Seasonality and competition select for variable germination behavior in perennials

Abstract

The occurrence of within-population variation in germination behavior and associated traits such as seed size has long fascinated evolutionary ecologists. In annuals, unpredictable environments are known to select for bet-hedging strategies causing variation in dormancy duration and germination strategies. Variation in germination timing and associated traits is also commonly observed in perennials and often tracks gradients of environmental predictability. Although bet-hedging is thought to occur less frequently in long-lived organisms, these observations suggest a role of bet-hedging strategies in perennials occupying unpredictable environments. We use complementary analytical and evolutionary simulation models of within-individual variation in germination behavior in seasonal environments to show how bet-hedging interacts with fluctuating selection, life-history traits, and competitive asymmetries among germination strategies. We reveal substantial scope for bet-hedging to produce variation in germination behavior in long-lived plants, when “false starts” to the growing season results in either competitive advantages or increased mortality risk for alternative germination strategies. Additionally, we find that lowering adult survival may, in contrast to classic bet-hedging theory, result in less spreading of germination by decreasing density-dependent competition. These models extend insights from bet-hedging theory to perennials and explore how competitive communities may be affected by ongoing changes in climate and seasonality patterns.

Introduction

Accurate timing of seasonal phenology is key to population persistence in unpredictable environments. Timing of emergence can have strong and direct effects on individual fitness and is expected to be subject to strong selection driving local adaptation (Donohue et al., 2010). Indeed, emergence behavior (e.g., patterns of germination or hatching) is often found to vary predictably along environmental gradients (Meyer et al., 1995; Pinceel et al., 2017; Rubio de Casas et al., 2017; Scholl et al., 2020; Simons, 2014; Torres-Martínez et al., 2017; Venable, 2007; Wagmann et al., 2012). In most plants and many animals, timing of emergence is controlled by dormancy (Baskin & Baskin, 2014; Finch-Savage & Leubner-Metzger, 2006; Vleeshouwers et al., 1995), and the evolution of emergence behavior is thus tightly linked to the evolution of dormancy mechanisms (Varpe, 2017).

Theoretical models of seed dormancy and germination behavior have a long history (Cohen, 1966; Ellner, 1985; Geritz et al., 2018; Hughes, 2018; Kortessis & Chesson, 2019; Venable & Lawlor, 1980). Most of these, however, have focused on specific systems such as annual plants in desert environments. This system provides a natural starting point because one striking observation demands an explanation: Some fraction of seeds produced each year fail to germinate the next year and instead lie dormant for another year before germinating at the beginning of the second growing season following their dispersal (Gremer & Venable, 2014). While this reduction in number of seedlings may seem a waste of resources most years, such a strategy has been identified as a risk-spreading adaptation to avoid complete recruitment failure in a bad year. Prolonged seed dormancy and variation in germination timing have come to represent the archetypical bet-hedging strategy, that is, a genotype-level strategy that sacrifices short-term (arithmetic-mean) fitness in order to lower fitness variance over time (Cohen, 1966; Levins, 1962; Venable, 2007). Such bet-hedging strategies have received considerable empirical and theoretical attention as a major mode of adaptation to unpredictable environments (Seger & Brockmann, 1987; Simons, 2011; Starrfelt & Kokko, 2012).

Empirical and theoretical studies of bet-hedging have yielded a good understanding of how different types of risk-spreading adaptations coevolve, interact, and cancel each other out. For example, if phenotypic polymorphisms or continuous variation ensures that fitness correlations among related individuals are sufficiently low, then there is less need for other costly bet-hedging strategies at the individual level such as “safer” offspring phenotypes that are weaker competitors but better able to cope with environmental variation (Escobar et al., 2021; Haaland et al., 2020; Starrfelt & Kokko, 2012; Venable & Brown, 1988). The scope for bet-hedging is also lowered if the spatiotemporal scale of environmental variation (often called environmental “grain” in bet-hedging terms) already ensures that related individuals experience different conditions and thus uncorrelated fitness returns. In spatially fine-grained environments, relatives may be exposed to a wide range of different conditions at any given time (as opposed to coarse-grained environments where all individuals experience the same conditions), and in such cases, genotype-level diversification or other bet-hedging strategies are not selectively favored (Levins, 1962; Starrfelt & Kokko, 2012). Furthermore, longer life spans with a larger number of selective events over which fitness can accumulate (e.g., an individual experiencing multiple consecutive breeding seasons with variable conditions) also reduce the need for any variance reduction if fitness payoffs among selective events are uncorrelated (Haaland et al., 2019).

Given these insights, it is unsurprising that most models of bet-hedging, as well as many of the best-documented empirical examples, consider rather specific types of short-lived organisms with discrete generations occupying highly variable, coarse-grained environments, such as germination strategies of desert annuals, or overwintering strategies for organisms in ephemeral ponds (Furness et al., 2015; García-Roger et al., 2017; Wang & Rogers, 2018). However, this focus has also led to a knowledge gap regarding the evolution of seemingly “risk-spreading” traits in longer-lived organisms, as these may require other explanations than bet-hedging in its strictest sense. Variation in seed germination behavior is seen not only in annuals and is at least sometimes associated with variation in seed size (Harel et al., 2011; Martins et al., 2019; Norden et al., 2009; Rees, 1996; Simons & Johnston, 2000; Susko & Lovett-Doust, 2000). A classic example of within-individual variation in seed size is seed heteromorphism, as observed, for example, in many Asteraceae and Chenopodiaceae (Imbert, 2002; Venable, 1985), where distinct seed morphs differ in their dispersal abilities and germination behavior (Brändel, 2004; Fumanal et al., 2007; Venable et al., 1987; Wang et al., 2012; Yao et al., 2010). Continuous variation in seed size is also common in natural populations, and may relate to variable germination behavior (Pélabon et al., 2021). Within species, larger seeds are generally more likely to germinate and/or germinate earlier than do smaller ones (Biere, 1991; Galloway, 2001; Pélabon et al., 2005; Simons & Johnston, 2000; Tremayne & Richards, 2000), but the opposite pattern of smaller seeds germinating earlier is also observed (Martins et al., 2019).

Seed size variation is thus a common mechanism for producing seeds with variable dormancy duration and/or variable germination time, both within individuals and within an inflorescence (Pélabon et al., 2021). As argued, existing bet-hedging models alone are not able to explain the ubiquity of seed heteromorphism or continuous seed size variation as observed in perennials (Martins et al., 2019). Although several other non-mutually exclusive hypotheses exist, including but not limited to variance sensitivity due to asymmetrical fitness costs versus benefits (Bårdsen et al., 2008; Bednekoff, 1996), fluctuating selection or fluctuations in priority effects (Chesson, 2000; ten Brink et al., 2020), competitive asymmetries among offspring types (Geritz, 1995), and negative frequency-dependent selection (Metcalf et al., 2015; Poethke et al., 2016), these have seldom been analyzed jointly (but see Rees et al., 2004). In Scholl et al.’s (2020) recent analysis of the flora of the south-east United States, annuals were not detectably more likely to exhibit seed heteromorphism than were perennials, suggesting that selection for within- and/or among-individual variation in germination behavior may be common also in long-lived plants where bet-hedging is less strongly favored.

Here, we explore the evolution of individual variation in dormancy of long-lived plants in seasonally varying environments, using both analytical and simulation models covering a range of ecological scenarios. First, our analytical model derives general predictions for when within- and/or among-plant variation in germination behavior can be favored as an adaptation to seasonal environmental variation in perennials. To this end, we use an adaptive dynamics approach assuming that plants produce two discrete seed morphs, “early” and “late” seeds with respectively short and long dormancy periods. This analysis examines the conditions favoring plants producing seeds of variable dormancy duration and identifies the shape of the function relating the (rainfall-dependent) benefits and costs of producing early relative to late seeds as the key determinant of whether mixed strategies are stable. The potential for among-individual variation is also examined. We complement this analytical model with individual-based evolutionary simulations of dormancy duration modeled as a near-continuous trait via freely evolving weekly germination probabilities. This model examines the predictions from the analytical model without the restriction of only allowing two discrete seed morphs and makes explicit the mechanisms affecting benefits and costs of early and late seeds. Specifically, early seeds germinating during the dry season gain a competitive advantage if they survive until reproduction, but suffer high mortality if there is not enough rain between their germination and the beginning of the wet season (“false starts”). We let spatiotemporal rainfall patterns vary predictably and unpredictably within and among years, thus emulating the wet- and dry-season dynamics seen in large parts of the tropics where intermittent dry-season rains can trigger the germination of certain seed types. However, this setup applies equally well to other stochastic seasonal changes between harsh and favorable conditions, such as the onset of warmer spring weather in temperate regions where “false starts” of warm temperatures may still be followed by harmful frosts. In concert, our two models enable teasing apart the relative effects of bet-hedging, competition, and fluctuating selection on the evolution of variable germination strategies.

Selection for within-plant variation in germination behavior

We first present an analytical model where we assume that plants can produce two seed morphs, here “early” and “late” seeds, that may differ in, for example, size or coat thickness and hence the amount of rainfall required for germinating (Norden et al., 2009). Each year consists of a dry and a wet season, where the dry season is characterized by scarce intermittent rainfalls affecting the germination and survival probability of early seeds. Early seedlings emerging during intermittent dry-season rains risk dying due to drought, but may persist if there is sufficient excess rain in the following weeks leading up to the wet season. Late seeds, on the other hand, remain dormant through any intermittent rains and germinate at the beginning of the safe wet season. However, any early seedlings that survived until the beginning of the wet season may now have a competitive advantage over late seeds, as they have a head start to growth, and therefore a higher probability of recruitment into the adult population. Thus, the relative advantage b of being an early versus a late seed in a given year depends on the amount of excess dry-season rainfall in that year, a random environmental variable we term X. In other words, if in a given year the amount of excess dry-season rainfall X equals x, this relative advantage will be b(x).

We designate as f the fraction of early seeds produced by a plant, so that 1 – f are late seeds. We model a density-regulated population of long-lived plants, where adult plants survive with probability s_a, and all seeds compete for recruiting into the vacant space 1 – s_a in the adult population. We incorporate asymmetric competition among early and late seeds in a “lottery” for vacant space. Early seeds get relative weight b(x)f against the weight 1 – f of all late seeds, such that the probability of drawing an early seed in the lottery for vacant space becomes

Next, assuming that the population is sufficiently isolated (no immigration) and that the quality of environmental conditions X vary randomly from year to year without any autocorrelation, the relative fitness w(f’, f) of strategy f’ (a rare mutant) against a resident population with strategy f is given by its geometrically averaged growth rate, which can be expressed through the expectation of its log growth rates $λ$⁠, that is,

where E indicates the expectation over the distribution of environmental conditions (see  Appendix A for derivation of λ). The sign of w(f’,f) determines whether the mutant can invade the population (positive) or not (negative)—examples are shown in Figure 1A and B where expectations are calculated over 10,000 realizations of X~Normal(0,1).

We now use an adaptive dynamics approach to analyze the evolutionary consequences of Equation 2 (Geritz et al., 1998; Kisdi & Meszéna, 1995). Assuming that E[X] = 0 (the expectation for “excess” rain is zero) and that the two seed types fare equally well in average years when there is neither excess nor deficit of rain between the early seeds germinating and the end of the dry season (i.e., b(0) = 1), we can examine the conditions leading to an advantage for early seeds.

The selection gradient acting on a rare mutant with a germination strategy (fraction of early seeds) f’ slightly different from the resident population’s strategy f, is obtained by differentiating w(f’, f) with respect to f’ (see  Appendix A) and evaluating at f’ = f, which yields

Intuitively, selection strength decreases with increasing adult survival 0 < s_a < 1, as the competition among seedlings for annual recruitment contributes less of the population. Examples of selection gradients for two functions b(x) with different s_a are shown in Figure 1C and D. Cases where $∂w∂f′|f′=f=0$ (colored lines cross the dashed black lines in Figure 1C and D) represent singular strategies (Geritz et al., 1998). To determine whether these are attractors or repellors, we can examine the sign of the derivative of Equation 3 taken with respect to the resident strategy f:

Because the squared term is positive, Equation 4 is always negative, indicating that all singular strategies are attractors. Furthermore, computing the second derivative of Equation 2 with respect to the mutant strategy f’ and again evaluating at f’ = f allows determining whether the singular strategies are evolutionarily stable strategies (negative sign) or branching points (positive sign). Thus, the ESS criterion is:

which reveals that $∂2w∂f′2(f′,f)$is always negative (both squared terms are always positive). Thus there is no potential for evolutionary branching and any singular strategy is necessarily a convergence stable ESS (Geritz et al., 1998). In other words, in this simple case of two discrete seed morphs (early and late seeds), the evolution of their frequency f cannot reach two distinct values at evolutionary equilibrium.

The need to compute expectations over realizations of the random variable X makes it difficult to exactly identify ESSs in the current model. However, we can approximate selection gradients using the delta method if we assume that X follows a sufficiently simple distribution with all odd-numbered moments equal to 0 (E[X] = 0, symmetric distribution), a small variance V, and even-numbered moments have an upper bound depending on V. Then, recalling b(0) = 1 by assumption, we obtain the approximation

Setting this selection gradient equal to 0, we see that there can be one singular strategy only,

In order for such an ESS to exist and represent a mixed strategy, it must lie between 0 and 1, with conditions given by the shape of the function b(x), which determines the advantage of early relative to late seeds for a given level of excess dry-season rain x. First, to ensure f > 0, b´´(0) > 0 is demanded (Equation 7), that is, b(x) must be accelerating (convex) around 0. Second, to ensure f < 1, Equation 7 gives the condition b´´(0) < 2b´(0)², that is, it must not accelerate too fast (there is an upper bound to how convex it can be, given by the steepness of the function). For example (as shown in Figure 1A and C, if b(x) = e^−βx, we have an ESS for all β > 0, since b´´(0) > 0 and b´´(0) < 2b´(0) is fulfilled. The ESS becomes f = b´´(0)/2b´(0) = 0.5. In contrast, if b is a logistic function b(x) = 2/[1+e^−αx] (Figure 1B and D), the conditions for an ESS are not fulfilled: b´(0) = 0 and b´´(0) < 0 whenever α > 0.

Overall, this model reveals that there is ample scope for within-individual variation in germination strategies when plants can evolve to produce both early and late seeds, but that among-individual variation in f should not occur in such a scenario because all ESSs are convergence stable. The evolution of a mixed strategy 0 < f < 1 requires accelerating rewards for germinating early with increasing amounts of excess rainfall x, but only within a limited range. If rewards are not accelerating, f evolves toward 0 (if benefits of being early are insufficient, producing risky early-germinating seeds is futile), whereas if rewards accelerate too much, f evolves toward 1 and all seeds germinate early. Interpreting b(x) as the sum of the functions relating early seed dry-season survival as a function of x and the competitive advantage of early seeds (given their survival) over late-germinating seeds in the lottery for vacant space in the adult population, this analysis provides a baseline expectation for our individual-based model with continuous variation in germination time.

Individual-based model of flexible dormancy durations

Model setup

Here, we build an individual-based simulation model that allows plants to produce a continuous distribution of seed types (rather than just “early” and “late” seeds). We model a population of asexually reproducing perennials occupying a wet–dry seasonal tropical environment where the wet and dry seasons both last half the year (26 weeks). We assume that seed germination is determined by its dormancy period d_z, which functions as an obligate “biological clock” preventing germination until a certain time d_z has passed (see Table 1 for an overview of mathematical notations and baseline parameter values). Germination occurs with probability 1 as soon as its age (in weeks) is greater than d_z. We set no constraints on the evolution of flexible dormancy strategies, as probability of germination is determined by 27 haploid genes d_i, with i between 1 and 27, each corresponding to a week in the dry half of the year, and the 27th indicating germination at the start of the wet season. Each gene determines the probability of a seed germinating in the corresponding week, and therefore has values bounded by 0 and 1, with the condition that the sum of all genes always equals 1. The actual phenotypic trait value (dormancy period d_z) of an offspring j is randomly drawn from the probability distribution determined by its parent’s genetic values.

Population initialization

Each replicate simulation starts with N₀ adult individuals. For computational purposes, we start each simulation with ample standing genetic variation. Therefore, each individual is independently assigned a random combination of gene values, with starting d_i values uniformly distributed between 0 and 1. After assigning each gene a random value, we standardize all values such that the sum of an individual’s 27 genes equals 1.

Abiotic conditions

We model time steps of 1 week and assign the first 26 weeks of a year as the dry season and the last 26 weeks as the wet season. Dry-season rainfall varies stochastically within years, with 26 weekly rainfalls randomly drawn from a beta distribution bounded between 0 (no rain) and 1 (high rain). Weekly rainfall in the wet season is always equal to 1. We parameterize the beta distribution in terms of its mode m, such that the shape parameters are given by

The mode mainly affects average rainfall (the higher the wetter), but note that it also affects weekly rainfall variance within years V$(=136m+12−m)$⁠, which is highest when m = 0.5.

To tease apart effects of bet-hedging resulting from the spatiotemporal scale of environmental stochasticity, we examine evolutionary outcomes under coarse-grained and fine-grained rainfall variation. In coarse-grained environments, we assume that all seeds experience the same sequence of weekly dry-season rainfalls R (a vector of 26 values), but R differs among years. Under fine-grained environmental variation, different R vectors are assigned to individual seeds within years at random. Specifically, we produce 10,000 sequences of weekly rainfall upfront and assign each seed a random R chosen among these. Thus, experienced rainfall will vary a lot among individuals within a year in this scenario, but average rainfall will vary little across years. In both scenarios, the weekly rainfall in the wet season (weeks 27–52) is constant and equal to 1, which represents high rainfall.

Survival of seedlings and adults

After setting the weekly rainfalls of a particular year, we determine the survival probability of seedlings. We assume that survival increases both with rainfall and seedling age, as could be the case if younger seedlings were more fragile in general, and particularly more vulnerable to rainfall shortages. The probability of survival for an individual i with age a_i,t in a given week t with rainfall R_t (or R_i,t in the fine-grained scenario) equals

that is, a sigmoid function of seedling age, the lower asymptote of which increases with increasing rainfall (Figure 2A and B). Note that rainfall also affects the horizontal position of the function (how far “along” the x-axis the seed has come in terms of survival) and that the strength of this effect increases with the parameter δ₂.

With the rainfall data of a particular year and the survival function (Equation 9), we calculate each seedling’s survival probability (Figure 2C), which is given by the product of its (age- and rain-dependent) survival probabilities of each week from germination time d_z until the end of the year:

We assume that weekly survival for adults is independent of age and rainfall and equal to s_ad, such that yearly survival becomes s_ad⁵² and expected life span (in weeks) is 1/(1 − s_ad).

Recruitment and density dependence

We assume that only K adult plants can live in the environment. At the end of the wet season, we determine which of the seedlings that germinated in this year will recruit into the adult population. We first calculate the number of available slots (K minus the number of surviving adults), and then fill the empty slots with seedlings. Recruitment success depends on seedling age, with older seedlings having a higher probability of recruiting. The relative recruitment probability of a seed is proportional to (a_i – 25)^c, where parameter c indicates the strength of competitive asymmetry. For c = 0, recruitment is independent of age, while for high values of c, young seedlings will be outcompeted by older seedlings. Because seeds germinate at the latest in week 27, the youngest seedling is 26 weeks old at the time of recruitment. By subtracting 25 from the age of each seedling, the youngest seedling has weight; 1 all other seedlings have weights exceeding 1.

Reproduction, inheritance, and mutation

At the end of the wet season, all adult plants (i.e., individuals older than 52 weeks, not the juveniles that were just recruited) reproduce asexually. Individual seed production is Poisson-distributed with a mean fecundity of γ. Offspring inherit their parent’s gene values for determining dormancy duration (d_i), but not their actual phenotype d_z. Each locus has an independent probability μ of experiencing mutation. Mutational effects are of constant effect, such that the new gene value is drawn from a normal distribution with mean equal to the previous value, and standard deviation of μ_σ. Negative values are absorbed at 0, ensuring that the new gene value is non-negative. After mutation, the values of all genes of an individual are normalized to sum to 1. We also explored the effects of an alternative mutational structure using a Dirichlet distribution with parameters given by the parent’s vector of allelic values, and a fixed concentration determining the size of mutational effects. Such a structure is suitable for discrete probability distributions as it ensures that all mutated allelic values are bounded by 0 and 1 and resulting multilocus genotypes sum to 1. To address the issue of absorbing-at-zero in the Dirichlet distribution, we added a small value (10⁻⁵) to each parental allelic value during parameterization to prevent gene values from becoming stuck at zero.

Data generation and analysis

Simulations ran for 1,000,000 years. Results presented are based on the populations at the end of each simulation. As there is hardly variation among replicates, results are presented for only three independent replicate runs of each scenario. We implemented the model in C++; the code is available in the Dryad data repository. Simulations were run using GNU parallel (Tange, 2021).

Results

Despite the added ecological complexity and evolutionary realism of the individual-based simulation model, with its potential for a flexible germination strategy allowing near-continuous variation in dormancy duration, we find overall that these results correspond well with those of the analytical model. First, despite the high potential for finely tuned germination strategies, our simulations showed remarkably little variation both among replicated simulations and within populations, in agreement with our prediction that any ESS is convergence stable and so no evolutionary branching should occur. Second, our simulations highlight the mechanisms modulating the (rainfall-dependent) benefits and costs of early relative to late seeds—namely the strength of age-dependent competitive asymmetries for recruitment and juvenile dry-season survival–and corroborate the finding from our analytical model that mixed germination strategies only arise at a certain balance point where the relative benefits of early seeds are neither too large nor too small (Figures 3 and 4, see Supplementary Figure S1 and S2 for weekly germination probabilities rather than grouped by early–intermediate–late).

Additionally, expanding on the findings from the analytical model, our simulations demonstrate that this within-individual dormancy variation evolves as an adaptation lowering genotype-level fitness variance, confirming that such strategies do indeed largely represent bet-hedging strategies (compare top vs. bottom rows of Figures 3 and 4). By comparing results obtained in temporally coarse-grained environments (all individuals experience the same rainfall in a given year, resulting in high within-year fitness correlations and high among-year fitness variation) with those obtained in fine-grained environments (rainfall is assigned independently for all individuals each year, resulting in low within-year fitness correlations and low among-year fitness variation), we observe that most of the spreading of germination disappears in fine-grained environments (but see Supplementary Figures S3; mixed strategies are still observed right at the switching point). Thus, the evolution of within-individual seed size variation in perennials can, across much of the parameter space, be attributed to the interaction between age-dependent survival, competition for recruitment, and bet-hedging. This result also importantly highlights that bet-hedging in germination strategies is not driven per se by weekly rainfall variation within years, V, but also by the spatial scale of rainfall variation, which affects correlations in environmental conditions experienced among individuals within populations.

When competitive asymmetries are weak, that is, competition for recruitment depends only weakly on seedling age, obligate dormancy evolves, causing germination at the beginning of the wet season (top row of Figure 3A and Supplementary Figure S1a). This holds even under higher rainfall, when dry-season germination and seedling survival may often be possible, because there are no competitive benefits to early germination and so even small risks are not worth taking. Conversely, when competitive ability depends strongly on seedling age, minimal dormancy periods evolve and seeds germinate as soon as possible (top row of Figure 3C and Supplementary Figure S1c). These seedlings then need to survive the entire risky dry season, but this pays off as long as the dry season is not too malign because later-germinating seeds have little chance of recruiting if there are even a few surviving early seeds. Accordingly, within-individual variation in dormancy period is low in both these scenarios. Bet-hedging has no effect on the evolution of dormancy in this case because there is no variance in expected fitness nor fitness correlations among related individuals (top and bottom rows are qualitatively identical in Figure 3A and C and Supplementary Figure S1a and c). Such fixed strategies and absence of evolutionary conflicts of interest in the short and long term are also predicted by our analytical model (Equation 7, no mixed strategies (0 < f < 1) can arise if the benefits b of germinating early do not increase sufficiently despite excess rain).

Similarly, only intermediate mortality risks select for mixed strategies. Because seedling mortality strongly affects the risks of early germination for a given rainfall level, any variation in germination timing occurs at intermediate levels of mortality risk in the dry season (Figure 4). In the scenario shown in Figure 4, we adjust the parameter a_inf, the inflection point of the survival function, that is, the age at which survival rises steepest, such that higher (later) a_inf entails higher overall mortality (see Figure 2). We find that low mortality (left column in Figure 4) always selects for germinating as soon as possible (because of age-dependent competitive asymmetries), whereas very high mortality (high a_inf; right column in Figure 4) always selects for germinating as close as possible to the start of the wet season. Only intermediate mortality risks (Figures 4 and Supplementary Figure S2, middle column) favor variable dormancy periods. Again, this general result corresponds well with our analytical model (Figure 1).

A final observation in this model is that, in contrast with predictions from previous bet-hedging theory, shorter life spans may select for less spreading of germination (Figure 5, weekly results shown in Supplementary Figure S4). This effect arises because of our implementation of density dependence (adult preemption), where lower adult survival means that more “slots” are available every year for seedlings to recruit into. This decreases the intensity of age-dependent competition, producing weaker selection for early germination with lower adult survival (Figure 5A shows results for high adult survival, vs. Figure 5B for low adult survival).

In situations where competition is strongly asymmetric (high value of c, bottom row of Figure 5), lowering adult survival may select for more spreading of germination (Figure 5D shows results for high adult survival, vs. Figure 5E for low adult survival). The reduction in density dependence now intensifies selection for late germination, resulting in the evolution of more spread in germination timing. In the analytical model, adult survival affects the speed of evolution only (Equation 3), and not the evolutionary endpoint (Equation 7). This discrepancy with the individual-based model is caused by the assumption in the analytical model that the strength of density dependence depends on the relative benefit of germinating early and the frequency of this strategy. In the individual-based model, however, the strength of density dependence is also affected by the number of free slots and competing seedlings. If we reduce adult survival and increase average seed production simultaneously, such that the strength of density dependence (expected number of seeds competing per open slot) remains constant, we no longer see an effect of adult survival on the resulting strategies (Figure 5C and F shows the same pattern of unimodal or bimodal germination as do Figure 5A and D).

As for Figures 3 and 4, removing any effects of bet-hedging by implementing fine-grained rainfall patterns (and thus removing environmentally induced fitness correlations among related individuals) leads to populations with only a single, fixed strategy in all scenarios depicted in Figure 5 (results not shown). Thus, within-individual variation in germination timing can arise due to interactions between life-history traits, bet-hedging, and intensity of intraspecific competition.

Discussion

Modeling results and insights

Our two complementary modeling approaches have shown how stochastic seasonal environments can select for within-individual variation in germination behavior through interactions between bet-hedging, life-history traits, and competitive asymmetries due to age-dependent seedling recruitment. First, our analytical model considering discrete variation (early- vs. late-germinating seeds) reveals ample scope for mixed germination strategies in long-lived species. This model revealed that the key determinant of whether variable germination evolves is the shape of the function relating how all benefits and costs of early versus late seeds change depending on environmental conditions (here, dry-season rainfall). Specifically, both the risks of early germination if conditions are too dry before the beginning of the wet season, and the benefits provided by competitive advantages over later-germinating seedlings (which will be smaller at the time of competition for recruitment), are captured in such a function, which is shown to have to be increasing and accelerating around 0 (expected dry-season rainfall), but not too quickly, in order for a mixed strategy to evolve.

Inspired by these results, we next built an individual-based simulation model of the evolution of the dormancy period, where we included both these benefits and costs to allow them to vary independently, as well as continuous within-individual variation in seed dormancy. To allow unconstrained evolution of flexible germination strategies, we modeled the joint evolution of 27 unlinked genes representing weekly germination probabilities of offspring. Despite this flexibility, the results from our analytical model with only two discrete germination strategies were largely recovered: Mixed strategies emerged only when the potential benefits (competitive advantage) and costs (dry-season mortality) of earlier germination were neither too strong nor too weak, but were still observed for a large range of parameter values. Furthermore, intermediate dormancy durations emerged very rarely, with evolution rather favoring mixed parental strategies producing some early- and some late-germinating offspring. Through comparisons with evolutionary outcomes in fine-grained environments, where the scope for such mixed strategies is much reduced, we conclude that this represents a diversifying bet-hedging strategy evolving due to genotype-level fitness correlations. In coarse-grained environments, phenotypically variable offspring reduces the fitness correlations among siblings, thus ensuring low genotype-level variance in fitness (Starrfelt & Kokko, 2012).

Our work demonstrates that explicit consideration of density dependence is necessary for understanding the adaptive value of within-individual variation in offspring phenotype in long-lived organisms. Variation in offspring size within individuals is not only common in perennial plants, but also in many other iteroparous organisms including arthropods (Fox & Czesak, 2000), birds (Amundsen & Slagsvold, 1998), fish (Einum & Fleming, 2004), and marine invertebrates (Marshall & Keough, 2007). While among-population variation is often interpreted as adaptive, within-individual variation, on the other hand, is mostly viewed as maladaptive (Fox & Czesak, 2000). This interpretation is possibly driven by the focus on optimality models (e.g., Einum & Fleming, 2004; Smith & Fretwell, 1974), which by definition predict a single offspring size to maximize fitness (Metz et al., 2008). Approaches that take frequency-dependent interactions into account, however, show that within-individual variation in offspring size can be adaptive, even in the absence of environmental unpredictability (Geritz, 1995). Our work shows that such an ecological approach is also necessary to understand evolution in unpredictable environments.

Germination strategies in seasonal environments

Our models were inspired by the wet–dry seasonal dynamics characterizing large parts of the tropics (Feng et al., 2013). Yearly patterns of seedling emergence such as those described by Garwood (1983) for Barro Colorado Island in Panamá suggest that germination during the early part of the rainy season predominates, although there is considerable variation (see also Escobar et al., 2018). Garwood’s study also hinted at an important role of asymmetric competition in that seedling emergence in highly competitive light gaps tended to occur earlier than did emergence in less competitive understory habitats. Our models provide a mechanistic explanation for these patterns and also suggest that ongoing changes in the predictability and temporal variation in precipitation patterns in the tropics may select for altered germination strategies in tropical plants (Feng et al., 2013).

The adaptive challenges faced by plants of seasonal tropical forests are in some ways analogous to those of arctic-alpine plants facing the problem of “false springs” followed by freezing events, which is thought to select for dormancy or other mechanisms to avoid detrimental fitness effects of premature germination (Mondoni et al., 2012; Schwienbacher et al., 2011). Arguing that within-individual variation in germination timing could be beneficial as a bet-hedging trait, Simons and Johnston (1997) used a model of such a system to illustrate their argument that developmental instability could be adaptive in annuals. During a time when developmental instability was largely seen as maladaptive (cf. the debate surrounding fluctuating asymmetry), substantial work on bet-hedging strategies has largely resolved this controversy (Devaux & Lande, 2010; Scheiner, 2014; Tufto, 2015; Zhang & Hill, 2005), and the dynamics considered by Simons & Johnston (1997) are now a canonical example of bet-hedging in seasonal phenology.

A second source of inspiration for our models was the extensive variation in seed size often observed in angiosperms (Michaels et al., 1988), and the many studies reporting relationships between seed size and germination behavior (Martins et al., 2019; Norden et al., 2009; Simons & Johnston, 2000). Although seed size is sometimes thought about as a highly canalized trait (Smith & Fretwell, 1974), both categorical (seed heteromorphism) and continuous variation in seed size are common (Susko & Lovett-Doust, 2000). In a recent phylogenetic analysis, Scholl et al. (2020) analyzed the occurrence of seed heteromorphism in a large sample of the flora of southwestern North America and detected weak associations between seed heteromorphism and several measures of environmental predictability (aridity and precipitation seasonality). While more likely seed heteromorphism in more unpredictable environments is consistent with our simulation model, these authors explicitly excluded species with continuous variation in seed size from their analyses. Although our simulation model suggests that seed heteromorphism may be a more likely evolutionary outcome for dealing with environmental variability than continuous seed size variation, there is no reason why continuous seed size variation could not also represent a bet-hedging strategy in unpredictable environments (cf. Simons & Johnston’s (1997) suggestion of developmental instability causing adaptive variation in germination timing). Interestingly, Scholl et al. (2020) failed to detect a correlation between seed heteromorphism and the annual life cycle, contrary to their expectations from previous bet-hedging theory. Although seed heteromorphism was more common in annuals than in perennials, they attributed the lack of a detectable effect to the small overall proportion of seed-heteromorphic species. However, the prevalence of seed heteromorphism in perennials suggests that the processes contributing to bet-hedging in our model and generating variation in germination timing may be common and important in natural systems.

Empirical guidelines and predictions

Our models yield several testable predictions about the relationship between germination behavior, seed size, and environmental predictability. The simplest prediction arising from our results is that within-individual variation in germination behavior and associated traits (e.g., seed size) can be adaptive, and possibly more so in more unpredictable environments. However, we also find that the distinctions between fine- versus coarse-grained environmental variation is important in driving germination patterns. This implies that caution is needed when interpreting measurements of environmental variation and using them to predict ecological gradients of germination strategies. For example, the measurement of rainfall variation used in Scholl et al. (2020) was based on among-year variation (coefficient of variation of annual rainfall measurements) and the smallest spatial grid used was 25 km², which is too large to capture whether a given genotype may experience environmental variation as fine or coarse grained. Thus, neither of these metrics provides information about the different outcomes observed in our models, which might explain the lack of a relationship between rainfall variation and the occurrence of seed heteromorphism. Another reason highlighted by our results could be that mixed germination strategies as adaptations to unpredictable environments may only evolve under certain conditions of how fitness costs and benefits vary among morphs across environments.

Recent studies of variation in seed size and germination behavior in the tropical vine Dalechampia scandens have revealed predictable covariation between measures of environmental predictability and germination behavior. Martins et al. (2019) found that seeds from populations occupying more seasonal environments required longer periods of after-ripening before germinating, and that within each population, smaller seeds required shorter periods of after-ripening. In a follow-up study, Pélabon et al. (2021) considered variation in seed size within individuals and detected a positive relationship between environmental stochasticity and variation in seed size. Environmental unpredictability as defined by Pélabon et al. (2021) more closely resembles our parameter V in describing stochastic variation in rainfall patterns, and our model thus provides mechanistic support for the hypothesis that the patterns of seed size variation and germination behavior in Dalechampia represents a bet-hedging strategy in unpredictable environments.

While observational studies of germination timing and seed size across ecological gradients may continue to yield insights into variation in these traits, experimental studies would be highly valuable. Seed-sowing experiments with seed families of known descent would specifically allow separating environmental and genetic causes of variation, and lead to insights into the evolutionary potential of germination behavior (e.g., Simons & Johnston, 2006). However, separating the presence of two distinct strategies from continuous variation may continue to prove difficult, especially if the difference in mean behavior between strategies is small, and variation around these means is large.

Limitations and caveats of the model

Our model results are broadly consistent with empirical patterns of seed size and germination behavior, yet some caution is needed when interpreting the model output. In particular, the specific genetic architecture we use (one freely evolving locus for each weekly germination probability) is admittedly highly unrealistic. Although we hope that this flexibility has allowed us to observe outcomes that explore all parts of unconstrained strategy space, some potentially beneficial combinations of germination probabilities may have been difficult to arrive at. For example, because weekly germination probabilities are constrained to sum to 1, loci with already large values could minimize the effect of potentially beneficial mutations at other loci increasing the germination probability in other weeks. However, our analysis using a Dirichlet distribution for genetic mutation, which allows for all loci to mutate together and reduces the likelihood of any single loci becoming stuck at a large value, did not qualitatively alter our results (Supplementary Figure S5), indicating that our evolved germination probabilities are indeed adaptive rather than model artifacts.

Next, while the above breach in realism aimed to limit bias and increase the robustness of our evolutionary interpretation, other limitations may in fact introduce biases to our conclusions. For example, it is difficult to say how our choice of asexual inheritance might have affected the ability to evolve discrete versus continuous strategies, or indeed the range of parameter space favoring variable germination, and so including sexual reproduction could provide an interesting next step for expanding our modeling work. Plant mating systems are highly variable, and near-complete selfing is uncommon compared to mixed and predominantly outcrossing systems (Moeller et al., 2017). If germination timing is indeed highly polygenic, outcrossing among individuals producing predominantly early- and predominantly late-germinating seeds might allow mixed strategies to evolve more easily than in our model, where such mixed strategies instead are dependent on the right mutations occurring sequentially. In addition to dormancy, germination timing is also driven by variation in flowering and fruiting phenology as well as the duration of fruit maturation (Escobar et al., 2018). Although we chose to keep these processes fixed in our model, variation in flowering time additionally leads to nonrandom mating and is therefore an interesting trait to add whether future studies consider sexual reproduction. Furthermore, germination timing may itself affect flowering phenology, such that later-germinating seedlings mature and flower later (e.g., García-Gusano et al., 2010; Mehlenbacher & Voordeckers, 1991), although the germination–flowering phenological correlation may also be null or even negative (Galloway et al., 2018; McKay et al., 2003). Under such a correlation, variable germination timing may cause suboptimal flowering phenology if, for example, seedlings miss a seasonal peak of pollinator abundance, potentially constraining the evolution of variable seed dormancy. We here assume that all seedlings recruit to the adult population and can reproduce at the same time regardless of germination timing, which if violated may interact with or even cancel out any competitive benefits of diversified germination timing.

Modeling multilocus evolution in the absence of any constraints, as we do here, may in itself introduce biases if evolution of optimal combinations is difficult to attain due to genetic constraints, covariation with other traits, or trade-offs. Importantly, we did not incorporate a trade-off between offspring quality and dormancy period, which could be expected if we assume that seed size is the mechanism by which variation in germination strategy is achieved (Stearns, 1989). Furthermore, we did not include a cost to seed size variation (Zhang & Hill, 2005). However, while such additional assumptions might affect our results (e.g., by narrowing the parameter space in which variable strategies are favored if adding costs of variation, and widening it if adding costs of canalization), they also reduce generality and do not subtract from the general point. Variation in germination strategies may arise from other sources than simply seed size variation resulting from per-offspring parental investment (Baskin & Baskin, 2014; Simons & Johnston, 2006) and as with costs of variation versus canalization, we note that the pattern may also go either way with regards to the seed size vs. germination strategy (offspring quantity vs. quality) trade-off: In many species, larger seeds germinate earlier (Biere, 1991; Pélabon et al., 2005; Simons & Johnston, 2000), but the opposite pattern is also observed (Susko & Lovett-Doust, 2000), and among species time to germination is usually longer for larger seeds (Harel et al., 2011; Norden et al., 2009). Thus, while adding some trade-off between seed set and germination strategy might increase realism with respect to certain systems, generality would again necessarily be lowered relative to our present model without such energetic constraints.

Finally, much remains to be explored regarding the effects of the abiotic conditions and their variation regimes. For example, we currently assume that adult survival is unaffected by fluctuations in rainfall, ignoring the possibility of events such as mass mortality resulting from prolonged drought. However, introducing negative correlations between seedling survival to recruitment (higher during relatively wet years) and recruitment probability (higher during relatively dry years, because many free “slots” may be available due to higher adult mortality) involves fluctuating density-dependent selection (Wright et al., 2019), disentangling these confounding effects are beyond the scope of the current paper. Another possibility that remains to be explored is separate effects of mode and variance in rainfall (Equation 8). Indeed, it should be noted that the variance changes with the mode under our current rainfall distribution parametrization. Although patterns of environmental variability relating to ecological processes are rarely measured in such ways, there may well be contrasting evolutionary responses to changes in these metrics for the distributions of environmental variables, and so a useful next step may therefore be to reparametrize our rainfall distribution to allow for such uncoupled effects. With our current parametrization, the concentration of the beta-distributed rainfall (α + β) is constant (and equal to 3), but by varying the concentration, one may achieve parameter settings yielding desired combinations of m and V.

Conclusions

This study has demonstrated novel mechanisms by which variation in germination strategies in perennial plants can evolve, shedding light on the prevalence of seed-size variation seen in perennials as well as annuals. Seed size was historically considered a highly canalized trait, to the point that the weight measurement “carat” was based on the remarkably invariant seeds of the carob tree (Ceratonia siliqua). However, it has since been discovered that substantial variation in seed size is widespread, even in carob seeds (Turnbull et al., 2006), and its universality begs an explanation. Bet-hedging in desert annuals has previously been the best-studied empirical and theoretical example of variable germination strategies, but there are arguably more perennial species occupying seasonal tropical or temperate environments than there are desert annuals. Our modeling results, where bet-hedging in perennials interacts with unpredictable seasonal variation and competitive asymmetries to produce within-individual variation in germination strategies, therefore provide a much-needed extension to existing theory on this topic. A better understanding of competitive dynamics in stochastic seasonal environments can help improve the predictability of species and community responses to ongoing changes in climate patterns and other anthropogenic challenges.

Data availability

All code, code output, and R-scripts are made available online at Dryad (https://doi.org/10.5061/dryad.8pk0p2nsq).

Author contributions

H.t.B., T.R.H., and Ø.H.O. initiated the study. H.t.B., T.R.H., and F.M. developed the models. H.t.B. and T.R.H. analyzed the models and visualized results. H.t.B. ran the simulations. Ø.H.O. reviewed the empirical literature. T.R.H. reviewed the theoretical literature and drafted the manuscript with input from all authors.

Conflict of interest: The authors declare no conflicts of interest.

Acknowledgments

The authors thank Hanna Kokko for helpful discussions, Philip Mostert for mathematical advice, and an anonymous reviewer for comments that greatly improved the manuscript. H.t.B. and T.R.H. were supported by the Swiss National Science Foundation, on grant no. 310030B_182836 awarded to Hanna Kokko. T.R.H. was additionally supported by the Forschungskredit of the University of Zurich, grant no. FK-21-122 awarded to T.R.H., and the Research Council of Norway, grant no. 313570 awarded to Jane Reid. F.M. thanks the CNRS for general support

Appendix A. Derivation of invasion fitness (Equation 2) and selection gradient (Equation 3)

Following a standard adaptive dynamics approach (Geritz et al., 1998), we assume sequential appearance of rare mutations of small phenotypic effect in populations of residents fixed for the wild type, where each mutation is assumed to go to fixation (if its invasion fitness is positive) before the next mutation occurs. Mutants are assumed to have negligible effect on ecological dynamics, such that the number of mutants N’ in a population of K residents can be derived. As in the main text, we designate respectively the resident and mutant germination strategies (fraction of seeds early) as f and f’, and probability of recruitment for an early seed is given by Equation 1. Then, the dynamics of number of mutants N’(t + 1) is given by the number of surviving mutant adults from the previous time step, N’(t)s_a, plus any mutant seedling recruitment (equation A1). As described in the main text, seedling recruitment is according to a lottery model where all seeds compete for a limited number of spaces in the adult population freed up after adult mortality; this number is (1 – s_a)K. Assuming equal yields of γ seeds per mutant and wild-type adult, the number of mutant seeds produced is N’(t) γ, and the number of resident seeds is K γ. In a year with × amount of excess dry-season rainfall their mean (averaged over small and large seeds) recruitment probabilities are, respectively, f’b(x) + 1 – f’ and fb(x) + 1 – f. Then the number of mutants in the next time step is given by

Canceling away K γ and dividing by N’(t) gives the growth rate λ of the mutant population used in Equation 2:

Differentiating the invasion fitness w(f’, f) (Equation 2) with respect to the mutant strategy f’ yields

The selection gradient is then obtained by evaluating equation A3 at f’ = f, shown in Equation 3.

References

Author notes