A Three-Way Trade-Off Maintains Functional Diversity under Variable Resource Supply

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1 vol. 18, no. 6 the american naturalist december 13 A Three-Way Trade-Off Maintains Functional Diversity under Variable Resource Supply Kyle F. Edwards, 1, *ChristopherA.Klausmeier, 1, and Elena Litchman 1,3 1. Kellogg Biological Station, Michigan State University, Hickory Corners, Michigan 96;. Department of Plant Biology, Michigan State University, East Lansing, Michigan 88; 3. Department of Zoology, Michigan State University, East Lansing, Michigan 88 Submitted November 6, 1; Accepted July 9, 13; Electronically published October 31, 13 Online enhancements: appendixes. Dryad data: abstract: The resources that organisms depend on often fluctuate over time, and a variety of common traits are thought to be adaptations to variable resource supply. To understand the trait structure of communities, it is necessary to understand the functional tradeoffs that determine what trait combinations are possible and which species can persist and coexist in a given environment. We compare traits across phytoplankton species in order to test for proposed trade-offs between maximum growth rate, equilibrium competitive ability for phosphorus (P), and ability to store P. We find evidence for a three-way trade-off between these traits, and we use empirical trait covariation to parameterize a mechanistic model of competition under pulsed P supply. The model shows that different strategies are favored under different conditions of nutrient supply regime, productivity, and mortality. Furthermore, multiple strategies typically coexist, and the range of traits that persist in the model is similar to the range of traits found in real species. These results suggest that mechanistic models informed by empirical trait variation, in combination with data on the trait structure of natural communities, will play an important role in uncovering the mechanisms that underlie the diversity and structure of ecological communities. Keywords: functional traits, coexistence, resource pulse, fluctuating environment, phytoplankton. Introduction Many organisms live in a world where the resources they depend on fluctuate greatly over time (Bode et al. 1997; Polis et al. 1997; Yang et al. 1). A variety of common traits are thought to be adaptations to fluctuating resource supply, such as resource storage, high maximum consumption rates, high growth or reproductive rates, high resource use efficiency during periods of scarcity, and dormant life stages or seed banks (Noy-Meir 1973, 197; Sommer 198; Grover 1991; Chesson et al. ; Evans and Dennehy 5). These traits are likely to be con- * Corresponding author; edwar66@msu.edu. Am. Nat. 13. Vol. 18, pp by The University of Chicago. 3-17/13/ $15.. All rights reserved. DOI: 1.186/67353 strained by trade-offs, such that an increase in one function causes a concomitant reduction in one or multiple other functions (Stearns 1989; Tilman 199). The particular phenotype(s) selected for by resource fluctuation will depend on the structure of trade-offs, in combination with environmental conditions. Therefore, in order to understand the distribution of traits that occur in nature, it is necessary to understand the nature of the relevant tradeoffs. Theory shows that trade-offs that constrain trait evolution may also promote temporal niche differentiation in afluctuatingenvironment,leadingtothecoexistenceof multiple strategies (Ellner 1987; Grover 1991; Chesson et al. ; Litchman et al. 9). A better quantification of empirical trade-off relationships can therefore enhance the mechanistic understanding of both the maintenance of species diversity and variation in the structure of communities across environmental gradients. This is especially likely if a trade-off is quantified in terms of covariation among functional traits that can be used to parameterize models of competition; in this case, one can use a model to ask whether different kinds of species are expected to prevail under different conditions and whether empirically supported forms of a trade-off can feasibly allow the coexistence of multiple species (Levine and Rees ; Litchman et al. 9). Here we investigate a potential trade-off inspired by classic experiments by Sommer (198), in which he found that a greater diversity of phytoplankton species could be maintained in culture when phosphorus was supplied in pulses, compared to that under a constant rate of P supply. He proposed that fluctuating nutrient supply promoted diversity because natural phytoplankton communities possess a variety of strategies related to varying resource concentration: velocity-adapted species grow quickly when nutrients are replete but decline steeply during nutrient scarcity; affinity-adapted species are competitively superior under periods of nutrient scarcity but do not grow This content downloaded from on Fri, 15 Nov 13 1:3:5 AM

2 Three-Way Trade-Off Maintains Diversity 787 as quickly during nutrient excess; and storage-adapted species take up and store nutrients when they are replete and use these stores to grow when ambient nutrients are depleted, but they do not exhibit the fast growth or persistence under prolonged nutrient limitation of species using the other strategies. If these three types represent extremes of adaptation, it is reasonable to posit a threeway trade-off between fast growth, competitive ability, and ability to store nutrients. We refer to this proposed mutual constraint as a velocity-affinity-storage trade-off. Our goal in this study is twofold: first to test for potential trade-offs among functional traits and then to use a model parameterized by these trade-offs to see whether they promote coexistence and/or constrain community trait structure to empirically plausible values. We use a compilation of phytoplankton functional traits to quantify variation across species in traits related to velocity, affinity, and storage strategies. We then use the empirical structure of trait covariation to parameterize a mechanistic model of competition under fluctuating nutrient supply. We use this model to explore how species sorting leads to shifting community trait structure and diversity across gradients of environmental conditions. This analysis expands on prior work by Grover (1991), who used a model of competition under pulsed nutrient supply to explore how nutrient storage and other traits affect competition and coexistence of phytoplankton. He examined several proposed bivariate trade-offs and found that storage-adapted species could dominate under large nutrient pulses, that affinity-adapted species could dominate under small pulses, and that uptake-adapted species could dominate under small or large pulses, depending on the particular trade-off. He also found that coexistence of multiple strategies occurred only under a restricted bandwidth of pulse conditions. Our work builds on these results in several ways to better resolve how fluctuating nutrient supply operates in natural communities. We test for multivariate trade-offs, which may explain the lack of bivariate correlations; we parameterize a model with empirical trait correlations (rather than hypothesized trade-offs); and we show how the likelihood of coexistence is affected by more complex modes of nutrient supply. Although proposed for phytoplankton, the velocityaffinity-storage trade-off has similarities to traits and trade-offs proposed for many kinds of organisms. Fast growth or high reproductive rates, efficient use of limiting resources, and storage of temporally variable resources are all considered important adaptations for both autotrophs and heterotrophs (Noy-Meir 1973, 197). A velocityaffinity trade-off is analogous to opportunist-gleaner (Grover 199; Litchman and Klausmeier 1) or powerefficiency (Smith 1976) trade-offs, as well as some aspects of r- versus K-selection (Reznick et al. ). Likewise, a trade-off in allocation to growth or reproduction versus that to energy storage is thought to be an important lifehistory constraint (Stearns 1989). Therefore, our analysis may shed insight on the general problem of how organisms persist and coexist in variable environments. Methods Functional Traits In order to test for a velocity-affinity-storage trade-off, we require lab-measured traits that quantify maximum growth rate, nutrient competitive ability, and ability to store nutrients. Maximum growth rate (m max ) is often estimated by measuring growth along a gradient of resource input (light or a nutrient). In order to use estimates of m max that are comparable across species, we compiled data from commonly performed experiments where exponential growth rate is measured as a function of irradiance. In all of these experiments, species were grown in monoculture at low density, with nutrients supplied at nonlimiting levels and temperature at or near C. Then, m max was estimated by fitting a curve to the growth-irradiance relationship (fig. 1A; app. A; apps. A C are available online). Because P is commonly limiting in freshwater systems (Lampert and Sommer 7) and to follow Sommer, we focus on it as the nutrient. As a metric of competitive ability for P, we use scaled uptake affinity for phosphate ( ), which is a composite of three functional traits: maximum cell-specific phosphate uptake rate (V max ), the halfsaturation constant for phosphate uptake (K), and the minimum phosphorus quota (Q min ). The uptake measures V max and K are the parameters of the Michaelis-Menten curve typically fitted to measurements of uptake rate as a function of nutrient concentration in the medium (fig. 1B). Uptake affinity ( V max/k) is the slope of the Michaelis- Menten curve at the origin, which quantifies the cell-specific clearance rate for a nutrient as its concentration nears (fig. 1B; Healey 198). The value of Q min is typically estimated in the fitting of the Droop model of phytoplankton growth (Droop 1973), which relates growth rate to internal nutrient content such that m p m (1 Q min/q), where m is specific growth rate, Q is cellular in- ternal nutrient concentration or quota, Q min is the minimum quota at which growth ceases, and m is asymptotic growth rate at an infinite quota (fig. 1C). Therefore, scaled uptake affinity ( V max/kq min p Psaff) combines these three traits in order to scale uptake ability (affinity) by the amount of phosphorus required for growth. Furthermore, in a model where Michaelis-Menten uptake is coupled to * the Droop growth equation as m r, R r m/, where * m is the density-independent mortality rate and R is the This content downloaded from on Fri, 15 Nov 13 1:3:5 AM

3 788 The American Naturalist A B C max V max inf Specific growth rate Uptake rate per cell Specific growth rate K Q min Irradiance Phosphate concentration Phosphorus quota Figure 1: Estimation of m max and. A, m max is estimated by fitting a curve to data measuring growth rate as a function of irradiance, with nutrients supplied at nonlimiting levels. The equation for the curve is given in appendix A, available online. B, Uptake kinetics are quantified with a Michaelis-Menten curve fitted to data measuring uptake rate as a function of phosphate concentration. The initial slope of this curve, V max/k, is the uptake affinity (dashed line). C, Q min is the cellular P content (quota) at which growth ceases, and it can be estimated by fitting the Droop growth curve, which intersects the X-axis at Q min and increases to the asymptote m inf as P content increases to infinity. break-even nutrient concentration where growth equals mortality (Tilman 198; Litchman et al. 7). Therefore, as mortality goes to, for competitors with equal mortality, predicts the winner of competition at equilibrium, because higher results in a lower R. In a com- * pilation of chemostat studies, we found that scaled uptake affinity is a good predictor of the winner in competition at equilibrium, even at relatively high mortality rates (i.e., dilution rates; Edwards et al. 1). We therefore consider to be a good proxy of competitive ability for phosphate * under long periods of P scarcity. Unlike R, it is independent of m, so it represents a pure expression of equilibrium competitive ability. We compiled estimates of V max, K, and Q min from studies in which monocultures were grown under P limitation, with other nutrients and light at nonlimiting levels, with temperature at or near C, and with uptake kinetics measured using P-depleted cells. As a metric of ability to store P, we compiledestimates of the maximum measured P quota ( ), that is, the maximum cellular P content, which approximates a cell s storage capacity for P. Reported estimates of were measured in monoculture in one of two ways: P content after a period of saturated phosphate uptake (3 hours) or P content during resource-saturated growth under high phosphate concentration. The measured with these methods may underestimate the true maximal P content (Elrifi and Turpin 1985; Flynn 8), but estimates of vary by orders of magnitude across species ( Results ), and therefore these values likely capture broad interspecific differences in storage capacity. We compiled estimates of m max,, and for freshwater species; insufficient data were available for a similar analysis with other nutrients, such as nitrate, or for marine species. The data set includes 9 species for which at least two of the focal traits were measured (app. B), including 1 chlorophytes, six cyanobacteria, six diatoms, four desmids, one prochlorophyte, one xanthophyte, and one euglenid. Cell volume for each species was also collected from the literature. The data set is deposited in the Dryad Digital Repository: (Edwards et al. 13). Statistical Analyses In order to test for a trade-off among more than two traits, it is necessary to use a technique, such as partial correlation, that quantifies the relationship between two variables while accounting for the effects of additional variables (van Noordwijk and de Jong 1986). For example, for a trade-off among three traits, an increase in trait A may result in a decrease in trait B, a decrease in trait C, or both; a partial correlation will appropriately test whether trait A is correlated with trait B while accounting for any dependence of A and B on C. The trait data set has 18 species for which all functional traits have been measured and 11 species for which one trait is missing. Thus, to make full use of the information in the data, we used a Bayesian approach that allowed us to quantify the multivariate structure of the trait data while accounting for the fact that some data are missing. Details of methods for estimating trait correlations are given in appendix A. This content downloaded from on Fri, 15 Nov 13 1:3:5 AM

4 Three-Way Trade-Off Maintains Diversity 789 Model of Competition under Pulsed P As described in Results, our analysis of trait correlations suggests a three-way trade-off among m max,, and. To explore the potential effects of this trade-off on phytoplankton communities, we use a model of nutrient competition parameterized with these traits. The model is derived from one analyzed by Morel (1987) and Grover (1991, 11) that has been shown to adequately predict the outcome of competitive interactions under fluctuating nutrient supply (Grover 1991; Ducobu et al. 1998; Chapelle et al. 1), and it largely follows one used by Litchman et al. (9) to model the evolution of diatom size. We model phytoplankton dynamics under nutrient limitation in a well-mixed layer. For each species i, the growth rate of cell density N i (cells L 1 ) increases with P quota Q i, following the Droop model (Droop 1973), with minimum P quota Q min (mmol P cell 1 )andtheoreticalgrowth rate at infinite quota m (day 1 ). Quota is increased by uptake of phosphate R (mmol L 1 ), following Michaelis- Menten kinetics, with maximum uptake rate V max (mmol P cell 1 day 1 ) and half-saturation constant K (mmol P L 1 ). We assume that increasing quota feeds back to reduce nutrient uptake, such that V max declines linearly from hi lo Vmax, when quota is at its minimum Q min, to Vmax, when quota is at its maximum (Gotham and Rhee 1981; Grover 1991; Ducobu et al. 1998). Mortality occurs at a density-independent rate m (day 1 ), and cell density also declines because of turbulent mixing across the thermocline at rate s (day 1 ). Phosphate mixes across the thermocline at rate s (day 1 ), with a fixed deep-water concentration R in, and is also supplied to the mixed layer in periodic, instantaneous mixing events where a fraction a of the mixed layer is replaced from water below the thermocline, with period T (days). This periodic mixing also dilutes phytoplankton, which are assumed to be absent from the deep waters. A fraction f of the phytoplankton biomass loss to mortality within the mixed layer is instantaneously recycled to yield dissolved phosphate. The model equations are and [ ] max,i min,i R Q min,i, i( ) i R Ki Qi Qmin,i, i( ) i i i dq Q Q hi hi lo p Vmax,i (Vmax,i V max,i) dt Q Q i i min,i # m 1 Q, (1) dni p m 1 N mn sn, () dt Q i dr p s(r in R) dt Qi Q hi hi lo min,i [ Vmax,i (Vmax,i V max,i) Q Q ] i max,i min,i R # Ni fmnq i i, (3) R K i with mixing events such that i R(jT ) p (1 a)r(jt ) ar in, N(jT ) p (1 a)n(jt ) for all positive integers j (which counts time in pulses), where T indicates conditions immediately before the pulse and T indicates conditions immediately after the pulse. The combination of slow turbulent nutrient input, pulsed input due to mixing events, and nutrient recycling within the mixed layer is intended as a minimal representation of the dynamics of phosphorus supply in lakes during stratified, P-limited conditions. Stratification leads to uptake of nearly all dissolved P, with low input from across the thermocline or other sources and the majority of production fueled by P remineralized within the mixed layer (Caraco et al. 199; Soranno et al. 1997; Kamarainen et al. 9). These conditions are interrupted by wind and/ or rainfall events that result in entrainment of nutrientrich water (Soranno et al. 1997; Robarts et al. 1998; Kamarainen et al. 9) or resuspension of sediments in shallow lakes (Istvánovics et al. ). These events cause a large transient increase in dissolved P and can represent a substantial fraction of total P supply during long stratified periods (Soranno et al. 1997; Kamarainen et al. 9). As we describe in Results, under relatively long pulse periods, some species can persist by growing sufficiently during the elevated nutrient conditions after a pulse occurs, while the population declines during the low-nutrient interim between pulses. Under these conditions, Q r Q min, production of new biomass approaches, and the population declines at a per capita rate of m s. Under natural conditions of prolonged nutrient starvation, cells likely adjust physiologically to enhance persistence (Dodson and Thomas 1977), but this process is poorly understood, and we do not model it here. Parameterization Variation across species in parameterization is derived from empirical relationships between m max,,and.athreeway constraint among these traits can be represented as a surface in three-dimensional trait space. We used expectation maximization to obtain the maximum likelihood estimate for the variance-covariance matrix of the log-trans- This content downloaded from on Fri, 15 Nov 13 1:3:5 AM

5 79 The American Naturalist formed traits, and we used that matrix to perform a principal-components analysis. The first two principal components define a best-fit plane, in the sense that this plane minimizes the sum of squared distances of the points from the plane; 9% of trait variation is accounted for by this plane. The trait values for all species in our simulations are constrained to lie on this plane. We took this approach in order to explore the effects of this trade-off when isolated from other sources of trait variation. The real species in our analysis presumably vary along many other trait dimensions, leading to residual trait variation not explained by the tradeoff plane. For example, a grazer-resistant species may be generally worse and a grazer-susceptible species may be generally better in terms of m max,,or.consistentwith this expectation, if we simulate competition using the trait values for the real species, coexistence does not occur, and asinglespecies(dictyosphaerium pulchellum) winsunder nearly all conditions (results not shown). This species has the second-highest value of,thesecond-lowestvalueof,andanintermediatevalueofm max (table B1; tables B1, C1 are available online). It appears that the combination of having very high competitive ability for P without a correspondingly low maximum growth rate allows this species to dominate under most conditions. Because this species does not dominate all natural phytoplankton communities, it likely possesses disadvantages not quantified in this analysis. By focusing on trait combinations that lie on the tradeoff plane, we can isolate the effects of this trade-off while recognizing that additional trait dimensions are surely important for fully explaining phytoplankton diversity. Scaled P affinity is a composite trait involving V max, K, and Q min, which are parameters in the model. Thus, in order to parameterize the model using the empirical tradeoff, we must translate from to these component traits. hi We chose to hold V max and Q min constant at their median values in the data set ( 3.89 # 1 7 mmol cell 1 day 1 and 1.7 # 1 9 mmol cell 1, respectively) and vary K across species to obtain the appropriate values of, that is, hi K p V max/psaff Qmin. This choice is justified because among the three component traits, covaries most strongly with K and is not significantly correlated with V max or Q min (fig. C1; figs. C1 C7 are available online). Growth rate in the model is parameterized with m, which can be calculated for each species with the constraint derived in Morel (1987): m p mmax/( Q min). lo lo Likewise, Vmax is constrained such that Vmax p mmaxq max (Morel 1987). For very high values of, this can result lo hi in Vmax 1 Vmax; that is, the maximum uptake rate increases with increasing quota. When this occurred, we set lo hi Vmax p Vmax, but removing this constraint did not signif- icantly alter the results (fig. C). Other parameters in the model (a, s, m, R in, f )werevariedacrosssimulations,as described in the next section. Simulation Our simulations were designed to mimic species sorting from a large regional pool that includes the range of feasible trait values, leading to varying community structure as a function of environmental conditions. The trade-off relationship that we use defines a plane in (log) trait space, but the space of trait values that corresponds to potentially persisting species is a bounded region of this plane, because of several constraints. First, in order for a species to persist, the nutrient concentration at which growth equals mor- * tality ( R ; Tilman 198) must be lower than R in,whichis the maximum possible value for dissolved nutrient concentration in the model. Second, m max must exceed the combined average loss rate, m s log (1 a)/t. Finally, in some regions of the plane! Qmin, that is, storage capacity is lower than the minimum subsistence quota, and we define these species a priori as impossible. Given these three constraints, the space of feasible species is nearly triangular, with exact boundaries that depend on parameter values and with extreme points corresponding to maximum possible values of m max,, and (fig. C3). For all simulations we used a common # array of trait values as the initial species pool (fig. C3); the number of species in this array that were feasible depended on parameter values. To speed up the simulations, some areas of feasible trait space were not included, because extensive preliminary simulation found that species persisting under competition never occurred outside of this region of the trait surface for the parameter values used here. All species were initiated at equal low densities relative to final abundances, and community dynamics were simulated until the density of each species at the end of a period changed by less than a factor of 1 between successive periods; species were removed from the community if their mean density over one period became less than 1 cell L 1. We performed invasibility analyses and found that when the simulation reached an attractor of coexisting species, this attractor was not invasible by any species from the initial species pool (fig. C). We explored how the frequency of nutrient pulses determines community structure. In order to vary the frequency of nutrient pulses while holding integrated mortality and nutrient supply constant, we made the fraction of mixed layer replaced with deep water proportional to m T pulse period, such that a p 1 e a, where m a is the instantaneous mortality rate that is equivalent to removing a fraction a of biomass every T days. Twenty-five period durations from 1 to 3 days, evenly spaced on a log scale, were used. We used a baseline value of m day 1 a p.55, which results in replacement fractions that vary from a p.5 for T p 1 to a p.3 for T p 1 and a p.9995 for T p 3. Baseline values of the other param- This content downloaded from on Fri, 15 Nov 13 1:3:5 AM

6 Three-Way Trade-Off Maintains Diversity 791 eters were m p.1, R in p 3, s p.1, and f p.7. To compare these results to the limiting case of pulses that are infinitely fast and small, we ran a simulation with no pulses and m p.155. We also used alternative param- eter values to explore how community structure varied with reduced lake productivity ( R in p.1), reduced crossthermocline nutrient flux ( s p.1), and increased mor- tality ( m p.). To evaluate whether our results were sen- sitive to uncertainty in the trait data, we resampled species with replacement two times and used the trade-off surfaces estimated from these bootstrap replicates to simulate communities under the baseline parameter values. We performed several analyses to explore how the complexity of the nutrient supply regime affects community structure. To create a scenario in which P comes solely from pulsed input, we performed a set of simulations with crossthermocline P flux and recycling set to. To evaluate the effects of stochastic variation in pulse period, we performed simulations where the period between pulses was sampled from an exponential distribution with mean T. Finally,to evaluate the effects of multifrequency pulse regimes, we performed simulations where high-frequency pulses occur with period T and the corresponding replacement fraction m T a a f p 1 e,andsuperimposedonthisregimeareslowfrequency pulses that occur with period 8T and corresponding replacement fraction a ma8t s p 1 e. In some simulations, we found that pairs of species that coexisted in the same simulation had very similar values for all traits. These species are adjacent on the species pool array (fig. C5), and the coexistence of these similar species likely implies that a species between them on the trait plane would persist in their stead if it were present in the initial species pool. In order to simplify visualization of the results and focus on large differences in functional strategies, we have averaged the trait values of these highly similar species pairs and plotted them as single species. Plots showing all persisting species for baseline parameter values are given in figure C6. Results Trait Covariation Raw bivariate relationships between m max,, and hint at negative relationships (fig. A C), but only m max versus is nearly significant (Pearson s r p.1, P p.56). In contrast, partial correlations among these traits are all negative, with 95% credible intervals that exclude (table 1; fig. D F; three-dimensionalscatterplot in fig. 3A); this is the case whether or not cell volume is controlled for in calculating the partial correlation (table 1). Thus, consistent with a three-way constraint among these traits, negative relationships between pairs of traits are most evident when dependence on the third trait is accounted for, and this constraint appears to be independent of cell size. Very similar patterns were found when the analysis was limited to the 18 species for which all traits were measured (table C1). There is some suggestion of differences between taxa in average strategy; in particular, cyanobacteria tend to have high, desmids tend to have a high, and nondesmid chlorophytes tend to have high m max (fig. 3B). Species-Sorting Simulations We first describe the effects of pulse frequency on community trait structure, with other parameters at their baseline values. With no pulses, a single species persists that has high, low, and low m max (fig. A). This species is at the edge of feasible trait space and represents an extreme affinity specialist (fig. 5). Under pulses with a 1- day period, the high-affinity species coexists with a second species that has higher, higher m max,andlower. With increases in pulse period, the second species continues to decline in while increasing in,andatthe same time m max for the second species initially increases and then decreases (fig. A). Thus, the high-affinity species initially coexists with a second species that has an intermediate strategy, but increasingly this second species becomes a storage specialist, and at a period of days it reaches a peak value of that is 1 times greater than Q min. Beyond this point, a transition occurs where the storage specialist is replaced by a fast-growing velocity specialist that has low, low, and high m max.further increases in pulse period result in the persistence of additional species that are intermediate on the -m max axis while having minimal (figs. A, 5). Example dynamics under pulse periods of 1 and 1 days are shown in figure 6. Under a period of 1 days, an affinity specialist and a storage specialist coexist (fig. A). Fluctuations in abundance are relatively small, with the affinity specialist reaching peak abundance at the end of the period and the storage specialist reaching peak abundance around day 6 (fig. 6A). Quota dynamics show that the storage specialist rapidly takes up dissolved P until its quota is near maximal and that its quota then declines throughout the period as it continues to grow (fig. 6B). In contrast, the affinity specialist has no variation in quota (fig. 6B), because its is only slightly greater than Q min (fig. 5). Dissolved phosphate declines rapidly at first, followed by a slow decline through the rest of the period (fig. 6C). Under a pulse period of 1 days, the dynamics are quite different. Three species coexist: one extreme affinity specialist and two species with successively higher m max and lower (fig. A). All species show substantial fluctuation in abundance, although the affinity specialist experiences This content downloaded from on Fri, 15 Nov 13 1:3:5 AM

7 79 The American Naturalist A B C e-9 e-8 e-7 e-9 e-8 e-7 D E F residual residual residual residual residual residual Figure : Relationships between, m max, and. A C, Raw bivariate scatterplots of versus m max, versus, and m max versus, respectively; D F visualize partial correlations between these pairs of traits. In order to display partial correlations, the two focal traits in each panel were each regressed against the remaining trait and cell volume, and the residuals of these regressions are plotted. For points for which one of the controlled-for traits was not observed, the posterior mean value of that trait was used in the regression. For example, in D, and m max have each been regressed against and cell volume, and the residuals of these regressions are plotted. For points for which was not observed, the posterior mean value from the Bayesian model was used. less fluctuation than the two faster-growing species; in addition, the faster-growing species have peak abundances in succession at 1 and days, after which they decline greatly, while the affinity specialist continues to increase to an asymptotic abundance throughout the period (fig. 6D). The quotas of all species do not vary, because they are on the boundary of trait space where is only slightly greater than Q min (fig. 6E). Finally, the dynamics of dissolved P have several phases. Initially, P declines very slowly because of the low abundance of all species. As the populations increase exponentially, they eventually cause a decline in dissolved P, depleting P to successively lower levels as species with greater increase in relative abundance (fig. 6F). By day, dissolved P is at a low level that is maintained through the rest of the period. Under alternative environmental conditions (higher mortality, lower productivity, lower nutrient flux), the same general pattern of shifting community structure with Table 1: Partial correlations between, m max,, and cell volume m max Volume (.86,.35).5 (.79,.).3 (.7,.6) m max.59 (.83,.9) (.86,.).37 (.3,.73).5 (.75,.1).5 (.76,.8) (.9,.9) Note: Posterior means are listed, with the 95% highest posterior density credible interval in parentheses. Above the diagonal are partial correlations that account for cell volume; below the diagonal are partial correlations among the other three traits with volume not accounted for. This content downloaded from on Fri, 15 Nov 13 1:3:5 AM

8 Three-Way Trade-Off Maintains Diversity 793 A B - 1 log PC (%) log log PC 1 (51%) Figure 3: Multivariate trait patterns. A, Three-dimensional scatterplot of, m max, and. Open circles are for species with all traits observed; filled circles are for species with two traits observed and the third trait estimated with the posterior mean from the Bayesian model. The fitted plane is the plane derived from the first two principal-component (PC) axes fitted to these points. The equation for this plane is Qmax p # Psaff 5.91 # mmax, where all traits are on a log 1 scale. B, The same data plotted in PC space, with taxon coded by symbol type; cyan p cyanobacteria; chlor p chlorophyte. shifting pulse period occurs, but the trait values of the most extreme specialist strategies are modulated by the parameters (fig. ). When mortality is increased, the minimum value of m max needed to persist is increased, and this in turn decreases the maximum possible value of. As a result, the most extreme affinity specialist under higher mortality has a relatively lower (fig. B). Higher mortality also causes the transition from a storage specialist to a velocity specialist to occur at a shorter period ( 7 days), and the most extreme storage specialist has a relatively lower,comparedtothatunderlow-mortality conditions. Finally, under the longest pulse periods, the communities have a maximum of two coexisting species, compared with three or four species under lower mortality. When lake productivity is reduced (reduced R in ), there is a moderate reduction in the highest achieved values of both m max and (fig. C). In other words, velocity and storage specialists grow relatively slower and store less P than under conditions of higher productivity. Reducing the rate of mixing across the thermocline results in negligible changes from baseline parameter values (fig. D). When communities are simulated with bootstrapped trade-off surfaces and baseline parameter values, the primary patterns in trait structure remain, with some alteration of the most extreme persisting trait values (fig. C7). We performed several analyses to explore how complexity of the nutrient supply regime affects community structure. When cross-thermocline P flux and P recycling are both set to, only a single species persists across all conditions, and the affinity specialist is restricted to conditions of small pulses with a short period, that is, conditions of less variable nutrient supply (fig. 7A). This loss of diversity requires that both recycling and turbulent P influx are removed; with only one of these sources removed, the results are similar to those in figure A (results not shown). In contrast, increasing the complexity of P by including multiple pulse frequencies promotes functional diversity. Notably, when the high-frequency pulse has a period ranging from to days, which corresponds to a period of 3 16 days for the low-frequency pulse, distinct velocity, affinity, and storage strategies coexist simultaneously (fig. 7B). Finally, when pulses occur randomly according to a Poisson process, patterns in trait structure are very similar to those under periodic pulses (results not shown). Comparison with Observed Trait Distributions Although our exploration of parameter space is not exhaustive, the different parameter values used in our simulations can be considered to represent a range of conditions that may plausibly occur in natural lakes; we can then compare the trait variation that occurs across simulations with the trait variation that occurs among real species. In general, This content downloaded from on Fri, 15 Nov 13 1:3:5 AM

9 79 The American Naturalist A Baseline C Low R in 1e+5 1e+3 1e+1 1e+5 1e+3 1e+1 1e-7 1e-8 1e-7 1e-8 1e-9 1e Period Period B High mortality D Low diffusion 1e+5 1e+3 1e+1 1e+5 1e+3 1e+1 1e-7 1e-8 1e-7 1e-8 1e-9 1e Period Period Figure : Persisting species in community assembly simulations for a range of pulse periods, using baseline parameter values (A), low R in (B), high mortality (C), and low cross-thermocline P influx (D). Each panel contains three subpanels that show the persisting trait values for,, and m max. For each pulse period, coexisting species are denoted with distinct symbols. For example, in A at pulse period 5, there are three coexisting species, coded with a filled circle, a triangle, and an open circle. The species coded with a filled circle has the highest and the lowest m max, while the species coded with the open circle has the lowest and the highest m max. The species coded with a triangle is intermediate for both of these traits. Units for are L day 1 (mmol P) 1 ; units for are mmol P cell 1 ; units for m max are day 1. there is substantial overlap between the observed range of traits and that predicted by the simulations (fig. 8). Both real and modeled m max range between.5 and.5 day 1, while ranges between 1 9 and 1 7 mmol P cell 1 (fig. 8). There is more discrepancy for,whichhasa minimum of 1 forrealandmodeledspeciesbutamaximum of 1 3 for real species and 1 6 for modeled species. There is a large region of feasible trait space where is very high and is low (fig. C3); species with these traits never persisted in the simulations, and likewise there are no real species with trait values in this region. Discussion Empirical Trait Patterns Our analysis supports the existence of a three-way velocityaffinity-storage trade-off for phytoplankton. An increase This content downloaded from on Fri, 15 Nov 13 1:3:5 AM

10 Period = 1 Period = log log1 Period = Period = log log1-6 log1 P saff log1 P saff log1-5 log Period = log1-6 log1 P saff log1-6 log1 P saff log1 P saff -8-7 log1 P saff -7 log1-5 log log1 This content downloaded from on Fri, 15 Nov 13 1:3:5 AM log1 Period =.5 Figure 5: Coexisting species for six example pulse periods, under baseline parameter values. Small gray circles show the array of species that are initially present in the simulations. Large black circles show the species that persist. The persisting species are the same as those plotted in figure A, replotted here to show their locations in three-dimensional trait space. Figure C3, available online, compares the array of initial species to the full range of feasible species. Period p indicates the simulation with no pulsed nutrient supply.

11 796 The American Naturalist A Abundance D Abundance Abundance (cells L 1 ) 1e+9 1e+8 1e+9 1e+7 1e+5 1e+3 1e B Quota E Quota Quota ( mol P cell 1 ) e-8 5e-9 e-9 e-8 5e-9 e C Dissolved phosphate F Dissolved phosphate Phosphate ( mol L 1 ) 3e+ 1e 1e- 1e-6 3e+ 1e 1e- 1e-6 1 Day 9 18 Day Figure 6: Example dynamics for a 1-day pulse (A C) and a 1-day pulse (D F). Coexisting species are indicated by distinct line patterns in A, B and D, E. A and D have Y-axes with different ranges, because of greater fluctuation in abundances for 1-day pulses. Note that abundances are reduced after each simulated period by the mixing event, so that these represent stable population cycles. in any one of m max,, and tends to be correlated with a decrease in both of the other traits (table 1). Within this constraint, species exhibit a wide variety of strategies (fig. 3). It is noteworthy that in this data set the trade-off is independent of cell volume. In general, tends to increase with increasing cell volume, while m max and decline with increasing cell volume (Grover 1989; Litchman et al. 9; Edwards et al. 1). Therefore, variation in cell volume alone should tend to cause to be negatively correlated with the other two traits. However, in this data set correlates with volume, while m max and do not (table 1). This is consistent with the fact that allometric relationships for many traits tend to be noisy (Edwards et al. 1), and in this data set the variation in cell volume is moderate ( 1,-fold), compared to the full range of variation among phytoplankton ( 1 8 -fold). We interpret these results to mean that the correlations among the three focal traits in this analysis represent trait variation that is orthogonal to variation in cell volume, while changing cell volume tends to cause additional correlated change in these traits. An interesting avenue for future research would be an analysis of the underlying physiological basis for these trait correlations. Our analysis of interspecific trait variation confirms the This content downloaded from on Fri, 15 Nov 13 1:3:5 AM

12 Three-Way Trade-Off Maintains Diversity 797 A B 1e+5 1e+3 1e+5 1e+3 1e+1 1e+1 1e-7 1e-7 1e-8 1e-8 1e-9 1e Period Period Figure 7: Effects of supply regime complexity on community structure. A, Community structure with no cross-thermocline nutrient flux or recycling ( s p, f p ) and other parameters at baseline values. B, Community structure under multifrequency pulsing. The period listed along the X-axis is the high-frequency pulse period T, and each community also receives a low-frequency pulse of period 8T. importance of using a multivariate approach when attempting to decipher how traits covary. A prior analysis of scaled phosphate affinity, scaled nitrate affinity, and cell volume also found that some important patterns emerged only when multiple trait dimensions were considered simultaneously (Edwards et al. 11). In order to extend these methods to a full consideration of phytoplankton ecology and evolution, it will be important to measure numerous key traits concurrently across a range of species and to better incorporate traits reflecting interactions with grazers and pathogens. It will also be important to extend the use of missing-data methods that allow all of the available information to be used in quantification of multivariate patterns. Across many kinds of organisms, traits analogous to m max,, and are considered to be important adaptations to fluctuating resource supply. For example, terrestrial plants in arid environments are often distinguished by their ability to grow rapidly after a pulse of rainfall, their ability to maintain metabolic activity during drought conditions, and their ability to store water and/or energy (Noy-Meir 1973; Chesson et al. ). An analysis of functional traits in a community of desert annuals found evidence for a trade-off between relative growth rate and water use efficiency (Angert et al. 9), analogous to a m max -versus- trade-off in phytoplankton. As research in this area accumulates, it will be interesting to consider whether such traits participate in multidimensional tradeoffs and whether the importance of such traits results in common responses of community structure to resource fluctuation across ecosystem types. Species-Sorting Simulations A primary result of the species-sorting simulations is that a wide range of strategies can persist, depending on environmental conditions. Species with high maximum growth rates tend to occur under large pulses of low frequency (period longer than days), presumably because these conditions result in long periods of P saturation that allow for sustained growth at maximal rates. This is consistent with the dominance of fast-growing species during the early stages of annual successional cycles (Sommer 1996), cycles that have some similarity to a large nutrient pulse with annual frequency. Relatively high P concentration below the mixed layer is also necessary to favor the greatest m max, because this increases the postpulse duration of prolonged growth at saturated rates. Species with high storage capacity are favored by pulses of intermediate frequency ( 5 days), presumably be- This content downloaded from on Fri, 15 Nov 13 1:3:5 AM

13 798 The American Naturalist A B C Frequency Frequency 8 Frequency 1e5 1e-1 1e e-9 1 1e+9 Figure 8: Observed and modeled ranges for (A), m max (B), and (C). Observed trait distributions are shown as histograms in gray. Modeled trait distributions are demarcated with dashed lines. The X-axes are scaled to include the range of feasible trait values in figure C3, available online. Units for are L day 1 (mmol P) 1 ; units for m max are day 1 ; units for are mmol P cell 1. cause these conditions allow for rapid uptake of pulsed P, followed by growth using stored P, followed by the occurrence of a new pulse around the time that stores have been depleted. In addition, high nutrient concentration below the mixed layer also benefits storage specialists, presumably by increasing the amount of nutrient that can be stored after a pulse. These results are consistent with prior models showing that a high storage capacity is favored under pulses of intermediate frequency with high nutrient concentration (Grover 1991, 11; Litchman et al. 9). We also find that high mortality rates reduce the magnitude of storage capacity that is favored (fig. B); this is likely because cells experiencing a high mortality rate are dying before they can fully utilize their stored resources. Species with high scaled affinity are always present in simulations that include cross-thermocline P influx or recycling of P from dead phytoplankton within the mixed layer. This usually results in the coexistence of multiple strategies (fig. ). This result contrasts with some prior models showing that a single species typically persists under pulsed nutrient supply, with the strategy of this species depending on conditions (Grover 1991, 11). The difference in our results appears to be due to the fact that our model contains additional sources of continuous nutrient supply, that is, mixing across the thermocline and nutrient recycling. Thus, it appears that multiple modes of nutrient supply can promote coexistence of multiple strategies, with a high-affinity species possessing a relative advantage during times of low nutrient supply, after pulsed nutrients have been consumed and transformed into biomass. Furthermore, inclusion of multiple pulse frequencies promotes additional diversity and allows velocity, affinity, and storage strategies to coexist simultaneously under a range of conditions (fig. 7B). This contrasts with singlefrequency pulses, which rarely allow strategies of rapid growth and high storage to coexist (fig. ). Multiple sources of nutrient loading are a common feature of pelagic ecosystems (Dugdale and Goering 1967; Caraco et al. 199; Hudson et al. 1999; Kamarainen et al. 9), and we suggest that incorporating this complexity will be important for understanding how the nutrient supply regime determines the structure of planktonic communities. We find a reasonable fit between the real and modeled ranges of trait values (fig. 8). Although the real trait values were used to fit the trade-off plane that parameterizes the model, our simulations were initialized with the full spectrum of trait values from the plane that could feasibly persist. Therefore, the simulations included a much broader range of trait values than is observed in our data set (fig. 8). Because the range of trait values that persist in the model is nonetheless similar to the range of observed trait values, it is plausible that the trade-off we have identified plays an important role in generating trait diversity in natural communities, as well as in constraining which trait values can exist in nature. Variation across lakes in productivity, mortality, and the temporal regime of nutrient supply may lead to spatial variation in dominant trait values, while temporal variation within lakes may maintain local functional diversity. A more direct empirical test of our simulation results will require the synthesis of spatial and temporal community survey data with functional trait data for the surveyed species. In general, we think that combining data on interspecific trait correlations with mechanistic models will be crucial for advancing trait-based approaches to community structure and better synthesizing these approaches with an understanding of the maintenance of species and trait diversity. Acknowledgments This research was supported by National Science Foundation grants DEB-8593 (to E.L.), DEB-8585 (to This content downloaded from on Fri, 15 Nov 13 1:3:5 AM

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