Amer. J. Bot. 74(12): 1893-1897. 1987.

A TEST OF SEVERAL HYPOTHESES FOR THE DETERMINATION OF SEED NUMBER IN AMELANCHIER ARBOREA, USING SIMULATED PROBABILITY DISTRIBUTIONS TO EVALUATE DATA'

DAVID L. GORCHOV AND GEORGE F. ESTABROOK Department of Biology, University of Michigan, Ann Arbor, Michigan 48109-1048

ABSTRACT Thenumberofseeds perfruitisvariable within Amelanchierarborea trees. Because A. arborea flowers are five-carpellate and eachcarpel contains two ovules, wewere ableto usethe pattern ofseed maturation within fruits to testwhether the failure ofsomeovules to develop intoseeds is determined by mechanisms operating at the level of carpels, suchas stigma-clogging, or by mechanisms operating at the level of ovules, suchas ovule infertility. The presence of one-, two-, and zero-seeded carpels demonstrated that the numberof ovules developing into seeds was not due entirely to carpel-level phenomena. In order to test the hypothesis of carpel independent seed development, without theassumption thatallovules havethesameprobability of developing into seeds, it was necessary to use simulation, since no conventional statistical models were appropriate. Analysis of this simulation allowed us to reject carpel independent processes as the only determinant of seed number. A mixed model of seed development, in which somecarpels fail entirely and ovules in the remaining carpels develop equiprobably, was shown to be consistent withthe data.

MANY, IF NOT MOST, plants have a variable of a fruit can be an additional tool for distin­ number of seeds per fruit. For these plants, guishing among competing hypotheses. seed number is one component ofyield or fit­ ness that the plant can adjust in response to MATERIALS AND METHODS-Amelanchier ar­ environmental conditions (Harper, 1977). In borea (Michx. f.) Fern. (Downy Serviceberry) some species seed number has a strong effect is a small tree of eastern North America that on fruit size (Wareing and Phillips, 1978, 123), bears fleshy fruits containing one to ten filled pulp: seed ratio (Herrera, 1981), mass: vol­ seeds. Unlike some congeners, it is self-incom­ ume ratio (Augspurger and Hogan, 1983), or patible and not apomictic (Robinson, 1982; fruit developmental time (Lee and Bazzaz, Gorchov, 1985). As in other members of the 1982), all ofwhich can have consequences for Rosaceous subfamily Maloideae, the gynoe­ seed dispersal. cium consists of five carpels each made up of Pollination, resources, and seed predation a single stigma, a style, and two ovules (see have all been proposed as mechanisms for the Campbell et aI., 1985, and Olson and Steeves, determination ofseed number per fruit, as well 1982, for detailed descriptions of other Ame­ as othercomponents ofplant reproductive out­ lanchier species). Thus, each flower should have put (for reviews, see Bierzychudek, 1981; Ste­ the potential to produce fruits with ten seeds. phenson, 1981; Rathcke, 1983; Bawa and Fruits usually do contain ten "seeds," but the Webb, 1984). Most studies to date have used number ofthese that are filled with an embryo pollen or resource augmentation to test wheth­ ranges from one to ten and is always variable er these factors limit seed number. A recent among fruits within a plant. Some of the re­ review (Snow, 1986) showed that seed number maining seeds are ofnearly full length but con­ is related to pollination intensity in only a mi­ tain no embryo ("empty seeds"), but most are nority ofspecies investigated to date, and these very small. The latter ("undeveloped seeds") are mostly species with a very large number of are not necessarily derived from fertilized ovules per flower. Here we show that analysis ovules: they can develop from ovules in carpels ofthe distribution of seeds among the carpels that had their styles pinched off before polli­ nation (Gorchov, 1987). I Received forpublication 10 December 1986; revision Filled seed number in A. arborea is nega­ accepted 26 March 1987. tively correlated with the number ofdays from We thank two anonymous reviewers for helpful com­ ments. Research supportto DLGfrom the University of fruit initiation to ripening, resulting in a with­ Michigan Museum of Zoology and Rackham School of in-plant ripening phenology that is much more Graduate Studies is gratefully acknowledged. asynchronous than the flowering phenology

1893 1894 AMERICAN JOURNAL OF BOTANY [Vol. 74

TABLE I. Hypothesesfor the determination offilled seeds one carpel, style/pollination related hypothe­ per A. arboreafruit. Rej. = rejected based on manip­ ses predict that both ovules in a carpel will ulation experiments (Gorchov, 1987). Seed predation share the same fate: either develop or fail to (3) reducesfilled seed number in some fruit, but filled seed number is variable among undamagedfruits develop. Hypotheses that attribute ovule fail­ ure to genetic or developmental factors predict Predicts failure that failure ofan ovule is independent offailure of single ovules, 0, or both ovules ofthe other ovule in the carpel (Table 1). While Hypothesis in a carpel, C the individual hypotheses might be testable by I. Limitation ofcompatible pollen C Rej. future experimental work, the two classes of 2. Local resource limitation after fruit hypotheses are potentially distinguishable by initiation 0 Rej. patterns of seed development within carpels. 3. Seed predation ? Carpel walls can be discerned in mature fruits 4. Pollen blockage if they are dissected carefully. It is easier to A. Stigma-clogging with self pollen C distinguish the carpel walls in immature fruits. B. Style blockage or breakage C This was done by one ofus (DLG) for a set of 5. Ovule infertility fruits collected from four individual plants

A. Ovule degeneration I 0 growing in an oak-hickory woods at the E. S. B. Ovule atrophy- O? George Reserve, southeastern Michigan. 6. Early abortion of fertilized ovules Four inflorescences on each of the plants A. Postzygotic incompatibility O? were thinned to two flowers at peakbloom (22­ B. Local resource limitation at the time 24 April 1985). On 4 May four other inflores­ offertilization ? cences on each individual were thinned to two 7. Carpel not adequately vascularized C developing fruits, and the leaves on each of these shoots were removed. Fruits from both I Premature cessation of development. the defoliation and control treatments were 2 Senescence of unfertilized ovules. collected one to two weeks before ripening be­ gan in the population (18 May for two plants, (Gorchov, 1985). Amelanchier arborea fruits 24 May for the other two). By this time seeds are eaten by a variety of birds and mammals, were approximately full-sized but had not yet many ofwhich are seed dispersal agents (Rob­ acquired hardened seed coats, and fruit abor­ inson, 1986; Gorchov, 1987), and this asyn­ tion was more than 90% complete. chronous ripening may be an adaptation to For each fruit the number of carpels con­ avoid satiation of seed dispersers (Thompson taining two, one, and zero developed seeds were and Willson, 1979). counted. (Developed seeds include both filled Seed predators (primarily moth larvae) re­ and empty seeds, since it is possible that some duce the number offilled seeds in some fruits, seeds that appear filled at this point in devel­ but filled seed number varies even among un­ opment abort before fruit ripening.) A few fruits damaged fruit (plant means range from 3.8 to (11%) had four rather than five carpels and 8.3 and with SD from 1.4 to 2.2). To test wheth­ were not included in this analysis. The fre­ er seed number in undamaged fruits is deter­ quency of these four-carpellate fruits did not mined by pollen or by resources, field manip­ differ significantly between the defoliation and ulations were carried out (Gorchov, 1987). control treatments. There was also no signifi­ Supplemental xenogamous pollination did not cant difference between the treatments in the affect the mean or variance of seed number, number of developed seeds per undamaged, indicating seed number is not limited by the five-carpellate fruit. This lack ofdifference be­ amount of compatible pollen arriving at the tween the treatments justified pooling the seed stigmas. Similarly, manipulations of local re­ distribution data. source levels at fruit initiation by defoliation, girdling, and fruit thinning did not affect seed HYPOTHESES- Ifseeddevelopmentor failure number, although they did affect fruit set and was entirely determined by a carpel-level seed weight. mechanism (Table 1), then we would expect These results suggest that seed number in A. each carpel to have either two or zero seeds. arborea is determined by neither pollen nor However, a large number ofcarpels (32%) con­ resources. Several post hoc hypotheses for seed tained one developed and one undeveloped number determination that are consistent with seed (Table 2), indicating that failure ofovules these data have been proposed (Gorchov, to develop is not solely dependent on carpel­ 1987). Because 82% of styles with any pollen level processes. tubes have a large number ofthem (Gorchov, If, instead, one of the ovule-level mecha­ 1987) and each style delivers pollen to only nisms (Table 1) is valid, we would expect seed December 1987] GORCHOV AND ESTABROOK-DETERMINATION OF SEED NUMBER 1895 development to be independent of carpel TABLE 2. Number ofcarpels with two, one, and zero de­ membership. It is difficult to predict the dis­ veloped seeds observed in a sample ofimmaturefruits tribution of seeds in carpels that would be ex­ and expected based on a constant ovule development pected under such a hypothesis, unless sim­ probabilityof(91 x 2 + 69)/2I5 = 0.58 that is random with respect to position. The observed distribution dif­ plifying assumptions are made. One such fers significantly from the expected (Goodness-of-fit simplifying assumption is that all ovules have x' = 24.7. df= 2, P < 0.001) the same probability, P, of developing into a seed. At least two distinct biological processes Carpels containing this number couldlead to thisassumption being valid. First, ofdeveloped seeds ovule failure may be due to some develop­ Developed seeds Observed Expected mental problem (e.g., hypotheses 5A, 5B, and 2 91 73.3 6A, Table I) that is equally likely to affect any 1 69 104.5 ovule. Second, resource allocation to different 0 55 37.3 flowers or fruits may be adjusted by the plant Total 215 215.1 so as to maintain a constant P despite differ­ ences in local resource levels. This would result in a binomial distribution ofseed number per binomial process rejected in Table 2 is con­ fruit. The latter pattern could be adaptive if, sistent with this first class ofremaining expla­ for example, it resulted in a variance in seed nations. number that, through the dependence of fruit A second possibility is that ovule failure is developmental time on seed number (Oor­ partly, butnotcompletely, dependenton carpel chov, 1985), generated an optimal degree of membership. This could involve two distinct ripening synchrony. but simultaneous processes, one operating at Under the simplifying assumption ofa glob­ the level of carpels to produce failure of both ally constant P the expected frequency oftwo-, ovules and the second at the level of ovules one-, and zero-seeded carpels is given by the independent ofcarpels. Partial dependence on binomial distribution. The observed distri­ carpels could alternatively be due to a process, bution has significantly fewer one-seeded fruits such as fungal infection, that tended to affect than expected (Table 2), allowing us to reject neighboring ovules, whether they were in the the hypothesis that ovules develop into seeds same carpel or not. Either process would in­ with a constant probability. crease the predicted number ofempty carpels Two classes of explanations remain for the and thus predict that the numberofone-seeded development of ovules into seeds. First, de­ carpels will be lower than expected by the con­ velopment ofovules into seeds may occur in­ stant P hypothesis rejected in Table 2. Because dependently (with respect to carpels) within both classes ofremainingexplanations are con­ fruits, but the probability that an ovule de­ sistent with (and thus cannot be distinguished velops into a seed may not be the global con­ by) the way in which the hypothesis ofglobally stant stated in the above hypothesis, but rather constant probability ofdevelopment is reject­ may vary among fruits or plants. This model ed, we must seek a more powerful means to would be consistent with any ofthe ovule-level distinguish these two classes. hypotheses in Table I. For example, flower Although the former ovule-based explana­ primordia experiencing different resource levels tion does not retain the assumption ofa glob­ may complete development ofovules with dif­ ally constant probability ofseed development, fering probabilities, but two ovules in the same it still assumes that seed development of one carpel would be as likely to both fail to differ­ ovule is independent of seed development of entiate as any two ovules in the same fruit. In another ovule. An important consequence of this case, the observed number ofcarpels with this assumption is that once given that a par­ two, one, or zero seeds would reflect mixed ticular fruit has a particular number, N, ofseeds, samples from two or more binomial distri­ those seeds will have developed from any N butions with different seed development prob­ of the 10 ovules with equal probability, in­ abilities corresponding to differing intensities dependent ofcarpel membership. By contrast, of the hypothesized ovule-level explanations the latter, carpel-dependent, explanation ex­ in Table I. One property of mixed binomial plicitly requires a violation of this indepen­ distributions is that the observed number of dence assumption. Thus, we can take the in­ one-seeded carpels is lower than predicted by dependence assumption of the ovule-level the single binomial distribution whose global hypotheses and derive distributions for statis­ probability is estimated from the data. Thus tics to test it. Its rejection will specifically im­ the trend in our data away from the number plicate carpel-level explanations. ofsingle-seeded carpels predicted by the global A difficulty arises in testing this hypothesis: 1896 AMERICAN JOURNAL OF BOTANY [Vol. 74

2000...------..., cannot be determined solely by ovule-level phenomena. This finding, when combined with the initial observation thata third ofthe carpels contain one seed, implies that ovule failure is ~ partially, but not completely, dependent on c s rooo carpel membership. Failure ofan ovule to de­ r velop into a seed therefore is either determined u, by a mechanism that tends to but does not always affect both ovules in a carpel(e.g., fungal infection) or it is partly due to a mechanism operating at the level ofcarpels and partly due o . to a mechanism operatingat the level ofovules. 60 70 80 90 tOO By simulating probability distributions for One-seeded carpels numbers ofcarpels with two, one, or zero seeds Fig. I. Frequency distribution of number of carpels with one seed resulting from 10,000 replications ofa pro­ under the specific conditions ofindependence gram simulating the assignment ofseeds into carpels based of ovule development, and of the numbers of on seed numbers in an observed set of 43 Amelanchier fruits with the numbers of seeds occurring in arborea fruit. Arrow indicates the number of one-seeded the data, we have shown that the tendency of carpels in the observed set of fruit (69). Realized signifi­ two ovules in a carpel to develop or fail together cance of this number of one-seeded carpels is 0.023. is statistically significant. Because experimen­ tally added xenogamous pollen failed to in­ what distribution of seeds in carpels does it crease seed set in naturally pollinated flowers predict? To answer this question, we generated (but produced seed set in bagged flowers) and these distributions by computersimulation. We 89% ofstyles from naturally pollinated flowers specified the number of fruits with each dif­ contained pollen tubes (Gorchov, 1987), it is ferent seed number. Then, for each fruit in the unlikely that zero-seeded carpels are the result data set to be simulated, we assigned the seeds of inadequate pollen delivery. Therefore, it is to the ovules equiprobably, without regard to likely that much ofthe style-mediated effect is carpels. Afterward, in the simulated data set, through the failure of styles by improper de­ the number ofcarpels with two, one, and zero velopment, clogging by incompatible pollen, seeds was observed and recorded. This process breakage, or some other cause of style failure. was replicated 10,000 times to obtain fre­ If carpels in which both seeds had failed due quency distributions for the number ofcarpels to style or whole carpel effects could be re­ with two, one, and zero seeds predicted by the moved from the data, the remaining carpels ovule based hypotheses. could be used to test ovule-related hypotheses. In particular, with ovules developing indepen­ RESULTS AND DISCUSSION-Figure 1 shows dently ofcarpels, the hypothesis ofa constant the frequency distribution of one-seeded car­ global probability of development could be pels among 43 fruits for which seed number tested. Ofcourse, we cannot tell which empty per fruit was specified by the data and seeds carpels failed for style/carpel reasons and which were assigned to carpels equiprobably, based just happened to contain ovules that indepen­ on 10,000 replications of the simulation. The dently did not develop. However, we can hy­ observed number of one-seeded carpels, 69, pothesize a constant global probability of de­ lies at the lower tail of this distribution; only velopment for ovules in carpels that did not 2.3% of the replicates resulted in 69 or fewer fail for carpel/style reasons, and see how well one-seeded carpels. Similarly, the observed our data can be made to fit. number of zero-seeded carpels (55) was For each proportion, f of zero-seeded car­ matched or exceeded in only 2.3% ofthe runs, pels attributable to carpel failure, we calculated and the observed number of two-seeded car­ how well the remaining distribution ofcarpels pels (91) was matched or exceeded in 2.3%. fit a binomial distribution. We found that if Thus, the observeddata include fewer one- and f= 76% of the zero-seeded carpels were at­ more zero- and two-seeded carpels than ex­ tributable to carpel-level failure, then the re­ pected under the assumption of ovule failure maining carpels (91 two-seeded, 69 one-seed­ independent ofcarpel membership, even after ed, and 13 seedless) best fit a binomial relaxing the assumption of globally constant distribution (X2 = 0.0003). This corresponds ovule failure probability. to an overall carpel failure rate of 20%. Thus These results demonstrate that the assump­ it is possible that about a fifth of the carpels tion that the failure ofan ovule is independent fail for carpel/style reasons and in the remain­ ofthe fate ofthe other ovule in the carpel does der seeds develop with a constant global prob­ not hold for A. arborea. Seed number per fruit ability. December 1987] GORCHOV AND ESTABROOK-DETERMINATION OF SEED NUMBER 1897

Impossible hypotheses can be rejected with­ distinguishing between hypotheses for the pat­ out statistical argument. The power of statis­ tern ofseed development within fruits or other tical argument is to determine how likely the similar processes. A critical advantage of this dataare given that a possible hypothesis is true; sortofsimulation is thatit allows for the testing data very unlikely under this condition argue of specific hypotheses without requiring as­ against the hypothesis. To assess this likeli­ sumptions that all other things are equal. hood in our case, we need a distribution for Readers wishing to receive Pascal source code chi-square under our unusual post hoc pro­ for these two programs on 5 1/4 floppy disk in cedure ofsuccessively removing empty carpels IBM/PC compatible format are invited to mail until goodness-of-fit chi-square is minimized. us such a formatted disk. The classical distribution of chi-square for df = 2 is clearly not appropriate. To determine LITERATURE CITED the distribution of chi-square appropriate for AUGSPURGER, C. K., AND K. P. HOGAN. 1983. Wind our application, we simulated our post hoc hy­ dispersal of fruits with variable seed number in a pothesis-fitting activity with a computer. tropical tree (Lonchocarpus pentaphyllusy: Legumi­ Our computer program determined every nosae. Amer. J. Bot. 70: 1031-1037. possible combination oftwo-seeded, one-seed­ BAWA, K. S., AND C. J. WEBB. 1984. Flower, fruit, and ed, and seedless carpels that added to a total seed abortion in tropical forest trees: implications for equal to a given number of carpels (in this the evolution of paternal and maternal reproductive patterns. Amer. J. Bot. 71: 736-751. example, 215, the numberofcarpels in the data BIERZYCHUDEK, P. 1981. Pollinator limitation of plant set). For each of these combinations (22,791 reproductive effort. Amer. Naturalist 117: 838-840. in this case), the program deleted seedless car­ CAMPBELL, C. S., C. W. GREENE, B. F. NEUBAUER, AND J. pels (i.e., attributed them to carpel failure), one M. HIGGINS. 1985. Apomixis in Amelanchier laevis, at a time, until all seedless carpels were deleted. Shadbush (Rosaceae, Maloideae). Amer. J. Bot. 72: At each step in this progressive deletion, the 1397-1403. GORCHOV, D. L. 1985. Fruit ripening asynchrony is re­ chi-square goodness-of-fit to a binomial dis­ lated to variable seed number in Amelanchier and tribution was calculated; then the program Vaccinium. Amer. J. Bot. 72: 1939-1943. found the minimum value for each of these --. 1987. Proximate and ultimate causes of fruit combinations. These 22,791 minimum chi­ ripening asynchrony in vertebrate-dispersed woody square values provided a distribution with plants in southeastern Michigan. Ph.D. dissertation, which to compare our observed chi-square of University of Michigan, Ann Arbor. HARPER, J. L. 1977. Population biology of plants. Ac­ 0.0003. The proportion ofthese minima falling ademic Press, London. below our observed value, and hence the re­ HERRERA, C. M. 1981. Fruit variation and competition alized significance ofour result, was P = 0.13. for dispersers in natural populations ofSmilaxaspera. In order to explore whether this result was Oikos 36: 51-58. affected by the inclusion of combinations in LEE, T. D., AND F. A. BAZZAZ. 1982. Regulation offruit which the total number of seeds was very dif­ maturation pattern in an annual legume, Cassia fas­ ciculata. Ecology 63: 1374-1388. ferent than the observed, we repeated this pro­ OLSON, A. R., AND T. A. STEEVES. 1982. Structural changes cedure confining the analysis to those combi­ in the developing fruit wall ofAmelanchier alnifolia. nations in which the total number ofseeds was Canad. J. Bot. 60: 1880-1887. close to the observed. In our data 58% of the RATHCKE, B. 1983. Competition and facilitation for pol­ ovules developed into seeds, so we confined lination. In L. Real [ed.], Pollination biology, 305­ 329. Academic Press, New York. this analysis to those combinations of two-, ROBINSON, W. A. 1982. Experimental taxonomy in the one-, and zero-seeded carpels that contained genus Amelanchier II: Do the taxa in the genus Ame­ 50-70% seeds. There were 7,417 combinations lanchier form an agamic complex? Rhodora 84: 85­ that met this criteria, and 8% had minimum 100. chi-square values below our observed value of --. 1986. Effect of fruit ingestion on Amelanchier 0.0003. seed germination. Bull. Torrey Bot. Club 113: 131­ 134. This analysis shows that the good fit of our SNOW, A. A. 1986. Pollination dynamics in Epilobium data to the binomial distribution, after a flex­ canum (Onagraceae): consequences for gametophytic ible proportion of seedless carpels was attrib­ selection. Amer. J. Bot. 73: 139-151. uted to carpel failure, was moderately surpris­ STEPHENSON, A. G. 1981. Flower and fruit abortion: ing. This enhances the plausability that seed proximate causes and ultimate functions. Annu. Rev. number in A. arborea is determined by two Ecol. Syst. 12: 253-279. THOMPSON, J. N., AND M. F. WILLSON. 1979. Evolution mechanisms: some carpels fail entirely and of temperate fruit/bird interactions: phenological those ovules in the remainingcarpels are equal­ strategies. Evolution 33: 973-982. ly likely to develop into seeds. WAREING, P. F., AND I. D. J. PHILLIPS. 1978. Control of We hope that this report will provide other growth and differentiatin in plants. 2d ed. Pergamon investigators with a statistical framework for Press, Oxford and New York.