Heredity 72 (1994) 522—535 Received 19 November 1993 Genetical Society of Great Britain

Simulations of flowering time displacement between two cytotypes that form inviable hybrids

P. VAN DIJK* AND R. BIJLSMA Department of Genetics, University of Groningen, P0 Box 14, NL -.9 750 AA Haren, The Netherlands

Theevolution of reproductive isolation by flowering time displacement between two cytotypes that produce inviable hybrids was studied by computer simulations in an isolation-by-distance model. Flowering time distribution was stabilized by mass-action, both by the mating procedure and by pollen-limited seed-production in early or late flowering plants. Coexistence had to last long enough for flowering time divergence to evolve. This could only be achieved in a mosaic of local patches or parapatry. The model showed that flowering time displacement occurred despite the stabilizing effect of mass-action and the restricted width of the interaction zone. Initially an inverse dine for flowering time was formed but after 200 generations this dine had become monotonic. In contrast to the possible swamping effect by gene flow from outside the zone, there was a spread of genes into the allopatric ranges.

Keywords:floweringtime, hybrid zone, polyploidy, reproductive character displacement, simulation.

Introduction types. In a sympatric cytotype population, seed-set was negatively correlated with flowering date in diploids Inthe grassland perennial Plantago media both diploid but positively correlated in tetraploids (van Dijk et at., and tetraploid cytotypes occur. Almost all triploid 1994). This suggests selection for earlier flowering in hybrids between the cytotypes are inviable because of diploids and for later flowering in tetraploids. Low endosperm collapse (van Dijk & van Delden, 1990). In seed-set was primarily due to seed abortion and endo- an area in the Pyrenees where diploids and tetraploids sperm collapse, suggesting that seed-set was reduced are sympatric, the cytotypes are almost completely by cytotype hybridization. separated in flowering time (van Dijk, 1991; van Dijk ci' A major problem in evolutionary studies is that the al.,1992). This may explain the local coexistence of events often occur on a time scale beyond the observa- cytotypes because otherwise frequency-dependent tion period of the investigator. Theoretical models may production of inviable hybrids would lead to exclusion then be the only possibility to gain insight into such of the minority cytotype (Levin, 1975). How could evolutionary processes. In this article we investigate by such flowering time differences evolve? Because P. computer simulation models whether flowering time media is wind-pollinated, flowering time differences differences could evolve as a consequence of reproduc- cannot be explained by competition for insect pollina- tive interactions between cytotypes. tors as has been suggested by Levin & Anderson The view that natural selection may strengthen (1970). Because P. media is strictly outcrossing due to reproductive isolation between incipient species has self-incompatibility, the hybridization handicap might been popularized principally by Dobzhansky (1951). be severe and differences in flowering time might have In Dobzhansky's words: 'if, for example, the hybrids evolved due to reproductive interactions between cyto- between species A and B are partly sterile, it is advan- tageous for these species to modify their breeding seasons in such a way that as few such hybrids be pro- duced as possible'. This evolutionary process has been *Correspondence: Department of Plant Population Biology, Nether- lands Institute for Ecological Research, P0 Box 40, NL-6666 ZG, described in the literature as reinforcement of repro- Heteren, The Netherlands. ductive isolation (reinforcement for short) (Blair, 1955) 522 FLOWERING TIME DISPLACEMENT 523

or reproductive character displacement (Levin, 1970). action' models, polymorphism at assortative mating Since the concept originally dates back to Wallace, loci is lost (Moore, 1979), owing to frequency-depen- Grant (1966) has suggested the use of the term Wallace dent mating probabilities. In contrast, in so-called 'con- effect for it. Experiments, mainly with Drosophila spe- stant fraction' models a fraction of the population mates cies, have shown that pre-zygotic isolation can indeed assortatively whereas the rest mates at random (Caisse be strengthened by selection against hybridization (e.g. & Antonovics, 1978; Felsenstein, 1981). In these con- Koopman, 1950). In plants, Paterniani (1969) achieved stant fraction models, there is no disadvantage for the complete flowering time separation between two corn minority mating type. Moore (1979) therefore con- varieties within five generations by selecting against sidered these models as less realistic. hybrids. However, in these experiments no initial gene Flowering time is a special kind of mate recognition flow was allowed between the incipient species. Later system because it affects both male and female compo- theoretical studies have shown that strengthening of nents (Butlin, 1989). Both single and multilocus pre-zygotic isolation is unlikely if hybrids can back- models have been used for theoretical studies of flow- cross with the incipient species (e.g. Caisse & Antonov- ering time evolution. Caisse & Antonovics (1978) used ics, 1978; Felsenstein, 1981; Butlin, 1987; Sanderson, a single locus constant fraction model whereas Moore 1989). Gene flow and recombination cause the break- (1982) used a single locus mass-action model for down of the associations between the genes for assorta- flowering time. These were general models without a tive mating and the genes that determine hybrid population structure. Multilocus flowering time simula- unfitness. Therefore, Butlin (1987, 1989) has sug- tion models have been used by Crosby (1970) and gested a distinction between reinforcement of repro- Stam (1982), taking both flowering onset and duration ductive isolation, in which intial gene flow was possible, into account. These models also included restricted and reproductive character displacement, in which gene flow and population structure. However, although gene flow was blocked intially by post-zygotic barriers. they were not constant-fraction models, neither incor- After reviewing cases of proposed reinforcement in porated mass-action on flowering time. nature, Butlin (1987, 1989) concluded that, in agree- Of these four studies only in those of Caisse & ment with theoretical considerations, well substan- Antonovics (1978) and Crosby (1970) was selection tiated examples of reinforcement are lacking. for reproductive isolation by flowering time studied. Although reproductive character displacement is Allowing initial gene flow, these models can be classi- not hindered by recombination between the incipient fied as reinforcement models. Moore (1982) was species, two main theoretical problems exist. Firstly, interested in the colonization of early flowering plants hybrid inviability or sterility itself causes instability of along a selection gradient whereas Stam (1982) studied sympatric populations (e.g. Crosby, 1970; Levin, 1975; how the environment could trigger flowering time Spencer et al., 1986). As hybrid production is fre- differentiation. Caisse & Antonovics (1978) showed quency-dependent, the minority type will be rapidly that the conditions for the evolution of flowering time eliminated, possibly before any significant character isolation along a selective dine were quite restrictive. displacement has evolved. In experiments such as those Crosby's simulations suggested that reinforcement by of Koopman (1950) and Paterniani (1969) the ratios of flowering time could occur, although this was a very the types were kept artificially constant. Two abutting slow and weak process. As Crosby only completed a parapatric cytotype populations will form a stable single simulation run, it is not clear to what extent his situation because across the border each cytotype model was affected by stochastic events. Crosby's experiences a minority disadvantage (Crosby, 1970; simulation results are considered to exemplify that Butlin, 1987). However, in this case the interaction will reinforcement may be possible (Butlin, 1987, 1989). be restricted to a narrow contact zone. Character dis- However, when we used similar mating schemes to placement may therefore also be restricted to the con- those of Crosby and Stam, the flowering time distribu- tact zone or possibly even here it may be swamped by tions had the tendency to segregate by themselves, in the influx of genes from the allopatric areas (Barton & the absence of interactions with other cytotypes or with Hewitt, 1985; Sanderson, 1989). the environment. The inherent instability of the flower- A second major problem in the evolution of flower- ing time distributions may have affected the flowering ing time displacement is that flowering time itself is time divergence in their models. likely to be under stabilizing selection and this will We are not aware of the existence of multilocus operate against displacement. Moore (1979, 1982) has models of flowering time displacement incorporating argued that the less frequent genotypes are less likely to mass-action. Here we describe stochastic multilocus find mates in the population. For example, in plants models of flowering time in populations with restricted seed-set may be limited early and late in the flowering pollen and seed flow, both with and without mass- season due to low pollen density. In so-called 'mass- action. Before investigating interactions between cyto- 524 P. VAN DIJK & R. BIJLSMA types, the stability of flowering time distributions in the or cytotype B; both cytotypes were diploid. Hybrids absence of cytotype interactions was studied. between the cytotypes were inviable. Unless otherwise indicated the initial frequencies of Themodel A and B were equal (0.50). Two different spatial start- ing patterns were used for the two-cytotype runs: para- Weused a stochastic isolation-by-distance model, patric and sympatric. In the sympatric starting pattern, similar to those of Rohlf & Scimell (1971), Turner et al. cytotypes were randomly distributed over a lattice of (1982) and Sokal & Wartenberg (1983). A simplified 60 X 50. All sites were occupied; the total density flow diagram is given in Fig. 1. therefore was constant. In the sympatric case the lattice The plants were considered to be annual herma- was constructed as a complete torus, therefore there phrodites, incapable of self-fertilizing. Generations were no edge effects. The parapatric model consisted were discrete, non-overlapping. Pollination resembled of two adjacent 50 x 30 lattices of different cytotype wind-pollination. Plants belonged either to cytotype A (see Fig. 8). In the parapatric model the upper and lower edges were connected by a torus construction. However, the left and right edges were not connected POPULATION INITIATION as this would have created two contact zones, which sample cytotypes from P =0.50 sample alleles from p =0.50 for 14 loci would have hindered the analysis of the processes. Plants near the left and right edges had fewer neigh- PLANT bours and received less pollen. In pollen limited simu- lations these plants produced less seeds than plants POLLEN LOAD A AND B further away from these edges. calculated by flowering time overlap —EXT PLANT Each generation there were four stochastic events: ants in pollen neighborhood y (i) the sampling of a female parent (weighted by its seed production); (ii) the sampling of a male parent; (iii) the SEED PRODUCTION if N0 >totalpollen load, then sampling of a female gamete and (iv) the sampling of a N8 = N0 domestic pollen ratio male gamete. These samplings were carried out by use else N5 domestic pollen load of the pseudo-random number generator of Turbo Pascal 3.0 (Borland International Inc.). ALL PLANTS DONE? I— NO Individual flowering onset was determined by 14

Y43 additive, unlinked loci each with two alleles (0,1). GO TO FIRST REGENERATION SITE Three loci had a major effect on flowering onset (major genes: 4 flowering time units delay per 1-allele), four SAMPLE SEED PARENT loci had a intermediate effect (medium genes: 2 units seed neighborhood GO TO N EXT S ITE delay per 1-allele) while the remaining 7 loci had a weighted by seed productio V minor effect (minor genes: 1 unit delay per 1-allele). [SAMPLE GAMETE FROM SEED PARENT Consequently flowering onset could vary between 'day' 0 to 'day' 54 (2X (3 X 4 + 4)< 2 + 7 X 1)). Although initial differences in flowering onset could be generated SAMPLE POLLEN PARENT within pollen neighborhood by stochastic variation, flowering onset in all plants of [9hted by flowering time overlap cytotype A was delayed 1 'day', to increase the rate of divergence. Initially alleles were sampled randomly [MPLE GAMETE FROM POLLEN PARENT from an allele frequency distribution of 0.50. Loci were stored as bits and manipulated by the methods [ALL SITES DONE? I—NO described in Fraser & Burnell (1970). Flowering dura- YES tion was the same for all individuals but could be {!CE EACH PARENT BY A ZYGOTE varied between runs (8, 16 or 32 'days'). Unless other- V wise indicated flowering duration of all individuals was —I--— NO ALL GENERATIONS COMPLETED? 16 'days'.

YES Both pollen and seed flow were restricted to neigh- bourhoods, within which mating was random with

STOP respect to distance. The neighbourhoods consisted of a sub-lattice centred on the individual to be pollinated or Fig. 1 Simplified flow diagram of the two-cytotype simula- replaced, respectively. Individual seed production was tion models with overlap weighted sampling. a function of flowering synchrony within the pollen FLOWERING TIME DISPLACEMENT 525 neighbourhood. In contrast to the models of Crosby bourhood sizes of the different runs are given in Table (1970) and Stam (1982), seed production was not 2. These sizes were chosen because of the gene flow (necessarily) equal for all plants. Therefore the mating distances measured in Plantago lanceolata (Bos et at., procedure was run first to determine seed production 1986) and the densities of flowering Plantago media in per plant and second to choose a male partner of a sympatric cytotype populations in the Pyrenees (Van female parent. The probability that offspring of a Dijk etal., 1994). certain plant gained a regeneration site was equal to its Initially a number of runs were done with a single proportion of the total seed load at that site. cytotype on a 50 x 30 lattice (complete torus) to For all plants the individual flowering period was analyse the evolution of flowering time in the absence calculated from its flowering onset genotype and the of cytotypic interactions. In these single cytotype runs, general flowering duration, which was the same for two methods of choosing a partner were tested: (i) ran- each plant in a simulation run. For each plant the dom mate choice weighted by its flowering time over- flowering time overlap with every potential mate in the lap with the seed parent (overlap weighted sampling), neighbourhood was computed. The overlap deter- and (ii) randomly choosing a mate at a random moment mined the number of pollen grains donated by that during flowering of the seed parent (random moment mate (maximum 64 pollen grains with exactly sampling), comparable to the method of Stam (1982). synchronous flowering). Pollen thus was uniformly dis- In the two-cytotype runs only overlap weighted samp- tnbuted through the plant's neighbourhood and ling was applied. uniformly throughout the plant's flowering period. A Most simulations were run for 200 generations; in a separate fertilizing pool of A and of B pollen was few runs the length was doubled. The following output determined. When the total pollen load within a pollen data were recorded every 25 generations for both cyto- neighbourhood was larger than the number of ovules types. to be fertilized on the central individual, seed produc- 1 Frequency of the cytotypes. tion was set equal to the proportion of con-cytotypic 2 Mean population flowering onset and standard pollen times the ovule number. Otherwise seed produc- deviation. tion was equal to the con-cytotypic pollen load. The 3 Allele frequencies, p(i)'s, at three major, three number of ovules per plant could be varied between medium and three minor loci which were previously runs (Table 1). Increasing the numbers of ovules per selected. plant caused a mass-effect because seed-set became 4 Flowering time overlap (combination of onset and pollen-limited in early and late flowering plants. Neigh- duration).

Tabte 1 Pollen (P) arid ovule (0) numbers for different 0/P ratios with pollen neighbourhood size of 134 self-incompatible plants (15 x 9— 1)

0/P production Pollen production Maximum pollen Ovules ratio per plant load per plantt per plant

0.01 8576 8576 86 0.20 8576 8576 1715 0.40 8576 8576 3430 0.50 8576 8576 4288 1.00 8576 8576 8576

tAssuming perfect synchronization.

Table 2 Some characteristics of the simulations

Neighbourhood size Population size Pollen Seed Edges

One-cytotype 50X30 120(11 xli— 1) 49(7x7) Torus Two-cytotypes Sympatric 50x60 120(lixll—1) 49(7x7) Torus Parapatric 100 x 30 134(15 x 9—1) 45(9 X5) Semi-torus 526 P. VAN DIJK & H. BIJLSMA

5 Mean seed-set percentage per plant (since all plants pollen grains than ovules. Within the pollen neighbour- produced an equal number of ovules this corresponds hood mating is random with respect to distance and is to seed-production and was considered as fitness). only determined by the flowering times. As there are 6 In the parapatric model these data were recorded 120 potential partners in the pollen neighbourhood, within 10 clinal blocks of 10 ><30lattice points (see even single flowering plants will be likely to receive Fig. 8). enough pollen for the fertilization of all their ovules. For 0/P= 0.01, then, there is pollen saturation and seed-set is pollen-unlimited (Fig. 2). For 0/P= 0.40, Results and discussion each plant produces 2.5 times as much pollen as ovules. In this case, even the modal classes of flowering Flowering time evolution in single cyto type onset, on average, do not receive enough pollen grains populations for full seed-set. Seed-set in early and late flowering We first simulated flowering time evolution in a single plants is strongly pollen-limited. For 0/P =1.00this cytotype population of 1500 plants to see how the effect is highly enhanced. flowering time distribution developed in the absence of Figure 3 shows the mean seed-set per plant at cytotype interactions. The inset of Fig. 2 shows the generation 0 for different ovule/pollen ratios, with a flowering onset distribution that was initially generated. pollen neighbourhood size of 120. For 0/P values of This distribution approximates to a normal distribu- 0.20 and higher, mean seed-set is lower than 100 per tion. cent and selection against early or late flowering will The strength of mass-action could be manipulated occur. by changing the ovule/pollen ratios (0/P ratios). In Fig. Under pollen-saturation (0/P= 0.01), the evolution 2 the relations between seed-set and flowering onset of the flowering onset distribution was markedly differ- date', after the first round of fertilization, generated by ent between overlap weighted sampling and random 0/P=0.01, 0.40 and 1.00 are shown, for a pollen moment sampling. Figure 4A shows the intial flowering neighbourhood size of 120. This can be considered as onset distribution whereas Fig. 4B and C show charac- a fitness graph. For 0/P ratios of 0.40 and 1.00, seed teristic flowering onset distributions after 200 genera- set is reduced in early and late flowering plants tions under both procedures. With the overlap whereas for 0/P=0.01, seed-set is independent of weighted sampling the kurtosis of the distribution flowering onset. This can be explained as follows. Early increased. However, with the random moment samp- or late flowering plants will find fewer partners that ling method the variation in flowering onset increased overlap in flowering time in their pollen neighbour- and the distribution segregated and finally became hood than plants with intermediate flowering onset. bimodal. With the latter procedure the original popula- When 0/P= 0.01, each plant produces 100 times more tion diverges spontaneously into two populations that

1) 100 0) I

C a) 80 Fig.2 Single-cytotype simulations, fit- 0 ness distribution. Seed-set after the first aa) round of fertilization in relation to the 60 flowering onset of a plant for three dif- 4-, ferent ovule/pollen ratios (0.01,0.40, ci) CD 40 1.00), causing pollen-saturated, moder- -o ate and severe pollen-limited seed-set, 1) respectively. Mean seed-set per flower- j) CD 20 ing onset class SE. The inset shows the distribution of the flowering onset in the population. The initial allele fre- 0 quencies for flowering onset (p(i)O's) 0 10 20 30 40 50 60 70 80 were all 0.50; flowering duration was 16 'days' and there were 120 plants per floweringonset (units) pollination neighbourhood. FLOWERING TIME DISPLACEMENT 527

100 400 A 0 0) 4-, a 300 4-, C 0 a. 0 60 9- 0) 200 a 0 4-, w 0) 40 a E100 D 0) C 0) 20 I— CD 0 0— 400 0.00 0.20 0.40 0.60 0.80 1.00 B ovule / pollen ratio 300 Fig. 3 Single-cytotype simulations. The mean population seed-set after the first round of fertilization for different ovule/pollen (O/P) ratios. The other parameters were similar 200 I to those described in Fig. 2. 100 are completely reproductively isolated by flowering 0 I..-----I period. It is well known that positive assortative mating 400 causes an increase in homozygosity. In a single locus C model this is obvious; with perfect assortative mating of 300 all the three genotypes, the percentage of heterozygotes is halved in each generation. In a multilocus model 200 segregation will occur more slowly as many different genotypes will have the same phenotype but eventually the result will be multilocus homozygosity. Moreover, 100 I this segregation will also be slowed down because flowering duration allows mating of plants with differ- 0 .— ent flowering onset dates. 0 10 20 30 40 50 60 How can the difference between the two mating schemes be explained? As intermediate flowering flowering onset onset genotypes are the most frequent, these are the Fig. 4 Single-cytotype simulations. Typical flowering onset most likely pollen parents in either mating scheme. In distributions under different mate sampling procedures at the overlap weighted method the whole flowering thestart and after 200 generations. (A) Initial distribution period of the female plant is taken into consideration. (s.d. =6.87).(B) Distribution after 200 generations with This gives a stronger bias towards intermediate flower- random moment sampling procedure (s.d. =18.05).(C) ing partners than in the random moment method in Distribution after 200 generations with the overlap weighted which the moment chosen is independent of the sampling procedure (s.d.3.82). Conditions: ovule/pollen ratio= 0.01 (pollen saturation); p(i)O's all 0.50; flowering number of plants flowering at that time. This is a mass- duration: 16 'days'; pollination neighbourhood size: 120 action effect not caused by frequency-dependent seed- plants; seed neighbourhood size: 49 plants. set but by frequency-dependent mating. In the overlap weighted mating scheme this mass-effect overcomes the natural tendency of segregation of the flowering 00 or 11 homozygotes for major and medium genes time distributions. In the random moment scheme, (0000000 /0000000 and 1111111 / however, the mass-effect is not strong enough to pre- 1111111 )(minorgenes are indicated as .).By vent segregation. contrast under the overlap weighted method all plants Inspection of the genetic composition of the individ- were homozygous 00 or 11 for alternating Joci(e.g. uals clarifies what is happening under the two mating 0011101 /0011101 ).Minorgenes were not schemes. After 200 generations, under the random yet completely fixed after 200 generations of simula- moment method the population consisted of multilocus tion. 528 P. VAN DIJK & R. BIJLSMA

The rate of segregation was shown to depend on the While the variation in flowering onset also contin- flowering duration. When the flowering duration was ued to increase after 20 generations in the random reduced from 16 to 8 'days', the segregation tendency moment sampling method, it stabilized after 20 genera- was much stronger for the random moment method tions in the overlap weighted method (Fig. 5)andafter and even under the overlap weighted method there was 80 generations clearly decreased. After 200 genera- a tendency for segregation. By contrast, a duration of tions the variation in flowering onset was less than the 32 'days' showed little segregation after 200 genera- initial variation (see also Fig. 4C). Under severe pollen tions in either mating scheme. limitation (O/P= 1.00), the initial differences between Figure 5showsthe change in the variation in flower- the local flowering time patches were much smaller ing onset during the first 200 generations for random than under pollen saturation. Variation in flowering moment sampling under pollen saturation (O/P= 0.01) time decreased rather rapidly because of stabilizing and for overlap weighted sampling under pollen satura- selection. At the same time the mean seed-set tion (O/P= 0.01) as well as under strong pollen limita- increased from 55percent in generation 0 to 80 per tion (O/P= 1.00). The standard deviation describes the cent in generation 200. In this case the stabilizing effect variation of the distribution. Under pollen saturation on the flowering onset distribution was caused by the the flowering onset variation initially increased for both effect of mass-action by biased mating and frequency- mating schemes because of the development of local dependent seed-set. early and late flowering patches as the result of The overlap method may be less realistic than the restricted gene flow. Local assortative mating enhanced random moment method as in this model fertilization initial chance differences and caused a patchy flower- takes place at the end of the flowering period of a plant. ing onset landscape, as has been noticed before by In reality early pollinations will pre-empt ovules for Stam (1982). This pattern must not be confused with later pollinations. However, the random moment the pattern of neutral genes caused by local genetic method of partner sampling cannot be used in a model drift in isolation-by-distance models by Rohlf and with two cytotypes with inviable hybrids. Moreover, Schnell (1971) and Turner eta!.,(1982) as flowering the overlap method causes a stabilizing force that pre- time is a multilocus phenotype. Moreover, as the neigh- vents segregation and operates against differentiation. bourhood sizes in our models are rather large, local If despite this stabilizing force, flowering time displace- genetic drift can not have played an important role, ment occurs, this is a robust result of the model. although flowering time variation by itself will have Neither Crosby(1970) nor Stam(1982) reported on reduced the effective neighbourhood size somewhat. the stability of their flowering time distributions in the absence of the interactions they studied. Stam used a longer flowering time duration and therefore the segre- 20 gation tendency in his model may not have been very strong. Crosby used a slightly different model, in which (D C 15 mating occurred on a weekly basis and was determined 0 by only three onset genes and three duration genes. C During his simulation flowering duration became very 10 short, possibly by selection against sub-species hybridi- 0 zation. As a consequence the flowering onset distribu- 4- tion probably became less stable. Moreover, plants that 5 (I) had no overlapping flowering partner in their neigh- bourhood were self-fertilized, which caused segrega- 0 tion at all heterozygous loci. It is hard to judge how 0 40 80 120 160 200 much spontaneous segregation of the flowering time distributions may have affected Stam's and Crosby's generaton results. At least it might have facilitated flowering time Fig. 5 Single-cytotype simulations. The change of the stand- differentiation. In this light it is noteworthy that in ard deviations of the flowering onset distributions under Crosby's simulations flowering time differentiation different mate sampling procedures during 200 generations. became greater than was necessary for reproductive Random moment sampling (A )(O/P=0.01; pollen- isolation. Obviously different alleles were fixed in the saturated seed-set); overlap weighted sampling (o) (O/P= two subspecies suggesting an intrinsic instability of the 0.01; pollen-saturated seed-set) and overlap weighted flowering time scheme of his model. sampling (•)(O/P=1.00; severely pollen-limited seed-set). Mean values of five different runs SE. per parameter set. Conditions are similar to those in Fig. 2. FLOWERING TIME DISPLACEMENT 529

Flowering time evolution in two-c yto type simulations cytotype hybridization was reduced by distance isola- tion during this process. Sympatry. Next we investigated whether it was This developing mosaic of different cytotype possible for two cytotypes to coexist long enough for patches enabled co-existence of cytotypes for many flowering time displacement to evolve. In these simula- generations. However, in simulations without genetic tions there was pollen saturation (O/P= 0.01) but seed- variation for flowering onset (P( i) =1.00),the smaller set was reduced by cytotype hybridization. These patches disappeared in the long run and after 200 sympatric simulations were started with a random generations generally only a single cytotype persisted. spatial distribution of the cytotypes (see Figs 7 and 8). Therefore this situation can be described as pseudo- It was found that in a sympatric starting pattern stable. In simulations with genetic variation for flower- when the frequency of one cytotype was less than 0.45, ing onset (P( i) =0.50),flowering time divergence could this minority cytotype was rapidly eliminated from the occur before elimination of the minority type and population. The rate of elimination was close to that in stable coexistence was the result. The initial contrac- the deterministic random mating model of Levin tion of the cytotype patches during the first 15 genera- (1975) (pollen saturation; no mass-action) (Fig. 6A). tions was followed by expansion in later generations Figure 7 shows the change in spatial pattern of a typical due to flowering onset differentiation. Sometimes com- minority cytotype elimination. Some patchiness plete flowering time separation was achieved within 30 developed due to local minority cytotype exclusion but generations. However, the development of stable these patches were not stable enough to persist longer sympatry was a matter of chance; often the stochastic than a few generations. Obviously, restricted gene-flow deviations from 0.50 were too large to build up patches does not expand time of co-existence significantly. of approximately the same size and elimination of the However, when starting frequencies of the cytotypes minority cytotype occurred within 20—30 generations were very close or equal to 0.50, occasionally a (Fig. 6B), despite the presence of genetic variation for pseudo-stable pattern developed (Fig. 6B). The flowering time. In six out of 10 runs one of the cyto- random starting distribution caused local chance types was eliminated before complete flowering time differences in cytotype frequencies. Due to the com- isolation was achieved. bined action of restricted gene flow and locally occurr- ing minority cytotype elimination, discrete single Parapatiy. The process of flowering displacement cytotype patches developed. These patches became can be better analysed in two abutting parapatric cyto- increasingly homogenous and tended to minimize the type populations. In transects perpendicular to the length of their contact zones, similar to the behaviour contact zone, the progress of the displacement through of tension zones (hybrid zones that are maintained by the population can be monitored. the balance between dispersal and selection against The initial situation is shown in Fig. 8 in which the heterozygotes) (Barton & Hewitt, 1985). This is to be pollen and seed neighbourhood areas are also shown expected, since in our simulations hybrids between on the same scale. The zone of interaction is restricted cytotypes are inviable. At the same time the mean seed- to the seed and pollen neighbourhoods along the con- set of both cytotypes increased dramatically since the tact zone of the two-cytotype populations and is

Fig. 6 Two-cytotype simulations. (A) Exclusion of the minority cytotype A, initial frequency of 0.45, according to the random mating model of Levin (1975), without flowering onset varia- tion (+ ) andaccording to the present isolation-by-distance model with tOO flowering onset variation and overlap A sampling (.)(O/P= 0.01; for other 4:o0 conditions see the legend of Fig. 2). 0 C0.60 (B) Changes in the frequencies of cyto- 3a) type A over 80 generations in four dif- 00.40 a) ferent runs when started at 0.50, accord- 9-020 ing to the isolation-by-distance model with flowering onset variation and 2 4 6 8 overlap sampling (O/P= 0.01; for other 0 10010 20 0 40 50 60 70 80 conditions see the legend of Fig. 2). generation 6 and7)flowering timedivergencehas become much that atgeneration25inthe interactionzone(blocks5, of thepopulationinFig.10. InFig.10itcanbeseen tion offloweringtimethe samerunisshowninFigs pattern ofacharacteristic simulation run.Theevolu- (O/P=0.01). Figure8showsthechangeinspatial 9 and11forthetotalpopulation andforcross-sections cytotype A. except thatfloweringonsetwasdelayedone'day'in time simulations,however,thecytotypeswereequal zones (Barton&Hewitt,1985).Duringourflowering behaviour hasbeendescribedformovingtension the zoneoflowdensity(datanotshown).This was modelled,thismovingcontactzonetrappedin the fewestgametes.Whenazoneof10percentdensity contact zonemovedintotheareaofcytotypewith one cytotypewasgivenmoreovulesorpollen,the distribution wasshowntobestable.However,when Without variationforfloweringonsetthisparapatric narrow 530 P.VANDIJK&ftBJJLSMA First thecaseofpollensaturationwillbeconsidered compared withtheareaswithoutinteraction. 0

0 01

p C.) Co displacement wouldbecompletedas theselective Spencer etal.(1986)doubted whethertheprocessof action causedbytheoverlap weightedmatingscheme. within thecytotypesdecreased becauseofthemass- in floweringonset,thevariation infloweringonset smaller interactionzone.While thecytotypesdiverged sympatric scenario,aswasexpectedbecauseofthe flowering timedivergencewasslowerthaninthe onset duringthefirst200generations.Therateof gradually theinversedinesdisappeared(Fig.10),while the interminglingprogressedmoreand(Fig.8). entiation progressedintotheallopatricareasand of floweringtimeseparation.Thediffer- intermingling cytotypesnolongerhybridizedbecause dispersal acrossthecontactzone;obviouslythese ling wasmuchstrongerthancanbeexplainedbyseed than fortheminorgenes.Atsametime,interming- dine wasmuchmorepronouncedforthemajorgenes dines wereestablished.Onthegenelevelinverse larger thanbetweenblocks1and10.Clearinverse Figure 11showsthedivergenceofflowering areas areshownonthesamescale. pollen (p)andseedneighbourhood(s) right atthebottomofmaps.The quencies ofcytotypeAaredisplayed other conditionsseeFig.2).Thefre- weighted sampling;O/P=0.01;for black square:cytotypeB;overlap generations (dottedsquare:cytotypeA; 0.45) insympatryafter0,2,4 type (initialfrequencyofcytotypeA: elimination patternofaminoritycyto- tial distributionofcytotypes.Atypical Fig. 7 Two-cytotype simulation: spa- and 6 FLOWERING TIME DISPLACEMENT 531

0

50

Fig. 8 Two-cytotype simulation: spatial distribution of cytotypes. The intermingling in space of two parapatric cytotype populations after 0, 50, 100 and 200 generations, indicated to the 100 right (dotted square: cytotype A; black square: cytotype B). Conditions: over- lap sampling; O/P= 0.01 (pollen saturation); p(i)O's all 0.50; flowering duration: 16 'days', pollination neigh- bourhood size: 120 plants; seed neigh- bourhood size: 45 plants. The pollen (p) and seed neighbourhood (s) areas are shown on the same scale. The num- bered blocks consist of 10 rows of 30 200 plants. 1 2 3 4 5 6 78 9 10

pressure would become weaker as the assortative However, the flowering sequence that evolved was mating characters are established. Although the rate of occasionally inverse to the initial sequence, indicating flowering time overlap reduction decreased, in the that genetic drift was an important factor in creating an end, it was complete. It can be seen that there is no initial difference that could be enhanced by selection. progress in flowering onset divergence after the Figure 12 shows the cross-sections of flowering average flowering time overlap had become zero onset after 200 generations under different 0/P ratios. (generation 160 in Fig. 11). At the same time, a con- It can be seen that the inverse dine under mass-action siderable amount of genetic variation for flowering disappeared but that the divergence after 200 genera- onset is still available as is indicated by the standard tions was less than under pollen saturation. Also the deviations in Fig. 11. Thus the model has no tendency degree of intermingling was reduced under pollen to segregate by itself. Probably mass-action accom- limitation. With 0/P= 0.40 complete flowering time plished the complete separation of the flowering time separation was achieved after 350—400 generations. distributions. Strong pollen-limitation, hence mass-acton (0/ Initially cytotype A was set to flower on average 1 P= 1.00), prevented flowering time displacement com- 'day' later than cytotype B, to initiate disruptive selec- pletely during the first 500 generations (data not tion. In most cases cytotype B diverged towards earlier shown). flowering and cytotype A towards later flowering. 532 P. VAN D!JK & R. B!JLSMA

400 tive isolation rather than reproductive character dis- B: 273 6.1 0 placement. ci) A 28. 6.2 C300 0 Evolutionaryperspectives of flowering time 0200 displacement a) -o Oursimulations indicate that a polygenic assortative E100 :3 mating character can be displaced in populations with C 0 restricted gene flow, leading to complete pre-zygotic reproductive isolation and coexistence of cytotypes. 400 Selection against hybridization was maximum due to a 16.8 5.1 100 hybrid inviability. This is not unrealistic as hybrids in 300 A 37.6 8.7 interploidy crosses are often inviable or sterile (Woodell & Valentine, 1961; Kay, 1969; Johnston et 200 al., 1980; van Dijk & van Delden, 1990). The simulations indicate that long individual flower- 100 ing periods will impede flowering time displacement. In species that have a long flowering season, flowering 0 .i1RIILh]JlEDfl Don displacement is therefore unlikely to occur. In partially selfing species the amount of hybridization will be 400 much reduced and consequently less flowering time B: 113 2.9 200 displacement than in outcrossing species is to be A 42.5 3.4 300 expected. Our models did not include environmental or 200 developmental variation for flowering time. These factors are likely to slow down the rate of flowering 100 time divergence between the cytotypes. Rathcke & Lacey (1985) have argued that although flowering time 0 II. flnD O.. can be easily altered as it is probably under simple 0 10 20 30 40 5060 genetic control, it is unlikely to cause effective isolation owing to phenotypic plasticity. Nevertheless, in flowering onset Piantago media flowering time causes effective repro- ductive isolation between sympatric diploid and tetra- Fig. 9Changein the flowering onset distributions in the simulation run shown in Fig. 8. Distributions after 0, 100 and ploid cytotypes (van Dijk et al., 1994). Flowering time 200 generations are shown together with the population displacement may be constrained by other selective means s.d. (open bars: cytotype A; closed bars: cytotype B). forces acting on flowering time (Rathcke & Lacey 1985; Ollerton & Lack, 1992; Fox & Kelley, 1993). Pollinator phenology in animal pollinated species and the seasonal development of the vegetation in wind- pollinated plants may also restrict flowering time When the flowering time duration was doubled from divergence. Flowering time divergence may also be 16 to 32 'days', no significant divergence developed constrained by developmental correlations between under pollen saturation. Clearly flowering duration of flowering time and other phenological stages in the individual plants has to be short for the development of annual cycle (e.g. the timing of leaf development in flowering time displacement. In reality in P. media a spring or the seed germination period). low level of gene flow between diploids and tetraploids The process of reproductive character displacement is possible because of low frequencies (about 0.1 per can be demonstrated in sympatric populations by the cent) of viable triploid and tetraploid hybrids (van Dijk, enhanced fitness of positive assortative mating 1991). Probably gene flow is mainly unidirectional individuals, provided that the character is heritable from diploids to tetraploids. A modification of the (van Dijk eta!., 1994). However, for the demonstration present simulation model, allowing an initial gene flow that reproductive characters are displaced (the of 0.05 (gamete per generation) from A and B did not products of character displacement), geographical notably affect the rate of flowering time divergence. In comparisons of the reproductive character are neces- fact this would be a case of reinforcement of reproduc- sary. As a consequence of reproductive character dis- FLOWERING TIME DISPLACEMENT 533

60 60 5° 0 50 4° 40

30 1 T 30 20 J f__f f f 20 10 10 6° 0 0)60 60 C 50 50 40 40 30 20 20 io 10

60 60 50 100 20050 40 40 Fig. 10 Spread of flowering time 30 "Ii' 30 divergence through the populations in 20 20 the simulation run shown in Fig. 8. 10 10 Cross-sections after 0, 25, 50, 75, 100 0 0 and 200 generations. Mean flowering 1234567891012345678910 onsets per block (see Fig. 8) s.d. are zit shown (+ : cytotype A; •: cytotype B). block

60 100 - vics,1968) and Pinus muricata (Millar, 1983). These 0) wouldbe cases of reinforcement rather than character displacement as post-zygotic isolation was not corn- •1- a 40 COT 60 plete. However, alternative explanations may be 30 equally likely (Stam, 1982; Butlin, 1989). Carter & 40 Murdy (1986) reported a likely case of displaced 20 flowering times in diploid Talinum mengesii and its allo- 10 20 tetraploid derivative T teretifolium. Hybrids between 0 o these species are sterile. In the glasshouse, diurnal 0 50 100 150 200 flowering time differences were shown to be larger between plants originating from sympatric populations generaton than between plants from allopatric populations. In many plant species cytotypes occur that produce Fig. 11 Characteristics of the simulation run shown in Fig. unfit hybrids. It is remarkable that there are only few 8. The divergence in flowering onset over generations (left reports in the literature on sympatric populations of axis); upper thick line: cytotype A; lower thick line cytotype such cytotypes. Although this may be due to poor B; given are population means s.d. The percentage flower- sampling or to ignorance, it may also be that sympatric ing time overlap (right axis) is indicated by a dotted line. The bar along the left axis indicates the flowering time duration populations are rare because reproductive character (16 units). displacement has not been strong enough to allow stable co-existence. Alternatively, niche overlap and competitive exclusion may have prevented co-exist- placement differences between sympatric taxa are ence. More population biological studies of such situa- expected to be larger than between allopatric taxa. Dis- tions are needed to elucidate this interesting problem. placed flowering times have been claimed in a number of wind-pollinated plant species (e.g. Agrostis tenuis and Anthoxanthum odoratum (McNeilly & Antono- 534 P. VAN DIJK & R. BIJLSMA

60 60 50 0.01 0.4050 -1-' ID 40 40 (I) "III' £ 030 30 0)20 20 10 111111 10 II) 0 -0 0 1 2 3 45 6 7 8 9 10 1 2 3 4 5 6 7 8 910 4- C60 (j50 0.50 ci) E40 30 20 Fig. 12 Cross-sections of the flowering onset distributions after 200 genera- 10 tions for three different 0/P ratios: 01 2 3 4 5 6 7 8 9 10 0.01,0.40 and 0.50. Mean flowering onset per block s.d. ( +: cytotype A; block •: cytotype B).

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