On selection for flowering time plasticity in response to density

Research On selection for flowering time plasticity in response to density Peter J. Vermeulen Centre for Crop Systems Analysis, Wageningen University, PO Box 430, 6700 AK, Wageningen, the Netherlands Author for correspondence: Peter J. Vermeulen Tel: +31 0317 484448 Email: peter1.vermeulen@wur.nl Received: 22 May 2014 Accepted: 10 July 2014 doi: 10.1111/nph.12984 Key words: density, evolutionarily stable strategy, flowering, game theory, optimization, plasticity, season length, selection. Summary Different genotypes often exhibit opposite plastic responses in the timing of the onset of flowering with increasing plant density. In experimental studies, selection for accelerated flowering is generally found. By contrast, game theoretical studies predict that there should be selection for delayed flowering when competition increases. Combining different optimality criteria, the conditions under which accelerated or delayed flowering in response to density would be selected for are analysed with a logistic growth simulation model. To maximize seed production at the whole-stand level (simple optimization), selection should lead to accelerated flowering at high plant density, unless very short growing seasons select for similar onset of flowering at all densities. By contrast, selection of relative individual fitness will lead to delayed flowering when season length is long and/or growth rates are high. These different results give a potential explanation for the observed differences in direction of the plastic responses within and between species, including homeostasis, as a result of the effect of the variation in season length on the benefits of delayed flowering. This suggests that limited plasticity can evolve without the costs and limits that are currently thought to constrain the evolution of plasticity. Introduction Plastic responses allow plants to adjust their phenotypes to different environmental conditions (Via & Lande, 1985; Sultan, 2000). Given these potential benefits of plasticity, a major question in evolutionary ecology is why different levels of plasticity, including stasis, exist among and within species. Several costs and limits have been proposed that may constrain the evolution of plasticity (DeWitt et al., 1998; van Kleunen & Fischer, 2005). The general focus has been on the costs of plasticity, and how these potentially can lead to a benefit of homeostasis (see van Kleunen et al., 2007; Sultan, 2009). However, such costs of plasticity are also thought to be generally low (Van Buskirk & Steiner, 2009; Maherali et al., 2010), and Sultan & Spencer (2002) have shown that, in a meta-population structure, plasticity can evolve even when the response does not lead to the optimal phenotype in each condition. Hence, there is still uncertainty about the selective forces that may constrain the evolution of plasticity. Here, I show that, for the onset of flowering, variation in population density itself may select for low levels of plasticity, including stasis, and even for selection in opposite directions, depending on the way in which selection is assumed to operate. The time of the onset of flowering (here defined as the flowering time) is an important trait for plants, as different components of their fitness are affected by the timing of the switch from vegetative to reproductive investment; thus, this timing can be expected to be under strong selection (Donohue et al., 2001; Hall & Willis, 2006; Franks et al., 2007; Anderson et al., 2012; Mendez-Vigo et al., 2013). In turn, such timing should be strongly influenced by season length, for instance as a result of changing latitude (Colautti & Barrett, 2010). Likewise, heterogeneous conditions may alter the selection pressure on flowering, and therefore plasticity in flowering time may be of great importance to maximize the fitness over different spatial or temporal scales (Amir & Cohen, 1990; Haggerty & Galloway, 2011; Quilot-Turion et al., 2013) or to allow for adaptation to novel environments (Levin, 2009). For instance, studies of several plant species have reported that there is selection for plasticity in flowering time in response to an increase in density (Thomas & Bazzaz, 1993; Donohue et al., 2000; Weinig et al., 2006). Interestingly, these studies show that genotypes differ in the level and direction of plastic responses to changing plant population density (i.e. number of plants per unit area). If all of these responses are adaptive to changes in density in the native environments of these different genotypes, this suggests that there may be different selection pressures that select for different plasticity in flowering times. One prediction is that, in competitive settings, direct selection should favour individuals that accelerate flowering in the face of increasingly scarce light resources (Callahan & Pigliucci, 2002). Indeed, as density increases, the available light per individual plant decreases. If flowering is an adaptive shade avoidance strategy to ensure that seed production occurs before light levels become too low (see Smith & Whitelam, 1997; Botto & Smith, 1

2 Research New Phytologist 2002), the signal to flower would arrive earlier at high density. This would select for flowering at smaller size at the individual plant level, and plants would need less time to reach that size with time. This, in turn, could explain the selection on earlier flowering found in the above-mentioned studies when density increases. It would also mean that plants with a higher growth rate can reach this optimal size sooner, and are thus predicted to flower earlier (also see results of Colautti & Barrett, 2010). However, competition for resources between individual plants is also predicted to lead to selection on increased investment in the resource-acquiring organs. This is because it would lead to a higher resource capture by the individual plant, conferring an advantage relative to its competitors. This would allow this individual to invade and to pass on its trait value to the next generation, allowing this larger trait value to increase in frequency. Over time, plants exhibiting this trait value will completely exclude the original resident population, until all individuals have the same, but raised, level of investment in resource-harvesting organs; hence, the initial advantage for the individual plant with this raised organ investment is lost. Then, this process of invasion and trait replacement could start again, until a stage is reached at which a further investment in the resourceacquiring organs has become too costly (see reviews of Falster & Westoby, 2003; McNickle & Dybzinski, 2013). Evolutionarily, game theory allows for the analyses of such invasion and replacement processes to determine its endpoint, called an Evolutionarily Stable State (ESS; Maynard Smith, 1982; see also Nowak & Sigmund, 2004). This endpoint is often predicted to be away from the optimal trait value at the stand level; that is, the optimization of the relative fitness of directly competing individuals can be proven mathematically to lead to different stand performance than the optimization of stand level performance (see review of Anten & During, 2011). Theoretically, examples of such aboveground competitive outcomes include increased height growth (Givnish, 1982; Iwasa et al., 1985; Falster & Westoby, 2003), increased specific leaf area (a tradeoff between light capture (m 2 ) and photosynthetic rate per unit area (mol m 2 ); see Schieving & Poorter, 1999; Anten & Hirose, 2001), leaf angle (shifting to more light capturing horizontal angles; Hikosaka & Hirose, 1997) and accelerated leaf turnover (Boonman et al., 2006). The shift from full vegetative investment to investment in reproduction is another well-known example. This is a result of the trade-off between the time it takes to reach the size that maximizes net photosynthetic rate that could subsequently be used for seed production, and the time that is left until the end of the season (or time of death). Hence, using simple optimization theory, Cohen (1971) and Iwasa (2000) showed that, when the growing season length is fixed, there exists an optimal strategy to invest all net photosynthesis into new vegetative mass, and subsequently plants should make a clear switch to full investment in reproductive mass. This optimum flowering time occurs as a result of a trade-off between the time it takes to reach the size that maximizes the net photosynthetic rate that could subsequently be used for seed production, and the time that is left until the end of the season. Consequently, the shorter the season, the earlier plants are predicted to flower. Similarly, the faster the plants reach the optimal size, the earlier they should flower. Using game theory, however, Vincent & Brown (1984) first showed that, when individual plants are competing for light, there should be selection for later flowering plants compared with the flowering time of plants that optimize seeds at the population or canopy level (see also Kawecki, 1993; Pronk et al., 2007). This leads to selection towards an ESS, where the whole population is flowering later than is optimal for seed production at the whole-stand level. To understand how an increase in density will affect the predicted optimal plastic response, it is important to realize the degree to which this selection away from the trait values that optimize the stand-level performance depends on the level of interaction between individuals. Game theoretical analyses show that the selection on overinvestment in resource-acquiring organs compared with stand-level optimization increases with the degree to which plants interact with non-self neighbours (see Vincent & Brown, 1984; Hikosaka & Hirose, 1997; Schieving & Poorter, 1999; Anten, 2002). This means that growth form and neighbour relatedness may influence the predicted trait value. For instance, plants that compete mostly with self, such as phalanx clonal species (Schmid & Bazzaz, 1994; Anten, 2005; Semchenko et al., 2007), or vegetation under the influence of kin selection, will have trait values that are close to those predicted to optimize stand-level production (Anten & During, 2011). In these stands, an increase in density has less influence on the change in selection pressure. However, for plants that compete strongly with neighbours, such as annual outcrossing plants, density will increase the influence of other competing individuals on the individual plant s performance; thus, in the latter stands, there should be a stronger selection for delayed flowering compared with the flowering time that would optimize stand-level investment in reproduction with increasing density. When one then defines the optimal plastic response as the response that leads to an ESS in flowering time at all densities, this means that there are two opposing selection forces when density increases: (1) direct selection for accelerated flowering as a result of decreased light availability per individual plant; and (2) indirect selection for delayed flowering compared with this optimal flowering time at the whole-field level as a result of increased competitive interactions, the strength of which can depend on the growth form. The combination of these two opposing selection forces leads to the following hypotheses: (1) when plants are selected to optimize performance at the stand level, there should always be selection towards accelerated flowering with increasing density; and (2) when there is selection on the individual plant to maximize its seed production, the level of plasticity of natural vegetation in response to density and, in the most extreme cases, even the direction of this plasticity (i.e. accelerated or delayed flowering) will depend on the balance between selection caused by reduced light availability per plant per se and selection as a result of the competitive interactions. As a special case, one could even imagine a scenario in which the ESS for flowering time at high density is very similar to the ESS for flowering time at low density. This

New Phytologist Research 3 latter case would indicate that there are conditions under which there would be selection for very weak or even no plasticity (i.e. homeostasis). Here, I have developed a simulation model based on logistic growth to analyse the conditions under which the abovementioned predictions may hold true. My objectives were to analyse: (1) when selection for maximum seed production at the stand level should lead to accelerated flowering at high density; (2) when selection as a result of competitive interactions may lead to selection for stasis in response to density, and when it may lead to a delayed flowering response; and (3) how changes in season length and growth rate affect these outcomes. Description Model assumptions The model follows most assumptions made by Cohen (1971) and Vincent & Brown (1984). It assumes that the combination of growth rate and season length is such that the production of more than one generation within a growing season is not possible. In addition, because the focus is on showing how selection on competitive traits works opposite to selection on resource availability per plant, the model assumes that season length is a constant (hence its effects are analysed through a sensitivity analysis), and the switch from vegetative to reproductive investment is assumed to be absolute (a so-called bang-bang strategy, i.e. at flowering time, the plant switches from 100% vegetative investment to 100% reproductive investment; see the Discussion section). Furthermore, flowering time is defined as the time at which the plant starts to allocate all of its net photosynthetic rate to reproduction, that is the onset of flowering. Hence, the costs of flowers and other structures to produce seeds are reflected in the total reproductive investment. This, in turn, means that plants are implicitly assumed to directly produce seeds from the time at which they start to flower, and that the net photosynthetic rate during seed production is directly related to size at flowering. Model description To date, the optimal plastic response has been defined as the difference between the trait values that maximize fitness in two different conditions, without considering direct competitive effects of competing neighbours, for instance, for resources (van Tienderen, 1991; Sultan & Spencer, 2002). Models based on this definition can be considered to be density independent (sensu Parker & Smith, 1990). In the model presented here, density has an effect on the performance, but in only one of the two scenarios does this result in a frequency-dependent model. The first scenario assumes that selection is equal to the optimization of stand-level seed production (from now on defined as stand-level selection, So). Here, the model is a frequency-independent model because all individual plants in the stand are assumed to have the same trait (or strategy). The second scenario assumes that there is selection for the individual plant to reach a higher fitness relative to its neighbours (here called the game theoretical model, Gt). Thus, this second scenario model becomes frequency dependent, as the fate of a mutant with a change in flowering time invading the vegetation depends on the fraction of shading by the resident neighbouring plants. Fitness (F) is assumed to be equal to the total investment in reproduction S of a focal plant, as a function of the flowering time of the focal plant (Ft_f, in d), the flowering time of the rest of the vegetation (Ft_r, in d), the plant density (D, in number of individuals per m 2 soil surface) and the season length (Ts, in d): F ¼ SðFt f ; Ft r; D; TsÞ Eqn 1 The flowering time Ft determines both the amount of time plants have to grow leaf area for photosynthesis (vegetative growth from time t = 0toFt) and the remaining period that is available for plants to produce seeds (from Ft to Ts). In their frequencydependent model, Vincent & Brown (1984) used an exponential growth function to model vegetative growth to keep the system analytically solvable. This would, however, give greater benefit to delayed flowering, as an ever greater size would lead to increasingly higher net photosynthetic rates. This, in turn, would increase the chance of confirming hypothesis 2. In reality, the increase in shading caused by selection for increased leaf area will, at some point, lead to a decrease in net photosynthetic rate (see also Fig. 1a,b), as it eventually entails self-shading, and hence to a decrease in the benefit of further delaying flowering time. Therefore, the simulation model here is based on logistic growth (see also discussion in Paine et al., 2012), using a forward Euler method to calculate the potential reproductive investment at each time step. The model is based on the classic Monsi & Saeki (1953) equation for light extinction in a canopy: P net ðtþ ¼L ue I o ð1 e^ð k LAIðtÞÞÞ C l LAIðtÞ Eqn 2 (P net (t), rate of net photosynthesis at time t (CO 2 m 2 soil surface s 1 ); k, light extinction coefficient; LAI(t), leaf area index (m 2 leaf m 2 ground surface) at time t; C l, cost of maintaining a unit of leaf area (lmol m 2 s 1 )). L ue can be seen as a conversion of captured light to gross photosynthesis, that is, the light use efficiency (lmol C lmol 1 intercepted photons). I o is the light intensity above the canopy (lmol photons m 2 s 1 ). The model focuses on a focal individual plant f, with a leaf area at time t = 0 that is equal to a set starting leaf area per individual (LAI fo ;m 2 m 2 ). The leaf area at t = 0 of the other plants is then set as: ðlai ro Þ¼ðD l ÞLAI fo Eqn 3 It should be noted that D represents the number of individuals whose leaf area occupies the same area of ground surface. Hence, a change in the absolute numbers represents the change in the number of individuals that are directly competing for light per m 2 of soil area. Following Eqn 2, the rate of net photosynthesis at time t for the focal plant then becomes:

4 Research New Phytologist (a) (c) (b) (d) Fig. 1 Modelled outcomes for a focal plant at low density (LD; one plant m 2, blue line) and high density (HD; four plants m 2, green line) for a season length of 180 d and light use efficiency set at 0.020. (a) The development of the leaf area index (LAI) per individual plant through time; (b) the development of the net photosynthetic rate (P net ) per individual plant through time; (c) the total seed investment per plant over the season, where t is the onset of flowering; (d) the change in seed production (dseeds), compared with the resident population that flowers at time t, if the mutant flowers on t+ a small delay (t + dt). The Evolutionarily Stable Strategy is represented by the intersection of the lines with y = 0. In (c) and (d), the semi-circles indicate the optimum values, and the level of plasticity that should be selected for is represented by the difference between these two points. P net f ðt Þ¼LAI f ðt Þ=ðLAI sðt ÞÞ b ð1 e^ð k LAI sðt ÞÞÞ C l LAI f ðt Þ Eqn 4 where b = L ue 9I o and LAI_s(t) is the sum of the LAI of the focal plant (LAI_f (t)) and the LAI of the rest of the plants with which the focal plant is competing at time t (LAI_r(t)). P net of the rest of the individuals (P net_r (t)) can be found by replacing LAI_f (t) with LAI_r(t). When t is not yet the flowering time Ft, P net (t) is used to produce additional leaf area. A forward Euler method is used to calculate the leaf area that is added at each time step (LAI 0 (t)) if the switch to full investment in reproduction has not been made: LAI 0 ðtþ ¼ðP net ðt Þ=C LAI Þdt Eqn 5 Here, dt is the length of the time step. C LAI is the cost of producing new leaf area (lmol C m 2 leaf area), as determined by the specific leaf area (SLA, m 2 leaf g 1 leaf), the allocation of mass towards the leaves (F la ) and the investment needed to produce 1 g of leaf, determined by the leaf carbon content (Lf c ; lmol C g 1 leaf) and the cost to build 1 g of leaf carbon (C built ; lmol C g 1 C): C LAI ¼ F la ðlf c C built þ Lf c Þ1=SLA Eqn 6 The production of new leaf area at time t for the focal plant (LAI_f 0 (t)) or that of the rest of the vegetation (LAI_r 0 (t)) can be found using Eqn 5: LAI f 0 ðtþ ¼ðP net f ðtþ=c LAI Þdt Eqn 5(a) LAI r 0 ðtþ ¼ðP net r ðt Þ=C LAI Þdt Eqn 5(b) If Ft < t Ts, P net (t) is used for reproductive investment. Thus, over the time interval dt, this investment for the focal plant (S_f ) is: S f ðt Þ¼P net f ðt Þdt Eqn 7 Hence, total investment in reproduction can be found as the summation over each time step for the onset of flowering until the season ends: SðFt f ; Ft r; D; TsÞ ¼ X Ts Ft f S f ðtþ Eqn 8 Optimization criteria The simple optimization approach (So) assumes that the vegetation can be treated as one unit (see Anten, 2005). Hence, Ft_f = Ft_r. To find the flowering time that maximizes the total seed production of the whole vegetation (Ft s ), one has to solve: @SðFt r; Ft r; D; TsÞ=@Ft r ¼ 0 which is numerically found by solving: Eqn 9(a) ðsðft r þ dt;ft r þ dt; D; TsÞ SðFt r; Ft r; D; TsÞÞ=dt ¼ 0 Eqn 9(b) By solving Eqn 9(b) for varying densities (D), the optimal plastic response to changing densities for this So model is found (shown as the optimal reaction norms in Fig. 2). By contrast, the game theoretical scenario assumes that there is selection on the focal individual. To find the flowering time that

New Phytologist Research 5 (a) (b) (c) Fig. 2 Modelled maximized reaction norms of flowering time (time of switch to reproduction) in response to an increase in density, depending on the selection criteria (So, optimal model; Gt, game theoretical model) and season length (number). (a) Reaction norms with light use efficiency (L ue ) = 0.020; (b) high L ue (0.025); (c) low L ue (0.015). is an Evolutionarily Stable State (Ft*; see Maynard Smith, 1982), Eqn 9(a,b) become: @SðFt f ; Ft r; D; TsÞ=@Ft f ¼ 0 and thus: Eqn 10(a) ðsðft r þ dt; Ft r; D; TsÞ SðFt r; Ft r; D; TsÞÞ=dt ¼ 0 Eqn 10(b) If there is a single solution for Eqn 10, and the solution is a maximum (around which the slope changes from positive to negative; i.e. the derivative of Eqn 10(b) is negative), this indicates that the population should evolve towards this point via small invasion and replacement steps. However, this only tests whether the population with flowering time Ft* is stable against mutations with a small deviation (either accelerated or delayed) from this value. To test whether this Ft* is also resistant to invasion from all other flowering times, and thus whether Ft* is also an Evolutionarily Stable Strategy (see Maynard Smith, 1982), it is tested whether the best strategy for a focal plant when growing in a population with flowering time FT* is to have a flowering time of Ft* itself: SðFt ; Ft ; D; TsÞ [ SðFt 1; Ft ; D; TsÞ Eqn 11(a) which should be true over the whole range of flowering times other than Ft*, indicated by Ft_1. This can be rewritten to compare relative fitness (e.g. graphical comparisons between densities; see Fig. 3):

6 Research New Phytologist shading of its neighbours. The adoption of a more cell-based approach, in which the rest of the vegetation experiences a higher level of shading by the mutant, would have increased the selection for delayed flowering. Four season lengths are shown in this article to illustrate the effects of season length on the results. In addition, the effect of changing the growth rate is analysed by varying L ue. The parameters I o, k, C l and C LAI all influence the growth rate, and thus the effect of a change in one of these parameters on the final results follows the direction shown by changing L ue. It should be noted that, in contrast with the other parameters, increasing C l and C LAI will decrease the growth rate. The parameters used to produce the presented figures can be found in Table 1. Fig. 3 Relative fitness of focal plants when growing in a resident population with flowering time (Ft*) for each density (D). Model settings are a growing season of 180 d and light use efficiency (L ue ) = 0.020. Circles indicate Ft*. For all other combinations of season length and L ue, the patterns are the same: relative fitness decreases away from Ft*. SðFt 1; Ft ; D; TsÞ=SðFt ; Ft ; D; TsÞ\1 Eqn 11(b) for all other possible flowering times Ft_1. If this holds, then Ft* is stable against invasion from all other flowering time strategies. The optimal reaction norms for the Gt scenario then follow from the way in which Ft* changes with density. It should be noted that, by analysing only the reproductive investment of the focal plant (see Eqn 7), it is assumed that the resident population is so large that the mean fitness of the population is not influenced by the mutant (see Schieving & Poorter, 1999); hence, the potential benefit of delayed flowering is rather conservatively estimated, as it purely lies with the increase in resource-acquiring organs of the mutant, and not in increased Results Figure 1 illustrates how the model functions. With time, the LAI of an individual plant increases (Fig. 1a) and, consequently, the net photosynthetic rate initially increases up to a maximum, where shading decreases the growth rate of the plant (Fig. 1b). For each time t, the investment in reproduction when t is the switch to reproduction (here called the flowering time, Ft) can then be calculated. Hence, the maximized reproductive investment at the stand level (So) can then be found (Ft s ; see Eqn 8; Fig. 1c). Similarly, for the game theoretical scenario (Gt), the ESS values can be found (Ft*; see Eqns 10 and 11 and Fig. 1d). By calculating these So and Gt values for more densities, the optimal reaction norms, and hence the optimal plastic responses, can be found across a wide range (Fig. 2). The analysis of the simple optimization scenario (So) follows hypothesis 1 from the Introduction: an increase in density leads to accelerated flowering, as the flowering time that maximizes seed production at the stand level (Ft s ) decreases with density. Sensitivity analysis shows that a decrease in season length reduces this difference between low and high density, and hence reduces the optimal plastic response that should be selected for (see Fig. 2). However, this decrease in plasticity as a result of Table 1 Parameters used in the model Symbol Parameter Value Units Source Remarks C l Cost of maintaining leaf area 3.32 lmol C m 2 leaf s 1 Pronk et al. (2007) Recalculated to account for total plant biomass with F la, assuming equal respiration costs for stems, roots and leaves C built Maintenance respiration 0.213 g C g 1 C in leaf Pronk et al. (2007) F la Fraction of mass in leaves 0.33 Assumed Assumed equal allocation to roots, stems and leaves I o Photon flux density above the canopy 1000.0 lmol photons m 2 surface area s 1 Schieving & Poorter (1999) k Light extinction coefficient 0.8 Schieving & Poorter (1999) LAI fo Leaf area index of individual plant at t = 0 0.0003 m 2 m 2 surface area Assumed Conversion of seed mass (=0.01 g) 9 SLA Lf c Leaf carbon content 0.45 g C g 1 leaf Pronk et al. (2007) L ue Light use efficiency 0.020 lmol C lmol 1 intercepted photons Hikosaka et al. (1999) SLA Specific leaf area 0.03 m 2 g 1 Pronk et al. (2007)

New Phytologist Research 7 decreased season length appears to be small in the examples used, indicating that the shifts in optimal flowering time for the different densities individually as a result of the shift in season length play a more important role at the current parameter setting. An increase in growth rate decreases the time to reach the maximum rate of photosynthesis, and hence, in general, the optimal flowering times decrease with higher light use efficiency (L ue ; see Fig. 2b) and increase with lower L ue (Fig. 2c). Hence, season length becomes more important in limiting Ft s with lower growth rates, and therefore the differences in optimal flowering time between seasons are largest when the growth rate is low. In the game theoretical scenario (Gt), for each density, an Evolutionarily Stable Strategy is found (Ft*; see Figs 1d, 2). These Ft* values are always an Evolutionarily Stable Strategy: all invasion plots follow the same pattern (relative fitness is always highest for the Ft* strategy and declines below 1 for all other flowering times); therefore, only the invasion plots for Ts = 180 are given in Fig. 3. Thus, all ESS flowering times are monomorphic (a single trait value is predicted to evolve). This indicates that these Ft* values will evolve, irrespective of the starting flowering time of the resident population, and will be stable against invasion. Consequently, when the optimal plastic response is defined as the response that leads to an ESS at every density, the way in which plasticity changes with density is markedly different from that of the So scenario. In general terms, the effect of the increase in competitive interactions with increasing density compensates for the size effect. For long growing seasons, this results in delayed flowering in response to an increase in density (Fig. 2a). For intermediate growing seasons (Ts = 180), delayed flowering with increasing density is only predicted when the initial density is low. Nevertheless, at higher densities, the competitive interaction effect largely compensates for the size effect. Hence, despite the apparent homeostasis that would be selected for in the Gt scenario at these high densities, the difference in optimal flowering time with the stand-level scenario still increases. Only with a short season is accelerated flowering predicted with increasing density in the Gt scenario. Similarly, the difference between the predicted optimal flowering response in the stand-level scenario (So) and the Gt scenario increases with increasing season length. Sensitivity analyses show that, when the growth rate increases (in Fig. 2b illustrated by increasing the light use efficiency by 25%), the flowering time is even more delayed in the Gt scenarios, also at higher densities. This is because the faster growth rate means that plants can reach their optimal size earlier, leaving more time for the increase in resource capture by the individuals that delay flowering to compensate for the decreased time for seed production. Interestingly, the differences between the So and Gt scenarios tend to increase with decreasing growth rate (see Fig. 2c). This is because, at low growth rates, the plants have not reached their maximum growth rate when they should switch to full investment into reproduction. At this point, a mutant that delays flowering has a larger benefit in terms of increasing its net photosynthetic rate (see slope of Fig. 1b before the maximum is reached), and thus selection for delayed flowering will be stronger. Effectively, this means that, in the Gt scenario, differences in season length and density can change the selection for a range of responses: from accelerated flowering when the season is short, albeit less early than the stand-level scenario would predict, to homeostasis and delayed flowering when the season is long. Discussion By analysing both selection at the whole-stand level and the way in which competitive interactions between direct neighbours drive selection, the model presented here provides insights into the difference in plastic responses triggered by varying density that may arise when the selection criteria differ. Optimizing the flowering time at the stand level is an important factor in optimizing crop yields where season length also plays a crucial role (Haussmann et al., 2012). In addition, for plants that grow in dense stands with close kin, such as some clonal plants, the optimization of their relative fitness may be similar to the optimization of stand-level performance (see Anten & During, 2011). However, in natural vegetation of non-clonal plants, or clonal plants with a guerrilla growth form (sensu Doust, 1981), strong non-self interaction may prevail, and these competitive interactions should be taken into account. By comparing a stand-level model (So) with the role played by competitive plant plant interactions on the selection for plastic responses, I wish to reinforce what was implicitly demonstrated by one of the first studies that showed that shade-induced height responses are adaptive (Dudley & Schmitt, 1996): that the benefits of plastic responses in natural vegetation can also strongly depend on neighbour performance, and that they are frequency dependent. Simple optimization and game theoretical results The analysis that focuses on optimal flowering time at different densities for the whole-stand level (So) confirms the first hypothesis: flowering time should be accelerated when density increases. Although the differences are small, the sensitivity analysis of season length shows that this difference between different densities will be greater when the season is longer. This is because, at low density, there is less shading within the stand and plants can therefore grow longer and larger before they reach their maximum photosynthesis. If the season length becomes shorter, they may not be able to reach this maximum size, and they may have to flower earlier. At higher densities, the flowering time that would maximize the net photosynthetic rate is already earlier. Therefore, when season length selects for earlier flowering at low density, this shift does not have to occur yet at high density. Consequently, the optimal flowering times at different densities will converge with shorter season length. Of course, there exist season lengths that are so short that, at all densities, plants should flower simultaneously as early as possible, just to be able to produce some seeds. The extrapolation of this into general terms results in the prediction that, when season length becomes shorter, and when one looks at maximizing the yield at the stand level, selection should lead to a plastic response to flower earlier in response

8 Research New Phytologist to density, but the absolute level of plasticity should decrease with decreasing season length. It should be noted, however, that a change in growth rate has a relatively stronger effect than changes in season length. Increasing the growth rate decreases the differences between season lengths and actually reduces the differences between densities, thereby reducing the absolute level of plasticity that will be selected for. This is because a higher growth rate allows plants the time to come close to the size that maximizes their net photosynthetic rate at all season lengths. Nevertheless, the optimal plastic response is always in the same direction. Hence, when selection requires that seed production at the whole-stand level should be maximized at all possible densities, the plastic response to an increase in density should always be an acceleration of flowering time. This is in line with studies that have found selection for accelerated flowering with an increase in plant density (Thomas & Bazzaz, 1993; Donohue et al., 2000; Weinig et al., 2006). Results are different in the game theoretical model (Gt), where the way in which vegetation should evolve as a result of selection on the relative fitness of individuals is analysed (Nowak & Sigmund, 2004). The flowering time that is predicted to lead to vegetation in a monomorphic ESS (Maynard Smith, 1982) is consistently later than that which maximizes stand-level performance, and this difference increases with density. This is a consequence of the fact that plants which delay flowering capture more of the available light, leading to an increase in their relative performance. Hence, through the increase in frequency of these lateflowering types, and the consequent competitive exclusion of early-flowering types, this will lead to later flowering of the whole canopy over time, until, after many generations, the season that is left to produce seeds is too short to make a further delay in flowering still profitable for the individual (see also Vincent & Brown, 1984). It should be noted that this process resembles the replacement of early-flowering species by late-flowering ones during succession. This shift towards later flowering confirms the idea that selection for relative performance goes in the opposite direction to selection as a result of lower light levels per individual. Hence, in such a competitive setting, the optimal plastic response should also have shifted to that direction over evolutionary time scales. However, as season length and growth rate affect the time during which the individuals that delay flowering can profit from the increase in net photosynthetic rate, the resulting optimal plastic responses (or better, optimal reaction norms) in the Gt model show a much more complex range of outcomes than in the So scenario: the level of plasticity, and even the direction, is changed by the interaction with season length. Selection for delayed flowering increases with increasing season length and growth rate. Hence, depending on the interplay between season length and growth rate, increased density can select for both accelerated and delayed flowering, including the possibility of stasis. Thus, the current game theoretical analysis may give a possible explanation for the occurrence of differences between naturally occurring genotypes in the direction of the plastic response in flowering time as a result of changes in density, sometimes against the predicted selection gradient reported in the experiment, which have been found in the literature (Dorn et al., 2000; Weinig et al., 2006; Dechaine et al., 2007; among others). Consequences of differences between optimization criteria An important aspect of the analyses presented here is that the two models that use different optimization criteria produce different results. Differences in the way in which fitness is calculated and interpreted are known to change the evolutionary trajectories of traits with populations (Burgess & Marshall, 2014). For instance, Stanton & Thiede (2005) showed that the analysis of absolute fitness or relative fitness within or between patches influenced which genotypes, and hence which trait values, were selected for. By defining the optimal plastic response as the shift in flowering time that optimizes performance at all the different densities, both within- and between-patch performance is optimized in the scenarios presented here. As a consequence, it does not allow for plastic genotypes that are not optimally adapted to still dominate the (meta)-population, as can occur in the Sultan & Spencer (2002) model. Although this assumption may seem rather strict, it shows how a basic assumption of whether plants are selected to maximize whole-stand fitness or to maintain a larger fitness than direct neighbour competitors will influence the way in which plasticity is predicted to evolve. Echoing the importance of using the correct fitness estimate (Burgess & Marshall, 2014), experimental tests should therefore take differences in the way in which selection may operate into consideration when setting up experiments. I distinguish three different selection criteria that could be used in experiments, only the last two of which are analysed through the current scenarios. First, setups that look at genotypic differences in plasticity by placing individual plants in different environments (Callahan & Pigliucci, 2002; Weijschede et al., 2006; van Kleunen et al., 2007; Vermeulen et al., 2008; Kover et al., 2009; Franks, 2011) are looking at a measure of absolute fitness, in the absence of a direct influence of the competitors with which the fitness measure is compared on the resource itself. Hence, these are density-independent models (sensu Parker & Smith, 1990). Second, there are experiments in which variation between genotypes is analysed with monogenotypic stands. Effects of density are often analysed using such a setup (see Dorn et al., 2000 among others; Weinig et al., 2006; Brock et al., 2010). However, one should realize that, in such a setting, the highest yields will be generated by individuals that grow with weak competitors (in reference to Donald s ideotypes Donald, 1968; see also the reasoning of Vermeulen & During, 2010); therefore, selection can seem to favour traits that maximize stand-level performance (thus, in the So model, accelerated flowering with decreasing density). Hence, such setups are quite suitable if the goal is to find traits that maximize crop yield, or for plants with a low level of competitive interaction with neighbours. To date, no experiments have mimicked the way in which plasticity is assumed to evolve in the third selection criterion (i.e. the Gt scenario presented in this paper). There are only a few experiments in which genotypes are directly competing with each other for the same resources (see Masclaux et al., 2010), and

New Phytologist Research 9 where seed production of an invading individual is expressed relative to the production of all the other plants forming the population. Yet, none have been repeated over multiple generations to follow the way in which changes in genotype frequency as a result of fitness differences affect the consequent selection on plasticity. However, as the difference between the two scenarios shows, such often implicit assumptions about what performance measure should be maximized can change the results and their interpretation. I therefore argue for a clearer explanation in studies on how the decision to use a particular setup logically follows from the decision on what kind of selection (i.e. yield maximization, absolute fitness or relative fitness) the experiment is thought to mimic, as it greatly influences the conditions for which the outcomes can be accurately interpreted. Selection on low levels of plasticity The analyses also show that costs and other constraints may not always be necessary to limit the evolution of plastic responses. On the basis of several theoretical studies (van Tienderen, 1991; Sultan & Spencer, 2002), Van Buskirk & Steiner (2009) argued that the costs and limits of plasticity that are most relevant for plants are genetic costs, including maintenance and developmental instability costs, plasticity history, environmental reliability and lag-time limits. Indeed, Stinchcombe et al. (2004) found costs for a plasticity in flowering in response to different temperatures, indicating that costs may limit the evolution of plasticity in flowering. Yet, several authors have argued that the costs of plasticity are quite low (Van Buskirk & Steiner, 2009; Maherali et al., 2010), casting doubt on how much such costs can constrain the evolution of plasticity (see also the model of Sultan & Spencer, 2002). The results presented in the game theoretical model offer a more direct explanation of why plasticity in response to heterogeneity in density may be limited: because the selection caused by reduced resource availability is partly offset by increased competitive interactions. In other words, the way in which selection pressure itself is altered can select for reduced plasticity, even though heterogeneity is large. Hence, this serves as an indication that the evolution towards apparent specialist genotypes or intermediate plastic ones does not have to depend on costs, nor on other limits of plasticity, such as negative pleiotropic effects (Weinig et al., 2003; Kover et al., 2009) and limits posed by selection on the trait value itself (Springate et al., 2011); it can evolve through selection on the responses in the heterogeneous conditions themselves, because the different conditions can still select for similar phenology. Conclusion Models of the evolution of plasticity are rarely tested experimentally (but see van Tienderen, 1991; DeWitt, 1998). In part, this runs parallel with the limited amount of long-term studies that focus on selection per se (but, see for example, Stuefer et al., 2009; Whitlock et al., 2010; Agrawal et al., 2013) rather than on diversity. To my knowledge, none of these have targeted selection on plasticity, although Springate et al. s (2011) experiment on selection directly on the trait value itself (instead of through seed production, i.e. fitness, itself) gives a promising direction of how to do so. Similarly, there is no experimental evidence on how the level of interaction between directly competing neighbours will affect selection. Along those lines, there are limited data on how the level of self vs non-self shading differs among individuals, species and vegetation types (Hikosaka & Hirose, 1997; Anten, 2002). 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