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Fine-scale genetic structure of a turkey oak forest.

Plant species and their populations are rarely randomly distributed within communities. Similarly, the spatial distribution of individuals within populations is often nonrandom, as are the distributions of genotypes and alleles. Genetic structure can result from several factors, including isolation in small patches, limited pollen and seed dispersal, and selection acting at the microhabitat level. Sewall Wright (1943a, 1946) argued that reproductive isolation can take place in a continuous population simply by means of limited gene flow. He described this process as "isolation by distance" and proposed that limited gene flow would generate patches of genetically similar individuals, which he called neighborhoods or demes. According to Wright's (1982) "shifting-balance" theory of evolution, if demes become ecologically adapted, then genetic structure can be enhanced. When environmental conditions change, some demes adapt to new conditions and are thus selected, whereas others become extinct. It is plausible that deme-structure can arise in physically isolated populations, but it is less easy to visualize its creation in a continuously distributed population.

Wright (1943b) used his isolation-by-distance model to describe the genetic differentiation of patches of white and blue flowers of the diminutive annual Linanthus parryae in the Mojave Desert. He divided the 130-km long range into a five-level hierarchy and found significant differences at every level of the hierarchy, attributing higher level differences to selection or drift, and lower-level differences to isolation-by-distance. On a much more local scale, Epperson and Clegg (1986) used spatial autocorrelation to measure patch size of flower colors in morning glory (Ipomoea purpurea) growing in soybean fields. On a still smaller scale, Schaal (1974, 1975) found considerable differentiation in 15 allozyme loci among 3-[m.sup.2] quadrats in an 18 x 33 m plot of the insect-pollinated prairie perennial Liatris cylindracea.

Wright (1946) defined a "neighborhood" as the number of individuals with which an organism mates at random. If offspring are distributed normally about their parents, a neighborhood of size N = 4[Pi][[Sigma].sup.2]d (a circle of radius 2[Sigma]) contains 86.5% of the potential parents of individuals at the center, where d is the density of the parents, and [[Sigma].sup.2] is the variance of the offspring distribution. For plants, this variance is the sum of half the pollen dispersal variance [[[Sigma].sup.2].sub.p] plus the seed dispersal variance [[[Sigma].sup.2].sub.s] so that [[Sigma].sup.2] = 1/2[[[Sigma].sub.p].sup.2] + [[[Sigma].sup.2].sub.s] (Crawford 1984).

Summarizing the effect of neighborhood size, Wright (1946) concluded that if N = 20 there can be great differentiation among neighborhoods. When N = 200 there can be moderate differentiation; and with N = 1000, the neighborhood effects disappear and the population is virtually panmictic.

Computer simulations of continuous annual populations with limited gene flow reveal that "neighborhoods" of genetically similar individuals arise rather quickly (within a dozen generations) among a random array of genotypes (Turner et al. 1982). A map of allele frequencies in such a differentiated population shows a persistent "hilly" character, with the hills and swales representing neighborhoods of genetic similarity. There is a characteristic depression of heterozygosity within [as measured by Wright's (1965) [F.sub.IS]] and among [as measured by Wright's (1965) [F.sub.ST]] neighborhoods, as evidenced by a monotonic temporal rise of allelic variance (Rohlf and Schnell 1971; Sokal 1979; Sokal and Wartenberg 1981; Turner et al. 1982; Bos and van der Haring 1988; Sokal et al. 1989).

The search for neighborhood structure in long-lived perennial plants has yielded mixed results, although one might argue that sampling strategies often have been too sparse and at inappropriate scales. Dewey and Heywood (1988) used a series of 20-m wide belt transects to sample the Florida hammock shrub, Psychotria nervosa, which is pollinated by insects and dispersed by birds. Their autocorrelation analysis yielded no significant spatial pattern for alleles at two loci. One of the most detailed studies to date is Epperson and Allard's (1989) study of lodgepole pine (Pinus contorta ssp. latifolia) on two dense, even-aged (50 yr), 4-ha stands, sampled every 15 m for 14 loci. Spatial autocorrelation of most genotypes showed no neighborhood structure, indicating that gene dispersal by wind-blown pollen and wind-blown seeds did not allow neighborhood structure to develop on a scale of 15 m to 250 m.

Studies with more intensive sampling, however, have documented that some genetic structuring does exist in long-lived perennials (Schaal 1974, 1975; Linhart et al. 1981; Schnabel and Hamrick 1990; and Schnabel et al. 1991). The two species examined in the latter study, honey locust (Gleditsia triacanthos) and osage orange (Maclura pomifera), both have long-distance pollen dispersal and relatively short-distance fruit dispersal. Spatial autocorrelation indicated that individuals are genetically correlated within 10 m or less of one another, probably because of the clumped spatial structure of individuals and limited seed movement.

Our study seeks to directly assess the applicability of Wright's (1943a) isolation-by-distance model in a population unconfounded by such factors as spatial patchiness, marked habitat heterogeneity, or substantial interspecific competition, factors that are potential sources of fine-scale genetic structure. A Quercus laevis Walt. (turkey oak) population was selected that is continuously distributed in a homogeneous habitat, with an apparently stable age distribution. We examined genetic structure separately in adult and juvenile size classes, because genetic structure can occur in younger plants but not appear in less dense, older cohorts on account of stand thinning. Moreover, some tree species exhibit a distinct increase in heterozygosity as cohorts mature, presumably because of heterosis (e.g., Mitton and Grant 1984; Plessas and Straus 1986).

To provide a comparative framework for our analysis, we simulated gene flow in an age-structured population, with parameters of pollen- and seed-dispersal distances. As in the earlier simulations, we found a pattern of homozygote patches embedded in a matrix of heterozygotes. By comparing a range of pollen- and seed-dispersal simulations with our observed data, we were able to estimate roughly the minimum neighborhood sizes for the study population. We applied our various spatial genetic procedures to simulated data with very restricted gene flow to obtain a "yardstick" for comparing our observed results.


Study Organism and Site

Quercus laevis is a wind-pollinated scrub oak endemic to the southeastern United States Coastal Plain, often growing with longleaf pine (Pinus palustris Miller) on poor, sandy soil (Radford et al. 1968; McGinty and Christy 1977; Berg and Hamrick 1993). The study site is a 60+ ha old-growth stand of Quercus laevis on the upland sandhills of the Savannah River Site (SRS) near Aiken, South Carolina. Air photo coverage beginning in 1943 shows no visible recent disturbance of this site. Stumps of longleaf pine indicate logging of the rather sparse pines on the site before establishment of the SRS in 1951. No cut stumps of Q. laevis were observed, although it is possible that some trees were cut for firewood before 1951. The random spatial pattern of the adult Q. laevis (diameter at breast height [DBH] [greater than] 0) indicates no substantial burning of the site for many years (Rebertus et al. 1989), although some old charred pine stumps were observed. The uniform white sand soil makes any history of agricultural use unlikely. The site lies on a gently sloping (3%-5% grade) south-facing sandhill, uncut by any stream drainages, and lacking any visible signs of disturbance, terrain irregularity, or moisture gradient.

The stand is continuous, with some variation in stem density (22.1 [+ or -] 6.3 [SD] stems of DBH [greater than or equal to] 2.5 cm per 10 x 10-m quadrat, N = 64). This carpetlike distribution approximates the mathematical assumptions of continuity and uniform density in Wright's (1943a) model more closely than do the patchy populations so commonly encountered in many tree species. The stand size is in excess of 200,000 individuals of all ages. The stem size distribution peaks in the juvenile size class (DBH = 0), with 50% of the adult stems [less than] 5.6 cm DBH ([approximately]40 yr). The maximum ring-based age is approximately 100 yr, although coppice-sprouted individuals could be considerably older.

Species growing on the site (nomenclature follows Radford et al. 1968) include Q. laevis at 2210 stems/ha (DBH [greater than or equal to] 2.5 cm), Pinus palustris at 123 stems/ha, Q. margaretta at 155 stems/ha, Q. incana Bartram at 107 stems/ha, Nyssa sylvatica var. sylvatica Marshall at 157 stems/ha, plus occasional Diospyros virginiana L., Carya pallida (Ashe) Engler & Graebner, C. tomentosa (Poiret) Nuttall, Prunus serotina Ehrhart, and Q. marilandica Muenchh. The understory consists of moderately dense Vaccinium arboreum Marshall and Crataegus spp., and occasional Sassafras albidum (Nuttall) Nees, Rhus copallina L., V. staminium L., and Aureolaria pectinata (Nuttall) Pennell. The patchy graminoid cover is presumably Aristida stricta Michaux, but no flowering stems were found for positive identification. The spatial pattern of the Q. laevis and the clonal structure of Q. margaretta are described in Berg and Hamrick (1994).

A 160 m x 160-m plot was surveyed by transit with a 10-m grid, and individual trees were located to [+ or -] 0.1 m. At least ten adult trees were genotyped from nearly every 10 x 10-m quadrat (N = 2693 adults). A more detailed study was made of an 80 x 80-m plot centered within the larger plot, in which nearly all juveniles lacking a coppice stem were genotyped (N = 651), every standing Q. laevis stem (dead or alive) was mapped for spatial analysis, and 47% of the adults (N = 768) were genotyped. Of the juveniles, 60% are coppice sprouts from old stems (commonly 2-5 cm diameter at ground level), which were revealed by digging with a claw trowel. Other juveniles appear to be seedlings, but excavation showed that many have a large taproot or an amorphous root mass weighing 1-2 kg. The unreleased growth of seedlings, as well as the coppice recycling of stages, makes it impossible to age these stems and creates the possibility that an apparent seedling beside a mature tree may in fact be the "recycled" parent of that tree. In some statistical tests described below, we analyze the trees in "adult" and "juvenile" size classes, but none of these tests require distinguishing parents and offspring, or relative ages of adult-size and juvenile-size trees.

To assess the spatial dispersion of the trees, Ripley's (1976, 1977) L statistics were calculated for the 80 x 80-m grid, where all stems were mapped. The spatial pattern of the adults (N = 1649) on the 80 X 80-m plot is random on a scale of 0-40 m, whereas the juveniles (N = 651) showed moderate clumping on a scale of 1-12 m. No significant spatial attraction or repulsion was found between adults and juveniles (Berg and Hamrick 1994).

We did however find some juveniles (and adults) quite close to adult trees, and a number of close pairs were genotyped to test for cloning from root sprouts. To assess the extent of cloning, we computed the proportion of identical nine-locus genotype pairs (assumed to be clones) about each individual in 1-m distance classes, to 10 m, and plotted the mean proportion of identical pairs as a function of distance.

We chose a grid size of 160 m, which would allow the data to be analyzed over a wide range of quadrat sizes in even multiples. Given that it was practical to genotype [approximately]3000 trees, we expected that a quadrat size of 10-16 m (with 10-30 samples) might be necessary to obtain an unbiased estimate of [F.sub.ST]. We suspected, however, that a scale of 10-16 m might be too coarse to resolve the finest structure, especially that resulting from acorn establishment near parent trees; thus, the nonquadrat and randomization methods described below were employed to assess structure at this level. Sample collection and enzyme electrophoresis procedures are described elsewhere (Berg and Hamrick 1994).

Data Analysis

Allele frequencies were calculated separately for juveniles and adults, and were compared with a [[Chi].sup.2] test (Workman and Niswander 1970), as were Wright's (1922, 1965) fixation index F, [F.sub.IS], [F.sub.IT], and [G.sub.ST] (Li and Horvitz 1953). A two-locus disequilibrium (linkage) analysis was done, using the LD86 program of Weir (1990). No significant two-locus disequilibria were found for any combination of alleles, when significance levels were adjusted with the Bonferroni procedure (Berg 1993).

Spatial genetic structure was analyzed in four ways: the number of alleles in common (NAC), randomized hierarchical [G.sub.ST] and [F.sub.IS], spatial autocorrelation of allele frequencies (on two scales), and spatial autocorrelation of genotypes (both nominal and interval).

The NAC method computes the average number of alleles in common per polymorphic locus between all individuals separated by a distance of r to r + [Lambda]r, where [Lambda]r = 2 m. A mean is calculated for each distance class by averaging the pairwise NAC values (for counting rules, see Surles et al. 1990), and a grand mean is obtained by averaging all possible pairwise NAC values without respect to distance. The grand mean is plotted as a horizontal line and represents the null hypothesis of spatial randomness of alleles. An excess of NAC at a certain distance suggests that individuals at that distance share more alleles. This excess must be offset by a deficit of alleles at other scales. The NAC can vary from 0 to 2, but in natural populations, values typically range from 1.25 to 1.75 (Hamrick et al. 1993).

The hierarchical [G.sub.ST] and [F.sub.IS] method partitions the grid into cells and calculates [G.sub.ST] and [F.sub.IS] weighted by sample size (Nei 1977; Wright 1978), as is conventionally done to assess among-population differentiation. The 160 X 160-m grid is repeatedly divided into 4, 16, 25, 64, 100, 256, 400, 1024, and 1600 cells. As the number of cells becomes large, there are empty cells and differences in allele frequencies can be quite large, generating inflated [G.sub.ST] values. Skewed allele frequencies can also generate low expected heterozygosities ([H.sub.S]) and reduced [F.sub.IS] values, since [F.sub.IS] = ([H.sub.S] - [H.sub.O])/[H.sub.S].

To assess significance of observed [G.sub.ST] for a given cell size, [G.sub.ST] values were computed for 999 randomized data sets to estimate the sampling distribution of [G.sub.ST]. For a given cell size, the 999 simulated and one observed [G.sub.ST] values were ranked from large to small, and the rank of the observed [G.sub.ST] was taken as its level of significance (P value). This method allows one to use the small cell sizes with inflated [G.sub.ST] values and still compare their significance against the null hypothesis of random structure. In similar manner, the randomized data sets were ranked by [F.sub.IS] to determine significance of observed [F.sub.IS]. The [G.sub.ST] and [F.sub.IS] randomizations are plotted against the mean number of individuals per cell, with cell sizes of 4, 5, 8, 10, 16, 20, 40, and 80 m.

Randomizations were conducted on three levels to test three null hypotheses. On the top level, multilocus genotypes were randomly permuted (sampling without replacement) and reassigned to the spatially fixed individuals. This tests only for spatial randomness of multilocus genotypes and is the primary test of interest in this study. It preserves both inbreeding and linkage (gametic phase) disequilibria among alleles.

The intermediate-level test randomly permutes single-locus genotypes, again sampling without replacement. Any multilocus linkage is broken up, but the overall level of Hardy-Weinberg disequilibrium (presumably caused by inbreeding) is maintained (in this case, [F.sub.IT] = 0.038 for juveniles, and [F.sub.IT] = 0.072 for adults). Differences between these results and the top-level randomization can thus be attributed to linkage.

The lowest-level test simply mimics random sexual mating and draws each allele (gamete) from the population allele-frequency table (sampling with replacement). This assumes Hardy-Weinberg equilibrium and no linkage. Differences between this and the intermediate simulation will thus be due to Hardy-Weinberg disequilibrium.

Envelopes of extremes (maxima and minima) of the randomizations, as well as observed [G.sub.ST] and [F.sub.IS] values are plotted. When an observed value falls above or below the envelope, it is significant at P = 0.001 with respect to the null hypothesis of that envelope.

A random number scrambler was routinely used in all calls to the DEC VAX pseudorandom number generator RAN(SEED). We noticed that a plot of successive calls as (x,y) coordinates exhibited a striped pattern of points, indicating that two successive calls were not independent. This was remedied by a further random scrambling of the calls in a file.

Spatial autocorrelations were done in two standard ways: as nominal correlations of genotypes (e.g., a 33 or 34 type) and as interval correlations of allele frequencies (e.g., with the frequency of the Fe1-2 allele in a given cell). In the nominal case, all pairs (called "joins") of like genotypes are counted for a given distance class (r to r + [Delta]t), for example, all pairs of 33-33 genotypes separated by 4-6 m. A similar count is made for unlike joins. Juveniles and adults were analyzed separately. Juveniles (N = 708) were sampled primarily in the 80 x 80-m central plot. Adults (N = 1608) were analyzed on a 120 x 120-m central plot instead of the full 160 x 160-m plot because of computer memory limitations.

The nominal autocorrelation test statistic is the standard normal deviate (SND) of the observed number of joins from the expected number of joins (Cliff and Ord 1973; Sokal and Oden 1978a, b):

SND(r) = Observed joins - Expected joins/[Variance.sup.1/2]

The SNDs are assumed to be normally distributed and hence have critical values of [+ or -]1.96 at the 5% level of significance. For both juveniles and adults, the analysis was made at increments of [Delta]r = 2 m.

For interval data (such as allele frequencies), Moran's I measures the degree of spatial autocorrelation:

[Mathematical Expression Omitted]

where [w.sub.ij] = 1 for all cells i and j falling in a distance class (r, r + [Delta]r), and otherwise [w.sub.ij] = 0; W is the sum of all the weights (i.e., the count of all pairs used in all classes); and [Z.sub.i] is the deviation of the allele frequency of the ith cell from the mean. The expected value of I = -1/(n - 1), which approaches zero for large n. Variance calculations followed the formulas of Sokal and Oden (1978a), and significance levels were calculated from SNDs on the assumption that Moran's I is normally distributed. The analysis was made on 256 10 x 10-m quadrats and 1024 5 x 5-m quadrats for alleles with frequency [greater than] 1%. Both juveniles and adults were pooled for this analysis in order to reduce the variance of cell allele frequencies.

To examine structure on a finer scale, interval autocorrelation was done on individual genotypes scored as frequencies, for both juveniles and adults. The homozygote of the most common allele was assigned a frequency of 1.0, its heterozygotes (of all types) were assigned a frequency of 0.5, and all other genotypes were assigned a frequency of 0.0. Moran's I was calculated for nearest sampled neighbors, and for all individuals in distance classes of [Delta]r = 1, [Delta]r = 2, and [Delta]r = 5 m. In most cases, I values of successive distance classes beyond the first class were not significant and are not reported. Connectivity matrices in all autocorrelation calculations were based on straight-line distances.


In our simulations, 10,000 bisexual individuals were fixed on a 100 x 100-unit grid, with a 10-unit buffer zone composed of non-replaced individuals who can contribute gametes. Fixed parameters were age of first reproduction at 10 yr and a half-normal survivorship ([l.sub.x]) curve described by the function exp[-[(age/36.7).sup.2]], which assumes the observed tree sizes represent a stable age distribution. Seed and pollen travel distances were scaled by the size of neighborhoods from which the seed and pollen parents were randomly drawn. For the first (smallest) neighborhood, the parent (either seed or pollen parent) was drawn from the first square annulus about the individual being replaced (N = 8 possible parents). The second neighborhood includes this eight plus individuals of the second square annulus (N = 8 + 16 = 24). No selfing was allowed, nor was there any provision for unreleased seedlings or coppice sprouting. By way of comparison, the simulations of Turner et al. (1982) annual plants, with used nearest-neighbor pollen donors ([N.sub.m] = 4 or 12) and very limited seed dispersal (80% probability of [N.sub.f] = 1, 20% of [N.sub.f] = 4).

For each setting of the neighborhood parameters, the grid was randomly initialized with genotypes of equal allele frequency, and the population was allowed to age, die, and reproduce for 1000 yr. Ninety-nine simulations were run for each setting. The envelopes of the extremes (maxima and minima) of [F.sub.ST] and [F.sub.IS] were plotted against the mean number of samples per quadrat (cell count). Observed [G.sub.ST] (which we use as a multilocus and multiallelic estimate of [F.sub.ST]) and observed [F.sub.IS] were also plotted for both juveniles and adults. A series of parameter values for [N.sub.f] and [N.sub.m] were chosen, which generated envelopes bracketing the observed curves as a means of estimating the magnitude of these parameters for the observed data.

For all parameter choices, the model was run for 10,000 yr in order to assess the stability of genetic structure. The [F.sub.ST] and [F.sub.IS] values increased rapidly from zero, but stabilized by 1000 yr. The maps of simulated genotypes at 10,000 yr exhibit the expected pattern of homozygote patches in a matrix of heterozygotes, on varying scales. For the minimum gene flow case ([N.sub.f] = [N.sub.m] = 8), the x- and y-coordinates of one-fourth of the 10,000 simulated genotypes were randomly jittered by 0-1.6 m to eliminate the small-scale pattern of the grid. This data set was used for randomization, NAC, and spatial autocorrelation analysis, providing a useful standard for the case of severely restricted gene flow.


Genetic Diversity and Inbreeding

Nine polymorphic loci were consistently scored, of which Fe1, Idh, Me and Pgi2 had high genetic diversities ([H.sub.T]) in excess of 40%, suggesting adequate variance for appreciable spatial genetic structure (table 1). The population as a whole has a modest amount of inbreeding (mean [F.sub.IT] = 0.053), and there is little overall differentiation between adults and juveniles ([G.sub.ST] = 0.001) in terms of allele frequencies.

Considering inbreeding within each size class, the fixation indices (F) showed significant deficits of heterozygotes for Lap, Me, and Skdh in adults and at Fe1 and Me in juveniles [TABULAR DATA FOR TABLE 1 OMITTED] (table 2). Lap had the greatest difference in fixation index between adults and juveniles (adult F = 0.186 [P [less than] 0.001] vs. juvenile F = 0.012 [P [greater than] 0.05]), but there was no significant difference in allele frequencies. Skdh had a smaller difference (adult F = 0.131 [P [less than] 0.001] vs. juvenile F = 0.044 [P [greater than] 0.05]), but allele frequency differences were significant at P [less than] 0.001. Inbreeding was not reduced in the adult trees, nor did the mean observed heterozygosities differ (adults [H.sub.O] = 0.252 [+ or -] 0.014 [SD]; juvenile [H.sub.O] = 0.244 [+ or -] 0.015).

Clone Analysis

The proportion of clones of two adult trees separated by [less than or equal to] 1 m is 15% [ILLUSTRATION FOR FIGURE 1A OMITTED]. The same proportion of two juveniles is 9%, and of an adult-juvenile pair is 4%. After 5 m, the proportion drops to a background level of less than 2% in all three cases. We identified 842 multilocus genotypes in 3402 individuals; the mean number of copies of each genotype was 4.04 [+ or -] 8.51 (SD). Genotype maps showed the copies to be mostly scattered across the 160 x 160 m plot, indicating independent generation of identical genotypes (for the nine polymorphic loci) by sexual reproduction. The largest sampled cluster of identical genotypes contained four individuals (Berg and Hamrick 1994).
TABLE 2. Fixation indices (F) and allele-frequency heterogeneity.
NS, nonsignificant [[Chi].sup.2].

Locus     Adults         Juveniles      heterogeneity

Fe1       0.058          0.093(*)           NS
Fe2      -0.001         -0.001              NS
Idh      -0.006          0.010              NS
Lap       0.186(***)     0.012              NS
Me        0.165(***)     0.151(***)         NS
Pgi2     -0.022         -0.017              NS
Pgm       0.040         -0.011              (*)
Skdh      0.131(***)     0.044             (***)
Tpi       0.059          0.028              NS

Overall [[Chi].sup.2] = 0.1, df = 17, P [less than] 0.005.

(*) P [less than] 0.05; (**) P [less than] 0.01; (***) P [less than]

Number of Alleles in Common

The NAC analysis indicates that both adults [TABULAR DATA FOR TABLE 1B OMITTED] and juveniles (not shown) have more alleles in common at a scale of 0-10 m. Hence, the trees are genetically more similar at this scale. The effect is very small, however, when compared with the NAC curve of the simulated population with strong neighborhood structure.

Hierarchical Analysis

The 999 randomizations of multilocus genotypes (top-level test) show that [G.sub.ST] is statistically significant at every scale for both juveniles and adults. Figure 2A shows the envelope of maxima and minima for this randomization (solid lines), with the observed values (dashed line) for the adults consistently falling slightly above the maximum (and hence P = 0.001). The [G.sub.ST] plot for juveniles is similar to that of adults [ILLUSTRATION FOR FIGURE 2B OMITTED]. The intermediate randomization (of single-locus genotypes) produced envelopes very similar to those of the multilocus randomization for both adults and juveniles, thus confirming that there is no appreciable linkage between loci (not shown). Single-allele randomizations for [G.sub.ST] also produced similar envelopes (not shown), shifted slightly lower by 5%-10% at small cell sizes.

For [F.sub.IS], the multilocus randomizations (which preserve Hardy-Weinberg disequilibrium) show values that are biased low at small cell sizes and that completely enclose the juvenile data, indicating no spatial effect in the positions of juvenile genotypes [ILLUSTRATION FOR FIGURE 2E OMITTED]. For adults, however, the observed data fall slightly below the multilocus envelopes at scales of 8-80 m ([similar to]10-650 individuals), indicating a slight but significant (P = 0.001) excess of heterozygotes at those scales [ILLUSTRATION FOR FIGURE 2D OMITTED].

For the single-locus simulated data with limited gene flow, we see that randomization locates the "observed" [F.sub.ST] and [F.sub.IS] far out in the tails of the sampling distributions (dashed lines in [ILLUSTRATION FOR FIGURES 2C AND 2F OMITTED], respectively). This shows quite vividly the magnitude of F statistics that can be expected in a strongly structured data set. The simulated pattern of homozygote patches in a heterozygote matrix [ILLUSTRATION FOR FIGURE 3D OMITTED] departs strongly from Hardy-Weinberg equilibrium ([F.sub.IT] [approximately equal to] 0.4). For small sample sizes, [F.sub.IS] underestimates the [F.sub.IS] component of [F.sub.IT] [ILLUSTRATION FOR FIGURE 2F OMITTED] and hence the [F.sub.ST] component of [F.sub.IT] must be inflated, because (1 - [F.sub.IT]) = (1 - [F.sub.IS])(1- [F.sub.ST]). The term (1 - [F.sub.IT]) is a constant here, independent of the sample size. Experimentally, we normally consider [F.sub.IS] and [F.sub.ST] as independent measures, but they are so only when the sample sizes [TABULAR DATA FOR TABLE 3 OMITTED] are large enough that estimates of [F.sub.IS] and [F.sub.ST] are unbiased (e.g., N [greater than] 20-30, according to these simulations).

Interval Autocorrelations

Of 21 alleles examined, 14 (67%) showed significant autocorrelation between adjoining 10 x 10-m cells (table 3). These cells contain an average of 13.3 individuals and have a moderate sampling variance. (For example, for an allele of frequency p = 0.5, the maximum binomial sampling variance is var(p) = p(1 - p)/n = [0.5.sup.2]/13.3 = 0.019 and SE = [var.sup.1/2](p) = 0.137 [Weir 1990, p. 31], [TABULAR DATA FOR TABLE 4 OMITTED] which decreases as p increases or decreases.) Inspection of the genotype maps does not reveal any distinct patchiness of the homozygotes; for example, figure 3A for Pgi2 is typical. Nevertheless, when allele frequencies are calculated on a 10-m grid and plotted as three-dimensional posts [ILLUSTRATION FOR FIGURE 3B OMITTED], one can see many adjacent pairs and trios of similar frequency. Figure 3C shows the Pgi2-2 correlogram for 10-m cells, with the typical largest I value in the first distance class. For all loci, the similarity drops off sharply at larger distance classes: for 10-20 m, 6 of 21 alleles are significant; for 20-30 m, 3/21; for 30-40 m, 2/21; and for 40-50 m, 3/21. This indicates appreciable allele frequency similarity at a scale of 10 m. This is generally confirmed by examining 5 x 5-m cells that have a quarter of the sample size and hence four times the sample variance (table 3). Each of the first three distance classes (5, 10, and 15 m) have 8 or 9 significant I values (of the 21 possible), with the number dropping off steadily for larger classes. The map, histogram, and correlogram of the simulated data set are shown for comparison, using 10-m cells [ILLUSTRATION FOR FIGURES 3D-F OMITTED].

When allele frequencies are scored 0, 0.5, or 1.0 for individual trees, the nearest sampled neighbors are significantly correlated only for the Skdh locus, for both adults and juveniles (table 4). Among juveniles, the 0-1 m class finds only Me significant; the 0-2 m class finds Idh, Me, Pgi2, and Skdh significant; the 0-5 m class finds Fe2, Idh, and Skdh significant. This suggests that the juveniles are most strongly correlated between 1 and 2 m. The adults, on the other hand, show no significant values in the 0-1 m or 0-2 m classes; the 0-5 m class finds Idh, Me, and Pgi2 significant, which suggests that the adults are most strongly correlated between 2 and 5 m.

Nominal Autocorrelations

There are significant positive SNDs of like-like joins for both heterozygote and homozygote pairings in a few loci at every scale (table 5). The effect is very weak, however, given that many like-like pairings are possible. The composite (and negative) unlike measures (e.g., 33-34, 33-44 joins) seem to best capture the magnitude of the genotypic similarity, because a negative correlation in unlike pairs indicates a positive correlation in like-like pairs considered as a group. This is clearly strongest in the 0-2 m class with four and five of the nine loci significant, in juveniles and adults, respectively.
TABLE 5. Nominal autocorrelations of genotypes. Numerators represent
the number of significant (P [less than or equal to] 0.05) joins;
denominators are the number of possible joins. Like-like joins
connect the same genotype (e.g., 34-34 joins). Unlike joins connect
all possible unlike genotype pairings (e.g., 33-34 joins). The
larger adult sample contains more rare genotypes than does the
juvenile sample, and hence more possible join types (36 versus 31,
respectively). Plot size is 120 m x 120 m.

Distance class                0-2 m   2-4 m   4-6 m   6-8 m   8-10 m

Juveniles (N = 708)

Proportions of significant
like-like joins                5/31    1/31    3/31    1/31    2/31

Proportion of significant
unlike joins                   4/9     1/9     1/9     2/9     1/9

Adults (N = 1608)

Proportion of significant
like-like joins                3/36    5/36    6/36    3/36    3/36

Proportion of significant
unlike joins                   5/9     1/9     3/9     1/9     1/9

Examination of the correlograms of unlike genotypes in 2-m classes for 20 m revealed that only the Skdh locus showed a consistent (nine of ten) pattern of significant (and negative) SNDs. This structure is corroborated by the many significant I values observed in the SKDH-3 and SKDH-4 allele frequencies, both in cells and especially in juvenile individual frequencies (tables 3, 4).


Each forest simulation was run 99 times for 1000 yr [ILLUSTRATION FOR FIGURES 4A-F OMITTED]. As the pollen-donor neighborhood ([N.sub.m]) is increased, the simulated [F.sub.ST] envelope is lowered toward the observed [G.sub.ST] values, and the simulated [F.sub.IS] envelope moves upward toward the observed [F.sub.IS] values; the homozygote patches become more diffuse and the proportion of heterozygotes increases toward Hardy-Weinberg equilibrium. The best fit of the model with observed values of [G.sub.ST] and [F.sub.IS] was obtained by expanding both seed-donor and pollen-donor neighborhoods to virtually panmictic levels (i.e., [N.sub.f] = [N.sub.m] = 440). Envelopes for this choice of parameters included the [G.sub.ST] values at all scales, as well as [F.sub.IS] values for scales above 10 m. The only discrepancy is the deficit of heterozygotes (high [F.sub.IS]) at the smallest scales ([less than] 10 m, cells of two to six individuals, [ILLUSTRATION FOR FIGURES 4E,F OMITTED]).


The genotype maps and the various statistical measures failed to reveal any well-developed genetic structure, such as the isolation-by-distance model predicts for limited gene flow. Nevertheless, a modest degree of small-scale genetic relatedness is detectable, especially in the autocorrelations, and is sufficient to reject the null hypothesis of complete panmixis.

Because we detected substantial cloning in the 0-1-m distance class (15% of adult pairs), one might ask if clonal sprouting from roots might account for the most of the fine-scale genetic structure. This seems unlikely, however, because none of the individual frequency autocorrelations were significant in the 0-1-m and 0-2-m adult classes, and only one of the nine loci was significant for the nearest-neighbor adult autocorrelations. When we consider pooled adults and juveniles on the 160 x 160-m plot (N = 3402) in table 3, the mean I value for cell frequencies for the 0-10-m class is nearly three times that of the 0-5-m class (0.095 vs. 0.037, respectively). This, too, suggests that the significant genetic correlation is developed over a distance of 10 m, rather than 1 or 2 m, as would result from cloning or, for that matter, from acorns establishing immediately beneath the seed parent.

The autocorrelation statistics obtained for Quercus laevis are in the range of those obtained for other forest trees. For example, Perry and Knowles (1991) used interval autocorrelation of individuals (with 5 loci and 11 alleles) in three stands of Acer saccharum (sugar maple). As with Q. laevis, the I values were generally low (I [less than] 0.100) but showed the greatest proportion of significant alleles in the first few distance classes. The proportion of significant alleles, however, was not as large as those of Q. laevis at similar scales.

Dewey and Heywood (1988) used interval autocorrelation of individual frequencies to examine fine-scale structure in the shrub Psychotria nervosa. They took clumped samples, with the expectation that nearest-neighbor pairings ought to show the highest autocorrelation if isolation-by-distance is present. For the five alleles examined, none of the nearest-neighbor pairs had significant I values, nor were there significant I values in the correlograms when the experimentwise error rates were adjusted using the Bonferroni procedure. They attributed the lack of structure to extensive gene flow through insect pollination and widespread seed dispersal by birds.

Epperson and Allard (1989) used nominal autocorrelation of genotypes in two stands of Pinus contorta spp. latifolia (lodgepole pine), sampled on a 15-m grid. Their first distance class (15-23 m) found only 12 of 184 single-locus genotypes to be individually significant in the Scar Mountain population and 11 of 158 in the Indian Creek population. (None of these statistics were significant, when the Bonferroni experiment-wise error rate was set to [Alpha] = 0.05.) These two populations are even-aged ([similar to]50 yr) stands that are presumably postfire cohorts established from semiserotinous cones opening on scorched seed donors within the plot. Densities of the P. contorta and Q. laevis stands are similar (2500 and 2200 [ha.sup.-1], respectively), and the modest structure in Q. laevis is most visible on a scale of less than 15 m. Wind-dispersed seeds of P. contorta, like samaras of A. saccharum, probably disperse more widely than acorns of Q. laevis. It is, therefore, not a foregone conclusion that the authors would have found more structure if they had sampled on a finer scale.

Schnabel and Hamrick (1990) examined the fine-scale autocorrelation structure of Gleditsia triacanthos in two populations. Comparisons of the (Gabriel-connected) near-neighbor I values for the two species showed higher values in G. triacanthos than in Q. laevis, (e.g., some significant values for adults were 0.293, 0.325, 0.682, 0.148, etc., and these values were in most cases raised by adding clonal members to the sample). The only significant I values of this type for Q. laevis are for Skdh-3 with I = 0.168 and 0.181, for juveniles and adults, respectively (table 4). Gleditsia triacanthos is pollinated by insects. Its seeds are borne in legumes, which have restricted dispersal about maternal trees, although secondary dispersal by animals is possible (Schnabel and Hamrick 1990). The weaker structure of Q. laevis probably is due to the wider dispersal of its wind-blown pollen. Of species discussed above, G. triacanthos appears to have the most restricted seed dispersal and definitely shows the most autocorrelation structure.

Sample sizes in our study are quite large, and comparison of observed [G.sub.ST] values with those of randomized data sets indicates that there is small but statistically significant genetic structure (of alleles) at all scales ranging from 4 m to 80 m. Because observed [G.sub.ST] values exceeded cell maxima of the 999 multilocus data randomizations, these values fall in the extreme tails of the sampling distributions (P = 0.001) for both adults and juveniles. This does not indicate any patch structure of the genotypes, however. Indeed, observed juvenile [F.sub.IS] values fall entirely within the multilocus randomization envelope, indicating no spatial structure (e.g., no genotypic patch structure) in the juveniles. As we have noted, there are significant [F.sub.IS] values for the adults on scales of 880 m, which are presumably caused by a slight excess of heterozygotes at these scales. Comparison with the simulations, however, show that this effect is not large [ILLUSTRATION FOR FIGURES 2D,F OMITTED].

Because [G.sub.ST] and [F.sub.IS] are averages over nine loci, we are examining the composite behavior of all loci. Furthermore, an isolation-by-distance pattern per se, like inbreeding, should affect all loci equally. If one can make the assumption that the loci are independent (as shown by the linkage test) and are not under selection (which we have tried to avoid with a homogeneous field site), multilocus average measures such as [G.sub.ST] and [F.sub.IS] should increase the signal-to-noise ratio.

It is instructive to examine the model simulations, because they exhibit the magnitude of structure produced by an extreme isolation-by-distance process. The case with most limited gene flow (from the nearest eight pollen and seed donors, [N.sub.m] = [N.sub.f] = 8) shows very strong autocorrelation signatures in allele frequencies for both 5-m and 10-m quadrats, starting with I [similar to] 0.5 in the first distance classes ([ILLUSTRATION FOR FIGURE 3F OMITTED] for 10-m cells). The correlogram intercepts the x-axis at 40-45 m, whereas the homozygote patches on the genotype map visually appear to be roughly 25 m in diameter [ILLUSTRATION FOR FIGURE 3D OMITTED]. Sokal and Wartenberg (1981, 1983) found that, for square patches, the x-intercept was a reasonable estimate of patch size, but this does not appear to be true for irregular patches. The NAC plot crosses the x-axis (mean NAC) at 28 m and appears to offer a more conservative estimate of patch size [ILLUSTRATION FOR FIGURE 1B OMITTED].

We have no good explanation for the deficit of heterozygotes (high [F.sub.IS]) observed with respect to the model at the smallest scales [ILLUSTRATION FOR FIGURES 4E,F OMITTED]. The neighborhood definition used in this model is essentially a step function (uniform distribution) for pollen- and seed-dispersal distances. A dispersal function monotonically decreasing with distance might generate a large enough small-scale [F.sub.IS] by near-neighbor mating to model this local deficit of heterozygotes, while providing enough gene flow to preserve the low [F.sub.ST] envelope.

The model also would be more realistic if it included cloning by root sprouting and coppice regrowth of stems. These processes would tend to preserve alleles in a region and would probably act only to retard the rate at which genetic structure changes (e.g., shifting of homozygote patches) but would not bias heterozygosity in a consistent direction. One could also add a small proportion of selfing, because oaks are considered to be predominant, but not obligate, outcrossers (e.g., Schwarzmann and Gerhold 1991). This could produce a deficiency of heterozygotes, but it is not clear that it would change the proportion of heterozygotes on any particular scale, such as the small scale observed here.

The need for a large seed-donor neighborhood in our forest simulation model would indicate that acorns on this plot do not establish close to their maternal trees. This is consistent with our autocorrelation results discussed above. It is also consistent with an auxiliary study, in which one of us (E.E.B.) attempted to model juvenile locations, conditioned on observed adult locations. A leptokurtic (negative exponential) distribution of offspring around a parent failed to fit the Q. laevis data, even when genetic offspring-parent probabilities were used to limit the possible juvenile-adult pairings. The model worked well for two clonal species (Q. margaretta and Rubus fruticosus), where juvenile clustering about adults was more visually apparent (Berg 1992).

Acorn production in this plot appears to be very erratic in both space and time. In 1989 acorns were observed in numbers of tens to hundreds on perhaps 100 of the larger trees. In 1990 and 1991, no trees were observed with more than two to three acorns. The remains of old acorns were observed to be quite dense under some trees, so it appears that intermittent masting is the normal mode of seed production. In pin oak (Q. palustris), Darley-Hill and Johnson (1981) found that 54% of the total mast crop of 11 pin oaks was transported and cached by blue jays (Cyanositta cristata). The birds carried 1-5 acorns (mean 2.2) per foraging trip for distances of 0.1-1.9 km (mean 1.1 km). The small number of Q. laevis masting at a given time could make them a target for intensive foraging and wide seed dispersal, which could account for our failure to detect strong near-parent genetic structure.

In summary, this detailed survey of genetic structure in a typical unburned Q. laevis population failed to reveal distinct patch structure, indicating that gene flow on the scale we examined is too extensive to fulfill the conditions of an isolation-by-distance process. Our randomizations and simulations suggest that graphs of [F.sub.ST] and [F.sub.IS] at various scales can be a powerful tool for revealing genotypic structure. The NAC and autocorrelation measures appeared to offer the best fine-scale assessment of genetic similarity. The presence of significant I values for some loci and some alleles at scales of 10 m or less presumably is due to limited seed dispersal and a small amount of cloning. This finest-scale structure, however, was below the resolution of our forest simulation model.


We wish to especially thank S. Sherman-Broyles for her technical assistance and J. Tyrell, L. Manning, and C. Desarno for their help in the laboratory. J. Arnold, R. Chesser, Y. Linhart, R. Sharitz, R. Wyatt, and an anonymous reviewer read earlier drafts of this paper and provided many useful comments. E.E.B. was supported by the Savannah River Ecology Lab (SREL) during the field phases of this work, under contract DE-AC09-76SR00-819 between the Department of Energy and SREL. Additional support was provided by National Science Foundation Dissertation Improvement Grant (BSR-9016351). This research was done in partial fulfillment of doctoral requirements in Botany, at the University of Georgia, Athens.


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Author:Berg, Edward E.; Hamrick, James L.
Date:Feb 1, 1995
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