Delayed fertilization facilitates flowering time diversity in Fagaceae

Abstract

Fagaceae includes typical masting species that exhibit highly synchronized and fluctuating acorn production. Fagaceae shows an interesting feature in that fertilization is delayed by several weeks to more than 1 year after pollination. Although delayed fertilization was recorded over a century ago, the evolutionary advantage of delayed fertilization is still poorly understood. Here, we present a new hypothesis that delayed fertilization facilitates temporal niche differentiation via non-overlapping flowering times among species. Comparing flowering and fruiting times in 228 species from five genera in Fagaceae, we first show that there is a close association between a wider spread of flowering times and the likelihood of a 2-year fruiting habit in which there is a long delay from pollination to fertilization. To study the coevolution of flowering time and delayed fertilization, we developed a mathematical model that incorporates the effects of competition for pollinators, seed predator satiation and unfavourable season for reproduction on fitness. The model shows that delayed fertilization facilitates the diversification of flowering time in a population, which is advantageous for animal-pollinated trees that compete over pollinators. Our new hypothesis about the coevolution of delayed fertilization and flowering time will provide new insight into the evolution of masting.

This article is part of the theme issue ‘The ecology and evolution of synchronized seed production in plants’.

1. Introduction

Among diverse species that exhibit masting, acorn production in Fagaceae, including beech and oak, has been intensively studied [1–4]. The Fagaceae dominate forests in the temperate, seasonally dry regions of the Northern Hemisphere, with a centre of diversity found in tropical southeast Asia [5]. There is rich phenotypic diversity in the Fagaceae, including the morphology of acorns and leaves, flowering time (spring to autumn), modes of pollination (wind or animal) and leaf habit (deciduous or evergreen). Because of this rich phenotypic diversity, Fagaceae is a good target to explore the genetic basis of masting [6].

Another less studied but interesting feature in Fagaceae is delayed fertilization. Fertilization takes longer than 21 days in most gymnosperms across both non-masting and mast-seeding species, but in most angiosperms, fertilization occurs within 1 or 2 days after pollination [7]. Unusually among angiosperms, in the Fagaceae, some species delay fertilization by several weeks to more than 1 year [8]. A delay in fertilization was recorded in several species of Fagales over a century ago [8,9]. In the Fagaceae, when the flower opens, ovules are immature and maturation takes several months or 1 year [8,10]. Pollen germinates after pollination, but pollen tubes are arrested and show discontinuous growth depending on the timing of ovule maturation [11]. Some species in the Fagaceae fertilize their ovule soon after pollination, e.g. five weeks after pollination in Fagus japonica [8], while some species (e.g. red oak and genus Lithocarpus) wait so long after pollination to be fertilized that fruit ripens the year after pollination. Although it has been discussed that sperm competition is one mechanism favouring delayed fertilization [8], a long delay from anthesis to fertilization (up to 1 year) is difficult to explain by sperm competition alone. Therefore, the evolutionary advantage of delayed fertilization is still unclear.

Here, we present a new hypothesis to explain the evolution of delayed fertilization using an integrated analysis of flowering and fruiting phenology data from China and a newly developed mathematical model. Of the Fagaceae, which total approximately 927 species in 10 genera, China hosts 294 species in six genera: Fagus, Trigonobalanus, Castanopsis, Castanea, Lithocarpus and Quercus, most of which are found in South and Southwest China [12]. Although long-term data on seed production are limited for these species, flowering and fruiting phenology data are available for 228 species from five genera. Based on the newly presented data in 228 species, we first show that flowering time is highly diverged within and between genera in the Fagaceae, especially in animal-pollinated species, Lithocarpus and Castanopsis, in which 2-year fruiting species are dominant. We then present a new hypothesis, the coevolution of flowering time and delayed fertilization, by integrating reproductive phenology data into a mathematical model that incorporates the effects of competition for pollinators and seed predator satiation.

Systematic comparisons of flowering and fruiting behaviours between species from multiple genera in the Fagaceae provide new insight into the evolution of masting, because masting is a consequence of the evolution of multiple reproductive processes, such as floral induction, pollination, fertilization and seed maturation [6,13]. We discuss the possibility that divergence at the stages of flowering and ovule fertilization plays a pivotal role in the evolution of masting traits because the delay from pollination to fertilization generates a period susceptible to environmental stress, which eventually regulates seed crop size and reproductive success.

2. Comparison of 228 species from five genera in the Fagaceae family

(a) . Data collection

We collected monthly flowering and fruiting phenology data of Fagaceae in temperate and subtropical zones in China where there is seasonality. The data were obtained from the eFloras database of China [14]. In addition to the flowering and fruiting month information, the data distinguish whether fruiting occurs in the same year of flowering (1-year species) or the next year of flowering (2-year species). Our study spanned five genera (Lithocarpus, Castanopsis, Quercus, Castanea and Fagus). In Quercus, five sections are included. The numbers of species in each genus (and in each section for Quercus) are summarized in table 1, and a full species list is given in electronic supplementary material, data S1. Pollination and leaf habits are also summarized in table 1. The mean annual temperature and annual precipitation in the overall habitat of each species were obtained from [15]. To explore the relationship between the probability of 2-year fruiting species and mean annual temperature or annual precipitation, logistic regression analysis was performed using the mean annual temperature or annual precipitation and genus (as factor) as independent variables and the probability of 2-year fruiting species as the dependent variable. Similarly, the relationship between the probability of 2-year fruiting species and flowering month was investigated by logistic regression analysis. To investigate the relationship between the length of the period from flowering to fruiting and mean annual temperature or annual precipitation, linear regression analysis was performed. The glm package in R v. 3.6.3 (R Core Team) was used for statistical analyses.

Table 1.

Number of target species of this study and fraction of 2-year fruiting in each genus.

genus	subgenus	section	no. of species	pollination	leaf habit	fraction of 2-year species
Lithocarpus	—	—	104	animal	evergreen	0.923
Castanopsis	—	—	47	animal	evergreen	0.833
Quercus	Cerris	Cerris	3	wind	mixture of evergreen and deciduous	1.0
	Quercus	Lobatae	1	wind		1.0
	Cerris	Ilex	18	wind		0.56
	Cerris	Cyclobalanopis	39	wind		0.308
	Quercus	Quercus	8	wind		0.0
Castanea	—	—	4	animal	deciduous	0.0
Fagus	—	—	4	wind	deciduous	0.0

(b) . Positive relationship between flowering time diversity and likelihood of 2-year fruiting

Flowering time was the most diverse, and the likelihood of 2-year fruiting was the highest in the animal-pollinated genus Lithocarpus (figure 1a,b). Flowering months in Lithocarpus were distributed in all seasons throughout the year from spring to winter, with a weak peak in June, and 2-year fruiting was seen in more than 90% of species (table 1 and figure 1b). Flowering time in the animal-pollinated genus Castanopsis also included spring-, summer- and autumn-flowering (figure 1a), with a peak of flowering in May (figure 1b). The percentage of the 2-year fruiting type was the second highest (83%) in Castanopsis. In the wind-pollinated genus Quercus sections Cerris, Lobatae, Ilex and Quercus, there were no autumn-flowering species (figure 1a). All species started flowering from spring (March) to early summer (June), and the fraction of the 2-year fruiting type decreased to 44% (table 1 and figure 1b). The reproductive phenology of Quercus section Cyclobalanopsis was similar to those including other sections in Quercus except that some winter-flowering species were included (figure 1a). The animal-pollinated genus Castanea and wind-pollinated genus Fagus showed highly synchronized flowering in spring (April–May), and all of them were 1-year fruiting types (figure 1a,b). Although only four species are included for each genus, it is less likely that the species in Castanea and Fagus would show flowering time diversity (flowering from spring to autumn or winter) because they are deciduous trees in which flowering in autumn or winter is less expected. These results suggest the close association between flowering time diversity, pollination type and the delay of fruiting time caused by delayed fertilization.

Figure 1.

Flowering and fruiting phenology of 228 Fagaceae species distributed in China. (a) A plot of the flowering month (green and black) and fruiting month (orange) for each species from five genera. In Lithocarpus and Castanopsis, there are six species in total that flower twice a year. For those species, the second flowering event is represented in grey as ‘Flower 2’. The Quercus group includes species from four sections: Cerris, Lobatae, Ilex and Quercus in the genus Quercus. The group ‘Cyclobaranopsis’ includes species from the section Cyclobaranopsis in the genus Quercus. Species names are listed in electronic supplementary material, data S1. (b) Histograms of the proportion of flowering (green) and fruiting species (orange) for each month for each genus or section.

Despite the flowering time diversity highlighted in Lithocarpus and Castanopsis, fruiting time is highly synchronized within and across genera. Fruiting from September to November included more than 72% of fruiting events in all species regardless of fruiting type (1 or 2 years) (figure 1b).

(c) . Habitat features and reproductive phenology

To explore the relationship between the probability of 2-year fruiting species and habitat features, we first plotted the mean annual precipitation against the mean annual temperature for each species. Lithocarpus and Castanopsis occur in relatively warm and wet environments with mean annual temperatures of 13–24.7°C (figure 2a), whereas Quercus species are found in relatively cold and dry environments with mean annual temperatures of 3.3–19.3°C (figure 2a). The probability of 2-year fruiting species showed no clear relationship with mean annual temperature (slope = −0.062, p = 0.37) or with annual precipitation (slope = −0.0025, p = 0.16). This finding suggests that environmental factors do not help predict which species will have 1- or 2-year fruiting.

Figure 2.

Relationship between reproductive phenology and environmental factors. (a) A plot of mean annual temperature and annual precipitation in the habitat of each Fagaceae species. (b) A plot of the first fruiting month against the first flowering month. (c) A plot of seed development period (months from first flowering to first fruiting) against mean annual temperature. These environmental factors do not help predict which species will have 1 or 2 years of fruiting.

To explore the relationship between the probability of 2-year fruiting species and flowering time, we plotted the first fruiting month against the first flowering month and detected a clear trend between the two. When the first flowering month was early, 1- and 2-year fruiting types were mixed, whereas species that began flowering later than June were all 2-year fruiting (figure 2b). Logistic regression analysis showed that there was a statistically significant positive relationship between the probability of 2-year fruiting species and flowering month (slope = 0.76, p < 0.001). This finding suggests that flowering times and 1- and 2-year fruiting types are closely interrelated. How these relationships are shaped and what the underlying evolutionary forces are will be answered from the analyses of a newly developed evolutionary model.

3. Modelling the coevolution of flowering time and delayed fertilization

We developed a model that describes the coevolution of flowering time and delayed fertilization in a population consisting of individuals with a phenotypic trait set of flowering time and period of delayed fertilization. Phenotypic variation within the population is assumed to be caused by genetic variation associated with flowering time and a period of delayed fertilization. Let i and j be the flowering time (duration of flowering was assumed to be one month) and period of delayed fertilization (which is defined by the interval from flowering time to fertilization), respectively (figure 3a). We here assume that the unit for i and j is months. Because we consider a cyclic environment with a period of 12 months, flowering month i = 1, 2, …, 12. The period of delayed fertilization j = 0, 2, …, J, where J is the maximum for the period of delayed fertilization. Although the maximum for i is 12 months, j can be longer than 12 months in 2-year fruiting plants. After fertilization, seed development takes place during the period of d, and mature seeds are dispersed in mod (i + j + d, 12) months for an individual with a trait set (i, j) because of the periodic boundary of 12 months. Here, mod (modulo or modulus) is the remainder after dividing one number by another to find the calendar month of dispersal when the process extends over more than 1 year.

Figure 3.

Model illustration of the coevolution of flowering time and period of delayed fertilization. (a) Time course of reproductive processes considered in the model. Flowering occurs in the month i followed by fertilization j months later. After fertilization, seeds develop over the period of d months, and seed dispersal takes place in mod(i + j + d, 12) months. (b) Phase plot of potential trait sets (i, j) that can have non-zero fitness given in equation (3.6) (open circles) and the trait set that enjoys the highest fitness among individuals with the same flowering time (solid circles). The trait sets illustrated as solid circles represent the potential trait sets Ω. τ_S and τ_E indicate the months when favourable environmental conditions begin and end, respectively, and L represents the length of the unfavourable period. As an example, seed development period d is set as three months.

In our unpublished data (collected between 2018 and 2020), seed maturation in Quercus acutissima takes five months (from June to November), and in Quercus glauca (Cyclobalanopsis glauca in electronic supplementary material, table S1), it takes seven months (from June to December). In Lithocarpus edulis (a Japanese species closely related to the Lithocarpus species in China), five months (from May to October) are needed for seed maturation. Although the seed maturation period may be influenced by habitat (e.g. temperature), the period from flowering to fruiting month (j + d in our model) did not show any clear relationship with annual mean temperature in our data (figure 2c; slope = −0.12, p = 0.27) or precipitation (slope = −0.0031, p = 0.16; we did not show the plot because of high correlation between temperature and precipitation: Spearman rank correlation coefficient = 0.69). Most 1-year fruiting species show four to seven months from flowering to fruiting (figure 2c), suggesting a requirement for a long seed development period in Fagaceae. We assume that survival and vegetative growth rates are the same among individuals in a population.

We first define the fitness of an individual with a trait set (i, j). Let x_ij(t) be the density of individuals with the trait set (i, j) at time t. Overlapping flowering times between individuals cause intraspecific competition for pollination resources that limit the population growth rate, thus allowing the coexistence of species that use different pollinators or the same pollinators at different times [16]. We incorporated this negative density dependence in the model by assuming that the fitness linearly decreases with an increased density of individuals with overlapping flowering time:

$$\mathrm{Pollination}\hspace{0.17em}\hspace{0.17em}\mathrm{success}=\left[1-a\sum _{l=0}^J{x}_{il}(t)\right],$$ 3.1

where a is a constant regulating the decreased effect of synchronized flowering on fitness. Because equation (3.1) cannot be negative, a ≤ 1. On the other hand, synchronized fruit production among individuals can increase the survivorship of seedlings by satiating seed predators [17,18]. We incorporated the effect of seed predator satiation by considering that fitness increased with the number of individuals that produce fruits at the same time, as follows:

$$\mathrm{Fruiting}\hspace{0.17em}\mathrm{success}\hspace{0.17em}=\hspace{0.17em}[1+b{\mathrm{\Sigma }}_{l,m\in U}{x}_{lm}(t)],$$ 3.2

where b is a constant regulating the increased effect of synchronized seed production on fitness. In equation (3.2), U represents the set of (l, m) that satisfies the following formula:

$$\mathrm{mod}(l\hspace{0.17em}+\hspace{0.17em}m\hspace{0.17em}+\hspace{0.17em}d,\hspace{0.17em}12)\hspace{0.17em}=\hspace{0.17em}\mathrm{mod}(i\hspace{0.17em}+\hspace{0.17em}j\hspace{0.17em}+\hspace{0.17em}d,\hspace{0.17em}12).$$ 3.3

We also considered the decreased survival rate for prolonged delayed fertilization. As the period of delayed fertilization becomes longer, the survival of ovules decreases because of increased risks of predation or disturbance-induced damage. This process is modelled as follows:

$$\begin{array}{r}\mathrm{Survival}\hspace{0.17em}\mathrm{of}\hspace{0.17em}\mathrm{ovules}\hspace{0.17em}\mathrm{produced}\hspace{0.17em}j\hspace{0.17em}\mathrm{months}\hspace{0.17em}\mathrm{before}\hspace{0.17em}\mathrm{fertilization}=c{\hspace{0.17em}}^j,\end{array}$$ 3.4

where c is a constant representing the monthly cost of fertilization delay $(0\le c\le 1)$, and j indicates the period of fertilization delay. Another factor influencing fitness is environmental quality. When environments are not appropriate for pollinator activity or photosynthesis owing to cold temperature or drought during the flowering or fruiting period, pollination success and proper fruit development become impaired, resulting in reduced fitness. Here, the quality of environmental conditions in month n is defined as a binary variable s(n)

$$\mathrm{Environmental}\hspace{0.17em}\mathrm{condition}\hspace{0.17em}s(n)\hspace{0.17em}=\hspace{0.17em}\{\begin{array}{cc}1& \mathrm{favorable}\hspace{0.17em}\mathrm{environment}\\ 0& \mathrm{unfavorable}\hspace{0.17em}\mathrm{environment}\end{array}.$$ 3.5

Here, we consider that unfavourable environmental conditions, such as winter cold below a certain threshold temperature, occur continuously with a length of L months (L < 12; figure 3b), and thus flowering and fruiting need to occur during the period of favourable conditions for positive fitness. We did not consider the case in which different conditions are favoured for flowering and fruiting.

Together, the fitness of an individual with a trait set (i, j) at time t is given as the product of the four processes explained above as follows:

$${\omega }_{ij}(t)=\left[1-a\sum _{l=0}^J{x}_{il}(t)\right]\left[1+b{\sum }_{l,m\in U}{x}_{lm}(t)\right]c^{j}s(i){\prod }_{n=i+j}^{i+j+d}\hspace{0.17em}s\hspace{0.17em}(n).$$ 3.6

Given the definition of environmental status s(n), the fitness of trait set (i, j) is zero when flowering time i and the period of delayed fertilization j are out of the following ranges: ${\tau }_S\le i\le {\tau }_E$ and ${\tau }_S\le \mathrm{mod}(i+j,12)\le {\tau }_E-d$, where τ_S and τ_E indicate the months when favourable conditions start and end, respectively (figure 3b). The trait sets (i, j) that have non-zero fitness given in equation (3.6) are illustrated as circles in figure 3b. Equation (3.6) further indicates that when individuals flower in the same month, the highest fitness is for the minimum period for delayed fertilization because the cost for delayed fertilization is minimized (figure 3b). The trait sets (i, j) that enjoy the highest fitness among individuals with the same flowering time are illustrated as solid circles in figure 3b. We call the trait sets illustrated as solid circles in figure 3b potential trait sets and denote them Ω.

Based on equation (3.6), we analytically derived the equilibrium in which each individual in the population has equal fitness. For this analysis, we first considered the case in which there was no effect of predator satiation (i.e. b = 0). We then incorporated the effect of predator satiation to examine how the results changed. The density of individuals increases if the fitness of individuals with a trait set (i, j) is greater than the mean fitness in the population, while it decreases when their fitness is smaller than the mean. When all existing individuals have equal fitness, evolution stops. We calculated the equilibrium as the set of densities for traits exhibiting equal fitness. Numerical calculation of the equilibrium density was also performed by iterations of the following dynamics:

$$x_{ij}(t+1)=\frac{{\omega }_{ij}(t)}{\overline{\omega }(t)}{x}_{ij}(t),$$ 3.7

where $\overline{\omega }(t)$ indicates the mean population fitness at time t given as

$$\overline{\omega }(t)=\sum _{i=1}^{12}\sum _{\hspace{0.17em}j=0}^J{x}_{ij}(t){\omega }_{ij}(t).$$ 3.8

(a) . Derivation of equilibrium density of each trait set

We derived the density of each trait set at equilibrium in which fitness is equal over all existing individuals with diverse trait sets in the absence of any predator satiation effect (b = 0 in equation (3.6)). When there is no unfavourable season for reproduction, the equilibrium becomes:

$$x_{ij}^{\ast }=\{\begin{array}{cc}1/12& \mathrm{if}\hspace{0.17em}j=0\\ 0& \mathrm{otherwise}\end{array}.$$ 3.9

Equation (3.9) means that when there is no predator satiation effect, delayed fertilization does not evolve when environmental conditions are always favourable for reproduction, such as ever-humid tropical rainforests in Southeast Asia. When the period for the unfavourable season is given as L, the equilibrium consists of potential trait sets Ω illustrated as solid circles in figure 3b. Because the sum of individual densities with trait sets of Ω equals one, the equilibrium density for individuals with each trait set $(i,j)\in \{\mathit{\Omega }$ is given as follows:

$$x_{ij}^{\ast }=\{\begin{array}{cc}\frac{1-(d-m)/a+{\sum }_{k=L+1}^{\hspace{0.17em}L+d-m}{c}^{-k}/a}{(12-L)-d+{\sum }_{k=L+1}^{\hspace{0.17em}L+d-m}{c}^{-k}}& \mathrm{if}\hspace{0.17em}j=0\\ \frac{x_{i0}^{\ast }-1/a}{c^{-j}}+1/a& \mathrm{otherwise}.\end{array}$$ 3.10

Because not all of the potential trait sets may be positive, m in equation (3.10) represents the number of potential trait sets that satisfy the criterion for positivity. If j = 0, $x_{i0}^{\ast }$ in equation (3.10) is always positive. If j > 0, the condition of positivity is satisfied when $((x_{i0}^{\ast }-(1/a))/c^{-j})+1/a\hspace{0.17em}>0$, which is reduced to the following inequality

$$a\hspace{0.17em}>\hspace{0.17em}\frac{1}{x_{i0}^{\ast }}(1-c^{-j}).$$ 3.11

From equation (3.10), $x_{i0}^{\ast }$ is given as

$$x_{i0}^{\ast }=\frac{1-(d-n)/a+{\sum }_{k=L+1}^{\hspace{0.17em}L+d-m}{c}^{-k}/a}{(12-L)-d+{\sum }_{k=L+1}^{\hspace{0.17em}L+d-m}{c}^{-k}}.$$ 3.12

Substituting equation (3.12) to (3.11), we have

$$a\hspace{0.17em}>\hspace{0.17em}(12-L)(1-c^j)-\frac{1-c^d}{1-c}{c}^{\hspace{0.17em}j-L-d}.$$ 3.13

The above equation is the condition for the evolution of delayed fertilization.

(b) . Theoretical predictions for the evolution of delayed fertilization

We derived three conditions that favour the evolution of a long delay of fertilization (equation (3.13)), (i) severe competition for pollinators (large a), (ii) long seed maturation period (large d), and (iii) the presence of an unfavourable season for flowering and fruiting (large L). When competition for pollinators is severe (a = 0.9) and the seed maturation period is long (d = 6) under environments in which there are unfavourable seasons (e.g. winter cold) from November to March (i.e. L = 5), the population consisted of diverse phenotypes varying in flowering time and period of delayed fertilization (figure 4a). The earliest flowering phenotype starts flowering when the favourable season begins in April and produces mature fruits immediately before winter starts in October without any fertilization delay, resulting in 1-year fruiting (figure 4a). Other phenotypes are 2-year fruiting types, with the longest period of delayed fertilization of 11 months in the earliest flowering phenotype that flowers in May (figure 4a). As the flowering time becomes later in the season, the period of delayed fertilization becomes shorter, and the autumn-flowering phenotype shows the shortest period of delayed fertilization (six months; figure 4a). Fertilization in 2-year fruiting types takes place in April in the year after flowering regardless of flowering time, and then seeds develop under favourable environmental conditions, and mature fruits are dispersed in October before the onset of winter (figure 4b).

Figure 4.

Predicted consequences of coevolution of flowering time and period of delayed fertilization. Note that seed development needs d months after fertilization. (a,b) Severe competition for pollinators (a = 0.9, b = 0, d = 6, L = 5). (c,d) Moderate competition for pollinators (a = 0.3, b = 0, d = 6, L = 5). (e,f) Low competition for pollinators (a = 0.1, b = 0, d = 6, L = 5). (g) Shorter seed development period under the condition of severe competition for pollinators (a = 0.9, b = 0, d = 4, L = 5). (h) Shorter period of unfavourable environment for reproduction under the condition of severe competition for pollinators (a = 0.9, b = 0, d = 6, L = 1). (i) Effect of predator satiation (a = 0.9, b = 0.5, d = 6, L = 5). For all plots, the monthly survival rate of ovules during delayed fertilization was c = 0.98. After fertilization, seed development needs d months.

When competition for pollinators is relaxed (a = 0.3), phenotypes that flower in early summer with a long period of delayed fertilization disappear, and the population consists of phenotypes that flower in spring without delayed fertilization and those that flower in autumn with delayed fertilization of approximately half of a year (figure 4c,d). When the competition for pollinators is further relaxed (a = 0.1), all individuals become a 1-year fruiting type that flowers in spring (figure 4e,f). When synchronized flowering has a positive effect on fitness (i.e. a < 0), the inequality in equation (3.13) is never satisfied, and thus delayed fertilization never evolves. These results demonstrate the important role of the negative effect of simultaneous flowering on the evolution of delayed fertilization.

Even when the seed maturation period becomes shorter (change of d from six to four months), 2-year fruiting types remain, although phenotypes that flower in early summer in May and June become a 1-year fruiting type (figure 4g). Similarly, even when the period of winter becomes shorter (from L = 5 to 1 month), 2-year fruiting types remain, although phenotypes that flower early in the season again become the 1-year fruiting type (figure 4h). The theoretical result that early flowering phenotypes are more likely to become 1-year flowering types is consistent with observations about the relationship between flowering time and the likelihood of 1- and 2-year fruiting types (figure 2b).

(c) . Predator satiation facilitates the evolution of delayed fertilization in less seasonal tropical environments

Thus far, our results suggest that the competition between simultaneously flowering individuals and the presence of an unfavourable season for reproduction are sufficient to explain the evolution of delayed fertilization. If the environment is always favourable for reproduction and if there is no effect of predator satiation, our model predicts that delayed fertilization is not advantageous even if there is severe competition for pollinators, and flowering and fruiting take place throughout the year, as shown in equation (3.9).

When predator satiation operates together with severe competition for pollinators (a = 0.9, b = 0.5), delayed fertilization can evolve even in a habitat where the environment is always favourable for reproduction (figure 4i). In the absence of competition for pollinators, delayed fertilization never evolved in this stable environment, stressing the more important role of competition for pollinators than predator satiation in the evolution of delayed fertilization. Predator satiation is essential only in tropical (less seasonal) environments, where it substitutes for the absence of seasonality in providing an advantage to fruiting in a subset of months.

4. Discussion

We proposed a new hypothesis for the evolutionary advantage of delayed fertilization: delayed fertilization facilitates temporal niche differentiation via non-overlapping flowering times among species. We first showed that flowering times, important phenological traits that are critical for fitness, reveal rich diversity from early spring to winter in animal-pollinated species, such as the genera Lithocarpus and Castanopsis, in which 2-year fruiting species are dominant. The observed association between flowering time diversity and the likelihood of 2-year fruiting species motivated us to theoretically examine the coevolution of flowering time and delayed fertilization. A newly developed mathematical model showed that delayed fertilization facilitates the diversification of flowering time at a population level, which is advantageous for animal-pollinated trees that compete over pollinators. The diversification of flowering times at a population level would strengthen the process of reproductive isolation as a species diverges, leading to full speciation and fixation of flowering time traits within species [19]. High diversity in flowering time in Lithocarpus and Castanopsis could be explained by these processes (figure 1). In wind-pollinated species, such as the genera Quercus and Fagus, the degree of competition between individuals that flower simultaneously is minimized. This weak competition would enhance synchronized flowering phenology in spring, with the result that fertilization delay becomes less pronounced. Interestingly, in the genus Quercus, 1- and 2-year fruiting types were mixed (figure 1). This feature suggests that another factor that is different from pollinator competition, such as interference by heterospecific pollen (e.g. stigma clogging), works to decrease fitness due to synchronized flowering in this genus. There may also be some selection for different Quercus species at the same site to have asynchronous seed production across years, as discussed below in relation to black versus white oaks in the USA.

It is difficult to evaluate how the strength of competition for pollinators in our model compares with empirical studies. Competition for pollinators can reduce maternal fitness (seed production) through lower visitation rates to flowers, lower deposition of conspecific outcrossed pollen, higher deposition of heterospecific pollen and reduced offspring quality [20,21]; it also reduces male fitness (paternity of seeds on other plants) through reduced pollen export and higher conspecific pollen loss [21]. Unfortunately, several of these effects (especially male fitness) are rarely studied, and measuring pollination effects on offspring quality may require decade-long experiments [22]. Additionally, in empirical studies, the current impact of competition may have been reduced by previous selection favouring diversification of flowering times, and measured impacts vary from year to year owing to external influences [21]. Thus, the empirical impacts of competition for pollinators in real-world systems are not well known but plausibly sometimes fall within the range of fitness costs in our model.

Although the degree of synchrony in flowering was different among genera, fruiting times were highly synchronized in all genera (most of the 1-year fruiting species needed four to seven months from pollination to fruiting, as shown in figure 2c). Our model predicted that the high synchronicity in acorn production can be formed by two different mechanisms. One is an adaptive strategy that completes seed maturation before the unfavourable winter season begins, and the other is predator satiation, which operates together with severe competition for pollinators. Because reproductive phenology data were collected in temperate and subtropical zones in China where there is seasonality, it is not possible to demonstrate which mechanism explains the data presented here. Collecting flowering and fruiting phenology data for the Fagaceae in less seasonal tropical forests in Southeast Asia and comparing these data with those presented here will be extremely interesting to identify which mechanism is involved in real ecosystems. Even in ever-humid tropical rainforests in Southeast Asia, sequential flowering and synchronized fruiting, called general flowering, have been reported [23–25]. The incorporation of a predator satiation effect facilitates the evolution of delayed fertilization, which can explain sequential flowering in tropical environments.

In addition to the severe competition for pollinators and predator satiation, long seed maturation periods favoured the evolution of delayed fertilization because seed maturation needs to be completed before the unfavourable season begins. Many Fagaceae species produce large acorns that need at least several months for maturation (figure 2c). Because a larger seed size contributes to an increased seedling survival rate and the successful establishment of seedlings [26], selection for increased seed size places increased selective pressure on delayed fertilization in Fagaceae. Because seed size is also associated with an intermast interval in oaks [27], it is tempting to speculate that the evolution of large seed size, delayed fertilization and masting occurred in relation to each other.

The relationship between the evolution of delayed fertilization and masting will be an interesting research topic in the future. To date, there is little evidence that the degree of synchrony and variability of seed production varies significantly between 1-year and 2-year fruiting species [28]. The intermast interval was greater in 1-year fruiting oaks than in 2-year fruiting oaks, suggesting that selection has been stronger for greater masting in 1-year fruiting oaks than in 2-year fruiting oaks [27]. Although the variability of seed production across years, measured by the coefficient of variation in seed production, and the level of synchrony of acorn production among individuals in a population were not different between 1- and 2-year fruiting oaks [29], seed production is asynchronous between species with different fruiting types [30]. This asynchronous seed production may facilitate the coexistence of species with different fruiting types by reducing competition during seedling establishment [30,31]. Mohler [30] showed that in the USA, oak subgenera co-occurred more often than expected by chance, which could be partly owing to different acorn maturation times (typically 1 year in white oaks and 2 years in black oaks). However, the subgenera still co-occurred frequently in the southwestern USA, where the common black oaks are 1-year fruiting species, suggesting that multiple niche differences must be involved [30]. Integration of our phenology-based hypothesis and the coexistence hypothesis will be fruitful for a comprehensive understanding of the evolutionary history of reproductive strategies in Fagaceae. Further research is needed to compare the relationship between masting, fruiting habits (1- and 2-year fruiting), and other traits, such as leaf habits (deciduous or evergreen), in diverse genera, not only in Quercus, and to understand how phylogenetic constraints contribute to the evolution of delayed fertilization and masting.

Knowledge about delayed fertilization provides a mechanistic understanding of fertilization failure owing to impaired pollen–ovule interactions. The failure of pollen–ovule interactions can act as an environmental veto that increases the degree of synchrony [2,32]. How climate conditions such as temperature and humidity affect the success of the pollen–ovule interaction needs to be studied to elucidate mechanisms for fertilization failure and quiescence of female flowers [33]. Long-term genome-wide transcriptome analysis under natural conditions and integrated analyses of the expression patterns of genes associated with ovule development, pollen tube growth and fertilization [34] will be the first step to unravel molecular mechanisms that potentially link masting and weather. In addition, the identification of genetic variability in the stress tolerance of pollen and ovule development would be useful to understand differential stress responses across species in future studies.

Data accessibility

Phenology data of Fagaceae species used in this study are publicly available from the eFloras of China [14].

The data are provided in electronic supplementary material [35].

Authors' contributions

A.S. collected the data, and performed modelling and data analyses. A.S. and D.K. prepared the manuscript.

Competing interests

We declare we have no competing interests.

Funding

This work was supported by JSPS KAKENHI Grant Number JP21H04781.