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Anatomy and Morphology |
/m) in the apical meristem1
Department of Biology, University of Miami, P.O. Box 249118, Coral Gables, Florida 33124-0421 USA
Received for publication February 22, 2006. Accepted for publication October 4, 2006.
ABSTRACT
The 
model for plant mating system evolution proposes a causal link between , the number of mitoses that occur within a plant's lifetime from zygote to gamete production, and constraints on the evolution of inbreeding depression and thereby on the evolution of plant mating systems. Through its use of plant stature, the model emphasizes the important role of morphology in creating developmental and genetic constraints on plant evolution. However, the estimation of itself is likely to be extraordinarily complex. Here I describe a protocol for estimating per meter linear growth by an apical meristem (/m) using medial pith cells from mature internodes of twigs. While such cells are produced by the apical meristem, during internode elongation, these pith cells also undergo further mitoses, and thus their measurement can only approximate a "true" /m via the application of a multiplier (the adjustment ratio) that partially corrects for the occurrence of cell divisions and cell growth beyond the apical meristem. I applied this method to Delonix regia (Caesalpiniaceae) and derived several adjustment ratios from the literature. Because variation in /m can have profound evolutionary implications, I also examined interspecific and intraspecific variation as well as within-individual variation in /m. Conifers apparently have lower /m than do angiosperms, while 20% of the total variance in /m for D. regia was found among individual trees, with the remainder found within trees. Given the large differences in stature between "high-" plants such as trees and "low-" plants such as herbs, these results support the idea that the total per-generation mutation rate for high- plants is likely to be many times higher than that for low- plants.
Key Words: adjustment ratio • apical meristem • diplontic selection • mitotic growth rate • mitotic mutation • model • pith
One of the more common evolutionary transitions in plants is a shift from a predominantly outcrossing to a predominantly selfing mating system (Stebbins, 1950
). The many intrinsic benefits to selfing (Uyenoyama, et al., 1993
; Morgan et al., 1997
; Goodwillie et al., 2005
) are offset by the presence of inbreeding depression, defined as the relative reduction in mean fitness of selfed progeny as compared to outcrossed progeny (Charlesworth and Charlesworth, 1987
; Husband and Schemske, 1996
). Although understanding the evolutionary dynamics of inbreeding depression is critical to a complete understanding of the evolution of plant mating systems, constraints on the evolution of inbreeding depression itself have rarely been considered. The recently proposed model for the evolution of plant mating systems describes a novel constraint on the evolution of inbreeding depression that is directly dependent upon , the number of mitotic cell divisions that typically occur in a plant's lifetime from zygote to gamete production (Scofield and Schultz, 2006
). The model predicts that while both small-statured ("low-") plants such as herbs and large-statured ("high-") plants such as trees may have high inbreeding depression and an outcrossing mating system, only in low- plants can inbreeding depression evolve to be low under nearly all natural conditions. Thus, only low- plants can evolve a mating system that includes selfing. The model emphasizes the importance of developmental and genetic constraints created by plant stature in plant mating system evolution and thus helps to unify diverse areas of research.
A reduction in fitness of selfed progeny due to inbreeding depression is largely the result of the deleterious effects of homozygous recessive alleles maintained via recurrent deleterious mutation at the per-generation genomic rate U (Lande and Schemske, 1985
; Charlesworth and Charlesworth, 1987
; Husband and Schemske, 1996
). The model assumes that U is a positive function of , based on two critical observations: (1) plants do not segregate a separate germ line (Klekowski, 1988
), and (2) there is a minimum error rate associated with DNA replication during mitosis (Maki, 2002
; Kunkel, 2004
). Thus, represents the lifetime opportunity for fixation of de novo deleterious mutations appearing during mitotic growth in meristems and the subsequent incorporation of these mutations into gametes. Just as the critical link between paternal age and disease occurrence in humans underscores the need to understand the quantitative link between germ line mitoses and mutation rate (Crow, 1997
), the model emphasizes the critical importance of recognizing the deleterious genetic effects of mitotic growth and thus the correlations that must exist between growth, stature, and mating system evolution (Scofield and Schultz, 2006
). A similar view with respect to plant developmental evolution has long been advocated by Klekowski (e.g., 1988
, 1998
).
Despite tremendous advances in our knowledge of plant growth and development, a precise determination of for any species is likely to be extraordinarily complex. Meristem structure influences fixation rates of deleterious mutations in plants (Klekowski and Kazarinova-Fukshansky, 1984a
, b
; Klekowski et al., 1985
), various meristematic organizations such as the méristèm d'attente (Romberger, 1963
; Klekowski, 1988
) complicate just what might represent a "meaningful" mitotic division in terms of correlated contributions to U, and subsequent cellular specialization obscures the relative contributions of meristematic vs. postmeristematic mitoses to specific tissues (Esau, 1965
; Brown and Sommer, 1992
). Perhaps most important from an evolutionary standpoint, the degree to which may vary among species and within and among individuals of high- species (Cloutier et al., 2003
; Scofield and Schultz, 2006
) can potentially have a large influence on variation in mutation rates and thus on the evolutionary histories of species and populations of high- plants. Genetic and/or environmental variation in may have a large effect on fitness variation among individuals of a population, while variation within individuals due to, e.g., within-crown differences in light environment may have an aggregate effect on individual fitness. The magnitude and structure of such sources of variation, if present, are entirely unknown. Furthermore, the effort required to estimate is likely to be large, so guidance in designing efficient sampling strategies would be useful.
Although linear growth itself (the length of the "developmental stream," Kearsley and Whitham, 1998
) is clearly a correlate of and must be a component of any empirical estimate of , it is preferable to begin by establishing the nature of via examination of direct mitotic products, to understand both the relationship between and its correlates and any underlying variational structure. One promising method for estimation of /m, the number of mitosis per meter linear growth of an apical meristem, is the rate of production of undifferentiated medial pith cells in proximity to the apical meristem (Cloutier et al., 2003
). The use of the overall growth rate of medial pith cells as a proxy for /m within the apical meristem has several apparent advantages. These pith cells originate within the apical meristem or in very close proximity to the apical meristem and remain relatively undifferentiated; they are of relatively constant size following maturation and are thus closely correlated with linear measures of growth attributable to a single apical meristem; and they are large and easy to observe in a variety of species.
A disadvantage to the use of medial pith cells as a proxy for /m is that it is unlikely that all pith cells are the direct products of cell divisions within the meristem, because pith cells typically undergo further divisions immediately below the meristem during internode elongation (Brown and Sommer, 1992
). However, regardless of the underlying physical mechanism that results in increased internode length, we may be able to assume that the rate of production of the direct products of the apical meristem, which may be called the "true" /m, and our medial-pith-cell-based proxy for /m are related, to a first approximation, via a species-specific multiplier (the "adjustment ratio") relating the mean number of "young" pith cells produced by an apical meristem per meter of initial internode to the mean number of mature pith cells per meter of mature internode. Thus, the adjustment ratio for a species corrects for changes in both cell number and size during internode elongation. Brown and Sommer (1992)
present medial pith cell size and number within internodes varying in developmental stage for several temperate tree species. For example, in Salix nigra L. (Salicaceae), a young "stage I" internode located just beneath the shoot apex averaged 69 cells/mm in a total internode length of 3 mm, while a mature "stage IV" internode that had reached its final putative length averaged 24 cells/mm in a total internode length of 33 mm. Thus, for S. nigra 207 young cells in a growing stage I internode became 792 larger cells in a mature, fixed-length stage IV internode, for an adjustment ratio of 0.26 young pith cells per mature pith cell.
The purposes of this study were to establish a protocol for the estimation of /m using medial pith cells, to examine variation in /m and in adjustment ratios among species, and, using the tropical leguminous tree Delonix regia, to examine variation in /m within species. I asked the following questions: What is the variation among species in /m? What are estimates of adjustment ratios among varied species? What are overall estimates of /m for D. regia, and what are the components of variation in /m among individual trees and among and within branches of the same tree? How can this variance structure be used to provide guidance for future sampling strategies? Finally, what are the implications of these results for mutation rates in high- plants?
MATERIALS AND METHODS
Study species
Delonix regia (Boj. ex Hook.) Raf. (Caesalpiniaceae) is a fast-growing, familiar tree planted as an ornamental throughout the world's tropical and subtropical regions. Delonix regia is native to the lowland, seasonal tropics of Madagascar but is very rare there (Corner, 1952
; Endress, 1994
). Trees used in this study were cultivated specimens growing on the University of Miami campus, Coral Gables, Florida, USA (25°43' N, 80°16' W). Growth axes of D. regia are sympodial, and the tree follows Troll's architectural model (Halle et al., 1978
; Tomlinson, 2001
). In south Florida, reproductively mature individuals grow to a center-canopy height of 6–15 m and a canopy diameter of 10–40 m (Tomlinson, 2001
).
Preparation of twig sections
In January 2003, I collected four apical twigs approximately 1 m in length and no more than 2 cm in diameter at their base from each of 25 separate D. regia. Each twig was collected from a different primary branch attached to the main trunk, and twig-bearing branches were chosen from several locations varying in exposure throughout the canopy. At the time of twig collection, tree size was measured as trunk diameter at 1.4 m height (dbh). Although individual D. regia may have multiple trunks originating below 1.4 m, all subject trees had a single unbranched trunk to at least 1.4 m.
In the laboratory, three 1-cm segments were cut from internodal locations selected at random between 30 and 60 cm from the growing tip; segments within this range had diameters of 1 cm. Thus, I attempted to avoid acropetal regions of the twig that might still be undergoing internode elongation (Brown and Sommer, 1992
). Each segment was stripped of its bark and cut in half longitudinally, and one half of each segment was selected at random.
The three segments of each twig were then fixed in 4% formaldehyde : 5% acetic acid : 47.5% ethanol : 43.5% H2O (FAA) for at least 24 h, dehydrated in 100% ethanol, impregnated with n-butanol, then impregnated with Paraplast+ paraffin (product 502004, Tyco Healthcare, Mansfield, Massachusetts, USA) using an initial bath of Paraplast+ and n-butanol in a 1:1 solution at 60°C followed by two baths of 100% Paraplast+ over at least 6 d. The hardened paraffin-segment block was trimmed, and four radial or nearly radial longitudinal sections of thickness 7–8 µm were cut from each segment on a Leica SM 2000R sliding microtome (Leica Microsystems GmbH, Wetzlar, Germany) with a Microm blade (Microm GmbH, Walldorf, Germany). These sections were affixed to a labeled slide using a single swiped drop of 0.1% albumin as an adhesive, and the slide was placed on a 40°C slide warmer for at least 48 h. Sections were deparaffined, stained in aqueous 0.05% toluidine blue O and 0.1% safranin O, dehydrated, and placed in a dust-free drawer until dry. Because of time constraints and with no further plans for examination of the sections used in this study, preparations were measured on the slide as described and were not embedded in resin nor covered with a coverslip.
Measurement of pith cell lengths
Cells were organized into clear longitudinal files, with cells within medial files clearly larger than cells within marginal files (Fig. 1A). The length of medial cells was measured along the longitudinal axis, using a Reichert microscope (C. Reichert, Vienna, Austria) with ocular micrometer. The ocular micrometer was calibrated with a 2 mm x 0.01 mm scale stage micrometer (Micromaster 12-561-SM3, Fisher Scientific, Hampton, New Hampshire, USA) prior to the first measurement. Following calibration at the measurement magnification of 200x, a single ocular micrometer unit was determined to be equivalent to 6.13 µm; this was reconfirmed several times during the course of measurement. Lengths were estimated to the nearest half unit, with the length of a cell extending between the middle of the cell walls shared with neighboring cells in the same file along the longitudinal axis. To reduce measurement error, the aggregate length of 10 contiguous cells within the same file was measured (Fig. 1B). Mean individual cell length was thus calculated as 0.1x the length measured, and the reported variance of cell length was determined from these calculated cell lengths. True variance of individual cell length would be 10x the reported variance, thus standard deviations and standard errors reported here should be multiplied by 
10 
3.2 to derive appropriate values for individual cells. Whenever possible for each segment, 10 files of 10 medial pith cells were chosen haphazardly for measurement from among the available files of medial cells.
|
/m and predictions of associated within- and among-tree variance components was performed using a random-effects analysis of variance with parameters estimated using restricted maximum likelihood ( 
; R Development Core Team, 2005
). For a given measurement taken of cell file l within segment k of branch j from tree i (ijkl/m), the effects of tree Ti, branch nested within tree Bij, and segment nested within branch Sijk were treated as normally distributed random effects with mean zero and variance 
ijkl assumed to be normally distributed with mean 0 and common variance 
2. In the analysis and discussion of the full model, I will assume that the large majority of the variance component 
ijkl may be assigned to among-cell file differences within segments, as additional sources of error at this physical scale, e.g., measurement errors, are expected to be minor in comparison to cell size (Fig. 1A). For statistical models other than the full model that incorporate a subset of the random effects (discussed later), the variance component due to residual error contains multiple strong sources of otherwise unassigned variation and is thus treated as true residual error. For notational convenience, "/m" will be dropped within statistical expressions.
The full statistical model for each measurement ijkl was thus the mean estimate of /m plus deviations due to each random effect:
|
| (1) |
). In addition to /m, which is the estimate reported in the Results, the quantities of interest are the four variance components of /m: 
2, which again, in the full model, is largely due to within-segment variation in cell size.
As is typical practice in fitting such models, the random effects (Ti, Bij, Sijk, ijkl) are assumed to be independent both within and between variance components. Thus there is no covariance between variance predictions, and we may sum variance components to form biologically plausible variance pools, as is done in the Results to examine the total within-tree variance (
Each variance component is reported as a deviance, the square-root of the variance prediction. Approximate normality of random effects and of residuals was confirmed visually using quantile-quantile plots. The improvement in the model fit due to the addition of each random effect was determined via observed decreases in negative log-likelihood values [–ln(L)] and the Akaike information criterion (AIC), as well as via likelihood ratio tests (LRTs) comparing fits after the sequential addition of each random effect, in order of decreasing physical size from
To test for an effect of tree size (measured as dbh) on pith cell size, the statistical model in Eq. 1 was augmented to include dbh as a linear covariate of ijkl. The dbh measurements were transformed to have mean zero so that the intercept of the augmented model estimated /m at mean dbh and the slope estimated the linear effect of dbh, if any. The fit of the augmented model was compared with that of Eq. 1 using LRTs after both models were fit via maximum likelihood, because models differing in fixed effects (via the addition of the slope estimate) cannot be compared using LRTs when fit using restricted maximum likelihood (Pinheiro and Bates, 2000
). Significance values of these LRTs were confirmed as conservative via simulation (
). RESULTS
Using the entire data set of 1380 measurements of medial pith cell files, mean /m (to three significant digits) was 26 600 ± 4510 (SD) cells/m, with a 95% confidence interval (CI) for the mean of (26 300, 26 800). Mean medial pith cell length (the reciprocal of /m) was 38.7 ± 6.54 µm. The measurements were approximately normally distributed (Fig. 2) with median (26 100 cells/m) similar to the mean and values at the 2.5% and 97.5% quantiles of 18 800 and 37 100, respectively.
|
/m and the variance components using the full statistical model given in Eq. 1, there were 876 measurements among the 92 segments within 44 branches of 11 trees. The data set contained a mean of 9.5 ± 1.7 measurements of medial files per segment, 2.1 ± 0.8 segments per branch, and 4 branches per tree for all 11 trees. Mean /m in the data subset (to three significant digits) was 27 000 ± 2870 cells/m with a 95% CI for the mean of (25 400, 28 600), and mean pith cell length in the data subset was 38.1 ± 6.86 µm; these estimates were similar to those found in the literature for several other species and represent neither an upper nor lower extreme among available data (Table 1). The confidence interval for mean /m calculated from the full statistical model is wider than that calculated for the mean only (Table 2) because the full statistical model takes into account the additional uncertainty due to the variance structure expressed in Eq. 1, which increases the imprecision in the /m estimate to the degree apparent in the confidence intervals.
|
|
/m in the full data set (LRT, 
2 = 2.09, df = 1, P = 0.15) nor in the data subset (LRT, 2 = 0.95, df = 1, P = 0.33).
Mean adjustment ratio among six diverse taxa was 0.19 ± 0.05 (Table 1). These adjustment ratios appear to be fairly tightly constrained around the mean, as the maximum adjustment ratio is just 2.5 times the minimum, and the mean adjustment ratio for just the five woody taxa (0.19 ± 0.06) was identical to the mean for all six. Notably, both the woody conifer Pinus taeda and the herbaceous annual Helianthus annuus have adjustment ratios within the range bookended by woody angiosperms. Using this mean ratio, from the estimate of /m from the full model analysis of the data subset, we calculated an adjusted /m for D. regia of 5130 cells/m with 95% CI of (4830, 5430). The use of this mean adjustment ratio calculated from six diverse temperate taxa to adjust cell sizes for the tropical legume D. regia is done with some reservation and will be discussed further. For simplicity, the remainder of the results and discussion will consider the unadjusted /m for mature pith cells unless otherwise indicated.
Within the data subset, there was clear variation in /m both among and within trees, with the pattern of variation differing from tree to tree (Fig. 3). All specified among- and within-tree deviance components were large and significant, and the addition of each variance component up to the full model presented in Eq. 1 resulted in a highly significant improvement in model fit, as determined by LRTs and a decrease in AIC and –ln(L) (Table 2). Of the total variance in the full model, 20% was among trees, 14% was among branches within a tree, 29% was among segments within a branch, and the remaining 37% was within segments (Table 2). For verification, mean-squared deviance components were calculated by hand from the data set (Sokal and Rohlf, 1995
). Though imbalance within the data set renders these mean-squared deviance components biased, it is notable that all such deviance components were significant as determined via F tests and were similar in both magnitude and rank order to the deviance components reported in Table 2 (data not shown).
|
2, excluding the among-tree variance component 
DISCUSSION
The estimates of /m given here (Table 1) indicate that, if plants have a per-mitosis rate of mutation similar to that observed in the human male germ line, then high- plants have per-generation genomic mutation rate U that may be dozens to hundreds of times greater than in low- plants or in any known animal. In human males, the mutation rate at age 20 yr is 8x that of a human female, with this difference apparently due to the male germ line having 170 more mitoses by age 20 yr than the 24 lifetime mitoses in the female germ line (Crow, 1997
). Using the adjusted /m for D. regia (Table 1), the total mutation rate of an apical meristem from a high- plant that has grown just 10 m would be approximately equal to that for a human male of age 5280 yr or 175x the human generation interval of 30 yr (Jack, 2005
).
There are a number of reasons to believe that the relative mutation rate in high- plants, as determined by this highly simplified analysis, is an overestimate. First, the assumption of equivalent per-mitosis mutation rates in plants and humans is almost certainly incorrect, because the large number of mitoses during mitotic growth in plants is likely to create strong selection to avoid the inevitable effects of deleterious mutation (Klekowski, 1988
) and thus plants may have a per-mitosis mutation rate that is lower than that within animal germ lines. Second, while there is clear evidence that genetic loads in high- plants are indeed higher than in low- plants and in animals (Lynch and Walsh, 1998
), the difference may not be as great as suggested earlier. For example, the average number of lethal equivalents among a group of high- conifer species is 14x that among a group of low- angiosperms (Table 10.6 in Lynch and Walsh, 1998
), and high- plants have 10–20x the number of chlorophyll deficiency mutations than do low- plants (Klekowski and Godfrey, 1989
; Klekowski, 1998
). Finally, the analysis ignores a nonlinear increase in the total mutation rate with increasing paternal age (Crow, 1997
); it is unknown whether there is a nonlinear increase in mutation rate with plant age. Thus, although the results presented here offer progress toward a more complete understanding of the interplay between plant stature, mitotic growth, and mutation, and thus contribute toward the further development of the model of plant mating system evolution (Scofield and Schultz, 2006
), a definitive synthesis comparing mitotic mutation rates among high- plants, low- plants, and animals remains to be made.
The use of adjustment ratios for /m
The use of the mean adjustment ratio among the six species in Table 1 to adjust /m calculated from mature pith cells of both D. regia and Pinus strobus requires some justification. Although we do not yet have adjustment ratios directly determined for any tropical species, D. regia is comparable to the temperate angiosperms in pith cell size (Table 1). The diverse temperate woody taxa also have adjustment ratios of similar magnitude, suggesting that differences in taxonomy, e.g., angiosperm vs. gymnosperm, that may affect cell size (Table 1), do not in turn affect the adjustment ratio. Additionally, and quite surprisingly, the adjustment ratio for the herbaceous Helianthus annuus (0.19) is equivalent to the mean adjustment ratio of the five woody taxa, despite having mature pith cells that are 2.7x larger than those of the largest woody species, P. taeda, as well as showing a much greater overall increase in size of mature pith cells over young pith cells (13x) than the 2–3x observed in woody species (Wetmore and Garrison, 1966
; Brown and Sommer, 1992
).
This suggests the occurrence of two different types of constraints active during pith development. First, there may be constraints on final pith cell size among woody taxa, perhaps due to wood development (Brown and Sommer, 1992
). Second, there may be a more general constraint on developmental changes expressed in the adjustment ratio that arises from, e.g., allometric or other developmental correlations that exist for both herbaceous and woody taxa. Certainly more study is required. Regardless of the underlying cause of similarity in the adjustment ratios, these results provide cautious support for the use of a mean adjustment ratio in correcting for changes in pith development in D. regia and P. strobus.
An important task for future work is to determine whether there exists significant intraspecific variation in the adjustment ratio. Other than the variance components analysis presented here, studies that examine the structure of such variation are rare in morphological work, but would certainly help to determine whether the patterns suggesting the constraints outlined are real or simply artifacts of the particular collection of species for which there are data.
Variance components of /m
Surprisingly, of the total variance in /m for D. regia, just 20% was explained by differences among trees (
The remaining 80% of the total variance fell among within-tree variance components (Table 2), with the overall range of /m measurements fairly well represented within each tree (Fig. 3). Regardless of statistical model, the among-tree variance component (Table 2,
+ Ti + Bij + Sijk + ijkl model.
Variation due to differences among branches within a tree (
). It has also been suggested that character trait differences among branches within tree crowns may be due to genotypic differences caused by mitotic mutation (Whitham and Slobodchikoff, 1981
; Gill et al., 1995
). Although the model is based on a similar mutational mechanism and would predict that the degree of mosaicism would be directly related to , it remains to be demonstrated whether the rate of mitotic mutation would be sufficient to create detectable genetic variance in quantitative traits such as /m. Regardless of the source of variation, the strength of 
/m from more than one branch per tree, with these branches varying in locations and exposures within the crown.
Variation due to differences among segments within a branch (
). Segments were collected from internodes located from 30–60 cm proximal to the apical meristem, a region in which it was assumed that internodes were mature and elongation had completed. This assumption, however, was based on morphological work involving four temperate angiosperm tree species and one temperate conifer (Brown and Sommer, 1992
) and may or may not have been correct in its details for D. regia, a tropical legume. Like the five temperate species, D. regia has a strongly seasonal pattern of twig growth (Tomlinson, 2001
). Regrettably, the linear positions within twigs from which segments were collected were not tracked, so this possibility cannot be tested.
The remaining source of variation in the full model, primarily due to differences in size among cells within a segment (2), may arise through, e.g., crowding effects leading to negative correlations between sizes of neighboring cells. While the degree of this variation complicates the estimation of /m (see Sampling design), it is unlikely to be evolutionarily important. This variance component predicts the variation in pith cell size among all medial pith cells created by a single apical meristem, thus variation in these measurements may be viewed as stochastic variation around the mean /m for the meristem.
Sampling design
The primary rate-limiting step in the protocol used here was the preparation of each segment and the sections from each segment. Thus, in addition to reducing the overall variance, a major consideration in selecting a sampling design is to reduce the total number of segments per tree. The deviance components reported in Table 2 may be used to determine sampling designs that will minimize the variance in the estimate of /m, by assembling progressively more inclusive variance predictions up to and including that among trees, while adjusting for differences in group sizes among levels (Sokal and Rohlf, 1995
). The predicted among-tree variance T2 derived from n measurements per segment from s segments taken from b branches is thus:
|
| (2) |
Equation 2 was used to examine the effectiveness of different sampling strategies in minimizing T 2 by adjusting n, s, and b. Our experience with D. regia suggests that adjusting sample sizes, rather than, e.g., tighter experimental controls, will be the most effective means to minimizing variance, as measurement error was minimized to the degree practicable and there was much true variation among /m measurements within segments (the 2 variance component).
In brief, the most effective means whereby T2 may be minimized is by increasing the number of measurements per segment to be n 
15 (see Appendix S1 in Supplemental Data accompanying the online version of this article). It is likely to be impractical to attempt >10 measurements per segment with the 1-cm-long segments used in this protocol, so longer twig segments should be used if greater n is desired. With n = 15, increasing the number of segments per branch s always reduces T 2, but for s > 5, there is much less reduction in T 2 per additional segment. Likewise, increasing the number of branches per tree b > 5 offers little additional improvement. With n = 20, the number of segments may be reduced to 4 per branch, and the number of branches to 4 per tree. Thus by increasing n, we also achieve time and cost savings in addition to reducing the variance in our estimate of /m.
Taxon-specific variation in /m
Curiously, conifers appear to have /m values that are about half those of angiosperms (Table 1). This may represent a real difference between conifers and angiosperms in true /m within the apical meristem or alternatively may indicate that conifers simply have larger pith cells than angiosperms and there is no such difference in true /m. It is not likely to be the result of differing patterns of pith cell development during internode elongation, because conifers and angiosperms are qualitatively similar in this regard and the difference in cell size is apparent in young internodes (Brown and Sommer, 1992
). If we assume that true /m for conifers is indeed about half that in angiosperms, then there are at least two possible implications that are not mutually exclusive. First, because lower /m leads to lower lifetime at a given height, conifers may simply have a lower per-generation genomic mutation rate U than angiosperms. Second, a lower /m in conifers may be the result of selection to reduce the overall mutation rate to that found in angiosperms, because the apical meristem structures found in most conifers are believed to be more susceptible to the fixation of deleterious mutations than the more tightly constrained tunica-corpus apical meristems of angiosperms (Klekowski et al., 1985
; Klekowski, 1988
). If plants are indeed under strong selection to avoid the inevitable effects of deleterious mutation occurring during mitotic growth (Klekowski, 1988
), it may thus be easier in conifers to reduce U via a decrease in /m than to alter meristem structure, and we may expect to find other taxon-specific correlations among suites of characters that potentially impact U.
Medial pith cells as a proxy for /m
The existence of both interspecies variation in pith cell size (Table 1) and strong intraspecies variation in /m (Table 2) emphasize that it is preferrable to examine directly, rather than one of its approximate correlates such as simple linear growth while ignoring /m. The use of linear growth alone may reveal patterns for further exploration (Kearsley and Whitham, 1998
), but failure to examine is likely to lead to failure to reveal evolutionarily significant variation in mitotic growth. Direct examination of also enables per-mitosis mutation rate comparisons with other studies based upon, e.g., animal-oriented germ line mutations (Crow, 1997
). It must be emphasized that while the variation in the proxy for /m revealed here would at first glance seem to preclude the use of these estimates and medial pith cells in general for estimation of a true /m, the analyses, estimates, and confidence intervals presented here arise from fits of well-defined statistical models in which multiple sources of variation were examined (Table 2). In combination with the preceding discussion of variance components, this argues for the possibility that the true /m may itself have strongly structured variation, and this work represents an important first step toward future progress.
This is the second study to examine medial pith cells specifically as a proxy for /m; the first was Cloutier et al. (2003)
. Recommendations for future work include the following. First, pith cells and internode lengths should be measured in both young and mature internodes, so that species-specific adjustment ratios may be calculated. Second, because of the necessity of adjustment ratios, /m calculated from mature medial pith cells will certainly be overestimated, at least with respect to the rate of pith cell production by the apical meristem itself. Third, confidence intervals for /m should be calculated from size variation among mature pith cells alone. Cloutier et al. (2003)
established a lower bound for /m from mature pith cells and an upper bound from young pith cells, but as the work of Brown and Sommer (1992)
makes clear, this practice lumps measurements from internodes expected to show systematic differences in pith cell size and number. Alternatively, it may be preferable to determine confidence intervals for the true /m from appropriately adjusted sizes of young pith cells, because these may show less among-cell size variation than mature pith cells. Finally, as I discussed in more detail earlier, adjusted /m as calculated from pith cells can only be a rough approximation to the "true" /m for a species. A detailed consideration of what the true value might be, and ultimately, appropriate values for itself, must wait for future work.
FOOTNOTES
101 This work was supported by U.S. National Science Foundation Doctoral Dissertation Improvement Grant DEB-0309253, a grant from Sigma Xi, and the University of Miami Department of Biology. The author is greatly indebted to the undergraduate students who contributed many of the nearly 1500 h of labwork required to complete the Delonix regia portions of this project: A. Abellard, A. Aldana, B. Beltran, D. Doeringer, J. Goldstein, A. Laird, T. Larrieux, J. Miles, C. Oliai, T. Prado, R. Raturi, M. Rodriguez, and A. Wright. D. Janos provided the microscope and J. Lu provided the laboratory facilities and equipment to produce the slides. Thanks to J. B. Fisher, J. Richards, S. T. Schultz, and two anonymous reviewers for helpful comments that greatly improved the manuscript. 
2 (E-mail: dgscofie{at}indiana.edu
), present address: Department of Biology, Indiana University, 1001 E. Third Street, Bloomington, IN 47405-3700 USA
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