# On selection for flowering time plasticity in response to density

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4 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 (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 r; Ft r; D; 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

5 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) f ; Ft r; D; 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 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 ) = 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 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 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 = 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 lmol C lmol 1 intercepted photons Hikosaka et al. (1999) SLA Specific leaf area 0.03 m 2 g 1 Pronk et al. (2007)

7 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 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

11 New Phytologist Research 11 Thomas SC, Bazzaz FA The genetic component in plant size hierarchies: norms of reaction to density in a Polygonum species. Ecological Monographs 63: van Tienderen PHV Evolution of generalists and specialist in spatially heterogeneous environments. Evolution 45: Van Buskirk J, Steiner UK The fitness costs of developmental canalization and plasticity. Journal of Evolutionary Biology 22: Vermeulen PJ, Anten NPR, Schieving F, Werger MJA, During HJ Height convergence in response to neighbour growth: genotypic differences in the stoloniferous plant Potentilla reptans. New Phytologist 177: Vermeulen PJ, During HJ Genotype density interactions in a clonal, rosette-forming plant: cost of increased height growth? Annals of Botany 105: Via S, Lande R Genotype environment interaction and the evolution of phenotypic plasticity. Evolution 39: Vincent TL, Brown JS Stability in an evolutionary game. Theoretical Population Biology 26: Weijschede J, Martınkova J, De Kroon H, Huber H Shade avoidance in Trifolium repens: costs and benefits of plasticity in petiole length and leaf size. New Phytologist 172: Weinig C, Dorn LA, Kane NC, German ZM, Halldorsdottir SS, Ungerer MC, Toyonaga Y, Mackay TFC, Purugganan MD, Schmitt J Heterogeneous selection at specific loci in natural environments in Arabidopsis thaliana. Genetics 165: Weinig C, Johnston J, German ZM, Demink LM Local and global costs of adaptive plasticity to density in Arabidopsis thaliana. American Naturalist 167: Whitlock R, Grime JP, Burke T Genetic variation in plant morphology contributes to the species-level structure of grassland communities. Ecology 91: Wong TG, Ackerly DD Optimal reproductive allocation in annuals and an informational constraint on plasticity. New Phytologist 166: New Phytologist is an electronic (online-only) journal owned by the New Phytologist Trust, a not-for-profit organization dedicated to the promotion of plant science, facilitating projects from symposia to free access for our Tansley reviews. Regular papers, Letters, Research reviews, Rapid reports and both Modelling/Theory and Methods papers are encouraged. We are committed to rapid processing, from online submission through to publication as ready via Early View our average time to decision is <25 days. There are no page or colour charges and a PDF version will be provided for each article. The journal is available online at Wiley Online Library. Visit to search the articles and register for table of contents alerts. If you have any questions, do get in touch with Central Office or, if it is more convenient, our USA Office For submission instructions, subscription and all the latest information visit

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