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

Homozygosity and patch structure in 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 nearest- ported sufficiently often for other and pollinators (5-15) neighbor pollination in an outcrossing plant species were investi- that it is clearly an important characteristic of pollination biol- gated through computer simulations. The genetic system consisted ogy. It is not universal, however, and there is at least one case of two alleles at a single locus in a self-incompatible plant that (7) in which one pollinator serving a plant species shows NNP, mates by random pollen transfer from a neighboring individual. while others do not. Several workers (6-10) have noted that Beginning with a random distribution ofgenotypes, restricted pol- predominantly NNP should restrict gene dispersal in plant pop- len and seed dispersal were applied each generation to 10,000 in- ulations. Schaal (11) reported extensive local differentiation for dividuals spaced uniformly on a square grid. This restricted gene 15 polymorphic loci coding for soluble enzymes in a population flow caused inbreeding, a rapid increase in homozygosity, and ofthe herb Liatris cylindracea. She found highly significant in- striking microgeographic differentiation ofthe populations. Patches creases in homozygosity within neighborhood-sized quadrats of homozygotes bordered by heterozygotes formed quickly and persisted for many generations. Thus, high levels of inbreeding, and significant differences between quadrats. homozygosity, and patchiness in the spatial distribution of geno- Although the effects of NNP on restricting gene dispersal in types are expected in plant populations with breeding systems plant populations have been discussed for many years, there based on nearest-neighbor pollination, and such observations re- appears to be no quantitative analysis of this specific case of quire no explanation by or other deterministic restricted gene flow, and information on several points such as forces. the number, size, and persistence of genotypic patches is not provided by more general studies ofbreeding systems. The the- over the habitats they ory of Wright (1) and the simulations of Rohlf and Schnell (4) Genetic differentiation of populations may not reflect the biological situation ofNNP. Hence we have occupy is a major factor in the processes ofadaptation and evo- undertaken computer simulations to study the manner in which lution. For populations subdivided into small colonies, it is easy of to picture this differentiation as the result of . homozygosity, population structure, and spatial patterns ge- Wright (1-3) showed that even large populations distributed notypes develop in plant populations in which breeding occurs continuously over an area will differentiate if gene dispersal mostly by NNP. In particular, our model allows seed dispersal. within them is sufficiently restricted. He termed this process Additionally, we have not allowed any self-fertilization, because isolation by distance. Many genetic characteristics of such con- the increased inbreeding and patchiness due to selfing is well tinuous populations depend on the size oflocal breeding units, known. We have attempted in this way to make our simulations or neighborhoods, within them. In particular, the smaller the more conservative than other models (1, 4). neighborhoods, the greater the genetic differentiation in the THE MODEL population, so these neighborhoods are essentially subdivisions created by limited gene dispersal. Inbreeding and increased We wrote a computer program to simulate the population ge- homozygosity result, as does a spatial differentiation ofgene and netics of an annual plant species visited by pollinators whose genotype frequencies. The genetic structure of a population flights are predominantly between nearest neighbors. Two al- departs considerably from that expected in a random-mating leles at a single locus composed the genetic system. The pop- population. Rohlf and Schnell (4), using computer simulations ulation of self-incompatible, bisexual diploid plants was uni- of Wright's model to examine spatial patterning and genetic formly distributed on the intersection points ofa 100 x 100 grid. differentiation in populations with various neighborhood sizes, Flowering and reproduction of all individuals in the population observed rapid establishment of spatial patterns in gene fre- were synchronized, so the generations were nonoverlapping, quency, which persisted for many generations. and population size remained a constant 10,000. Our simulation Many plant species have reproductive systems ideally suited was similar in basic design to that of Rohlf and Schnell (4), al- to isolation by distance. Pollinator flight behavior and seed dis- though our model was structured to fit the particular biological persal determine gene flow, and both are often severely lim- situation of NNP. Our assumptions about selfing, seed disper- ited. The restriction on pollen movement is particularly strong sal, and mate selection were somewhat different than theirs, when pollinators fly between nearest-neighboring plants, a and our spatial analysis was based on the distribution of geno- common behavior. Levin and Kerster (5), for example, observed types rather than gene frequencies. A simplified flow chart of almost exclusively nearest-neighbor pollination (NNP) in Liatris the computer program is presented in Fig. 1. aspera (Compositae), as well as highly localized dispersal of A male parent is selected from plants neighboring the female seeds. Even with some carryover ofpollen from previous visits, parent in one ofthe two ways diagrammed in Fig. 2. With strict gene dispersal was highly leptokurtic (6). NNP has been re- NNP the four nearest plants on the grid have equal probabilities (P = 0.25) of serving as male parent. With relaxed NNP the 12 of The publication costs ofthis article were defrayed in part by page charge nearest neighbors of the female parent have probabilities payment. This article must therefore be hereby marked "advertise- ment" in accordance with 18 U. S. C. §1734 solely to indicate this fact. Abbreviations: NNP, nearest-neighbor pollination. 203 Downloaded by guest on September 30, 2021 204 Population Biology: Turner et al. Proc. Nad Acad. Sci. USA 79 (1982)

1 Initiate Population in 2 Hardy-Weinberg Proportions Calculate F and and Randomly Place Other Parameters on a 100x1OO Grid I 5 Randomly Choose .4 Randomly Select 3 Go to Plant at a Gamete from 4- Parent from Nearest First Position on Grid Each Parent Neighbors of Parent and Use as g Parent ? L I I 8 6 7 Combine df and g NO 8 Go to Plant at Next Gametes to Form an Have All Plants Been Position on Grid and Offspring Genotype Used as ? Parent? Use as g Parent YES 10 9 Replace Each Plant NO Have All Generations A with the Offspring Been Completed? Formed in Box #6 YES 11 L--p STOP

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 fe- RESULTS AND DISCUSSION male parent. There are two ways this latter case can be inter- preted biologically. Pollinators can move to plants which are Inbreeding and Homozygosity. The inbreeding effect of first, second, and third nearest to the maternal parent with the NNP was measured by the coefficient of inbreeding, F. We probabilities given. Alternatively, pollinators could move to calculated F as simply the proportional loss of heterozygosity nearest-neighboring plants only, carrying mostly pollen from from Hardy-Weinberg expectation: F = (expected heterozy- the last plant visited, but in addition some pollen from earlier gosity - observed heterozygosity)/expected heterozygosity. In visits to other plants. The plant visited next to last contributes this paper the values of F reported are exact, because all indi- most of this carryover pollen, with rapidly declining contribu- viduals in our simulated populations were censused. tions from successively earlier visits. The results of our simulations are summarized as values of Each individual has a probability of0.8 ofbeing replaced by F in Fig. 3. Simulations with the same parameters but different its own maternally derived seed. Seed dispersal was incorpo- sequences of pseudorandom numbers gave strikingly similar rated by allowing a probability of 0.2 that an individual would results. In all cases the variability of F among the 10 replicate be replaced by a seed formed from a neighboring (strict NNP, populations was quite small, with standard deviations less than Fig. 2 Left) individual. Computer runs were made with three 0.03. choices ofgene frequencies: P = 0.5, P = 0.8, and P = 0.9, each It seems that the gene frequency has little effect on either with both strict and relaxed NNP (Fig. 2). Ten replicate pop- the trajectory or the final value ofF (Fig. 3B). Thus we feel jus- ulations were simulated for each choice of gene frequency and tified in comparing our results to studies, such as that of Schaal neighborhood size, each utilizing a different sequence of pseu- (11), which present F values averaged over loci having alleles dorandom numbers for the chance events of pollination and at different frequencies. seed dispersal. In specified generations the entire population Genetic drift at the level ofthe whole population was not an was represented visually with a different symbol for each important factor in our study. For instance, in simulations with genotype. relaxed NNP and an initial gene frequency of 0.5, gene fre- quencies after 120 generations differed from the initial value STRICT NNP RELAXED NNP by an average of 0.041 in 10 replicate simulations. However, 0 0 0 . * * D * 0 genetic drift within small areas is one of the most significant outcomes of our simulations. * * A 0 0 * C B C A striking result of the simulations is the rapid increase in F, representing large increases in inbreeding and homozygosity. In * A X A 0 D B X B D all ofthe populations we studied, F reached values greater than 0.25 within 20 generations and went on to increase until about * * A 0 * C B C generation 200. It then stayed between 0.3 and 0.5, depending on the parameters specified for a population. Increases in F

* 0 0 0 * * D * were also seen by Rohlf and Schnell (4) in their simulations of isolation by distance, although their increases occurred more NNP: FIG. 2. Mating schemes. X is the female parent. (Left) Strict rapidly and their ultimate values were higher. 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 The effect of NNP was thus to increase homozygosity by a B, C, or D has probability 0.2125, 0.025, 0.0125, respectively, of being third to a half over the amount expected under random mating. the male parent. Values ofF as small as 0. 1 are statistically significant for a sample Downloaded by guest on September 30, 2021 Population Biology: Turner et al. Proc. Natl Acad. Sci. USA 79 (1982) 205

0.5 -

0.4 - 0.3 - Strict NNP 0.2- P = 0.5 0.1 0 ) 80 160 240 320 400 480 560 640 720 9 - O..5 -B 0.15L c O..4 0.04 _

. O..3 - _0.A AdO AII j I~~~~~~~~~~~~~~~~~~~~~~~~~~ ~.2:-/ P=0.5 0.".2 -{ - Strict N;NP = -/--- P = 0.8 Strict NNP U -. = 0.9 O. O~~~--Rlxe N . v0 20 40 60 80 100 12 0 20 40 60 80 100 120 140 Generation

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.

of400 individuals, so that the inbreeding effect of NNP should dividuals potentially involved in each mating event. Because be detectable in most field surveys of plant populations. their comparable models allowed no seed dispersal but did in- Values of F as large as those we found in our simulations of clude selfing at a high rate, the neighborhood sizes in terms of NNP-on the order of 0.4-are not unrealistic biologically. Wright's theory are actually quite small. Using Wright's (1) for- Schaal (10, 11) examined 15 polymorphic enzyme loci in a pop- mulas we calculate them to range between 0.5 and 3. ulation of Liatris cylindracea, a self-incompatible herb polli- Populations with smaller neighborhoods developed and nated by insects practicing NNP. F, averaged over all 15 loci, maintained a larger homozygosity, and hence F, than those with was 0.43, and she suggested that homozygosity and local dif- the larger neighborhoods (Fig. 3C). Inbreeding and homozy- ferentiation in this population might be caused by restricted gosity developed rapidly under both pollination schemes. The pollen and seed dispersal. Our simulations show it is indeed neighborhood sizes we employed are like those known for sev- possible to get F values of this magnitude with nothing more eral plant species with predominantly NNP; for example, neigh- than NNP; in particular, neither selection nor self-pollination borhood sizes have been estimated to be 2-5 in Lithospermum need be invoked. caroliniense (12), 8-23 in bumblebee-pollinated Senecio (7), Neighborhood Size. Wright (2) defined a neighborhood size and 10-100 in parryae (13). as "the number of individuals in an area from which parents of Genotypic Patches. A primary consequence of NNP is the central individuals may be treated as if drawn at random." development and persistence of genotypic patches. Our find- Neighborhood size is important because it governs the differ- ings on this topic are exemplified by Figs. 4 and 5, which depict entiation that results from short-range dispersal ofgenes in con- the distributions of genotypes in a model population. Both the tinuous populations. Wright (1-3) showed that neighborhood initial (Fig. 4) and long-term (Fig. 5) development of patches size was a simple function ofthe variance in the distance genes are shown. move from parents to offspring. Two forms ofNNP were utilized Beginning with a random distribution of genotypes, small in our simulations, and we have calculated the neighborhood patches of black or grey homozygotes appear within five gen- sizes associated with each. erations and grow steadily with time (Fig. 4). The proportion Seed dispersal contributes about 40% ofthe overall variance of homozygotes in the population continues to grow, and the in gene dispersal. The rest comes from pollen movement ac- black and grey patches consequently expand in area. This rapid cording to either strict NNP, in which only the four neighboring increase in homozygosity continues for about 25 generations and plants could contribute pollen, or relaxed NNP, in which 12 accounts for the initial increase in F (Fig. 3). plants surrounding a female parent could contribute pollen. Most heterozygotes are found at the borders between patches Applying Wright's (1) formulas, the neighborhood sizes are ap- of the two homozygotes, although a few are contained within proximately 4.4 and 5.2 for our models involving 4 and 12 pollen the large homozygous patches. Patches of each homozygote co- donors, respectively. Pollen dispersal from the 12 plants in- alesce, so that by generation 100 there are very large patches. volved in our relaxed NNP is not uniform but declines rapidly At this stage the population has undergone a striking micro- with distance from the female parent; it is no surprise that this geographic differentiation oflocal gene and genotypic frequen- pollen movement, coupled with the same seed dispersal, leads cies due to NNP, with little or no change in overall gene fre- to a neighborhood size only 18% larger than that for our strict quency. This differentiation or substructuring under restricted NNP. gene flow is just what Wright (1, 2) predicted in his model of Rohlf and Schnell (4) referred to neighborhood size in their isolation by distance. The genotypic patches which evolved in simulation models as 9 or 25, on the basis of the number of in- our simulations of plant species breeding under NNP have Downloaded by guest on September 30, 2021 206 Population Biology: Turner et al. Proc. Nad Acad. Sci. USA 79 (1982)

GENERATION 1 GENERATION 5

GENERATION 15 GENERATION 20 GENERATION 25

---dL.-l - _ GENERATION 30 GENERATION 35 GENERATION 40 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 pop- ulation. Heterozygotes are represented by white rectangles, the two homozygotes by black and grey rectangles.

counterparts in nature; they are, for example, like the pheno- appreciably from generation 300 to generation 800, but these typic patches of blue and white flowers described in a natural changes occur with little change in F (Fig. 3A). population of the desert annual Linanthus parryae (13, 16). The patches that arose in our simulated populations persisted Presumably, electrophoretic variants would also show such spa- for many generations, even for many tens of generations, al- tial clustering, although there do not seem to be published data though their shapes and sizes changed. Rohlf and Schnell (4) on spatial patterns of electrophoretic genotypes. noted persistence of gene frequency patterns in their simula- Wright's theory of isolation by distance (1, 2) predicts both tions; it is apparently a regular feature of geographic differen- local differentiation and the increase in F found in our simu- tiation under restricted gene flow. For instance, several large lations. Wright's theory is ageneral one, whereas we have based patches of the black homozygote that had appeared by gener- our simulations on the specific biological situation of NNP, ation 100 in Fig. 5 continued until generation 400. By gener- through use ofa model that we have tried to make realistic but ation 500 these patches had begun to be displaced by patches simple. Several features ofour model depart from the assump- ofgrey homozygote, and new patches ofthe black homozygote tion of Wright's theory of isolation by distance, and the corre- were forming along the upper and lower right corners of the spondence between our results and the expectations ofhis the- population. ory attests to the robustness of the theory's major predictions. There appears to be little regularity in the shape of patches The computer simulations are particularly useful in providing evolving in our simulations. Analysis of the spatial differentia- a visual image ofthe spatial relationships ofgenotypes in a large tion of our simulated populations into genotypic patches re- population, a picture of geographic patterning that would be quires some sort of "patchiness index. " One form ofthis index difficult to deduce from the mathematical theory alone. Mea- is calculated as the fraction of individuals whose four nearest sures such as F do not carry much information about spatial re- neighbors are ofthe same genotype. For the population shown lationships in a population. For instance, the size, shape, and in Fig. 4, this index began at 3.5% in generation 1 and increased location ofpatches in the population depicted in Fig. 5 change to 30.7% in generation 800. The fraction ofisolated individuals, Downloaded by guest on September 30, 2021 Population Biology: Turner et al. Proc. Natd Acad. Sci. USA 79 (1982) 207

.Mi-j I WIW.% Iq- liamalgo-- RIO

GENERATION I GENERATION 100 GENERATION 200 I I

GENERATION 300 GENERATION 400 GENERATION 500

GENERATION 600 GENERATION 700 GENERATION 800 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, This research was supported in part by the National Science Foundation decreased over the same period. under Grant DEB-7918493X to W.W.A. and U.S. Public Health Ser- Beginning with a random distribution ofgenotypes, the total vice Training Grant Awards to M.E.T. and J.C.S. number ofpatches decreases rapidly as many. small patches ag- gregate, increasing the mean patch size. Patches persist as 1. Wright, S. (1943) Genetics 28, 114-138. changing but recognizable units for many generations-for time 2. Wright, S. (1946) Genetics 31, 39-59. periods long in terms ofpopulation dynamics. It is striking that 3. Wright, S. (1978) Variability Within and Among Natural Popu- at generation 800 only 0.8% ofthe patches were larger than 100 lations, Evolution and the Genetics of Populations (Univ. Chi- individuals, but about 52% of the individuals were contained cago Press, Chicago), Vol 4. in them. 4. Rohlf, F. J. & Schnell, G. D. (1971) Am. Nat. 105, 295-324. It is worth 5. Levin, D. A. & Kerster, H. W. (1968) Evolution 22, 130-139. reemphasizing thatthe considerable homozygosity 6. Levin, D. A. & Kerster, H. W. (1974) in Evolutionary Biology, and patch structure that evolved in our model populations were eds. Dobzhansky, T., Hecht, M. K. & Steere, W. C. (Plenum, due solely to the NNP and limited seed dispersal that constitute New York), Vol. 7, pp. 139-220. the mating system ofour simulated plants. No selective differ- 7. Schmitt, J. (1980) Evolution 34, 934-943. ences between genotypes were involved, nor did the popula- 8. Augspurger, C. K. (1980) Evolution 34, 475-488. tions as a whole undergo any significant degree ofgenetic drift. 9. Schaal, B. A. (1980) Nature (London) 284, 450-451. NNP restricts flow 10. Schaal, B. A. (1974) Nature. (London) 252, 703. gene sufficiently that even in young pop- 11. Schaal, B. A. (1975) Am. Nat. 109, 511-528. ulations significant patchiness and homozygosity are expected. 12. Kerster, H. W. & Levin, D. A. (1968) Genetics 60, 577-587. Our results indicate caution against uncritically invoking selec- 13. Wright, S. (1943) Genetics 28, 139-156. tion as an explanation of persistent patch structure in a plant 14. Allard, R. W., Jain, S. K. & Workman, P. L. (1968) Adv. Genet. species whose mating system includes NNP. 14, 55-131. 15. Price, M. V. & Waser, N. M. (1979) Nature (London) 227, We thank Drs. J. Antonovics, M. Clegg, M. Price, L. Real, N. Waser, 294-297. S. Wright, and R. Wyatt for their thoughtful comments on this work. 16. Epling, C. & Dobzhansky, T. (1942) Genetics 27,'317-332. Downloaded by guest on September 30, 2021