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Proc. Nati Acad. Sci. USA Vol. 79, pp. 203-207, January 1982 Population Biology

Homozygosity and patch structure in plant populations as a result of nearest-neighbor pollination (inbreeding/population structure/isolation by distance)

MONTE E. TURNER, J. CLAIBORNE STEPHENS,

AND

WYATT W. ANDERSON

Department of Molecular and Population Genetics, University of Georgia, Athens, Georgia 30602

Communicated by G. Ledyard Stebbins, August 24, 1981

ABSTRACT The population genetic consequences of nearestneighbor pollination in an outcrossing plant species were investigated through computer simulations. The genetic system consisted of two alleles at a single locus in a self-incompatible plant that mates by random pollen transfer from a neighboring individual. Beginning with a random distribution of genotypes, restricted pollen and seed dispersal were applied each generation to 10,000 individuals spaced uniformly on a square grid. This restricted gene flow caused inbreeding, a rapid increase in homozygosity, and striking microgeographic differentiation of the populations. Patches of homozygotes bordered by heterozygotes formed quickly and persisted for many generations. Thus, high levels of inbreeding, homozygosity, and patchiness in the spatial distribution of genotypes are expected in plant populations with breeding systems based on nearest-neighbor pollination, and such observations require no explanation by natural selection or other deterministic forces. Genetic differentiation of populations over the habitats they occupy is a major factor in the processes of adaptation and evolution. For populations subdivided into small colonies, it is easy to picture this differentiation as the result of genetic drift. Wright (1-3) showed that even large populations distributed continuously over an area will differentiate if gene dispersal within them is sufficiently restricted. He termed this process isolation by distance. Many genetic characteristics of such continuous populations depend on the size of local breeding units, or neighborhoods, within them. In particular, the smaller the neighborhoods, the greater the genetic differentiation in the population, so these neighborhoods are essentially subdivisions created by limited gene dispersal. Inbreeding and increased homozygosity result, as does a spatial differentiation of gene and genotype frequencies. The genetic structure of a population departs considerably from that expected in a random-mating population. Rohlf and Schnell (4), using computer simulations of Wright's model to examine spatial patterning and genetic differentiation in populations with various neighborhood sizes, observed rapid establishment of spatial patterns in gene frequency, which persisted for many generations. Many plant species have reproductive systems ideally suited to isolation by distance. Pollinator flight behavior and seed dispersal determine gene flow, and both are often severely limited. The restriction on pollen movement is particularly strong when pollinators fly between nearest-neighboring plants, a common behavior. Levin and Kerster (5), for example, observed almost exclusively nearest-neighbor pollination (NNP) in Liatris aspera (Compositae), as well as highly localized dispersal of seeds. Even with some carryover of pollen from previous visits, gene dispersal was highly leptokurtic (6). NNP has been re-

ported sufficiently often for other plants and pollinators (5-15) that it is clearly an important characteristic of pollination biology. It is not universal, however, and there is at least one case (7) in which one pollinator serving a plant species shows NNP, while others do not. Several workers (6-10) have noted that predominantly NNP should restrict gene dispersal in plant populations. Schaal (11) reported extensive local differentiation for 15 polymorphic loci coding for soluble enzymes in a population of the herb Liatris cylindracea. She found highly significant increases in homozygosity within neighborhood-sized quadrats and significant differences between quadrats. Although the effects of NNP on restricting gene dispersal in plant populations have been discussed for many years, there appears to be no quantitative analysis of this specific case of restricted gene flow, and information on several points such as the number, size, and persistence of genotypic patches is not provided by more general studies of breeding systems. The theory of Wright (1) and the simulations of Rohlf and Schnell (4) may not reflect the biological situation of NNP. Hence we have undertaken computer simulations to study the manner in which homozygosity, population structure, and spatial patterns of genotypes develop in plant populations in which breeding occurs mostly by NNP. In particular, our model allows seed dispersal. Additionally, we have not allowed any self-fertilization, because the increased inbreeding and patchiness due to selfing is well known. We have attempted in this way to make our simulations more conservative than other models (1, 4). THE MODEL We wrote a computer program to simulate the population genetics of an annual plant species visited by pollinators whose flights are predominantly between nearest neighbors. Two alleles at a single locus composed the genetic system. The population of self-incompatible, bisexual diploid plants was uniformly distributed on the intersection points of a 100 x 100 grid . Flowering and reproduction of all individuals in the population were synchronized, so the generations were nonoverlapping, and population size remained a constant 10,000. Our simulation was similar in basic design to that of Rohlf and Schnell (4), although our model was structured to fit the particular biological situation of NNP. Our assumptions about selfing, seed dispersal, and mate selection were somewhat different than theirs, and our spatial analysis was based on the distribution of genotypes rather than gene frequencies. A simplified flow chart of the computer program is presented in Fig. 1. A male parent is selected from plants neighboring the female parent in one of the two ways diagrammed in Fig. 2. With strict NNP the four nearest plants on the grid have equal probabilities (P = 0.25) of serving as male parent. With relaxed NNP the 12 nearest neighbors of the female parent have probabilities of

The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U. S. C. §1734 solely to indicate this fact.

Abbreviations: NNP, nearest-neighbor pollination.

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FIG. 1. Simplified flow chart of the computer program used to simulate plant populations breeding under NNP.

serving as male parent according to their distance from the female parent. There are two ways this latter case can be interpreted biologically. Pollinators can move to plants which are first, second, and third nearest to the maternal parent with the probabilities given. Alternatively, pollinators could move to nearest-neighboring plants only, carrying mostly pollen from the last plant visited, but in addition some pollen from earlier visits to other plants. The plant visited next to last contributes most of this carryover pollen, with rapidly declining contributions from successively earlier visits. Each individual has a probability of 0.8 of being replaced by its own maternally derived seed. Seed dispersal was incorporated by allowing a probability of 0.2 that an individual would be replaced by a seed formed from a neighboring (strict NNP, Fig. 2 Left) individual. Computer runs were made with three choices of gene frequencies: P = 0.5, P = 0.8, and P = 0.9, each with both strict and relaxed NNP (Fig. 2). Ten replicate populations were simulated for each choice of gene frequency and neighborhood size, each utilizing a different sequence of pseudorandom numbers for the chance events of pollination and seed dispersal. In specified generations the entire population was represented visually with a different symbol for each genotype. STRICT NNP

RELAXED NNP .

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FIG. 2. Mating schemes. X is the female parent. (Left) Strict NNP: each of the four nearest plants (A) has probability of 0.25 of being the male parent. (Right) Relaxed NNP: each of the four plants designated B, C, or D has probability 0.2125, 0.025, 0.0125, respectively, of being the male parent.

RESULTS AND DISCUSSION

Inbreeding and Homozygosity. The inbreeding effect of was measured by the coefficient of inbreeding, F. We calculated F as simply the proportional loss of heterozygosity from Hardy-Weinberg expectation: F = (expected heterozygosity observed heterozygosity)/expected heterozygosity. In this paper the values of F reported are exact, because all individuals in our simulated populations were censused. The results of our simulations are summarized as values of F in Fig. 3. Simulations with the same parameters but different sequences of pseudorandom numbers gave strikingly similar results. In all cases the variability of F among the 10 replicate populations was quite small, with standard deviations less than 0.03. It seems that the gene frequency has little effect on either the trajectory or the final value of F (Fig. 3B). Thus we feel justified in comparing our results to studies, such as that of Schaal (11), which present F values averaged over loci having alleles at different frequencies. Genetic drift at the level of the whole population was not an important factor in our study. For instance, in simulations with relaxed NNP and an initial gene frequency of 0.5, gene frequencies after 120 generations differed from the initial value by an average of 0.041 in 10 replicate simulations. However, genetic drift within small areas is one of the most significant outcomes of our simulations. A striking result of the simulations is the rapid increase in F, representing large increases in inbreeding and homozygosity. In all of the populations we studied, F reached values greater than 0.25 within 20 generations and went on to increase until about generation 200. It then stayed between 0.3 and 0.5, depending on the parameters specified for a population. Increases in F were also seen by Rohlf and Schnell (4) in their simulations of isolation by distance, although their increases occurred more rapidly and their ultimate values were higher. The effect of NNP was thus to increase homozygosity by a third to a half over the amount expected under random mating. Values of F as small as 0. 1 are statistically significant for a sample NNP

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FIG. 3. Values of the inbreeding coefficient F in simulated plant populations breeding under two forms of NNP. Initial gene frequencies and the type of NNP are given on each graph. (A) F in a single population over 720 generations. (B) Mean F in sets of 10 replicates begun at each of three gene frequencies. (C) Mean F in sets of 10 replicates with strict or relaxed NNP.

of 400 individuals, so that the inbreeding effect of NNP should be detectable in most field surveys of plant populations. Values of F as large as those we found in our simulations of NNP-on the order of 0.4-are not unrealistic biologically. Schaal (10, 11) examined 15 polymorphic enzyme loci in a population of Liatris cylindracea, a self-incompatible herb pollinated by insects practicing NNP. F, averaged over all 15 loci, was 0.43, and she suggested that homozygosity and local differentiation in this population might be caused by restricted pollen and seed dispersal. Our simulations show it is indeed possible to get F values of this magnitude with nothing more than NNP; in particular, neither selection nor self-pollination need be invoked. Neighborhood Size. Wright (2) defined a neighborhood size as "the number of individuals in an area from which parents of central individuals may be treated as if drawn at random." Neighborhood size is important because it governs the differentiation that results from short-range dispersal of genes in continuous populations. Wright (1-3) showed that neighborhood size was a simple function of the variance in the distance genes move from parents to offspring. Two forms of NNP were utilized in our simulations, and we have calculated the neighborhood sizes associated with each. Seed dispersal contributes about 40% of the overall variance in gene dispersal. The rest comes from pollen movement according to either strict NNP, in which only the four neighboring plants could contribute pollen, or relaxed NNP, in which 12 plants surrounding a female parent could contribute pollen. Applying Wright's (1) formulas, the neighborhood sizes are approximately 4.4 and 5.2 for our models involving 4 and 12 pollen donors, respectively. Pollen dispersal from the 12 plants involved in our relaxed NNP is not uniform but declines rapidly with distance from the female parent; it is no surprise that this pollen movement, coupled with the same seed dispersal, leads to a neighborhood size only 18% larger than that for our strict NNP.

Rohlf and Schnell (4) referred to neighborhood size in their simulation models as 9 or 25, on the basis of the number of in-

dividuals potentially involved in each mating event. Because their comparable models allowed no seed dispersal but did include selfing at a high rate, the neighborhood sizes in terms of Wright's theory are actually quite small. Using Wright's (1) formulas we calculate them to range between 0.5 and 3. Populations with smaller neighborhoods developed and maintained a larger homozygosity, and hence F, than those with the larger neighborhoods (Fig. 3C). Inbreeding and homozygosity developed rapidly under both pollination schemes. The neighborhood sizes we employed are like those known for several plant species with predominantly NNP; for example, neighborhood sizes have been estimated to be 2-5 in Lithospermum caroliniense (12), 8-23 in bumblebee-pollinated Senecio (7), and 10-100 in Linanthus parryae (13). Genotypic Patches. A primary consequence of NNP is the development and persistence of genotypic patches. Our findings on this topic are exemplified by Figs. 4 and 5, which depict the distributions of genotypes in a model population. Both the initial (Fig. 4) and long-term (Fig. 5) development of patches are shown. Beginning with a random distribution of genotypes, small patches of black or grey homozygotes appear within five generations and grow steadily with time (Fig. 4). The proportion of homozygotes in the population continues to grow, and the black and grey patches consequently expand in area. This rapid increase in homozygosity continues for about 25 generations and accounts for the initial increase in F (Fig. 3). Most heterozygotes are found at the borders between patches of the two homozygotes, although a few are contained within the large homozygous patches. Patches of each homozygote coalesce, so that by generation 100 there are very large patches. At this stage the population has undergone a striking microgeographic differentiation of local gene and genotypic frequencies due to NNP, with little or no change in overall gene frequency. This differentiation or substructuring under restricted gene flow is just what Wright (1, 2) predicted in his model of isolation by distance. The genotypic patches which evolved in our simulations of plant species breeding under NNP have

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FIG. 4. Spatial distribution of genotypes in a simulated plant population breeding under strict NNP. Genotypic distributions at five-generation intervals are shown. The population was begun at P = 0.5, with genotypes in Hardy-Weinberg frequencies and randomly distributed in the population. Heterozygotes are represented by white rectangles, the two homozygotes by black and grey rectangles.

counterparts in nature; they are, for example, like the phenotypic patches of blue and white flowers described in a natural population of the desert annual Linanthus parryae (13, 16). Presumably, electrophoretic variants would also show such spatial clustering, although there do not seem to be published data on spatial patterns of electrophoretic genotypes. Wright's theory of isolation by distance (1, 2) predicts both local differentiation and the increase in F found in our simulations. Wright's theory is a general one, whereas we have based our simulations on the specific biological situation of NNP, through use of a model that we have tried to make realistic but simple. Several features of our model depart from the assumption of Wright's theory of isolation by distance, and the correspondence between our results and the expectations of his theory attests to the robustness of the theory's major predictions. The computer simulations are particularly useful in providing a visual image of the spatial relationships of genotypes in a large population, a picture of geographic patterning that would be difficult to deduce from the mathematical theory alone. Measures such as F do not carry much information about spatial relationships in a population. For instance, the size, shape, and location of patches in the population depicted in Fig. 5 change

appreciably from generation 300 to generation 800, but these changes occur with little change in F (Fig. 3A). The patches that arose in our simulated populations persisted for many generations, even for many tens of generations, although their shapes and sizes changed. Rohlf and Schnell (4) noted persistence of gene frequency patterns in their simulations; it is apparently a regular feature of geographic differentiation under restricted gene flow. For instance, several large patches of the black homozygote that had appeared by generation 100 in Fig. 5 continued until generation 400. By generation 500 these patches had begun to be displaced by patches of grey homozygote, and new patches of the black homozygote were forming along the upper and lower right corners of the population. There appears to be little regularity in the shape of patches evolving in our simulations. Analysis of the spatial differentiation of our simulated populations into genotypic patches requires some sort of "patchiness index. " One form of this index is calculated as the fraction of individuals whose four nearest neighbors are of the same genotype. For the population shown in Fig. 4, this index began at 3.5% in generation 1 and increased to 30.7% in generation 800. The fraction ofisolated individuals,

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Proc. Natd Acad. Sci. USA 79 (1982)

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FIG. 5. Spatial distribution of genotypes in the simulated plant population of Fig.. 4 at intervals of 100 generations.

whose genotypes were different from all nearest neighbors, decreased over the same period. Beginning with a random distribution of genotypes, the total number of patches decreases rapidly as many. small patches aggregate, increasing the mean patch size. Patches persist as changing but recognizable units for many generations-for time periods long in terms of population dynamics. It is striking that at generation 800 only 0.8% ofthe patches were larger than 100 individuals, but about 52% of the individuals were contained in them. It is worth reemphasizing that the considerable homozygosity and patch structure that evolved in our model populations were due solely to the NNP and limited seed dispersal that constitute the mating system of our simulated plants. No selective differences between genotypes were involved, nor did the populations as a whole undergo any significant degree of genetic drift. NNP restricts gene flow sufficiently that even in young populations significant patchiness and homozygosity are expected. Our results indicate caution against uncritically invoking selection as an explanation of persistent patch structure in a plant species whose mating system includes NNP. We thank Drs. J. Antonovics, M. Clegg, M. Price, L. Real, N. Waser, S. Wright, and R. Wyatt for their thoughtful comments on this work.

This research was supported in part by the National Science Foundation under Grant DEB-7918493X to W.W.A. and U.S. Public Health Service Training Grant Awards to M.E.T. and J.C.S. 1. Wright, S. (1943) Genetics 28, 114-138. 2. Wright, S. (1946) Genetics 31, 39-59. 3. Wright, S. (1978) Variability Within and Among Natural Populations, Evolution and the Genetics of Populations (Univ. Chicago Press, Chicago), Vol 4. 4. Rohlf, F. J. & Schnell, G. D. (1971) Am. Nat. 105, 295-324. 5. Levin, D. A. & Kerster, H. W. (1968) Evolution 22, 130-139. 6. Levin, D. A. & Kerster, H. W. (1974) in Evolutionary Biology, eds. Dobzhansky, T., Hecht, M. K. & Steere, W. C. (Plenum, New York), Vol. 7, pp. 139-220. 7. Schmitt, J. (1980) Evolution 34, 934-943. 8. Augspurger, C. K. (1980) Evolution 34, 475-488. 9. Schaal, B. A. (1980) Nature (London) 284, 450-451. 10. Schaal, B. A. (1974) Nature. (London) 252, 703. 11. Schaal, B. A. (1975) Am. Nat. 109, 511-528. 12. Kerster, H. W. & Levin, D. A. (1968) Genetics 60, 577-587. 13. Wright, S. (1943) Genetics 28, 139-156. 14. Allard, R. W., Jain, S. K. & Workman, P. L. (1968) Adv. Genet. 14, 55-131. 15. Price, M. V. & Waser, N. M. (1979) Nature (London) 227, 294-297. 16. Epling, C. & Dobzhansky, T. (1942) Genetics 27,'317-332.