53.0 ± 4.1), 58.7 ± 3.1, 58.8 ± 6.2, 63.5 ± 2.4 (57.2 ± 3.2, 60.3 ± 3.8, 68.6 ± 4.3), 67.5 ± 3.2, 68.1 ± 3.0, 68.4 ± 2.6 (69.3 ± 3.3, 67.0 ± 4.2), 68.8 ± 4.6
C3H/HeJ 60.8 ± 2.6 (59.1 ± 3.2, 64.1 ± 4.4), 65.6 ± 8.0, 66.8 ± 4.1, 68.3 ± 4.7, 69.5 ± 4.7, 71.3 ± 4.3
C57BL/6JAx1 58.6 ± 2.9 (59.8 ± 4.3, 57.6 ± 4.0), 59.3 ± 3.4, 64.2 ± 5.0, 66.9 ± 2.7 (67.5 ± 3.7, 66.4 ± 3.8), 67.2 ± 3.5, 67.8 ± 3.7, 69.4 ± 3.2 (72.9 ± 5.5, 67.6 ± 3.9), 69.5 ± 3.4, 71.8 ± 5.0
C57BL/6J 47.1 ± 1.9 (48.4 ± 3.3, 46.3 ± 2.4), 47.8 ± 4.9, 49.0 ± 4.2, 49.4 ± 3.4, 49.8 ± 3.6, 51.1 ± 3.5, 52.8 ± 3.3, 53.6 ± 4.2, 54.3 ± 2.4 (56.6 ± 4.3, 53.2 ± 2.9), 56.0 ± 3.2, 57.3 ± 5.6, 57.5 ± 3.6, 58.1 ± 3.1, 59.0 ± 3.8, 60.7 ± 3.6, 65.7 ± 5.5
C57BLKS/J 56.4 ± 4.0, 58.6 ± 4.7, 62.0 ± 3.8, 63.9 ± 2.8 (65.2 ± 3.6, 61.9 ± 4.5), 66.0 ± 3.4, 67.3 ± 4.7, 75.5 ± 4.6
CBA/CaJ 52.8 ± 2.6 (47.7 ± 4.0, 56.2 ± 3.3), 54.2 ± 3.2 (48.2 ± 4.5, 60.6 ± 4.6), 55.7 ± 3.1, 56.3 ± 3.1, 56.9 ± 4.6, 60.3 ± 3.2, (62.4 ± 4.9, 58.6 ± 4.3)
CE/J 55.2 ± 2.4 (59.2 ± 4.4, 57.5 ± 2.8, 52.5 ± 4.9), 64.7 ± 4.0, 64.8 ± 3.7, 66.3 ± 2.2 (68.9 ± 3.9, 68.9 ± 4.1, 63.7 ± 3.4), 66.9 ± 3.4 (63.0 ± 4.6, 71.7 ± 5.1)
DBA/2J 57.6 ± 2.5 (56.8 ± 3.3, 58.7 ± 3.7), 57.9 ± 4.0, 59.0 ± 3.7, 60.0 ± 4.7, 61.7 ± 2.2 (61.0 ± 2.6, 63.8 ± 4.4), 62.0 ± 4.2, 63.0 ± 3.8, 64.7 ± 3.4, 65.5 ± 3.5 (68.7 ± 4.7, 61.4 ± 5.2), 66.0 ± 5.8, 66.9 ± 3.9 (64.3 ± 4.8, 71.5 ± 6.4), 69.4 ± 4.8, 69.8 ± 2.7
LP/J 46.2 ± 2.6, 46.2 ± 2.8, 50.2 ± 3.6, 50.4 ± 2.6, 51.7 ± 3.7, 55.3 ± 3.5, 58.8 ± 3.3, 59.1 ± 4.8 (54.7 ± 6.8, 63.5 ± 6.9)
NZB/BinJ 56.1 ± 2.5, 60.7 ± 2.3 (55.3 ± 3.0, 59.3 ± 3.5, 64.3 ± 4.4), 61.0 ± 3.1 (65.4 ± 4.1, 55.5 ± 4.7), 62.5 ± 5.1, 62.6 ± 2.2 (61.4 ± 2.4, 66.6 ± 4.5), 64.0 ± 3.9
NZW/LacJ* 62.1 ± 3.1, 62.9 ± 3.6, 64.2 ± 3.6, 67.5 ± 3.8, 67.8 ± 5.3, 69.5 ± 3.4, 72.8 ± 53.6, 76.9 ± 5.7
PL/J 50.5 ± 2.0 (52.7 ± 3.1, 49.4 ± 3.6, 49.7 ± 3.6), 52.5 ± 3.4, 54.6 ± 3.6, 56.2 ± 2.1 (55.3 ± 2.6, 57.9 ± 3.5), 56.8 ± 4.2, 57.2 ± 1.8 (63.7 ± 3.4, 62.7 ± 3.4, 51.2 ± 2.7), 59.6 ± 4.4, 60.3 ± 3.1
SJL/J 45.6 ± 3.2, 51.8 ± 3.0, 52.4 ± 2.9, 53.9 ± 2.7, 54.7 ± 4.2, 56.4 ± 3.7
Wild Strains
CASA/Rk 45.1 ± 2.3, 45.5 ± 2.9, 48.9 ± 3.6, 56.2 ± 3.6
CAST/Ei 41.3 ± 3.3, 41.6 ± 3.1, 43.2 ± 4.7, 44.0 ± 2.6, 44.5 ± 4.1, 44.9 ± 4.4, 44.9 ± 3.2, 46.3 ± 4.3, 49.4 ± 3.5, 50.0 ± 4.8, 50.2 ± 3.4
CZECHII/Ei 49.3 ± 3.6, 54.0 ± 4.0, 54.8 ± 3.8, 56.8 ± 5.6, 61.0 ± 3.4, 65.3 ± 3.6, 73.6 ± 3.7
MOLD/Rk 32.3 ± 2.2 (35.5 ± 3.0, 32.1 ± 3.4, 31.5 ± 1.6), 37.7 ± 1.8 (40.3 ± 2.5, 34.9 ± 2.5), 47.2 ± 2.3, 49.2 ± 3.1, 52.4 ± 3.2
PANCEVO/Ei 61.3 ± 3.4, 61.5 ± 7.4, 62.3 ± 6.4, 65.7 ± 4.5, 67.3 ± 5.8, 67.7 ± 5.3
SPRET/Ei 53.3 ± 3.8, 55.8 ± 2.5 (54.6 ± 2.7, 62.0 ± 6.3), 57.6 ± 3.5, 58.2 ± 3.2, 61.8 ± 2.1 (63.2 ± 3.1, 60.6 ± 3.0), 64.4 ± 3.6
WSB/Ei 50.8 ± 2.7, 51.2 ± 4.1, 56.9 ± 3.3, 57.1 ± 5.0, 58.6 ± 4.7, 59.1 ± 5.1, 62.3 ± 3.9, 63.0 ± 2.9
F1 hybrids
B6AxCF1 56.7 ± 2.4 (57.4 ± 4.8, 56.5 ± 2.8), 59.3 ± 2.7 (59.0 ± 3.0, 60.3 ± 6.1), 63.6 ± 4.4, 64.9 ± 3.0, 65.8 ± 4.2 (61.0 ± 8.7, 67.3 ± 4.7), 69.5 ± 5.2 (69.6 ± 7.0, 69.3 ± 7.7), 74.2 ± 5.2
CAF1 51.8 ± 2.4 (48.4 ± 3.0, 58.6 ± 4.2), 52.3 ± 2.9, 55.6 ± 3.1, 56.4 ± 3.8, 58.2 ± 3.6, 62.6 ± 3.2 (62.8 ± 4.2 62.4 ± 5.0)
CB6F1 63.4 ± 4.2, 65.4 ± 3.8, 66.0 ± 2.8 (61.1 ± 4.3, 69.5 ± 3.7), 66.2 ± 3.7, 69.0 ± 3.9, 70.1 ± 2.6 (71.2 ± 3.7, 68.9 ± 3.7)
PLSJF1/J 50.0 ± 2.8 (50.0 ± 4.0, 50.1 ± 4.0), 54.0 ± 3.1, 56.1 ± 2.5 (51.0 ± 3.3, 63.2 ± 3.9), 57.5 ± 2.5, 57.9 ± 3.4, 58.2 ± 2.9, 59.0 ± 4.1
BXD Recombinant Inbred Strains
BXD1 55.7 ± 3.0, 59.6 ± 3.9, 60.4 ± 4.6, 60.4 ± 5.8, 60.8 ± 3.6, 61.2 ± 6.6, 67.2 ± 6.0, 67.2 ± 5.3
BXD2 60.4 ± 3.7 (61.8 ± 5.3, 59.1 ± 5.2), 64.0 ± 3.1 (69.6 ± 4.3, 58.3 ± 4.4), 65.1 ± 3.6 (72.2 ± 6.4, 61.8 ± 4.3), 67.7 ± 2.5 (66.0 ± 3.9, 68.9 ± 3.2), 68.4 ± 3.4 (70.4 ± 4.3, 64.9 ± 5.6), 70.8 ± 4.0 (70.2 ± 5.6, 71.4 ± 5.7)
BXD5 72.6 ± 7.0, 73.3 ± 3.7, 73.7 ± 4.6, 76.7 ± 6.5, 77.3 ± 4.9, 79.9 ± 3.9
BXD6 59.9 ± 2.8 (63.0 ± 4.7, 58.1 ± 3.60), 60.1 ± 2.9 (66.6 ± 4.9, 56.8 ± 3.5), 62.9 ± 1.9 (65.1 ± 2.6, 60.2 ± 2.9), 63.1 ± 2.5 (64.3 ± 3.2, 61.3 ± 3.9), 63.6 ± 3.7 (62.7 ± 6.2, 64.1 ± 4.6), 64.5 ± 3.5 (64.0 ± 4.5, 65.4 ± 5.6), 64.7 ± 2.7 (64.9 ± 4.3, 64.6 ± 3.4)
BXD8 52.9 ± 3.4, 53.8 ± 4.7, 53.9 ± 5.2, 56.0 ± 4.0, 59.4 ± 5.0, 60.6 ± 4.9, 61.7 ± 4.0
BXD9 59.8 ± 2.9 (55.6 ± 3.9, 64.9 ± 4.2), 61.3 ± 3.0 (66.6 ± 5.3, 58.9 ± 3.6), 66.9 ± 3.4 (69.2 ± 4.7, 64.4 ± 4.8), 68.3 ± 3.3 (62.1 ± 5.5, 71.7 ± 4.2), 68.8 ± 4.1 (75.8 ± 5.5, 60.1 ± 6.1), 69.3 ± 3.6 (68.5 ± 4.3, 71.2 ± 6.3)
BXD11 56.1 ± 2.9 (53.1 ± 5.0, 57.7 ± 3.6) 59.7 ± 3.3, 61.6 ± 2.5, 65.3 ± 2.6 (69.8 ± 4.7, 63.2 ± 3.2), 65.8 ± 3.5 (65.2 ± 4.1, 67.0 ± 6.5), 66.5 ± 2.9 (69.3 ± 4.0, 63.1 ± 4.4)
BXD12 48.0 ± 4.1, 53.0 ± 4.1, 53.7 ± 4.1, 55.2 ± 5.0, 57.9 ± 2.9 (55.0 ± 5.0, 59.4 ± 3.6)
BXD13* 49.2 ± 2.3 51.6 ± 3.6, 56.3 ± 3.4, 58.1 ± 3.3 58.1 ± 3.4 59.1 ± 4.2
BXD14 60.4 ± 3.6, 61.7 ± 5.3, 62.8 ± 4.4, 66.2 ± 4.5, 69.1 ± 4.2, 70.3 ± 5.1, 71.4 ± 5.3
BXD15* 58.4 ± 3.9, 62.8 ± 5.2, 63.8 ± 4.5, 64.9 ± 5.6, 65.8 ± 4.2, 67.0 ± 5.8
BXD18 52.7 ± 3.3, 53.8 ± 4.9, 55.0 ± 4.2, 55.3 ± 3.2, 58.2 ± 5.2, 59.5 ± 5.1
BXD19 62.5 ± 3.3 (57.4 ± 4.9, 66.6 ± 4.4), 62.7 ± 2.7 (58.7 ± 3.8, 66.6 ± 3.8), 64.8 ± 3.9 (61.7 ± 6.1, 66.9 ± 5.0), 66.3 ± 2.7 (62.3 ± 4.0, 69.7 ± 3.7), 66.9 ± 3.5 (62.9 ± 4.4, 73.8 ± 5.8), 67.0 ± 3.1 (67.1 ± 5.9, 67.0 ± 3.6), 70.9 ± 2.6 (69.5 ± 3.0, 74.8 ± 5.0), 72.8 ± 3.3 (70.4 ± 4.5, 75.6 ± 4.9), 74.7 ± 4.6 (76.3 ± 5.9, 72.3 ± 7.3)
BXD20 55.9 ± 3.7 (52.0 ± 5.6, 58.9 ± 4.9), 58.8 ± 5.1, 59.5 ± 6.1, 59.8 ± 4.3, 60.9 ± 6.1, 62.2 ± 4.7, 65.0 ± 4.6, 66.8 ± 7.2, 68.3 ± 3.7
BXD21 54.9 ± 3.4, 55.5 ± 4.9, 56.6 ± 4.8, 57.2 ± 3.9, 60.3 ± 2.8 (56.0 ± 4.4, 63.3 ± 3.7), 62.5 ± 3.0, 63.5 ± 3.8, 63.5 ± 4.4
BXD23 50.8 ± 4.5, 50.9 ± 3.3, 52.0 ± 3.9, 53.4 ± 4.9, 59.3 ± 5.6, 60.9 ± 4.8
BXD24 57.7 ± 5.8, 61.4 ± 4.4, 61.5 ± 3.0, 61.6 ± 4.5, 62.6 ± 2.8, 65.4 ± 4.7, 65.6 ± 4.0
BXD25 53.1 ± 2.4, 53.9 ± 4.9, 54.1 ± 3.2, 58.8 ± 5.1, 64.3 ± 4.9
BXD27 47.6 ± 3.5, 48.2 ± 2.5, 52.1 ± 1.9, 52.6 ± 3.1, 53.3 ± 4.0, 55.7 ± 5.1
BXD28 44.4 ± 2.6, 45.0 ± 4.9, 47.9 ± 3.4, 57.8 ± 4.9, 60.5 ± 3.2
BXD29 58.1 ± 3.2, 60.6 ± 3.8, 62.0 ± 3.7, 65.3 ± 5.3, 65.3 ± 4.3, 69.9 ± 6.2
BXD31 59.8 ± 6.0, 60.2 ± 3.1, 66.3 ± 3.3, 68.4 ± 4.6, 70.5 ± 5.1, 71.8 ± 5.7
BXD32 72.0 ± 4.5, 72.9 ± 4.0 (68.9 ± 5.5, 77.3 ± 5.7), 77.9 ± 5.3, 85.3 ± 4.1 (89.8 ± 4.9, 75.3 ± 7.3), 85.6 ± 4.8
Outbred Inbred Strains
CARL/ChGo 39.5 ± 1.6 (38.9 ± 1.8, 41.9 ± 3.5), 43.5 ± 1.3 (43.6 ± 1.4, 43.5 ± 2.9), 46.7 ± 3.5, 46.9 ± 3.6, 47.3 ± 2.3 (45.8 ± 2.8, 50.4 ± 4.0), 52.5 ± 4.4, 54.8 ± 3.6, 54.9 ± 2.5, 57.5 ± 2.9, 57.5 ± 4.2, 62.8 ± 2.1 (64.1 ± 2.5, 59.6 ± 3.9)
CD-1 57.2 ± 2.7 (59.9 ± 3.6, 53.6 ± 4.2), 61.8 ± 2.6 (58.6 ± 3.5, 65.3 ± 3.8), 62.4 ± 2.5, 62.6 ± 4.5, 64.9 ± 3.0, 65.4 ± 2.8, 65.7 ± 3.2, 65.9 ± 3.1, 69.1 ± 2.4, 69.2 ± 2.4, 73.6 ± 3.7, 74.0 ± 2.7 (74.5 ± 3.1, 74.8 ± 5.7, 73.6 ± 2.4), 77.7 ± 2.2, 87.2 ± 2.5 (88.8 ± 3.3, 85.2 ± 3.8)
BALB/cJ x CAST/Ei Cross
BCBN2 53.1 ± 2.0 (47.1 ± 4.9, 54.3 ± 2.2), 57.8 ± 4.0, 62.1 ± 5.6, 62.2 ± 6.9, 62.9 ± 6.5, 63.3 ± 3.2, 63.4 ± 5.1
BCCN2 50.3 ± 2.7, 50.6 ± 2.6, 51.5 ± 2.6, 60.0 ± 2.7, 62.8 ± 3.7, 64.9 ± 3.3
BCF1 55.2 ± 3.1 (54.5 ± 5.8, 55.6 ± 3.7), 55.3 ± 4.9, 56.1 ± 4.0, 57.8 ± 5.6, 61.3 ± 4.3 (60.5 ± 6.1, 62.0 ± 6.1), 61.7 ± 5.7, 61.8 ± 4.7, 63.7 ± 3.1 (68.5 ± 5.4, 61.4 ± 3.7), 64.4 ± 3.3
BCF2 40.6 ± 3.8, 45.4 ± 2.1 (44.9 ± 2.7, 46.0 ± 3.1), 46.6 ± 3.0, 47.1 ± 3.6, 47.2 ± 3.6 (51.9 ± 6.1, 44.7 ± 4.5), 47.6 ± 3.3, 48.1 ± 3.1, 48.3 ± 4.6, 48.5 ± 2.6, 49.9 ± 2.4, 50.5 ± 2.7, 50.8 ± 3.2, 50.8 ± 4.2, 51.2 ± 2.9 (44.4 ± 5.1, 54.3 ± 3.5), 52.7 ± 4.0, 52.7 ± 3.5, 53.0 ± 5.0, 53.6 ± 3.2 (63.2 ± 6.4, 50.4 ± 3.7), 53.9 ± 3.8, 54.6 ± 5.6, 54.9 ± 5.8, 56.6 ± 5.0, 57.2 ± 4.2, 57.3 ± 2.7, 58.2 ± 1.8, 58.3 ± 3.8 (53.4 ± 5.0, 64.4 ± 5.7), 60.4 ± 4.1, 60.7 ± 4.2, 60.9 ± 3.9, 61.3 ± 3.1, 62.0 ± 5.7, 62.6 ± 2.6, 63.6 ± 3.2, 64.0 ± 4.0, 64.7 ± 3.2, 65.4 ± 2.7, 65.7 ± 3.8 (77.1 ± 5.9, 57.8 ± 5.0, 65.2 ± 5.3), 66.6 ± 3.0, 68.0 ± 4.1, 70.1 ± 5.0, 70.2 ± 2.3, 71.0 ± 3.3, 73.7 ± 5.6, 77.4 ± 5.3, 77.5 ± 3.9 (82.8 ± 5.1, 70.5 ± 5.9)
Other Types
B6C3Fe/J 55.0 ± 2.2, 55.6 ± 3.1, 58.1 ± 1.8 (53.5 ± 5.1 left, 54.3 ± 1.9 left, 53.7 ± 3.1 left, 62.2 ± 3.0 right), 62.9 ± 2.0, 69.9 ± 2.4, 78.6 ± 4.3
TgN(Hbb-b1)LoGo 50.8 ± 2.9 (49.2 ± 3.9, 52.7 ± 4.4), 52.6 ± 2.5, 58.0 ± 2.3 (62.9 ± 3.3, 53.6 ± 3.1), 58.2 ± 4.8, 59.3 ± 2.5, 62.6 ± 1.9 (65.0 ± 2.6, 60.6 ± 2.8, 60.2 ± 5.1)

*Updated or new cases since publication in 1996.


 

Results

The Results are divided into four sections. The first is a summary of data pooled across all strains analyzed with respect to age, sex, and brain weight. The second part surveys differences in cell number between strains and includes an analysis of the bimodality of strain averages. The third section summarizes variation in ganglion cell numbers within isogenic mice. The final section deals with heritability and variation in cell number among Mendelian test cross progeny.

 

Distribution of cell number and correlations with age, sex and brain weight

Distribution of individual values. The average and standard deviation for all cases listed in table 1 is 59,692 ± 7,953 ( ± 375 SE). The distribution is unimodal and close to normal (Figure 3). We have included a wide diversity of types of mice (Fig. 1) and for this reason the distribution might have been expected to have extended tails. However, near normality extends over a range of four standard deviations. There is a small but significant deficit in the expected number of cases with populations close to the average (asterisk in Fig. 3) that gives the distribution a slightly flattened shape compared to the expected Gaussian distribution. This deviation has a straightforward explanation—we sampled many homozygous mice (Table 1), and these homozygous mice tend to have polarized phenotypes.

Legend to Figure 3. Distribution of individual counts. In this stem and leaf display each case is encoded as a single digit (see Interpretation). The figure can be read as a vertical histogram with bins of 1,000 cells and bars made up of rows of digits. The bold black curve is the observed probability density calculated from the sum of 451 individual Gaussian probability functions. In contrast, the predicted Gaussian probability density (fine line and gray region) is based on the sample average and standard deviation of 59,692 ± 7,953. The median is 60,000 and the quantiles are at approximately 54,300 and 65,100. The asterisk highlights the deficit of expected cases close to the mean. Values below 40,000 and above 80,000 are enclosed within parentheses. Excluding the 23 animals that do not belong to the M. musculus complex (Fig. 1; CARL/Go, SPRET/Ei, and PANCEVO/Ei) does not alter the distribution in any significant way.

Age and the ganglion cell population. The average longevity of strains of mice ranges from 300 to 850 day (Green and Witham, 1991). Our estimates were taken from animals averaging 82 days old, but with a range extending from 21 to 765 days. The youngest 66 mice—between 20 and 36 days old—had an average population of 58,542 ± 925 (SE). The oldest 54 animals—retired breeders between 180 and 765 days old—had an average population of 57,636 ± 1,128. This difference is not significant. As expected from these age averages, the correlation coefficient for the entire set of animals is very close to zero (r = - 0.03).

Sex and the ganglion cell population. There are no sex differences in retinal ganglion cell number. The average population for 236 females is 59,422 ± 520 SE (average age of 87 ± 6 days), whereas that for 215 males is 59,989 ± 543 SE (average age of 76 ± 4 days). There is no evidence of sex difference within any strains.

Brain weight and the ganglion cell population. We were interested in assessing whether differences in ganglion cell numbers among mice are closely associated with differences in brain weight (cf. Williams et al., 1993). The correlation between neuron number and brain weight across all cases for which both parameters were measured is 0.32 (n = 372). A stronger correlation between brain weight and the ganglion cell number emerges when strain averages are used. The correlation is 0.59 both for the set of species and subspecies listed in table 2 and for the 17 standard inbred strains listed in table 3. The correlation among the BXD strains listed in table 4 is 0.54. Collectively, this analysis indicates that as much as 30% of the variance between strains in ganglion cell number may be associated, directly or indirectly, with differences in brain weight. However, the correlation coefficient among the genetically heterogeneous BCF2 progeny (see Test cross progeny below) is 0.28, and the explained variance for this group is only 8%. Finally, the correlation within isogenic strains between these two variables is close to zero (r = 0.14 ± 0.08 SE; based on 40 within-strain correlations). This low correlation (r² = 2%) is particularly important because it indicates that environmental factors do not have significant common effects on both ganglion cell number and brain weight.

 

Survey of variation among species, subspecies, and strains of mice

Variation among species and subspecies. We examined animals belonging to four different species of the subgenus Mus. Given the significant ecological, biogeographic, and genetic differences between these species (Nowak, 1991; Bonhomme 1992), the ganglion cell population has a comparatively narrow range extending from about 45,000 to 60,000 (Fig. 1, Tables 1, 2). We also examined several subspecies of M. musculus that are known to have contributed to the genome of the common laboratory mouse (Fig. 1, Tables 1, 2). These wild inbred M. musculus strains also have averages that range between about 45,000 and 60,000 ganglion cells. An analysis of variance demonstrates a significant difference between species and subspecies (F [7, 50] = 11.2, P < 0.001).

 

Table 2. Ganglion cell population size in wild strains*
Type** Species Mean SE SD N
CASA/Rk M. m. castaneus 48,915 2,958 5,123 4
CAST/Ei M. m. castaneus 45,484 999 3,160 11
CZECHII/Ei M. m. musculus 59,207 3,341 8,183 7
MOLD/Rk*** M. m. molossinus 43,758 4,207 8,414 5
WSB/Ei M. m. domesticus 57,380 1,698 4,492 8
PANCEVO/Ei M. spicilegus 64,300 1,316 2,943 6
SPRET/Ei M. spretus 59,049 1,804 4,035 6
CARL/ChGo M. caroli 51,263 2,214 7,000 11

*Abbreviations in this and all other tables are SE: standard error of
sample mean, SD: standard deviation, CV: coefficient of variation.
No correction has been applied for the systematic but slight (about
4%) underestimate of the population standard deviation associated
with small sample size (Diem and Lentner, 1975, p. 47).
**All types are inbred with the exception of CARL/ChGo, an
outcrossed strain.
***The low value for M. molossinus is suspect because of the high
incidence of necrotic axons in the optic nerve of the MOLD/Rk
inbred strain. Estimates from the two youngest MOLD/Rk
cases (49,200 and 47,200) are probably more representative.


Variation among standard laboratory strains. Estimates of ganglion cell number in the 17 standard inbred strains range from 51,200 in A/J to 67,000 in C3H/HeJ (Tables 1, 3, Fig. 1, middle group). The variance between strains is also much greater than that within strains (F [16, 113] = 11.4, P < 0.001). The inbred strains are in many cases closely related by descent. Yet we find that even closely related strains have large differences in ganglion cell number (Fig. 1, Table 3). For example, strains 129/J and LP/J originated from a common ancestor in the mid-1920s but their mean populations now differ by 11,500 cells or 20% (Scheffé t = 4.75, P < 0.05 two-tailed for six comparisons). An equally large difference of 11,200 cells exists between the closely related strains, C3H/HeJ and CBA/CaJ (t = 6.22, P < 0.05).

We discovered a remarkable difference of about 11,800 cells between groups of C57BL/6 mice (Table 3). The initial ten animals received from the Jackson Laboratory prior to the summer of 1994 included six standard pigmented C57BL/6J animals (4 females, 2 males) and four coisogenic c2J albinos (2 females, 2 males). These two subsets gave averages of 53,800 ± 2,000 and 52,800 ± 2,600, respectively (see Rice et al., 1995a and Table 1) that are close to the previous estimate of 56,700 ± 3,200 obtained by M.A. Williams and colleagues (1990) using similar methods. However, C57BL/6J mice obtained from the Annex 1 production colony of the Jackson Laboratory in three separate shipments in the second half of 1994 gave estimates averaging 66,100 ± 1,600 (5 females, 4 males; Table 1). This is far above the average for the first ten cases (t = 6.29, P < 0.05). More recent estimates of C57BL/6J animals obtained from a different Jackson Laboratory production colony (Annex 10) match the low number phenotype (56,026 ± 2,928, n = 6). Brain weights in the high and low groups do not differ appreciably—459 ± 5.3 mg for Annex 1 cases versus 471 ± 4.6 mg for the C57BL/6J mice. We have not identified any non-genetic factors that could have caused this difference. The difference is probably due to the fixation of a single mutation in the Annex 1 colony.

 

Table 3. RGCs in Inbred Laboratory Strains (updated July 1996)
Type Mean SE SD N
129/J 63,772 ± 1,771 ± 4,339 7
A/J 50,615 ± 1,319 ± 3,490 8
AKR/J 62,788 ± 935 ± 2,091 6
BALB/cBy 55,859 ± 1,178 ± 3,331 7
BALB/cJ 63,393 ± 2,290 ± 6,058 8
C3H/HeJ* 67,029 ± 1,696 ± 3,793 6
C57BL/6** 54,630 ± 874 ± 3,910 21
C57BL/6JAx1 66,082 ± 1,708 ± 4,832 9
C57BLKS/J 65,667 ± 1,886 ± 4,217 7
CBA/CaJ 56,028 ± 1,203 ± 2,691 6
CE/J 63,593 ± 2,536 ± 5,072 5
DBA/2J 63,351 ± 1,208 ± 4,186 13
LP/J 52,225 ± 1,989 ± 5,262 8
NZB/BinJ 61,063 ± 1,600 ± 3,579 6
NZW/LacJ 63,711 ± 727 ± 1,259 4
PL/J 55,976 ± 1,309 ± 3,462 8
SJL/J 52,473 ± 1,770 ± 3,958 6

*SD and SE have been corrected using the Gurland and Tripathi (1971) equation.
**Pooled data from 3 C3H/HeJ and 3 C3H/HeSnJ mice.
***Pooled data from 17 pigmented and 4 coisogenic albino mice.

 

Variation among the BXD recombinant inbred strains. The BXD strains were generated by crossing C57BL/6J and DBA/2J mice (Taylor, 1978). The two parental strains have populations of 54,600 ± 900 and 63,400 ± 1,200 cells, respectively. Average neuron numbers of the 26 BXD recombinant strains extend well beyond the parental limits—from 50,900 ± 1,100 to 75,800 ± 2,200 (Tables 1, 4). The broad range is associated with a high F ratio (F [22, 119] = 16.0, P < 0.001). Two of 26 BXD strains had populations near 75,000, a level not approached in any of the other strains.

 

Table 4. BXD Recombinant Inbred Strains (July 1996)
Type Mean ± SE ± SD N
BXD27 50,818 ± 1,120 ± 2,504 6
BXD23 52,977 ± 1,049 ± 2,532 6
BXD13 53,169 ± 1,883 ± 3,766 5
BXD28 53,628 ± 2,327 ± 5,699 7
BXD25 53,823 ± 1,480 ± 3,624 7
C57BL/6J 54,630 ± 874 ± 3,910 21
BXD18 55,058 ± 870 ± 1,945 6
BXD12 56,789 ± 2,096 ± 4,192 5
BXD20 59,872 ± 1,873 ± 5,619 10
BXD21 59,968 ± 1,474 ± 3,899 8
BXD1 60,289 ± 1,138 ± 3,597 11
BXD11 61,049 ± 1,108 ± 3,135 9
BXD24 62,395 ± 1,034 ± 2,532 7
BXD6 62,688 ± 839 ± 2,055 7
BXD8 63,016 ± 2,568 ± 5,135 5
DBA/2J 63,351 ± 1,208 ± 4,186 13
BXD29 63,585 ± 1,361 ± 3,044 6
BXD15 63,831 ± 1,120 ± 2,504 6
BXD14 64,047 ± 1,615 ± 3,957 7
BXD16 64,049 ± 1,360 ± 3,042 6
BXD22 64,459 ± 1,194 ± 2,389 5
BXD9 65,622 ± 1,702 ± 3,806 6
BXD2 65,880 ± 1,798 ± 3,597 6
BXD30 66,518 ± 1,672 ± 3,740 6
BXD31 66,553 ± 1,212 ± 2,709 6
BXD19 67,054 ± 1,313 ± 3,7136 9
BXD5 75,548 ± 1,338 ± 2,991 6
BXD32 75,727 ± 2,200 ± 6,600 10

*SEs and SDs are corrected (see Materials and Methods).

 

Bimodality of strain averages. The average number of neurons across all 43 homozygous strains listed in Tables 3 and 4 is close to 60,000, but this value corresponds to a surprising gap in the distribution (Fig. 4). A chi-square test confirms that this distribution is not Gaussian (chi^2 [7] = 16.1, P < 0.025). A simple alternative is that the underlying population has two modes. To test this idea we computed the normalized probability densities for the set of 17 inbred strains and for the set of 23 BXD strains. This procedure involves calculating the Gaussian probability density for each strain average (see the small functions labeled C57BL/6J and DBA/2J in Fig. 4). These functions are then summed to give a cumulative probability density. In essence, a probability density is a histogram in which Gaussian functions rather than single values are tallied. The probability functions for both groups are bimodal (Fig. 4), and both are remarkably similar in shape. The main difference between the two functions is the third mode at about 75,000 in the recombinant inbred group generated by BXD5 and BXD32.

Collectively, 13 of the 43 inbred strains have populations that range from about 51,000 and 56,000. They make up a low phenotype group that has a mode near 55,500. Among these 13 strains the 95% t-distribution confidence interval extends no higher than 59,000. A second, and more sharply resolved group is made up of 24 strains, all of which have means between 61,000 and 68,000. In none of these strains does the lower limit of the 95% t confidence interval extend below 58,000. Four of the BXD strains—BXD1, BXD12, BXD20, and BXD21—have intermediate cell populations between 56,500 and 60,500. Finally, two strains—BXD5 and BXD32—have averages far above the second mode and may represent a third very high cell number phenotype. The two probability densities in figure 4 can themselves be summed. The modes of this cumulative function are at 55,000 and 63,500. The low point between the two modes falls at 58,000.

Legend to Figure 4. Bimodal distributions of ganglion cell numbers. The function labeled 17 inbred strains is based on data in Table 3. For each inbred strain, the Gaussian probability density of the sample mean was computed at 500 cell intervals. Values were summed and divided by 17 to obtain a normalized cumulative probability for this group. The plot labeled BXD strains was computed in the same way using data listed in Table 4 (the parental strains were excluded). The individual distributions are shown for C57BL/6J and DBA/2J—the two strains used to generated the BXD recombinant inbred strains. These strain-specific Gaussian distributions provide a sense of the contribution that single strains make to the cumulative density (values for these two small distributions have been divided by 23).

 

Variation within isogenic strains

The level of variation within isogenic and non-isogenic groups. Variation in neuron number within members of isogenic groups is due to environmental and non-genetic developmental effects. We have already discounted the likelihood that sex differences or age contribute to normal variation among mice, but this still leaves room for numerous non-genetic sources of variation, including maternal care, litter size, and developmental noise (Wright, 1968, chapter 5). But the dominant source of quantitative variation within isogenic groups in this study is technical error. This technical variance had to be measured and eliminated before we could estimate the magnitude of genuine non-genetic effects. By repeating counts of 116 cases—in several cases three or even four times (Table 1, and see Material and Methods)—we determined that the standard deviation between pairs of counts from the same nerve averaged approximately 4,000 ± 400 (SE). Of this technical variance, 60-70% was due to the density with which we sampled each case (about 25 samples per nerve) and the remainder was due to calibration and measurement error. Had we sampled six adjacent thin sections from a single nerve, rather than six sections from different cases, our apparent non-genetic coefficient of variation would still have amounted to about 6.5%/ This is our average technical variance for a single estimate. The average variation within isogenic strains prior to any replication was 7.9%. We subtracted the square of the technical variance from the square of the mean total variance to obtain a more realistic estimate of non-genetic effects on the ganglion cell population (see Materials and Methods). For all of the inbred strains listed in tables 3 and 4 the corrected environmental coefficient of variation averages 4.60% ± 0.4%.

Sensitivity to environmental factors is likely to vary among groups of inbred strains. The uncorrected coefficients of variation for single isogenic strains range from 3 to 10%. The average coefficient of variation for 17 standard inbred strains prior to any corrections for technical error, is 6.5% ± 0.5%. The average corrected variation of the BXD recombinant inbred strains is 5.8% ± 0.4%. Compared to these laboratory strains, the coefficient of variation for seven wild inbred strains is higher—9.7% ± 2.3%. The higher variability in wild mice is presumably due to adverse gene-environment interaction effects associated with their often poor adaptation to laboratory rearing conditions. While we have not been able to formally demonstrate a significant level of non-uniformity of variance between individual strains (Bartlett's chi-square [39] = 32.6) this is probably due to the masking effect of the fixed technical error that is included in uncorrected estimates of strain variance. [Due to the small sample number within single strains (n < 10), most strain variances cannot be effectively corrected for technical error.]

 

Heterosis, heritability, and test-cross results

F1 heterosis and inbreeding depression. To assess the effects of inbreeding and the magnitude of gene dominance effects on neuron number we compared the population size and its variation between inbred strains and five sets of F1 hybrids (Table 5). Each set of hybrids is isogenic (Falconer, 1989), but because these F1s are generated by crossing very different strains, they have an especially high level of heterozygosity. The crosses included low-low, low-high, and high-high parental strain pairs. The ganglion cell population in F1 hybrids was on average somewhat higher (+1,600 cells) than the midpoint between parental strains. The largest positive deviation from the midpoint was about 5,300 cells in the F1 cross between CAST/Ei (45,000 cells) and BALB/cJ (63,400 cells). In general, the F1 results are consistent with mild heterosis and mean positive dominance at loci affecting ganglion cell number (Table 5). The relatively high population of cells in the out bred laboratory strain CD-1 (n = 68,300, Table 7) is also consistent with mild heterosis. The variation in isogenic F1s and isogenic inbred mice (wild strains excluded) do not differ significantly (Table 5 versus Tables 3 and 4; 5.8% ± 0.8% versus 6.2% ± 0.3% prior to a correction for technical variance). Thus, there is no evidence that cell number in homozygous mice is more easily perturbed by developmental or environmental factors than it is in isogenic F1 hybrids (cf. Waddington, 1957; Wayne et al., 1986; Leamy, 1992).

 

Table 5. Ganglion cell population size in F1 hybrids and their parentals
Type Mean SE SD N Maternal Mean Paternal Mean Mid* Delta**
CAF1/J 56,147 1,794 4,010 6 BALB/cJ 63,393 A/J 51,238 57,315 -1,169
BCF1 59,705 1,278 3,615 9 BALB/cJ 63,393 CAST/Ei 45,484 54,439 5,267
PLSJF1/J 56,096 1,279 3,134 7 PL/J 55,976 SJL/J 52,473 54,225 1,871
B6AxCF1/JGo 64,854 2,408 5,898 7 C57BL/6JAx1 66,082 BALB/cJ 63,393 64,738 116
CB6Ax1F1/J 66,688 1,094 2,446 6 BALB/cJ 63,393 C57BL/6J 66,082 64,738 1,950

*Mid is the midpoint between maternal and paternal strain averages.
**Delta is the difference between the midpoint and the actual F1 hybrid estimate.

The strength of genetic determination. A comparison of the level of variance within and between groups of inbred strains can provide an estimate of the strength of additive genetic control on neuron number (Hegmann and Possidente, 1981). Our analysis of variance demonstrates far greater variation between strains than among individuals within strains. The total variance within isogenic laboratory strains averages 15.1 (variance units are x10^6 cells^2). Estimates of this variance for two different sets of strains are close (Table 6, column Vwt). When technical error is subtracted, the average environmental variance within all isogenic inbred mice drops to 5.00 (Table 6, Vw). In comparison, variance across strains is far higher (Table 6, Vb). From these values we estimate that the narrow sense heritability, h2 is about 0.8 (Table 6). The internal errors of these estimates were computed using a jackknife procedure (Mosteller and Tukey, 1977), and the error across independent data sets is under ± 0.10. When the same estimates are made, but now without compensating for technical variance, estimates of additive genetic control range between 0.45 and 0.74. Comparable estimates of omega-squared (Wahlsten, 1992) are 0.56 for inbred and 0.70 for BXD strains. These latter estimates are lower primarily because they also do not subtract the technical error.

 

Table 6: Estimates of heritability*
Type Vwt Vw Vb h^2 SE N
Inbred 15.8 5.68 29.0 0.72 ± 0.09 17
BXD 14.7 4.61 48.8 0.83 ± 0.06 23
Combined 15.1 5.00 40.3 0.82 ± 0.04 40

*Vwt = variance within strain, including technical error;
Vw = variance within strain after correcting for technical error;
Vb = variance between strains; h^2 = narrow-sense heritability;
N = number of strains used in estimate. Variance units are x10^6 cell^2.
Wild strains listed in Table 2, which comprise different species
and subspecies, were excluded from this analysis.


 

Table 7: Genetically heterogeneous groups
Type Mean SE SD N
CARL/ChGo 51,263 ± 2,270 ± 7,177 11
BCF2/JGo 56,660 ± 697 ± 7,280 110
CD-1 68,338 ± 2,183 ± 7,869 14

In comparison to isogenic strains, the coefficient of variation within three groups of genetically heterogeneous mice (CARL/ChGo, CD-1, and BCF2) averaged 12.8% ± 0.9%. This high value represents both a small environmental component (about 4 to 5%) and a much larger genetic component (11 to 12%). The increment in variance between isogenic strains and these outbred mice is due principally to genetic factors in a broad sense, including both dominance interactions between alleles and epistatic interactions between recombinant loci. From these values we estimated broad-sense heritability. The first estimate of 0.90 was generated by comparing the average variance in genetically heterogeneous strains (Table 7) with that in isogenic strains (Tables 3, 4, 5). The second estimate of 0.95 was generated by taking the ratio of the variance in the BCF2 progeny to the average variance within the parental strains, BALB/cJ and CAST/Ei, and their F1 hybrid, BCF1. This second value is likely to be inflated by the substantial genetic differences between the parental strains, CAST/Ei and BALB/cJ.

Test cross progeny. The relative importance of additive gene effects, gene dominance, and heterosis can often be estimated by comparing intercross and backcross progeny (Falconer, 1989; Crusio, 1992). The magnitude of the additive genetic variance in F2 progeny is approximately equal to the summed variance in both backcrosses (Crusio, 1994). However, in our CAST/Ei x BALB/cJ cross the variance in the F2 progeny was substantially higher than the summed variance in the two backcrosses. This may be due to sampling error in the backcross progeny or to the disruption of epistatic complexes that stabilize neuron number in the F2s. A Mendelian test cross can be useful in estimating the approximate numbers of genes that contribute to variation (Wright, 1978; Barton and Turelli, 1989). We crossed BALB/cJ females (a high strain) to CAST/Ei males (a low strain), and then backcrossed and intercrossed these F1 progeny. If a small number of loci, each with additive effects, contribute to variation in ganglion cell number, then phenotypes of individual F2 progeny will occasionally have parental phenotypes (Falconer, 1989). In contrast, if many gene loci affect the phenotype, then the random assortment of alleles at many loci should lead to only a modest increase in variance in the F2 generation and these progeny should have intermediate phenotypes that are distributed normally. We found that variance in the BCF2 progeny was extremely high—greater even than the summed variance in both groups of backcross progeny (Table 8, Fig 4B). Many of the F2 progeny have ganglion cells populations close to, or even exceeding, the parental values (Table 1). This suggests a very small number of segregating loci. The Castle-Wright formula gives a minimal estimate of one major factor (Wright, 1978). But the relatively large number of F2 mice with very high cell numbers (overdominant phenotypes) suggests that there is at least on other locus with major effects. The unusually high variance may also be due to novel epistatic interactions introduced in the F2 generation.

 

Table 8: Test cross between CAST/Ei and BALB/cJ
Type Mean SE SD CV N
CAST/Ei 45,484 ± 999 ± 3,160 6.9% 11
BCF1 59,705 ± 1,278 ± 3,615 6.1% 9
BCF2 57,805 ± 1,523 ± 9,013 15.6% 45
BCCN2* 56,673 ± 2,970 ± 6,642 11.7% 6
BCBN2* 60,679 ± 1,571 ± 3,847 6.3% 7
BALB/cJ 63,393 ± 2,210 ± 5,846 9.2% 8

*Mothers of BCCN2 and BCBN2 progeny were BCF1.

Maternal factors. The observation that both the BCF1 intercross and the BCCN2 backcross progeny have higher average cell populations than expected suggests either that BALB/cJ alleles are dominant or that there are positive BALB/cJ maternal effects (Wahlsten, 1983; Cowley et al., 1989; Bulman-Fleming et al., 1991). We do note that the average population in both F1 and F2 test cross progeny are closely matched (Table 8). This is of interest because the mothers of the BCF1 mice were fully inbred BALB/cJ females, whereas the mothers of the F2 mice were hybrid F1 females. Both types of females had approximately the same adult body size (25-30 gm). But in this case, reproductive heterosis in the F1 generation is clearly not associated with F2 progeny that have higher cell number. However, these hybrid females did produce F2 progeny with populations that ranged over a remarkably wide range—from 45,000 to 70,000 in single litters. Maternal effect is not a source of variation because the BCF1 mothers are isogenic. Furthermore, the marked differences in ganglion cell numbers among the F2 progeny are not related to differences in brain weight (r2 = 0.08), also indicating that maternal effect is not a significant factor in this cross.
 

 

Discussion

Synopsis. The population of retinal ganglion cells varies twofold even among closely related mice. Seventy to ninety percent of this variation can be traced to genetic differences. Sex and age differences are negligible. The coefficient of variation within groups of isogenic animals averages only 4%—a result that demonstrates that large populations of neurons in mammals can be regulated precisely. The reproducible bimodality of ganglion cell numbers among different populations of mice is an important result because it indicates that normal allelic variants at single gene loci can exert high levels of control over neuron number in the vertebrate CNS.

 

Environmental variation and the precision of genetic control in isogenic mammals

An analysis of isogenic animals makes it possible to assess the consistency with which the genome guides the generation of traits such as neuron number. When environmental differences are minimized, the residual variance is due to microenvironmental effects and developmental noise (Waddington, 1957; Stent, 1981; Gavrilets and Hasting, 1994, Scheiner 1993; Cheetham et al., 1995). In a systematic analysis of the grasshopper nervous system, Goodman (1976, 1979) found a remarkable level of variation in neuron number both within and between isogenic groups that had been reared in a tightly controlled environment. In one exceptional group, half of the animals had the standard set of six ocellar interneurons whereas the other half had seven to nine interneurons. In contrast, in a survey of optic nerves from a set of more than 100 isogenic crustaceans, Macagno (1980) found only a single exception to the rule of 176 axons. The question immediately arises whether large populations of neurons in the CNS of isogenic vertebrates are subject to high or low levels of variation? The cellular composition of the vertebrate CNS is known to be variable. But in the absence of an analysis of isogenic vertebrates, this variation could be due to genetic polymorphisms rather than lax developmental regulation.
     It has been difficult to carry out a biometric analysis of neuron populations in vertebrates, first because technical errors intrude into all estimates (Williams and Rakic, 1988b; Gundersen et al., 1988), and second, because large numbers of isogenic animals must be studied. In this study, we have resolved the technical problem by independently replicating more than 100 cases to determine the cumulative reliability of the counts (Table 1). We can now provide an accurate answer to the question of how precisely a large population of neurons can be regulated in a vertebrate. After subtracting technical error, we find that the coefficient of variation in ganglion cell numbers among isogenic mice averages 4%. If a typical isogenic mouse strain has a mean population of 60,000 neurons, individuals will occasionally (1 in about 50 cases) have numbers lower than 55,000 or higher than 65,000. This low level of variation is impressive, and corresponds nicely to the 3.5% coefficient of variation in total brain weight within isogenic mice (Lande, 1979, p. 411).
     Despite the reassuring similarity in these two estimates, the level of variation we have measured in the ganglion cell population should not be taken as a good estimate for other neuronal populations or even for the ganglion cell population of an uncharacterized strain of mouse. There are unpredictable differences in the range of phenotypes that single genotypes can generate (Williams, 1992). For example, BALB/cJ, C57BL/6J, and several wild inbred strains have levels of nongenetic variation that range up to 10%, even in a stable environment. An even more forceful example is the belly spot and tail (Bst) mutation that we have recently characterized in the mouse (Rice et al., 1995b). In Bst mice the entire ganglion cell population is often eliminated just on one side. This asymmetric effect illustrates just how important epigenetic developmental factors can sometimes be in determining final neuron number. Two conclusions can be drawn: 1) variation is itself variable, and 2) the magnitude of nongenetic variation is under partial genetic control (Scheiner and Lyman, 1989).
     To what extent is variation among isogenic mice due to developmental differences in the kinetics of neuron production, commitment, or cell death, and to what extent is variation due to conventional environmental factors such as litter size, parental care, food, climate, and disease? One way to begin answering this question is to measure the correlation between the ganglion cell population and total brain weight within isogenic strains. A reasonable presumption is that major environmental factors—for example, nutrition—will have widespread and common effects. Consequently, the correlation between brain weight and ganglion cell number within an isogenic strain might be high. However, we find that this correlation is actually remarkably low (r= 0.14). This indicates that little, if any of the variance in retinal ganglion cell number within strains is associated with differences in brain weight. The "environmental" effects that we have measured are probably the result of intrinsic developmental noise in ganglion cell production and survival.

 

Genetic variation

Genetic differences account for most of the variation in ganglion cell numbers among mice. Seventy to eighty-five percent of the variation is due to the independent and additive effects of allelic variants—what is termed narrow-sense heritability. Estimates of total genetic determination, or broad-sense heritability—a value that includes gene dominance effects and epistatic interactions among loci—are in the neighborhood of 90%. These estimates neatly bracket the 80% estimate of genetic control over granule cell number in the dentate gyrus of mice (Wimer and Wimer, 1982, 1989). Heritability estimates such as these are based on ratios between genetic and nongenetic variance. Consequently, minimizing environmental variance increases measured heritability. In this study, all mice were reared in a pathogen-free laboratory environment—a situation that eliminates numerous sources of environmental differences, and that almost certainly increases estimates of genetic control compared to dispersed wild populations of mice. However, it is worth emphasizing that we included mice of a wide range of ages, both sexes, and taken from different litters and different mothers within strains. The environmental range that we have sampled is appreciable and is typical of most research colonies, perhaps even stable wild populations.
     There are several reasons why the high estimate of genetic determination is significant. The pace of brain evolution under selection is critically dependent upon a reservoir of normal allelic variants that modulate brain development (Romer, 1969; Kruska, 1987; Lipp, 1989; Finlay, 1992; Williams et al., 1993). The fact that the ganglion cell population is strongly controlled by additive gene factors suggests that selection could produce rapid phenotypic change. Given our results, even a short period of direct selection (<20 generations) might change numbers twofold (Falconer, 1989; Barton and Turelli, 1989). A interesting question is whether selection for high or low ganglion cell number would be matched by a correlated response in either body size, brain weight, or eye size (Lande, 1979; Purves, 1988, Finlay and Darlington, 1995). In an analysis of evolutionary change in the cat's visual system, we found that several cell populations were reduced neatly in proportion to the reduction in total brain weight (Williams et al., 1993). This is consistent with the idea that common gene mechanisms link the proliferation and survival of neurons in different parts of the brain. However, in this same study two important populations—rod photoreceptors and alpha ganglion cells—did not scale with brain size. This independence is consistent with the idea that regional and cell-specific differences in gene expression (e.g., Lipp, 1989; Rubinstein et al., 1994; Usui et al., 1994) can adjust the size of individual neuron populations.
     Levels of phenotypic variation provide insight into the contribution of specific traits to fitness (Wright, 1978; Levinton, 1988; Barton and Turelli, 1989; Williams, 1992). In general, traits that are highly variable within a population contribute less to fitness than those that are tightly regulated (Yablokov, 1974). Intense directional selection trims away the maladapted extremes, a process that can reduce allelic diversity at key gene loci. It has also been noted that traits that are important in fitness tend to have low heritability and high levels of directional dominance (Hahn and Haber, 1978). In contrast, traits that are only weakly selected display greater additive genetic variation and comparatively high heritability (Roff and Mousseau, 1987; Mousseau and Roff, 1987). From this perspective, the relatively high heritability that we have measured, coupled with the wide range of phenotypes in outbred groups of animals, suggests that the particular size of the retinal ganglion cell population does not materially affect the fitness of mice, and that polymorphisms having large phenotypic effects have been allowed to accumulate. Given the high variance even in the wild non-inbred group of M. caroli mice, this characteristic is probably not due to relaxed selection associated with 400 or more generations of laboratory breeding. While, it would be useful to confirm this by further analysis of wild populations, this idea is also consistent with the seminocturnal niche of most mice and the reliance that they presumably place on nonvisual sensory modalities (Fuller and Wimer, 1966). Less variation and lower estimates of heritability might be expected in the murine trigeminal system.

 

Significance of the bimodal distribution

The bimodality of strain averages is a surprising and important finding that provides evidence that there are single polymorphic genes that have comparatively large effects on neuron number. This conclusion is strengthened both by the bimodality of the F2 test cross progeny and by the large differences between three pairs of very closely related inbred strains. A speculation based on these findings is that variation in other neuron populations may also be controlled by relatively small numbers of quantitative trait loci that have major effects.
     What differences in development might account for the two modes? A simple idea is that the modes trace back to early differences in numbers of retinal founder cells. For example, low strains may have an average of six progenitors, whereas high strain have an average of seven. If we assume that progenitors contribute equally to the population, then each would produce a net of roughly 8,000 ganglion cells, giving modes at about 56,000 and 64,000. Quantal variation is striking in the Purkinje cell and facial motor neuron populations of mice (Wetts and Herrup, 1983; Herrup et al., 1984; Herrup, 1986). If the modes in retina have this quantal origin then numbers of many other retinal cell types should also be high in strains with high ganglion cell number. An alternative hypothesis is that the bimodality reflects strain differences in gene expression that specifically target precursors of retinal ganglion cells or the young postmitotic ganglion cells themselves at a later stage of development. If the bimodality is specific to ganglion cells then the correlation between ganglion cell number and that of other retinal cell types should be weak. It would be useful to focus on the three pairs of closely related mice that have population differences of 11,000 to 12,000 cells.

 

Prospects for the functional and genetic analysis of natural variation in brain structure

The wide range in the ganglion cell population among mice provides excellent material to study the functional consequences of differences in neuron number. For example, it should be practical to test whether differences in receptive field size and visual performance correspond to the 50% difference in cell number between BXD28 and BXD32—two related strains with closely matched brain weights (405 ± 8 and 429 ± 4 mg). Exploiting the robust and large variation among inbred strains could complement experimental studies in which dendritic diameter, receptive field size, and contrast sensitivity have been studied with reference to total ganglion cell number following prenatal and early postnatal lesions (Shook et al, 1983; Kirby et al., 1985; Kirby and Chalupa, 1986; Heywod et al., 1988). One advantage of using strains of mice is that many individuals with well characterized phenotypes can be compared. Sampling and technical error can be reduced to very low levels compared to experimental manipulations (Fuller and Wimer, 1966; Lipp et al., 1989). Strain differences also provide excellent material for developmental studies—to determine whether variation between strains arises during cell generation or after cell death (Linden and Pinto, 1985; Williams et al., 1990; Strom et al., 1995).
     Variation in neuron number is widespread among rodents. Strain differences ranging from 25% to 100% have been discovered in hippocampus (Wimer et al., 1976, 1978, 1988; Wimer and Wimer, 1989), neocortex (Wimer et al., 1969), forebrain cholinergic regions (Albanese et al. 1985), olfactory bulb (Smith, 1928), substantia nigra (Ross et al. 1976), locus coerulus (Berger et al., 1979), and cerebellum (Wetts and Herrup, 1982). In several cases the numerical differences have clear biochemical and functional correlates (Berger et al., 1979; Albanese et al., 1985). There are good reasons for renewed interest in these robust quantitative differences in CNS structure. The foremost reason is that is it now practical to map genes associated with these types of complex quantitative traits (Lander and Botstein, 1989; Belknap, 1992; Johnson et al., 1992; Belknap et al., 1993; Plomin and McClearn, 1993; Dietrich et al., 1994; Lander and Schork, 1994; Lai et al., 1994; Crabbe et al., 1994; Silver, 1995). The rapid progress in generating high resolution maps of chromosomal regions containing genes expressed in the CNS will greatly improve the efficiency of cloning quantitative trait loci (Adams et al., 1993a,b; Polymeropoulos et al., 1993; Durkin et al., 1994). Given the extraordinarily large numbers of genes expressed in the vertebrate nervous system—no less than 30,000 (Sutcliffe, 1988; Adams et al., 1993b)—it is encouraging that an important subset of genes with unambiguous effects may be mapped and ultimately sequenced using this forward genetic approach (Takahashi et al., 1994).

 

Acknowledgements

This research was supported by grants from the National Institutes of Health to RW and DG and a grant from the University of Tennessee Physicians Foundation to RW. Institutional and mouse colony support was provide by the Center for Neuroscience at the University of Tennessee. R. C. Strom and D. S. Rice were supported by training grant USPH SGRNS-07323. We are indebted to Richard Cushing, Toya Kimble, and Kathy Troughton for technical support. We thank Drs. Douglas Wahlsten, Benjamin Taylor, John Belknap, Eric Lander, Muriel Davisson, and Richard and Cynthia Wimer for comments and advice. Evan Williams helped count.

 

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