Satoki Sakai

A model for seed size variation among plants

SummaryI developed a model for seed size variation among plants assuming that the pollen captured per flower depends on both the allocation to pollen capture mechanisms per flower and the number of flowers on each plant. I showed that the optimal seed size increases with (1) the total resource allocation to reproduction, (2) decreasing outcross pollen availability, (3) decreasing probability of seedling establishment and (4) decreasing selfing rate. However, optimal seed size does not depend on the total resource allocation if the total number of pollen grains captured by a plant increases linearly with its flower number. In addition, the optimal seed size is not always positively correlated with the optimal resource allocation to pollen capture mechanisms per flower. I discussed implications of the results for seasonal decline in seed size and seed size variations among populations, such as alutitudinal variation.

Evolutionarily stable growth of a sapling which waits for future gap formation under closed canopy

SummaryA model was developed to examine the ESS sapling growth waiting for future gap formation under closed canopy. Assumptions are: a sapling has two parts, a trunk and a photosynthetic part, and allocates annual photosynthates to these two parts; and a sapling with a larger photosynthetic part has a larger production rate, but a sapling with a larger trunk is more successful in competition after gap formation. The ESS growth schedule of a sapling typically consists of three phases: (1) the sapling first allocates all annual photosynthates to the photosynthetic part, then (2) it allocates annual photosynthates both to its trunk and to photosynthetic part, and both parts grow simultaneously, and finally (3) it also allocates annual photosynthates to both parts, but the size of the photosynthetic part stays constant due to annual loss, and only the trunk size increases. A sapling should allocate photosynthates more to the trunk if mortality or probability of gap formation is large. However, a sapling should allocate photosynthates more to the photosynthetic part if large trunks are strongly advantageous in competition after gap formation.

Evolutionarily stable resource allocation for production of wind-dispersed seeds

We developed a game-theoretic model for wind-dispersed seed production to examine the seed mass–dispersal ability relationship and the evolutionarily stable distance of seed dispersal in terms of exploitation of safe sites. We assumed trade-offs between masses of the embryo (including albumen) and the wind-dispersal structures per seed, and also between seed mass and number of seeds per parent. We showed that ESS wing-loading is independent of embryo mass; that is, heavy seeds are not poor dispersers if the cost of producing wind-dispersal structures per unit area is constant. The ESS embryo mass per seed depends only on the factors which determine the probability of a seedling being established from a seed. However, wing-loading was found to increase with embryo mass when the change in length was isometric and there was a negative correlation between seed mass and dispersal ability. Thus, the area–mass relationship in wind-dispersal structures may have large effects on the ESS production of wind-dispersed seeds. On the other hand, given that only a limited number of adults can be established at a safe site, the ESS seed dispersal distance depends on the relative degree of sib to non-sib competition. A parent disperses its seeds over a wide area to exploit many safe sites if sib competition is strong. However, it disperses its seeds within a narrow area if the mean number of parents per unit area is large, or if non-sib competition is strong. Thus, in addition to an upper limit on the number of adults per safe site, the degree of sib and non-sib competition may be important for the ESS dispersal distance in wind-dispersed seeds.

A model for nectar secretion in animal-pollinated plants

SummaryA game theoretic model was developed for nectar secretion in animal-pollinated plants in order to examine how the total amount of resources allocated to flowers affects the spread of nectarless plants. It was assumed that pollinators concentrate on patches whose nectar rewards are relatively large compared to other patches and if pollinators visit a patch, they concentrate on the plants whose nectar rewards are relatively large compared to other plants in the patch. It was shown that plants are more likely to secrete nectar in populations where the total amount of resources allocated to flowers is large. It was also shown that strong interplant competition, strong interpatch competition and the nectar discrimination of the pollinators are also important factors for nectar secretion. However, if the total amount of resources allocated to flowers is sufficiently large, plants would secrete nectar even if competition is not very strong and nectar discrimination is not so precise.

Patterns of wing size variation in seeds of the lily Cardiocrinum cordatum (Liliaceae).

We examined the patterns of variation in wing-loading and its related characteristics in Cardiocrinum cordatum to clarify the factors that determine the variation in seed dispersal ability in this species. The square root of wing-loading of a seed of a plant was not significantly correlated with basal stem diameter of a plant, indicating that large plants did not necessarily produce seeds with high dispersal ability. This result was inconsistent with the hypothesis that large plants produce seeds with high dispersal ability to avoid high mortality of seeds and seedlings in the vicinity of the parents. On the other hand, the square root of wing-loading of a seed of a fruit was negatively dependent on seed number of a fruit. Thus, many-seeded fruits produced seeds with high dispersal ability. This was because the projected surface area per seed was large in large fruits and large fruits contained large numbers of seeds. The cost per seed of producing fruit structures was small for many-seeded fruits. Thus, high dispersal ability of seeds in many-seeded fruits may be a result of an effective resource allocation pattern in which a high proportion of resources are allocated to those many-seeded fruits, enabling seeds to develop large wings and thus reducing the structural cost of fruits per seed.

DOES THE TRADE-OFF BETWEEN GROWTH AND REPRODUCTION SELECT FOR FEMALE-BIASED SEXUAL ALLOCATION IN COSEXUAL PLANTS ?

We analyzed sexual allocation in cosexual plants while taking the trade‐off between growth and reproduction into consideration and showed that this trade‐off does not select for female‐biased sexual allocation. There are two problems in sexual allocation: optimizing the amount of resources allocated to reproduction in a growing season and equalizing the resources allocated to the male and the female functions. If these two are possible at the same time, equal resource allocation to the male and the female functions is the evolutionarily stable strategy (ESS; given that the fitness gains through the male and the female functions are proportional to the amount of the resources allocated to these functions). Biased sexual allocation only occurs when constraints make it impossible to simultaneously optimize allocation to reproduction and allocation to male and female functions. However, even if female‐biased sexual allocation occurs due to the addition of other constraints, the trade‐off between growth and reproduction itself is not an important factor that selects for female‐biased sexual allocation.

Using phylogenies to explain seed size variation among plants

Seed size varies among plants within single populations in many species (e.g., Janzen, 1977; Michaels et al., 1988; Sakai and Sakai, 1995) and among populations within a single species (e.g., Melzack and Watts, 1982, Marshall et al., 1985; Winn and Werner, 1987, Stromberg and Patten, 1990, Winn and Gross, 1993). However, in contrast to empirical evidence, the standard size-number trade-off model (Smith and Fretwell, 1974) predicts that plants growing in the same environment should respond to resource changes by varying their seed number, while keeping seed size constant. In their model, although larger seeds are advantageous, increasing seed size must result in decreasing seed number due to the size-number trade-off of seeds. Thus, there is an optimal seed size (S*‘) that maximizes the reproductive success of the plant, and this optimal seed size is independent of the resource status of the plant (Fig. lc). Several hypotheses were proposed to explain the factors for seed size variation (see Haig and Westoby, 1988; Sakai and Sakai, 1995) but this inconsistency between predictions of seed size constancy and observed seed size variation has not yet been fully explained. Recently, Sakai and Sakai ( 1995) proposed, and Sakai ( 1995) modified the “fertilization efficiency hypothesis”, which can explain mean seed size variation among plants within single populations. That is, Sakai (1995) predicted that larger plants produce larger seeds than the seeds of smaller plants if the number of pollen grains captured by a plant is an increasing but diminishing function of the