Seed size and dormancy are reproductive traits that interact as adaptations to environmental conditions. Here, we explore the evolution of these traits in environments that differ in overall mean favorability and in the extent of temporal predictability.
Our model simulates a population of annual plants living in a range of environments that differ in aridity, namely mean annual precipitation and inter-annual variation of this mean precipitation.
The optimal fitness curve is investigated assuming density dependence, three alternative hypothetical relationships between seed mass and seed survival in the soil (negative, positive, and independent of mass), and three alternative relationships between survival in soil and precipitation (strong and intermediate negative relationships, and no relationship).
Our results show that seed size and dormancy are not two substitutable evolutionary traits; that specific combinations of these two traits are selected in environments that differ in favorability and temporal predictability; that a certain degree of seed dormancy is advantageous not only in temporally unpredictable environments but also in temporally predictable environments with high competition; and that more than one combination of seed size and dormancy (defined in terms of germination fraction) can be optimal, even in spatially homogeneous environments, potentially allowing selection for more variation in these traits within and among species.
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It is recognized that seed traits are crucial plant adaptations that interact to optimize plant fitness under given environmental conditions (Cohen, 1966; Venable & Brown, 1988). Therefore, an attempt to understand how different environments select for specific seed traits must be based on the joint evolution of these traits. Seed size, dormancy, and dispersal are three traits that allow plants to adapt to environments that vary in their temporal and spatial heterogeneity. It has been shown that dormancy and dispersal allow spreading of the risk of encountering unfavorable conditions in time and space, respectively (Schupp & Fuentes, 1995; Wenny, 2001; Venable, 2007). In this work, we will discuss only the temporal aspects of environmental quality and predictability. Seed size is positively related to seedling growth and establishment (reviewed in Leishman et al., 2000; Moles & Westoby, 2004). However, larger seed size may be associated with a lower probability of escaping pre- and post-dispersal predation (Moegenburg, 1996; Gomez, 2004), or escaping unfavorable conditions by lower persistence in the soil seed bank (Thompson et al., 1993; Bekker et al., 1998). Larger seeds, being heavier, can also be dispersed shorter distances from the mother plant compared with smaller seeds of the same shape (Ganeshaiah & Uma Shaanker, 1991; Hedge et al., 1991; Bohrer et al. 2008). The relationship between seed size and seed persistence in the soil, in general, is negative (reviewed in Leishman et al., 2000) because large seeds are preferentially harvested by predators (e.g. Abramsky, 1983) and small seeds can more easily penetrate cracks in the soil or be washed in by rainwater and thus escape post-dispersal predation (Thompson et al., 1993; Bekker et al., 1998). This relationship, however, is not universal (Yu et al., 2007).
Joint evolution of these three traits was investigated in several theoretical studies. Venable & Lawlor (1980) and Levin et al. (1984) modeled optimal germination in response to dispersability under density-independent and density-dependent conditions, respectively, and found substitutable effects of dormancy and dispersal in a response to high temporal unpredictability. Templeton & Levin (1979) and Brown & Venable (1986) modeled joint evolution of dormancy and an abstract suit of traits determining fitness in a temporally varying environment. They came to a similar conclusion: an increase in temporal unpredictability leads to an increase in dormancy and an increase in specialization for ‘good-year conditions’. And, conversely, increasing specialization to ‘good-year conditions’ selects for a more persistent soil seed bank. In addition, Brown & Venable (1986) concluded that, under decreasing environmental favorability, selection operates on non-seed traits until a ‘seed-bank threshold’ is crossed at which point seed dormancy becomes selectively advantageous and is selected for. Venable & Brown (1988) explored the selective interaction of the three seed traits in a spatially structured and temporally varying environment under no frequency or density dependence, with patches experiencing environmental conditions independently. They found that dormancy, seed size, and dispersal have positive effects on geometric mean fitness. In other words, the optimal fitness in temporally heterogeneous environments can be achieved by an increase in either seed dormancy or seed size, and therefore these traits are substitutable to cope with environmental unpredictability. However, in their model fecundity was a function of seed size by its interaction with environmental favorability (seed size was positively related to fecundity under unfavorable conditions while the opposite was true under favorable conditions). The last relationship may not be universally true, because it ignores the positive effect of seed size on growth and establishment and, as a result, small-seeded plants will be outcompeted by large-seeded plants under favorable conditions. In this study, we revisit these conclusions and explore the evolution of seed dormancy and seed mass in temporally heterogeneous environments that differ in overall mean favorability and in predictability, as expressed by the extent of inter-annual variation.
Our model simulates a population of annual plants living in an arid environment. The model uses empirically based and realistic assumptions about the environment and its interaction with the three seed traits. Thus, in our model, environmental favorability is determined by the total seasonal precipitation; which, given the complete lack of precipitation during the dry season, is also the annual precipitation. Inter-annual variation in total annual precipitation represents temporal heterogeneity. Environments that are highly heterogeneous in time are less predictable, because in highly variable environments the information about precipitation that is available to the annual plant population in the current year is less indicative of the precipitation in the next year.
We chose an approach of optimization and sensitivity analysis. Under this approach, the mean population size after many generations of a population composed exclusively of individuals of a given trait or trait combination value(s) (i.e. of a single genotype) is considered as an indication of the genotype fitness. Thus, our model cannot simultaneously estimate the fitness of more than one genotype in a common environment, as is done in an alternative evolutionary stable strategy (ESS) approach. The ESS was previously used by Ellner (1985a,b), Rees (1994), Tielbörger & Valleriani (2005) and Satterthwaite (2010) to study the evolutionary effects of seed dormancy, and by Kobayashi & Yamamura (2000) to study those of seed dormancy and dispersal. However, the ESS approach is impractical when several axes of continuous traits are considered simultaneously. Here, we conducted a sensitivity analysis of the fitness effect of two interacting continuous traits: seed mass and seed germination fraction (i.e. dormancy). The analysis was conducted using all combinations of these two traits within the prescribed ranges under a broad range of environmental conditions. The environmental conditions were defined by the two axes – environmental favorability and its predictability. In our simulated semiarid climate conditions of the Mediterranean, these two axes corresponded to mean annual precipitation and inter-annual variation in precipitation, respectively.
For simplicity, we assume that the reproductive biomass produced by a plant is fixed (i.e. differences in yield among the plants are solely determined by seedling survival) and is converted to seed number through the inverse function of seed mass. Following Weiner et al. (2001), we assign conventional units (0–1) to measures of mass for ease of interpretation; however, these units are essentially arbitrary and should not be taken literally. This relationship between seed mass and number is independent of environmental conditions. We assume that seeds are identical in shape and therefore seed mass is equivalent to seed size. Several mechanisms of plant adaptation through seed traits, seed mass and dormancy are well accepted in the literature and are listed below as model assumptions.
Further model assumptions
Assumption 1: There is a trade-off between the number of seeds and the size of seeds produced for a given amount of available resources for reproductive allocation
A negative correlation between seed number and seed weight was detected in studies encompassing a range of life histories, habitats, and continental floras (Stevens, 1932; Primack, 1979; Shipley & Dion, 1992; Greene & Johnson, 1994; Turnbull et al., 1999; Jakobsson & Eriksson, 2000; Aarssen & Jordan, 2001; Henery & Westoby, 2001). Those studies where this relationship was estimated quantitatively found the slope not to differ significantly from −1 (Aarssen & Jordan, 2001; Henery & Westoby, 2001).
Assumption 2: Seedlings from larger seeds have a higher probability of establishment in general and under water stress conditions in particular
Larger seeds usually produce larger and more vigorous seedlings, and an advantage of seedlings originating from large seeds in establishment or survivorship was demonstrated in both species comparisons (Jurado & Westoby, 1992; Leishman & Westoby, 1994; Turnbull et al., 1999; Baraloto et al., 2005; Bruun & Ten Brink, 2008) and intraspecific studies (Lewis & Garcia, 1979; Schaal, 1980; Dolan, 1984; Stanton, 1984; Weller, 1985; Marshall, 1986; Wulff, 1986; Seiwa et al., 2002; Baraloto et al., 2005). Larger seeds usually have higher germination percentages, higher or advanced emergence from deeper sowing (Harper & Obeid, 1967; Maun & Lapierre, 1973; Schimpf, 1977; Weller, 1985; Wulff, 1986; Gulmon, 1992), and less stringent requirements for emergence with respect to litter and herbaceous cover (Gross, 1984; Winn, 1985; Facelli & Pickett, 1991; Molofsky & Augspurger, 1992; Reader, 1993; Bosy & Reader, 1995; Rebollo et al., 2001; Dalling & Hubbell, 2002).
Large-seeded species survive longer under deep shade than small-seeded species (Grime & Jeffrey, 1965; Marañon & Bartolome, 1989; Leishman & Westoby, 1994; Saverimuttu & Westoby, 1996; Westoby et al., 1996; Walters & Reich, 2000). This was attributed by Leishman & Westoby (1994) to either a larger initial energy reserve, which is advantageous in habitats where gaps in the canopy are regularly created, or the increased seedling height, which can be advantageous in habitats with a steep gradient of light such as in herbaceous vegetation or for seeds germinating below litter. Under water stress conditions, intraspecific mortality rates are higher for smaller seedlings (Cook, 1980; Parker, 1982; Wulff, 1986) and larger seed mass is predicted to be favored as a result of the greater energy reserves, which allow seedlings to produce more extensive root systems to obtain water and to better tolerate drought (Baker, 1972; Wulff, 1986; Marshall, 1986; Leishman & Westoby, 1994; Seiwa et al., 2002).
These seed-size effects on seedling growth and establishment were found to be important at the early stage of plant development (Newbery & Newman, 1978; Howell, 1981; Zimmerman & Weis, 1983; Dolan, 1984; Houssard & Escarre, 1991; Weiner et al., 1997; Tremayne & Richards, 2000; Walters & Reich, 2000; Dalling & Hubbell, 2002), and in some cases to persist beyond early establishment (Arnott, 1969; Schaal, 1980; Weis, 1982; Stanton, 1984; Ellison, 1987; Lloret et al., 1999; Simons & Johnson, 2000; Baraloto et al., 2005; Metz et al., 2010). The positive seed-size effect may not be evident under conditions of extreme hazard, for example, drought, when survival is low for all seed masses.
Assumption 3: Larger seeds have a better chance of success in competitive environments
An overwhelming majority of competition studies have reported a positive correlation between seed mass and seedling success in competitive environments, that is, that seedlings from small seeds are poorer competitors (Black, 1958; Anderson, 1971; Gross & Werner, 1982; Winn, 1985; McConnaughay & Bazzaz, 1987; Reader, 1993; Rees, 1995; Burke & Grime, 1996; Eriksson, 1999; Jakobsson & Eriksson, 2000; Leishman, 2001; Dalling & Hubbell, 2002; Turnbull et al., 2004). Seedling–seedling competition is considered to be important for vegetation dynamics in communities dominated by annual plants, that is, in communities where biomass is produced each year mostly from seeds (Leishman, 2001).
Seedlings from large seeds have a better developed root system and larger root mass and length, enabling them to reach deeper soil levels. This assumption has strong empirical support (Evans & Etherington, 1991; Jurado & Westoby, 1992; Lloret et al., 1999). In arid environments, the upper 5–10 cm of soil can dry out within 5–25 days after the first effective rain when mass germination of seeds occurs (Noy-Meir, 1973). The initial seedling size differences, associated with a difference in root system development, may allow large-seeded seedlings to survive better the initial stage of establishment after germination. High seedling mortality is known for Mediterranean and desert annual plant communities (Bartolome, 1979; Rice, 1989; Rebollo et al., 2001).
Assumption 4: Seed dormancy is independent of seed mass
This effect was empirically shown by Philippi (1993) in his study of six winter annuals. This means a lack of developmental (physiological or morphological) interdependence, but does not exclude the possibility that a selective trade-off between the two traits, such as either increased dispersal or increased dormancy, is selected for.
Assumption 5: Survival of seeds in the soil may be dependent on seed mass
Because there are conflicting views concerning the relationships between seed mass and persistence in the soil, our model tested the effects of three different relationships: negative, positive, and independent of mass.
Negative relationship – the predominant view is that small seeds have a higher probability of survival in the soil because of a positive correlation between seed mass and risk of seed predation (Mitchell, 1975; Davidson, 1977; Nelson & Chew, 1977; Chew & De Vita, 1980; Abramsky, 1983; Nelson & Johnson, 1983; Napela & Grissell, 1993; Reader, 1993; Fox & Mousseau, 1995; Moegenburg, 1996; Hulme, 1998; Gomez, 2004; Azcárate & Peco, 2006; Traba et al., 2006). Lower post-dispersal survivorship of large, as compared with small, seeds is expected because large seeds are more likely to be discovered by predators because they are more apparent (Feeny, 1976) and have a lower chance of penetrating into the soil profile (Van Tooren, 1988; Chambers et al., 1991; Thompson et al., 1993; Bekker et al., 1998; Hölzel & Otte, 2004). A decrease in seed size was shown in several studies to be an evolutionary response to herbivory (Smith, 1970; Davidson et al., 1985; Gomez, 2004). A strong negative correlation between seed mass and seed longevity in the soil, independent of phylogeny and of any relationship with life history, was reported by Hodkinson et al. (1998). Although a negative correlation between seed size and persistence in soil may not hold universally (Yu et al., 2007), it was clearly shown to be the case in a study of the Mojave Desert flora of California (Price & Joyner, 1997), the closest analog to the environmental conditions modeled here.
Positive relationship – a positive correlation between seed mass and persistence may apply to environmental conditions and ecosystems where pathogen infestation, which is more detrimental for small seeds, outweighs an effect of seed predation by rodents and birds (Yu et al., 2007). This can also be the case when seed mass is associated with ease of manipulation (e.g. with thickness of seed cover structures such as the endocarp or testa) (Lee et al., 1991; Blate et al., 1998). In this case, the larger the seeds the longer the time that is needed to reach the edible part of the seed (Kaufman & Collier, 1981; Alcántara et al., 2000)
No relationship – as an intermediate alternative, we also tested a scenario under which seed survival in the soil is independent of the seed mass. Such a scenario may, for example, apply to situations in which seeds have tough seed coats and therefore small seeds survive the conditions in the soil as well as large ones, or contain features making them unpalatable or poisonous, and therefore avoid seed predation (Kollmann et al., 1998).
Assumption 6: Survival of seeds in the soil may be affected by soil moisture
As very little quantitative information is available about these relationships, we tested two alternatives.
Negative relationship – survival in the soil is inversely proportional to soil moisture. Survival is maximal when the soil is dry during years with no precipitation and decreases with increases in precipitation and soil moisture. High soil moisture creates conditions favorable for soil fungi and bacteria, thus increasing the chance of seed infestation (Mickelson & Grey, 2006).
No relationship – the negative effect of soil moisture on seed survival in the soil can be reduced or avoided by a seed if it possesses a hard impermeable coat. Therefore, as a null hypothesis, we also tested a scenario in which seed persistence in the soil is independent of precipitation amount.
Our model is based on the approach of Cohen (1966), subsequently used by Brown & Venable (1986) and Venable & Brown (1988). The model describes the population fitness of an annual plant species in terms of the geometric mean of its population size over the last 9000 yr of a 10 000-yr simulation experiment. At any annual time-step, t, the model calculates the total number of seeds in a population just before the start of the next growing season, Nt+1, that is, the number of seeds that will be available after seed production, distribution, and mortality before germination.
where the evolutionary traits being tested are G, the fraction of the seed bank that germinates each year, and M, the seed mass. The variable environmental forcing is represented by the mean annual precipitation, μ [P], and its standard deviation, σ[P]. We ran simulations for each combination of G and M values within a relevant range under each of the ranges of mean annual precipitation regimes with each of the standard deviation levels. The values we used for all parameters in the simulations described here, following the formulation detailed below (equations 2-5), are presented in Table 1. Nt is the current seed population size, V is the survival fraction in the soil, S is seedling survival after germination and Y is fecundity. These three variables are functions of G, M, Nt and the actual annual precipitation in each year, Pt, as follows:
Table 1. Variable symbols and parameter values used in simulations
Shape parameter for precipitation and size-dependent seedling survival
Shape parameter for size–survival in soil relationship
Maximal fecundity in seed mass units
Shape parameter for precipitation and size-dependent seedling survival
Shape parameter for size–survival in soil relationship
Shape parameter for density dependence of survival to maturity
Scale parameter for precipitation and size-dependent seedling survival
Proportionality coefficient for the effect of precipitation (soil moisture) on survival in soil
0 – no effect 0.003 – intermediate 0.004 – strong
Shape parameter for density dependence of survival to maturity
Shape parameter for precipitation and size-dependent seedling survival
Annual germination fraction
0.02 : 1
Sign of survival-in-soil and seed mass relationship
Autocorrelation time-scale of random precipitation time series
0.02 : 1 [arbitrary units]
Number of seeds in the current population
[number of seeds]
Number of seeds after annual seed production
[number of seeds]
Vector of autocorrelated actual annual precipitation rates
2, 3, 5
Actual annual precipitation
Vector uniform random numbers
1 : 10 000 [yr]
Survival fraction of seeds in the soil
Maximal annual survival in soil
Number of seeds produced by a germinated seed (fecundity)
Number of seeds
Vector of random autocorrelated values
Kronecker delta for size-dependent or -independent survival in soil
0 – size-independent 1 – size-dependent
Mean annual precipitation
100 : 280 [mm]
Mean of random vector (for normalization)
Inter-annual standard deviation of precipitation
0 : 40 [mm]
Standard deviation of random vector (for normalization)
V, the survival fraction of seeds in the soil:
V is a sigmoid-shaped survival function which is dependent on seed mass, M, with two empirical shape parameters, av and bv. Vmax represents the maximal mean survival-in-soil rate under favorable conditions; av and bv were parameterized such that the inflection point of the sigmoid will be around the median seed mass (Fig. 1). cv is a parameter describing the sensitivity of survival-in-soil to annual precipitation, Pt. cv was set to 0.004 or 0.003 in the set of tests that assumed a negative effect of soil moisture on survival in soil, and 0 in the set of tests that did not include this effect. Setting cv to values larger than 0.004 led to almost complete mortality of the seeds in the soil under the ranges of precipitation amounts in our model. δPN is a Kronecker delta and used as a switch: δPN = 1 when the modeled relationship between seed survival in the soil and seed mass is either positive or negative (as detailed in assumption 5) and δPN = 0 for an independent relationship, in which case the function (Eqn (Eqn 2)) is reduced to V = Vmax − cvPt. In these independent cases, we tested three different fixed mean survival rates in the soil: Vmax = 0.1, 0.5 and 0.9. The formulation is further reduced to V = Vmax when there is no dependence on soil moisture (i.e. cv = 0). We used Vmax = 0.9 in that case. IPV is a sign function that corresponds to the type of relationship between mass and survival-in-soil: it is +1 for the case of a negative relationship and −1 for a positive relationship (Fig. 1).
S, seedling survival:
The survival function describes a precipitation, Pt (subscript t indicates a specific year), and a seed mass, M, dependent Weibull function with four empirical shape and scale parameters, aS, bS, cS, and dS, which were parameterized such that the shape of the survival curve will correspond to observations on seedling survival of two annual grasses, Avena sterilis and Hordeum spontaneum, in semi-arid and desert conditions (S. Volis, unpublished) and the range will fit the arbitrary mass units. This parameterization allows spanning of the full range of possible values by changing only M while keeping the shape parameters constant (Fig. 2a).
Y, the number of seeds produced by a germinated seed (fecundity):
Y describes a density-dependent and seed size-dependent yield function of seedlings, which includes both the probability of the seedling survival to maturity and their seed production, where M is seed mass. ay is an empirical coefficient for the maximal fecundity (per unit seed mass) and by and cy are shape parameters for the density and size dependence of young plants’ survival to reproductive maturity (Fig. 2b).
[P] is a random vector of actual annual precipitation rates in all years composed of elements, Pt, of the precipitation in each particular year, t. [T] is a vector of all years (1:10 000). The precipitation is calculated as an autocorrelated time series with a random phase, prescribed autocorrelation time, L (2 yr in this case), and prescribed mean and standard deviation. [R] is a vector of 10 000 uniform random numbers. [λ] is a resulting vector of random autocorrelated values (Bohrer et al., 2007). [λ] (in arbitrary units) is converted to precipitation with a prescribed mean and standard deviation (μ[P] and σ[P], respectively, in mm yr−1) by normalizing it against its own mean and standard deviation (μ[λ] and σ[λ], respectively).
Results and Discussion
Independence of seed survival in the soil from seed mass
When seed survival in the soil is high (90%), large seeds (M > 0.8) with little dormancy (G = 0.86) are selected for, except for a situation with low and highly variable precipitation: μ[P] = 100; σ[P] = 40 (Fig. 3, lower panel). In this harsh and temporally variable environment, seed dormancy is selected for (G = 0.25), but large seeds still have an advantage over small ones. With increases in environmental favorability, in terms of higher precipitation and soil moisture with lower variability (μ[P] = 220–280; σ[P] = 0–20), a second optimal peak arises and approaches in magnitude the peak for large seeds with no dormancy. This peak is characterized by small seeds and little dormancy (G = 0.92) (Fig. 3, bottom panel).
An intermediate rate of seed mortality in the soil (0.5) results in similar trends for seed mass and dormancy, but the magnitude of the second peak under favorable conditions is always lower than that of the large seeds with little dormancy (Fig. 3, middle panel). However, that secondary peak for small seeds is more pronounced, indicating a faster reduction in the trait advantage around the peak itself, with less advantage to intermediate forms between the two maxima.
Under low seed survival in the soil (Vmax = 0.1), a single optimum exists in all the environments. Large seeds (M > 0.8) with no dormancy are selected for, except for a situation with low and highly variable precipitation: μ[P] = 100; σ[P] = 40 (Fig. 3, upper panel). Under these conditions, the optimal strategy is a combination of intermediate seed mass, M = 0.6, and germination fraction, G = 0.7.
Negative relationship between seed mass and survival in the soil
Under no temporal variation, harsh environmental conditions (i.e., a persistently low amount of precipitation: μ[P] = 100–120; σ[P] = 0–10) select for increased seed mass and a high germination fraction (Fig. 4, lower panel). However, with increased precipitation μ[P] ≥ 160, production of small seeds becomes a secondary optimal (or near-optimal) strategy. In this environment, the competitive advantage of large seeds over small ones is partially offset by their reduced survival in the soil. The competitive disadvantage of small seeds can be further compensated for by producing greater seed numbers. Because the effect of density dependence becomes stronger in more favorable environments, the contribution of seeds remaining ungerminated in the soil seed bank and avoiding competition by delaying germination to a less favorable year becomes more important (Fig. 4, lower panel).
Temporal unpredictability (i.e., inter-annual variation in precipitation) selects for a decrease in seed mass and stronger dormancy (i.e. a decrease in the germination fraction) as compared with a constant environment with a single optimum. However, these effects can be observed only when the environment is stressful. In environments where precipitation is not strongly limiting survival (in our model, these conditions correspond to precipitation of > 140 mm yr−1), the effects of decreased predictability are negligible.
One important difference between the results with negative relationships between seed mass and survival in the soil (Fig. 4, lower panel) and the scenario in which survival in the soil does not depend on seed mass (Fig. 3) is the lack of the secondary optimal peak for small seeds in the latter scenario, even in environments with high uniform survival in the soil and high precipitation. Another important difference is that harsh environmental conditions (low precipitation and high variability) with uniform survival select for larger seeds (M = 0.6–1.0, depending on the uniform survival rate), while conditions with a negative seed size–survival in soil relationship favor small to intermediate seed masses (M = 0.3–0.4).
Positive relationship between seed mass and survival in the soil
When small seeds have a lower probability of survival in the soil than large ones, large seeds are always selected (Fig. 4, upper panel). The optimal germination fraction in a temporally invariant environment is G =0.86, but when the amount of precipitation is low (100 mm or lower in our model), variation in precipitation selects for seed dormancy. Thus, an optimal strategy in a harsh and unpredictable environment is large seeds with a low germination fraction, 0.23 < G < 0.41 when μ[P] = 100 and 20 ≤ σ[P] ≤ 40. This outcome may apply to a situation in which large seeds are preferentially harvested but not consumed, and have higher survival in the new places of storage (Mark & Olesen, 1996; Bas et al., 2009). For example, many seeds possess adaptations for ant dispersal, and burial by ants provides seeds with a nutrient-rich environment and protects them from surface-foraging predators and lethal temperatures during fire (Espadaler & Gomez, 1996; Christian & Stanton, 2004; Garrido et al., 2009).
The most important difference between the outcomes of the negative and positive relationships between seed mass and persistence in the soil is that small seeds with high dormancy are strongly suboptimal in all cases under the latter hypothetical relationship. While a single optimal peak is observed under the full range of precipitation and predictability for the positive relationship, for the negative relationship, there is a broad range of possible trait combinations that are similar in fitness under almost the full range of precipitation and predictability (Fig. 4).
Negative relationship between seed survival in soil and soil moisture
When soil moisture has an effect on survival of seeds in the soil seed bank, selection is acting against delayed germination (Fig. 5). Therefore, a germination fraction G < 0.8 can be optimal only if the effect of soil moisture is greatly reduced, that is in xeric environments with low annual precipitation and intermediate to high inter-annual variation in precipitation. In this environment, delayed germination was selected for under both positive and negative relationships between seed mass and survival in the soil, and the optimal seed mass corresponded to whether larger or smaller seeds had higher survival in the soil. Under all other environmental conditions, a negative dependence between seed mass and survival in the soil led to a single optimal strategy of large seeds with no dormancy (Fig. 5). This is surprising because, with no dormancy, there should not be an effect of seed mortality in the soil. This is indeed the case (Fig. 6). Under a negative effect of precipitation on survival in the soil, increased mortality in the soil in wet years negates the advantage of small seeds with dormancy. Therefore, with higher mortality in the soil, the optimal trait combination becomes unimodal favoring large seed mass. A high germination fraction is selected for under all environmental conditions except the most limiting and unpredictable ones.
These results show that, in xeric temporally fluctuating environments, a strategy in which some seeds enter the soil seed bank is always advantageous, and the optimal seed mass depends on the importance of seed predation and/or infestation, the presence of a hard seed coat, etc. In a species having seeds that are not subjected to predation because of some biological features or because the granivorous species are absent in the environment they occupy, large seeds are selected. However, if these conditions are not met, a decrease in seed mass becomes important for seed escape from predation. Species having small seeds with no special adaptations to persist in the soil bank can be highly successful in xeric (desert) environments, because even seeds without hard coats can be well preserved in dry soil.
In Mediterranean conditions where soil moisture is less limiting and conditions are more predictable, some degree of dormancy can still be advantageous if seeds are well protected from the effects of high soil moisture, that is, have a hard impermeable coat. If predation is strong, species having small seeds with or without dormancy can be as successful as species with large nondormant seeds, but only if they have features allowing tolerance of high soil moisture.
In our study, we investigated how the optimal combination(s) of two seed traits, dormancy and size, evolves along the aridity gradient, which is characterized by two parameters, the amount of annual precipitation and its inter-annual variation. In our simulations, we tried to embrace a variety of interactions, both biotic and abiotic, between seeds and environment. The complexity of the results produced can be summarized as the following key findings (Fig. 7).
Α low amount of precipitation selects for dormancy, but only when precipitation fluctuates greatly from year to year. When precipitation is low and temporally predictable, dormancy is always selected against. Under high precipitation, a high (but not 100%) germination fraction is selected for regardless of inter-annual fluctuations in precipitation amount.
Optimal seed mass depends on a relationship between seed mass and soil moisture, and susceptibility to seed predation and infestation, in addition to the amount and predictability of rainfall. Either only large or both small and large seeds can be optimal or nearly optimal under high precipitation regardless of the magnitude of inter-annual fluctuations in precipitation. Environments with constantly low precipitation always select for large seeds, while under low and highly fluctuating precipitation, either small or large seeds can be optimal (Fig. 6).
In productive environments, that is those with high precipitation, bimodality is often observed (Fig. 6) with optimal peaks being flat and resembling a plateau, while in low-productivity environments the peak is always single and narrow.
In this study, we simulated simplistic environmental conditions while preserving a natural range of two critical environmental properties, the mean and variability of annual precipitation, representing a gradient of aridity from xeric desert to more mesic Mediterranean climates. The typical Mediterranean climate is characterized by rainy winters when annual vegetation sprouts, and long dry summers when annual vegetation is present only in the soil seed banks. The inter-annual precipitation variability and probability of reproductive failure increase along the gradient of aridity. Several of our findings correspond well with those of experimental studies conducted in this region. The prediction that small seed mass will be optimal under conditions of low precipitation, low predictability and a negative relationship between seed mass and survival in the soil (or constant and low survival in the soil) (Fig. 3, upper panel; Fig 4, lower panel) was observed in a comparative study by Harel et al. (2011) and in two annual grasses (Volis, 2007, 2012). The latter two species also demonstrated a positive relationship between germination fraction and precipitation predictability at the population location (Volis et al., 2002, 2004; Volis, 2009; Fig. 6).
Our study does not only provide theoretical support for already known phenomena. In a previous model analyzing the evolution of seed traits in temporally varying environments, seed mass and dormancy were found to be substitutable traits (Venable & Brown, 1988). The results of our model suggest the opposite; that is, that there is an interaction between these two traits and this interaction is environment-dependent. Specifically, under different environmental favorability and temporal predictability, different combinations of seed mass and dormancy are selected. Our results also show that several combinations of seed traits (i.e. seeds of a range of sizes with low and high germination fractions) can be optimal or near-optimal in a given spatially homogeneous environment when temporal heterogeneity is considered. These results are in contrast with several ESS models that simulate germination rates in spatially homogeneous environments with density dependence (Bulmer, 1984; Ellner, 1985a,b). At the same time, our results support the hypothesis that some level of seed dormancy is selected for even in temporally constant environments with population density at the equilibrium via a reduction of competition among siblings by spreading their germination over time (Ellner, 1986). In our model and those of others, such as the model of Nilsson et al. (1994), density dependence was introduced through symmetric competition of a single genetically identical cohort. Therefore, sib-competition could not be distinguished from generalized intraspecific competition. However, because genetic relatedness was irrelevant in our and Nilsson et al.'s (1994) simulations, generalized competition appears to be a reasonable interpretation of the observed phenomenon. Delayed germination reduces competition among intraspecific cohorts and not exclusively among siblings. Similarly, generalized competition was suggested to be a more realistic natural phenomenon than sib-completion in several recent theoretical and empirical studies (Tielbörger & Valleriani, 2005; Lalonde & Roitberg, 2006; Satterthwaite, 2010; Eberhart & Tielbörger, 2012).
Although we use an overly simplistic representation of the environment and the phenotypic trait space, our model provides quantitative predictions about a range of seed mass and germination fractions optimal under specific environmental conditions, and the results apply to both intraspecific processes such as evolution of life history traits, and to inter-specific processes such as community structure and species coexistence. In particular, we found that harsh environmental conditions of low precipitation and/or increased mortality rates in the soil allow only a single optimal combination of the two traits’ values, thus strongly limiting the potential number of coexisting species. As the favorability of the environment increases, as a function of both an increased amount of precipitation and reduced temporal variation in precipitation, the choice of optimal values for the two-trait combinations becomes wider. This could potentially allow more species to co-exist, and select for more phenotypic plasticity within species.
The role of differential seed size in promoting species coexistence was predicted by several game models (Geritz, 1995; Rees & Westoby, 1997; Geritz et al., 1999), but received no empirical support (Eriksson, 2005). While our model did not directly test multi-species systems, the simulation results provide further details about the conditions under which larger and smaller seeded species may coexist. Cases that showed a clear bimodal solution may indicate not only such natural phenomena as seed dimorphism (i.e. production of both large and small seeds) but also conditions under which specialization leading to the creation of two distinct co-optimal species is possible. We found that this state of multiple co-optimal trait combinations is expected in productive environments, and in situations in which there is either a negative relationship between seed mass and survival in the soil or high survival of seeds in the soil independent of seed mass. Thus, our results indicate that seed survival in the soil can be important for the coexistence of large and small seed size strategies in a given environment.
The results reconcile two alternative explanations for the selective role of seed dormancy and the presence of the soil seed bank, that is, bet-hedging and reduced competition. It is evident from the results that both processes took place but under different environmental conditions. Bet-hedging operates and causes a decrease in the germination fraction when environmental favorability is low and temporal unpredictability is high, while escape from local crowding through dormancy becomes important when the environment is favorable and therefore competition is strong.
The work was funded in part by grant #10R-05 from the International Arid Land Consortium Project to S.V. and G.B., and NSF grant #DEB-0918869 to G.B. Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We are grateful to Ashley Matheny for editing the manuscript, and Dan Cohen and Benoit Pugol for helpful comments on an early version of the manuscript.