How Does Masting Happen and Synchronize?

J. theor. Biol. (1997) 187, 231–239

How Does Masting Happen and Synchronize? Y. I, K. S, A. S  H. I Kansai Research Centre, Forestry and Forest Products Research Institute, Momoyama, Kyoto 612, Japan (Received on 25 July 1995, Accepted in revised form on 6 March 1997)

Masting is an intermittent synchronous production of large seed crops by plant populations. The cause and mechanism of masting were analysed using a resource budget model for an individual plant. The model produced characteristic masting behavior that is made up of intermittent large crops, crop failures and semi-regular masting cycles. The ratio of seedling cost to flowering cost (RC ) played the most important role in the model. The species with a large RC value (RC e 1) showed intermittent fruiting whereas species with a small value (RC Q 1) showed constant fruiting. With increasing RC values, the fruiting interval became longer, and the occurrence became more unpredictable. When the model ignored the dependence of fruiting efficiency on the ratio of flowering individuals, flowering and fruiting did not synchronize among individuals in a population. In contrast, when the model included the dependence of fruiting efficiency on the ratio of flowering individuals, synchronization of flowering and fruiting within a population occurred. The synchronization was also dependent on the kind of pollination system. The present model suggests that masting can take place due to the resource balance of each plant even without any interannual environmental fluctuations, and may result in evolutionary benefits to each individual. 7 1997 Academic Press Limited

1. Introduction Masting is the episodic synchronous production of large seed crops by plant populations (Janzen, 1976; Kelly, 1994). The production of fruits by such trees as Quercus and Fagus varies by several orders between mast and non-mast years (Gysel, 1971; Feret et al., 1982; Kawada & Maruyama, 1986; Sork et al., 1993; Koenig et al., 1994). Bird populations (Smith & Scarlett, 1987), reproductive success of bears (Elowe & Dodge, 1989) and young deer weight (Feldhamer et al., 1989) are affected by the masting behavior of plants. Although evolutionary advantages of masting behavior for plants such as swamping predators (Janzen, 1971; Silvertown, 1980; Ims, 1990a, b), increased efficiency of wind pollination (Norton & Kelly, 1988; Smith et al., 1990), and attraction to seed distributors (Christensen & Whitham, 1991) have been proposed, most of these explanations deal only with the evolutionary advantages of masting, and not the mechanism. 0022–5193/97/140231 + 09 $25.00/0/jt970442

Weather conditions are known to affect the amount of seed production (e.g. Sharp & Sprague, 1967; Rehfeldt et al., 1971; Allen & Platt, 1990; Sork et al., 1993) or cue masting (Ashton et al., 1988). However, Kelly (1994) and Koenig et al. (1994) did not accept weather conditions as the major cause of large interannual fluctuations of seed crops because annual weather conditions did not vary as much as the fluctuations in seed production. Silvertown (1980) also pointed out a flaw in this hypothesis, that the weather conditions determine the annual fluctuation of seeding, because the hypothesis does not explain why all species do not share the same masting habit in temperate forest ecosystems. Moreover, there remain other questions about masting. First, Kelly (1994) divided masting behavior into three categories: strict, normal and putative masting, according to the yearly CV of seed production. Yet, it has not been established how such differences in CV for each species can arise. Secondly, most of the well-known masting species in temperate 7 1997 Academic Press Limited

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ecosystems are wind-pollinated (Smith et al., 1990; Kelly, 1994), and it is unclear how masting behavior is related to the means of pollination. Masting behaviors have been recognized in many ecosystems in the world, and there exist wide variations in the degree of masting from one or a few tree species making a large amount of fruit in occasional years (Sork et al., 1993), to many species making a large amount of fruit with synchronization among species (Appanah, 1985; Ashton et al., 1988; Corlett, 1990). Against this background of such a wide variety of masting phenomena at the landscape level, we developed a resource budget model for an individual plant in order to analyse the masting phenomena of single tree species that intermittently makes a large amount of fruit with or without synchronization among individuals in a population. The model successfully produced some characteristics of masting behavior: (i) years of large fruiting with an intermast interval of several years; (ii) variations in the intermast intervals among species from 0 (every year) to several years; (iii) synchrony of fruiting of a species within a population; and (iv) large variations in the degree of synchronization among species with different fruiting efficiency. 2. Resource Budget Model In order to reveal the mechanism of masting based on the resource budget of an individual plant, a simple compartment model was constructed (Fig. 1).

It concerns mature plants within a population and assumes that there is a constant amount of photosynthate produced by each plant every year, given that the environmental conditions are constant during the years. The photosynthate is consumed for growth and maintenance of the plant, and the plant stores the rest of the photosynthate (PS ) in a pool in the plant body. In order to keep the model simple we did not incorporate an effect whereby increasing activity of the sink for photosynthetic products leads to increasing activity of the photosynthetic source, although such an effect is known in many plants (Dickson, 1991). Neglecting this factor did not essentially affect the behavior of the model. The amount of PS was constant from year to year. In a year when the accumulated PS exceeded a certain amount (LT ), the amount of accumulated PS minus LT was used for flowering as the cost of flowering (Cf ). Hence, if the amount of photosynthate accumulated in the preceding years was large, the plant was inclined to flower more; the amount of flowering in a year also depended on the amount of photosynthetic products accumulated in previous years. The amount of accumulated PS was decreased to LT after the flowering. The flowers were pollinated and bore fruits, whose cost was designated as Ca . The ratio of Ca /Cf was assumed to be constant: RC . After the fruiting is completed, the accumulated amount becomes LT − Ca = LT − RC Cf . In the model PS is accumulated annually, until the tree flowers again when the amount exceeds LT .

Photosynthate Respiration Turnover of leaves, branches, roots.... Ps Surplus photosynthate

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      (e) R C: 3.5

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It has been observed for several tree species that the amount of allocation to non-reproductive organs such as leaves and trunks decreases in mast years because larger amounts of resources are allocated to reproductive organs in mast years (Eis et al., 1965; Innes, 1994). The decrease in leaf amount may result in a reduced amount of net production, and hence a longer time for the accumulation level to recover to the level of LT . However, the change in allocation to non-reproductive organs in mast years is quite a species-specific parameter and hard to generalize; therefore we did not incorporate this parameter into the present model. The removal of this factor did not essentially affect the behavior of the model.

3. Results           Using the model described above, we conducted several numerical simulations, which indicated that

the parameter RC played an important role in the behaviors of the model. When RC Q 1, the amount of seed production was constant every year [Fig. 2(a)]. When RC e 1, mast years appeared [Fig. 2(b–g)]. The higher the RC value, the larger the intervals between mast years, that is, the higher the rate of crop failure. The autocorrelation values between seed production and lagged values of the prior seed production reciprocated between −1 and 1 when RC = 1 [Fig. 3(a)]. In this case, the mast and non-mast years are predictable due to the regular interval. When RC = 1.5 [Fig. 3(b)], the absolute values of the autocorrelation were less than 1, but negative and positive values appeared in turn, showing a regular masting cycle of 2 years. With increasing RC values, the first positive values of autocorrelation appeared later, indicating that the intermast interval became larger [Fig. 3(c d, e) and (f)]. In addition, the absolute values of the autocorrelation became smaller with increasing RC values, showing the lower predictability of masting when RC was large.

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234      

We estimated the RC value for Fagus crenata from the construction costs of flowers and fruits. Williams et al. (1987) developed a method to determine the construction cost of plant tissues using the ash-free heat of combustion, ash content, oxidation state of the nitrogen substrate and nitrogen content. The construction cost determined here is in units of grams of glucose per gram of dry mass and represents the amount of fixed carbon required to provide carbon skeletons, reductant, and ATP for synthesizing all of the biochemical components in plant tissues (Williams et al., 1987). Using this method, we

1.0

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(d) R C = 3.5 1.0 0.8 0.6 0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1.0

Autocorrelation values

0.8 0.6 0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1.0 1.0 0.8 0.6 0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1.0 1.0 0.8 0.6 0.4 0.2 0

determined the construction costs of reproductive organs of Fagus crenata (Table 1). Kawada & Maruyama (1986) measured the net production of flowers and fruits of Fagus crenata for 3 years. Fagus crenata has unisexual flowers, and the male flowers make up most of the weight (Kawada & Maruyama, 1986), so we neglected the amount of female flowers when estimating the flowering cost. We estimated Ca and Cf by multiplying the net production of male flowers and fruits (cupules and seeds) by the construction cost for the unit weight of each organ, and then calculated the RC (=Ca /Cf ) values (Table 1). There were distinct differences in the production of male flowers, cupules and seeds between mast (1981)

(b) R C = 1.5

(e) R C = 4.5 1.0 0.8 0.6 0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1.0

(c) R C = 2.5

1.0 0.8 0.6 0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1.0

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F. 3. Autocorrelation values between seed crop of current year and lagged values of seed crop prior n years. The model was run with an initial Cf value of 2.5, and with parameters of LT = 6.0 and PS = 3.0. Results were excluded for the initial 50 years.

      T 1 Net production and construction cost of reproductive organs, and estimation of RC values for Fagus crenata Construction cost (g glucose g−1 ) Male flowers Cupules Seeds Cf (g glucose m−2 ) Ca (g glucose m−2 ) RC (=Cf /Ca )

1.31 1.37 1.82

Net production (g m−2 )* 1979 1980 1981 3.0 12.5 2.6 3.9 21.9 5.6

2.8 10.3 0.3 3.7 14.7 4.0

702 2060 861 920 4389 4.8

* After Kawada & Maruyama (1986)

and non-mast years (1979 and 1980). The estimated RC values fell into a relatively narrow range, from 4.0 to 5.6, irrespective of the wide fluctuation of seed and flower productions (Table 1). The masting patterns reported in stands of F. crenata (Maeda et al., 1985), Fagus grandifolia (Gysel, 1971) and Nothofagus solandri (Allen & Platt, 1990) resemble the patterns shown in Fig. 2(e, f) and (g) (RC between 3.5 and 5.5) in terms of the intervals and the large variation among years.         In the model behavior described above, when RC q 1, small differences in the resource budget among individuals became larger with time. Therefore, given slightly different initial values of Cf for each plant, the seeding did not synchronize in a population. How, then, would synchronized seeding among individuals often reported in many plant communities occur? One explanation for this phenomenon is that weather conditions act as cues for flowering, such as reported for single tree species (Augspurger, 1981), or interspecific synchronization in the aseasonal tropics (Ashton et al., 1988). Here we focused on synchronization of fruiting for a single species in a population with the present resource budget model regarding fruiting efficiency as one of the rhythm makers. The fertilization success of trees from outcrossing is higher than from self-pollination (Ledig, 1986; Nilsson & Wa¨stljung, 1987; Sork, 1993) as a result of the effects of inbreeding depression by homozygous recessive deleterious genes and self-incompatibility, which occurs through plants recognizing genes at the incompatibility locus, and determining the acceptance or rejection of pollens. Thus, the pollination efficiency is expected to vary according to the number of plants flowering by chance in a population (Nilsson & Wa¨stljung, 1987; Smith et al., 1990). In addition, even for the same proportion of flowering trees in a population, the efficiency of pollination is expected to

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be higher in the case of entomophilous flowers than that of anemophilous flowers because animals help trees to pollinate more efficiently than wind (Regal, 1982; Watanabe, 1994). Consequently, even a given small proportion of plants flowering in a population may result in a higher rate of fertile seed production for an entomophilous species than for an anemophilous species. Such effects were incorporated in the resource budget model as follows. In the present model, the maximum payable cost for flowering of each individual is equal to PS . A population consisting of n individuals then has the maximum flowering cost of n PS . We designated the flowering proportion of a population (x) as n

x = s Cfi /nPS i=1

where Cfi is the flowering cost of the i-th individual. The dependence of the fruiting efficiency of a tree (y) on the flowering proportion of a population (x) can then be expressed, for example, with a power function of y = xa(0 Y y Y 1, 0 Y x Y 1, a y 0). The pollination success increases as the flowering proportion of a population increases. In addition, we expect that a should reflect the difference in pollination and fruiting efficiency among the different pollination systems and other factors affecting reproductive processes as follows. (i) a = 0. In this case, y = 1 for all x; the flowering proportion of a population does not affect the fruiting efficiency of a tree. (ii) a = 1. The fruiting efficiency increases linearly with increasing flowering proportion of a population. (iii) 0 Q a Q 1. In this case the y − x relationship becomes convex, and represents animal pollination, because animal pollinators carry pollen between plants more effectively than wind does (Regal 1982; Watanabe, 1994), and the probability of fruiting efficiency might become higher irrespective of the small flowering proportion of a population. (iv) a q 1. In this case, the curve becomes concave, and corresponds to ineffective fruiting. In the case when immature fruits are attacked by predators and some of them could escape by the effect of predator swamping, the number of mature fruits will increase exponentially with increasing number of flowers in the population, but when their number is small most of them are attacked. It is also known that the proportion of pollen germinating may increase as the number

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of pollen grains per stigma increases (Marshall & Folsom, 1991). We can describe these situations with parameter a q 1.

proportion necessary to complete the pollination and fruiting becomes higher. The level of resource accumulation of a plant becomes LT when it flowers (Fig. 1). Therefore, if plants flower and fail in fruiting, each of them has a similar resource accumulation level, and consequently individuals within a population become synchronized in fruiting at last, even without any environmental cues [Fig. 4(a–d)]. The standard deviation of Ca among individuals decreased with an increasing a value (Fig. 4). Most previous studies on masting used or analysed the total amount of seeding in populations. However, detailed observations of individual plants in a population have revealed that there can be some out-of-synchrony individuals in a masting population (Koenig et al., 1994). Within the continuum of a in our model, variations in the proportion of out-of-synchrony individuals were produced (Fig. 4). The actual values of the standard deviation or CV of Ca among

We used this density-dependent efficiency of pollination and fruiting in the present model, in which the amount of flowering was determined by the resource balance of the plant. The fruiting success of a tree was then determined by the amount of flowering of a tree (Cf ), the flowering proportion of a population (x) and the several factors reflected in the parameter a, that is, a plant investing Cf in a year would pay a fruiting cost of RC Cf x a. We then conducted simulations for a population. When a = 0, y becomes 1 for all x(0 Y x Y 1), and the proportion of flowering individuals has no effect on the fruiting efficiency; flowering and fruiting are caused by their own material balance, and synchrony does not occur [Fig. 4(a)] As the values of a increase, the flowering

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Time (years) F. 4. Synchrony of fruiting among 20 individuals in a population with the density dependent efficiency of fruiting. (a–d) Various figures were given for the various a values of x a, shown in each plate to assess the effect of the fruiting efficiency. A random initial value of Cf was given to 20 individuals in the population. Results were discarded for the initial 50 years. (e) Changes in the standard deviation of Ca among 20 individuals: r, a = 0; Q a = 0.5; w a = 1; R a = 2; r a = 3. Values of parameters were given as RC = 4.5, LT = 6.0 and PS = 3.0.

      individuals for most natural plant populations may fall within the range from complete synchrony to asynchrony according to the factors that might affect the value of a, such as pollination system, predation swamping for immature fruits and density-dependent pollen germination. 4. Discussion Silvertown (1980) showed that masting happens at irregular intervals but with a periodicity that is characteristic of the species. Using our model, we also found such irregular, but species-specific intervals; they were longer with increasing RC (Figs 2 and 3). Waller (1979) found that among trees of six genera (Acer, Betula, Fraxinus, Pinus, Populus and Quercus), the masting species had a larger mean seed size except in Populus. Sork (1993) found that there was a positive correlation between the log of the intermast interval and the log of the seed weight for 18 species of North American eastern deciduous oaks. Sork et al. (1993) found species-specific intervals of masting for Quercus species by analysing autocorrelation values of the current fruit production with the prior fruit production, and interpreted the results in terms of the species-specific intervals depending on difference between species in the amount of stored resources needed to produce a mast crop. Silvertown (1980) also stated that such phenomena might be a reflection of the time required for the accumulation of assimilates necessary to produce an eventual mast crop capable of saturating predators. In the present model, RC was defined as the ratio of the cost for flowering to the cost for fruiting, and representing the differences among species. It is reasonable to consider that species with larger seeds have larger RC values and longer intermast intervals, which coincided with the results shown in Figs 2 and 3. However, there are species with regular crops of large seeds and also species that show masting but have small seeds such as Populus. By expanding the definition of the parameter RC as the ratio of the latter cost to the initial cost in the whole reproductive procedure, the present model can deal with such species. Species with small fruits do not necessarily have a small value of expanded RC , and species with large fruits do not necessarily have a large value of RC because the initial cost might be large for the development of supporting organs such as receptacles. The present model predicts that even species with small fruits might show masting if the latter/initial cost ratio were equal to or larger than 1, and conversely, even species with larger fruits might show

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regular crops if the latter/initial cost ratio were less than 1. Another confusing matter for the description and interpretation of masting is asynchrony within a tree. For example, Aesculus turbinata bears relatively large fruits (around 4 cm in diameter), but is known for the constant fruit production among years in Japan. However, a recent study revealed that the fruiting fluctuated remarkably at the branch level (H. Nakajima, personal communication) although the annual amount of fruiting was constant at the individual level. In the case of Aesculus turbinata, each branch might be a semi-independent unit of the material balance, and each module repeats good and bad years similar to the patterns produced by the present model. In some tree species a series of reproductive processes—the initiation of the reproductive organs, pollination, fertilization and maturation of fruits— takes several years. For such species allocation between organs and between successive years must be taken into consideration. Observations on masting behavior at the individual level (Koenig et al., 1994) or module level are scarce. Thus we can hardly consider the relationships between the masting behavior of various species and the cost of the reproductive organs. In order to verify whether the present model is applicable to such phenomena, we need studies that describe reproductive behaviors at the module level, and also physiological studies that monitor the resource level and amount of transport between organs or modules. Resource matching and economies of scale have been considered as distinct causes of masting (Norton & Kelly, 1988; Koenig et al., 1994; Kelly, 1994). Resource matching corresponds to the proximate causes of masting, that is, the abundance of seed crops is correlated with the resource level. Koenig et al. (1994) outlined possible hypotheses of masting, and tested the predictions of each hypothesis against observations on Quercus species. They concluded that the following four observations could not be explained by the resource matching hypothesis: (i) annual variation in crop production was high; (ii) most species showed a bimodal distribution of reproductive effort among years; (iii) crop failures occurred; and (iv) regular masting cycles were observed. The present model assumed accumulation of surplus resources in a plant, and a certain threshold resource level for flowering and seeding as described in Fig. 1. Hence, the present model is based on the resource matching hypothesis. However, it could produce the four characteristic masting observations mentioned above as opposed to the predictions of

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.  ET AL .

Koenig et al. (1994) on the resource matching hypothesis. In order to satisfy the wind pollination hypothesis and predator saturation hypothesis, which are the most popular and representative of the supposed ultimate causes of masting (Silvertown, 1980; Nilsson & Wa¨stljung, 1987; Norton & Kelly, 1988; Sork, 1993; Koenig et al., 1994), flowering and fruiting of individuals in a population must synchronize with each other and realize economies of scale (Norton & Kelly, 1988; Kelly, 1994). As previously mentioned, fluctuations in environmental conditions have been considered as the causes of the annual fluctuation of seeding, but Kelly (1994) and Koenig et al. (1994) concluded that they are insufficient as the causes of synchrony. Silvertown (1980) argued that the evolution of synchronized masting was caused by the forced synchrony of seed release due to environmental fluctuations, followed by predator saturation. Of course, certain environmental conditions could act as a cue for gregarious flowering for some species in a forest (Ashton et al., 1988), and result in interspecies synchronization in fruiting. We did not deal with such specific cues. In the present resources budget model, plants with slightly different initial conditions did not synchronize their flowering, even under the same environmental conditions, because small differences in the resource balance among individuals resulted in larger differences in later years. However, taking the density dependent fruiting efficiency into consideration, intermittent flowering of plants within a population was synchronized even without any environmental cues. Besides, asynchronized and synchronized individuals could exist within a population according to the parameter a, which wholly represented fruiting efficiency. It is noteworthy that the present model, which does not involve environmental fluctuations but a resource balance of individuals and fruiting efficiency, produces not only annual variation in fruiting but also synchrony among individuals. Our model is deterministic, yet stochastic environmental factors should also be important in ecological systems. For example, in addition to the cues of weather conditions for flowering in natural conditions, fruiting failure after ample flowering can be caused by adverse weather conditions and herbivore attacks (Sharp & Sprague, 1967; Stephenson, 1980; Matsuda, 1982), and they may also play an important role in the development of synchrony. In our model, fruiting failure after ample flowering makes the accumulated resource level similar between individuals and acts as a synchronizer. We think that the pollination efficiency is also likely to elucidate the

formation of synchrony because (1) it would affect individuals in a population every year, and (2) most of the masting behaviors have been reported for tree species, in which outcrossing is more common than for shrubs and herbaceous perennials (Ledig, 1986; Bawa, 1990); fertilization success depends on the proportion of flowering individuals in a population most heavily in the case of tree species. No upper limit of the RC Cf (the seeding cost) is assumed in the present model, in which the cost is always paid, and plants pay back the debt later. However, there may be an upper limit of available resources (Stephenson, 1981) that is species specific, or dependent on plant size. Incorporating such a capacity for accumulation, and examining the definition of RC , the present model will help in analysing and understanding further various types of masting behavior. Masting is recognized in many different kinds of forests in the world, and the phenomena are quite manifold. Each masting species has distinct characteristics with respect to reactions to environmental condition, size of minimum unit of material balance, allocation patterns and reproductive schedule. However, it is obvious that the amount of fruit production depends more or less on the available amount of resources in unit modules of material balance (Silvertown, 1980; Allen & Platt, 1990; Houle & Filion, 1993; Sork et al., 1993; Innes, 1994). We thus believe that masting behavior can be largely explained using the model describing the resource balance of an individual plant. As discussed above, further studies on reproductive behaviors at the module level, and also physiological studies on the resource level and amount of transport between organs, are necessary to analyse masting behaviors. We wish to thank H. Miguchi and M. Shibata for providing samples of Fagus crenata, and T. Masaki and K. Odani for discussions. We are also grateful for the improvements suggested by an anonymous reviewer.

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