We studied the evolution of the correlation between growth rate r and yield K in experimental lineages of the yeast Saccharomyces cerevisiae. First, we isolated a single clone every approximately 250 generations from each of eight populations selected in a glucose-limited medium for 5000 generations at approximately 6.6 population doublings per day (20 clones per line × 8 lines) and measured its growth rate and yield in a new, galactose-limited medium (with ∼1.3 doubling per day). For most lines, r on galactose increased throughout the 5000 generations of selection on glucose whereas K on galactose declined. Next, we selected these 160 glucose-adapted clones in the galactose environment for approximately 120 generations and measured changes in r and K in galactose. In general, growth rate increased and yield declined, and clones that initially grew slowly on galactose improved more than did faster clones. We found a negative correlation between r and K among clones both within each line and across all clones. We provide evidence that this relationship is not heritable and is a negative environmental correlation rather than a genetic trade-off.

Correlations among traits underlie much of evolutionary ecology, including the evolution of life history (Walsh and Blows 2009) and niche breadth (Kawecki and Ebert 2004; Cobey et al. 2010). Negative genetic correlations, or trade-offs, have two possible genetic origins: pleiotropy (multiple phenotypic effects of genetic variation at a single locus), and, less often observed, linkage to selected mutations (Futuyma and Moreno 1988; Rose 1991; Maclean et al. 2004; Chen and Lübberstedt 2010). Pleiotropy is thus central to our understanding of genetic correlations (Falconer and Mackay 1996). Although the importance of pleiotropy is firmly established (Stearns 2010), limited efforts have been devoted to testing the stability of genetic correlations over evolutionary time (e.g., Begin and Roff 2003), especially using experimental evolution. This led us to study the correlation between growth rate and yield in long-term selection lines of the budding yeast Saccharomyces cerevisiae before and after an environmental change.

Population growth rate r and yield K have been shown to correlate with fitness in theory and in previous experiments with Drosophila (Mueller 1997), bacteria (Luckinbill 1978; Velicer and Lenski 1999), yeast (Spor et al. 2008, 2009), and animals in nature (Reznick et al. 2002). In the classical theory of life-history evolution (MacArthur and Wilson 1967), populations are thought to evolve a suite of adaptations specific to their own and other species’ densities (Pianka 1970; Prasad and Joshi 2003). A second classical view asserts that demographic factors influencing population age structure underlie the evolution of life-history traits (Charlesworth 1994). Recent research has focused on how the spatial structure of populations can favor altruistic behavior and K-selected traits that increase population productivity (Pfeiffer et al. 2001; Maclean 2008; Eshelman et al. 2010). This latter perspective is most useful for our experimental system as it predicts that, in the absence of spatial structure, selection will favor fast intrinsic per capita growth rate when organisms are selected under exponential or logistic growth, even if this reduces yield (Vasi et al. 1994; Maclean 2008). The phenotype of the ancestral population relative to the optimal phenotypes is also crucial for understanding the evolution of life-history trade-offs, such as those between growth rate and yield (Novak et al. 2006). If genotypes grow slowly and produce a low yield in comparison to their optimum, selection is not expected to generate a life-history trade-off until mutations adaptive for both traits are exhausted (Roff and Fairbairn 2007).

To test these ideas, we measured the correlation between growth rate r and yield K among clones of S. cerevisiae in galactose-limited batch cultures at high cell density (∼1.3 population doublings per day) under two circumstances. We first measured the correlation between r and K in galactose that evolved as a correlated response to selection in a glucose-limited batch culture with lower cell density (∼6.6 doublings per day). Next, we selected these clones isolated from the glucose selection lines into galactose and measured the changes in both r and K as direct responses to selection in galactose (Fig. 1). The glucose–galactose pair of substrates is a model system for the regulation of gene expression in yeast (Johnston et al. 1994), and previous studies suggest large pleiotropic effects of mutations affecting galactose metabolism (Hittinger et al. 2004; Maclean 2007). We also changed the cell density between the glucose and galactose environments to maintain a large effective population size in galactose. Our aims were to (1) monitor changes in life-history traits as a correlated response to selection, (2) find predictors of the magnitude of changes in the life-history traits caused by selection in a new environment (galactose), and (3) test the evolutionary stability of the relationship between r and K among clones and replicate selection lines.

Figure 1.

Design of the selection experiments and of the assays of life-history traits for single-clone isolates. Black arrows represent selection, gray arrows represent assays, dashed lines represent the galactose environment, and filled lines represent the glucose environment. The experiment had eight replicate selection lines in glucose, however the figure presents the design for a single line.

We found that correlated responses on galactose to selection in glucose generally increased growth rate and decreased yield, and that their magnitude changed little over 5000 generations of selection in glucose. Selection on galactose increased growth rate, and initially slow growers adapted more than fast growers. Finally, r and K were negatively correlated among clones within each glucose line. However, replicate assays of any given clone—among which there is no heritable variation—consistently showed a negative correlation between r and K. We take this result as strong support that the negative correlation between life-history traits was primarily environmental.



The S. cerevisiae strains are derived from the selection experiment by Zeyl et al. (2003). Otherwise isogenic, haploid and diploid leucine auxotroph strains (S288c background) were selected with fivefold replication in a glucose-limited minimal medium (glucose 2.5 g/L, ammonium sulfate 5 g/L, YNB 1.7 g/L, leucine 0.06 g/L) at 30°C under daily 100-fold dilution, or 100 μl of day-old culture transferred into 10 mL of fresh medium. The 2 × 5 lines were propagated for about 5000 doublings at 6.6 doublings per day. Population aliquots sampled every approximately 15 days from all lines were preserved at –80°C in 15% glycerol. For all five haploid populations and three of the diploid populations, we sampled here 20 single-clone isolates every 200–300 generations across the 5000-generation frozen record of selection in glucose. We measured the competitive fitness of these 8 × 20 clones in the glucose-limited environment using head-to-head competition against the ancestral haploid strain marked with a deletion in the ade2 gene (which causes colonies to turn pink on agar plates containing 15 mg/L adenine). The conditions for these fitness assays were the same as for selection except that 80 mg/L adenine was added to the assay medium. Competitive fitness was estimated by the change in frequency of the focal clone relative to the common competitor in a model with non-overlapping generations, W=[(p1 (p0– 1))/(p0 (p1– 1))](d− 1), where p0 and p1 are the frequencies of the focal clone before and after two daily cycles of selection, respectively, and d is the number of doubling expected during two cycles of selection (i.e., 2 × (ln100)/ln2 = 13.3). Note that all diploid lineages (lines F–H) became haploid before 3000 generations of the selection in glucose (J. N. Jasmin, A. C. Gerstein, and C. Zeyl, unpubl. data), therefore ploidy level is not a treatment in our experiments.

We then selected these 8 × 20 clones in triplicate for 90 days in a galactose-limited medium otherwise identical to the original glucose-limited medium and at 30°C (Fig. 1). However, selection on galactose was carried out in 96-well plates (CoStar; Corning Incorporated, Corning, NY) and with a daily serial transfer of 80 μl of day-old culture into 120 μl of fresh medium, resulting in about 1.3 doubling per day (cells spent the majority of the cycle in stationary phase). After 90 days of selection (∼120 doublings) in the galactose-limited environment, a single evolved clone was isolated from each of the 160 × 3 selection lines and frozen. Growth curves for these 480 clones and their 160 ancestors were generated in 96-well plates in an incubating spectrophotometer (PowerWave XS2; BioTek Instruments, Winooski, VT) that measured the optical density at 630 nm of cultures every 30 min for 24 h (same 96-well plates, medium, and temperature as during selection). Each evolved clone was paired in a well adjacent to a well of its ancestor to control for possible heterogeneity of growth conditions on the plates. This assay was carried out in replicated blocks where each block is one set of 160 evolved clones with their 160 ancestors.


The population growth curves were fitted to the Beverton–Holt model (Beverton and Holt 1957; see Supporting Information) of density-dependent growth using the FindFit function of Mathematica 8 (Wolfram Research Inc., Champaign, IL). The Beverton–Holt model has the form


where N0 and Nt are the population size at 0 and t units time after initiating the 24-h selection cycle, r is the intrinsic growth rate of the population, and K is the limiting population density. K and r in galactose were first analyzed for the 160 ancestral clones to obtain the correlated response in galactose to selection in glucose. To analyze variation in r and K, we both centered and reduced these two traits across all 160 clones (e.g., for r, inline image, with inline image the mean and inline image the SD of the r values). This standardization gives each trait an average of 0 and a variance of 1 and provides values with no unit, but it does not alter the within-trait structure of data.

To compare the life-history traits of the 160 clones before and after selection on galactose, we calculated for r and K the direct response to selection as Δx= (xevolvedxancestral), with x being r or K (centered and reduced), separately for each replicated block. We averaged these effects across three evolved clones isolated from the triplicate selection lines and obtained 160 responses to selection, henceforth Δr and ΔK. We estimated the effect of ancestral life-history traits and evolutionary history in glucose (EH; the number of generations in glucose) on Δr and ΔK using structural equation modeling performed in Amos 20 (IBM Inc. and SPSS Inc., Chicago, IL) with the path shown in Figure 5. Structural equation modeling allows testing the effect of EH on r or K in the ancestral clones, and the effect of each of these three variables on Δr and ΔK. For example, the model specifies that EH may influence r and K, but not the reverse.

Figure 5.

Structural equation model of the change in intrinsic growth rate Δr and cell limiting density ΔK in galactose. Arrows represent causal links and values attributed to arrows are standardized regression weights averaged across replicate lines. The bold arrows are strong links according to the standardized regression weights (Table 3).

Estimates of parameters of quadratic and linear regression models of life-history trait evolution were obtained using the NonLinearModelFit function of Mathematica 8 (Wolfram Research, Inc.). P-values were obtained for each parameter by the rank of the observed parameter among parameters generated from randomly permuted datasets, in which the observed values of the dependent variable were shuffled without replacement, to account for the fact that the 20 data points within each lineage were not independent. Other statistical analyses were performed with JMP 9.0.0 (SAS Institute Inc.).



For most of the eight lines, competitive fitness of single clones isolated from replicate populations selected for 5000 generations in glucose (evolutionary history in glucose, EH) increased rapidly over the first hundred generations and much more slowly afterwards (Fig. 2). Lines adapted at different rates over the last 3000 generations of selection, as indicated by significant differences in fitness among lines (F15,88= 14, P < 0.001) when relating fitness in glucose to line, and EH nested within line. Therefore, we analyzed the direct responses of each line separately.

Figure 2.

Fitness through 5000 generations of evolutionary history in glucose for eight replicate selection lines (A–H). Linear regressions were fitted to data between generations 2000 and 5000. Lines F–H started as diploids but haploidized after approximately 150 (F) and approximately 3000 (G and H) generations (vertical dashed lines); lines A–E were haploid from the start.

Decelerating adaptation is supported by the good fit of the hyperbolic model Wglucose=aEH(b+EH)−1+c EH, where a, b, and c are fitted parameters, over all 5000 generations of selection for six of the eight lines (Table 1). For the remaining two lines, G and H, a linear regression model fits better (Table 1). The different behavior of the G and H lines may result from their change from diploidy to haploidy after approximately 3000 generations of selection on glucose (J-N. Jasmin, A. C. Gerstein, and C. Zeyl, unpubl. data; Zeyl et al. 2003). Line F also started as diploid but it haploidized much earlier than G or H and behaved similarly to the haploid lines A-E (Fig. 2). Most importantly, fitness increased in all lines over the last 3000 generations of selection, except line D (P-values < 0.005 for all lines except B, P= 0.09, and D, P= 0.24; gray regressions on Fig. 2). Thus, adaptation in the glucose-limited environment occurred over the entire 5000 generations of selection, and the rate of adaptation varied among lines and decelerated with time.

Table 1.  Hyperbolic (A–F) or linear (G–H) models fitted to competitive fitness in glucose over the evolutionary history in glucose (mean ± SE) for each of eight replicate populations (A–H).
Hyperbolica P-valueb P-valuec (×10−6) P-value
  1. Line H was split into sections a and b to accommodate the large step at generation 3000 (Figure 2).

  2. P-values are for t-statistics of Student's t-tests.

A1.07±0.008<0.000115±30.0001 14±2.0<0.0001
B 1.12±0.010 <0.0001 24±3 <0.0001 0.5±2.0 0.8
D 1.06±0.020 <0.0001 14±7 0.05 8.0±4.7 0.1
F 1.07±0.012 <0.0001 18±5 0.0009  14±3.2 0.0003
Linearslope (×106) P-value    
G 24±2.2 <0.0001     
Hb 12±5.7 0.07     


We estimated the growth rate r and limiting cell density K in galactose for the same clones shown in Figure 2. Again, replicate lines diverged, as indicated by a significant line effect in a linear model with EH nested within line, for both r (F15,144= 7.7, P < 0.001) and K (F15,144= 4.0, P= 0.0005). Therefore, we analyzed the correlated response of each line independently, first with a quadratic model (EH2+EH), and with a simple linear regression when EH2 had no significant effect. During adaptation to glucose, r in galactose increased linearly whereas K declined linearly in most lines (Table 2; Fig. 3). However, in line C, r increased for the first approximately 2000 generations and declined for the last approximately 2000 generations, whereas r reached a plateau in line D after approximately 2000 generations (Table 2).

Table 2.  Linear and quadratic models fitted to correlated responses in galactose to selection in glucose (Figure 3).
Line r K
EH (10−3) P EH 2 (10−7) P R 2 EH(10−3) P EH 2 (10−7) P R 2
  1. Dashed cells indicate that the linear model provided a better fit than the quadratic model.

  2. P-values for each estimate correspond to t statistics of Student's t-tests.

  3. The Bonferroni-corrected alpha is 0.05/21=0.0024.

B 2.6±0.6 0.01    0.85 –0.4±0.1 0.004    0.41
D 1.2±0.3 <0.001 –1.5±0.5 0.05 0.78 –0.9±0.3 0.005 1.5±0.5 0.006 0.46
F 0.3±0.1 0.003    0.34 –0.7±0.02 0.009 1.1±0.5 0.04 0.49
G0.2±–0.1±0.1   0.20.06
H 0.4±0.1 <0.001    0.2 –0.4±0.1 <0.001    0.46
Figure 3.

Correlated evolutionary change of standardized life-history traits r (filled circles) and K (empty circles) on galactose after experimental selection in a glucose-limited environment over 5000 generations. Panels show the same lines (A–H) and clones as in Figure 2. Statistics for regression lines are in Table 2. Regression lines are not shown for G because neither was significant.

Next, we analyzed the differences (steps) in r and K between clones sampled at intervals of 200–300 generations. Adaptation to glucose had opposing effects on r and K in galactose, generating a negative relationship between steps for r and K among clones (Fig. 4A) and within each line (r/K correlations in Table 3). Over all clones, twice as many steps (differences between two consecutive time-points) contributed to a negative correlation between r and K (102 steps in top-left and bottom-right quadrants of Fig. 4A) than to a positive relationship (50 steps in top-right and bottom-left quadrants), and slightly more mutations increased r at the expense of K (61 steps) than the converse (41 steps; inline image= 4, df = 1, P= 0.05; Fig. 4A). The negative relationship between r and K was further supported by the linear decrease of r with K nested within line (F8, 151= 121, P < 0.0001, R2= 0.71; see also Table 3). The r/K relationship differed among lines, suggesting replicate lines were not moving on the same trade-off line (there was a significant interaction between the K and line effects for explaining r; F7, 152= 4.8, P < 0.0001). The differences among clones in their fit to the overall r/K negative relationship were not generally predicted by their values of r or K, or by EH, even among clones from the same selection line.

Figure 4.

The relationship between changes in r and changes in K between time-steps during selection in glucose (A), or after selection in galactose (B). The area of each of the four bubbles is proportional to the number of data points in its quadrant.

Table 3.  Standardized regression weights (RW) in the structural equation model shown in Figure 5 estimated for each line.
Line R2 EHr EH→Δrr→ΔrΔr→ΔK r/K correlation
  1. R 2 are the proportion of variance in Δr and ΔK explained by each model, the P-values are associated to the RW for each causal link, and ρ are the correlation coefficients between r/K among the 20 ancestors for each line. ***P < 0.0001. The Bonferroni-corrected alpha is 0.05/40 = 0.0013.

B 0.35 0.29 0.70    0.64 0.01 –0.82 0.001 –0.54 0.005 –0.39  
C0.360.690.77*** 0.100.73–0.680.02–0.83***–0.64***
D 0.62 0.14 0.87   –0.42 0.16 –0.40 0.17 –0.37 0.09 –0.17 0.01
E0.720.560.78*** 0.120.52–0.94***–0.75***–0.68***
F 0.27 0.37 0.23 0.30  0.14 0.50 –0.54 0.008 –0.61   –0.67  
H 0.70 0.51 0.56 0.003 –0.38 0.1 –0.56   –0.71   –0.76  

In summary, lines varied in the correlated responses of their growth rates and yields to selection in glucose. This variation provides the opportunity to estimate the effects of evolutionary history in glucose (EH), and of r and K in galactose, on the subsequent direct response to selection in galactose for each clone.


On average, the growth rates of the 160 clones selected on galactose for approximately 120 doublings accelerated in that environment by 0.71 SD (calculated as the difference between averages after and before selection, over the SD before selection) at the expense of lowering yield by 0.65 SD (paired t-test, t159= 14 for r and –8.6 for K, P < 0.0001). Not all lines A–H increased r to the same extent (line explained changes in r, F7,152= 3.5, P= 0.001, R2= 0.14). Specifically, line B responded more than lines A, D, and E (Tukey–Kramer test, P < 0.03). However, and in contrast to the correlated response to selection in glucose (previous section), all lines showed a similar negative relationship between Δr, the change in r, and ΔK, the change in K (line was not a significant cofactor of Δr, nested in line, in predicting ΔK; F7,152= 1.3, P= 0.23). Lastly, because selection on galactose directly increased r, the region of the r/K relationship occupied by the clones shifted toward the top-left quadrant of Figure 4B; there are 113 points in the top-left quadrant and only 22 at the bottom right of Figure 4B2= 88, df = 1, P < 0.0001). Thus, the direct response to selection in galactose increased r and reduced K much more consistently than did the correlated response to selection on glucose.

We used structural equation modeling to test simultaneously for the effect of EH on r in the ancestral clones, and for the effects that these two variables had on the response to selection in galactose. We assumed that Δr was the target of selection in galactose and was influenced by EH and r, and that Δr could influence ΔK (Fig. 5). This assumption would be misleading only if selection favored lower K while larger r was an indirect consequence. This scenario does not seem plausible given that we selected in batch cultures, which generally favors rapid growth over some other traits (Vasi et al. 1994), especially if survival during stationary phase is high (cell density did not decline once K was reached in galactose).

Overall, the number of generations in glucose did not influence the response to selection on galactose Δr (Table 3; Fig. 5). The standardized regression weights (similar to partial regression coefficients in structural equation modeling) for EH were small and not statistically significant, except for line B. Instead, the analysis suggests that it was mainly variation among clones in ancestral growth rates that explained the variation in Δr; fast-growing clones tended to adapt less than slow-growing clones in all lines (Fig. 6). Note that this model even held for lines that did not show a temporal pattern in Δr (Fig. 3; Table 3). However, the relationship between r and Δr was not homogeneous among lines (the line×r interaction effect was significant in a model with line and r, F7,152= 3.2, P= 0.003, model R2= 0.59). Multiple comparisons showed that lines C, F, and G had slopes of Δr over r that were shallower than those of the other five lines (–0.24 vs. –0.56, on average; Fig. 6). In conclusion, within lines, r increased with the number of generations in glucose (Figs. 3, 5; Table 2, 3), and this reduced the adaptive response in r during subsequent selection in galactose (Figs. 5, 6; Table 3). The cost imposed on K of faster growth (Fig. 4) is further suggested by the significant negative effect of Δr on ΔK (except for line D; Table 3).

Figure 6.

The response to selection on galactose of clones isolated from glucose selection lines, as a function of their ancestral growth rate in galactose. The response of a clone is the trait value after selection on galactose minus the trait value before selection on galactose. Population growth rate r (filled circles) and carrying-capacity K (empty circles) on galactose are shown for replicate lines A–H. Panels I and J show the responses for all lines A–H together.


The correlation between r and K may have resulted in part or in whole from an environmental correlation between these traits rather than a genetic trade-off. For example, if stochastic variation in the initial population size N0 directly affects r (e.g., because of resource competition, but other mechanisms are possible), r and K may be correlated environmentally because of the positive correlation between N0 and K for the 160 clones (Theil–Sen nonparametric linear equation and P-value; ancestral: 0.344K– 0.028, P < 0.0002; evolved: 0.349K– 0.31, P < 0.0002). To test for this environmental correlation, we measured the r/K relationship resulting from the nonheritable variation among replicate assays for a given clone. The slopes of r over K were consistently negative, even when differences among assays were due solely to environmental variance (test on abundances for each sign, for ancestors, χ2= 69, for evolved clones, χ2= 46; df = 1, N= 160; P < 0.0001 in both cases). Moreover, the slopes of r over K among the 20 clones isolated from each glucose line after selection on galactose were not significantly different from the nonheritable correlations observed in either ancestral or evolved clones (Kruskal–Wallis ANOVA, χ2= 2.3, df = 3, P= 0.51; ranks of slopes were analyzed because their distribution was highly leptokurtic; Fig. 7). We also found no evidence that the r/K relationship among replicate assays had evolved within the A–H selection lines (no significant EH or EH×line interaction effects in likelihood ratio tests for ancestral clones, χ2 < 11, P > 0.15, and galactose-adapted clones, χ2 < 5, P > 0.3).

Figure 7.

The intensity of density dependence estimated by the slope of linear regressions of r over K among the three replicate assays for ancestral and evolved clones (N= 160), among the 20 clones within a line before or after selection on galactose (N= 8), or among replicate assays with a smaller dilution ratio (1.5% instead of 40%). Ranks out of 456 slopes are shown because the distribution of slopes is leptokurtic. Error-bars are 95% confidence intervals. Negative slopes indicate that r decreased when K increased, even among replicates of the same clone (i.e., without genetic variation).

Finally, to test the idea that the large bottleneck size (i.e., 40% of final cell density) in galactose caused the environmental correlation between r and K, we estimated these parameters for 120 ancestral clones experiencing a bottleneck of 3 μl in 200 μl of fresh glucose-limited medium (∼1.5% bottleneck size). The r/K correlations, calculated from four replicates of each clone, were generally negative (93 of 120 slopes, or 78%, were negative, which is significantly greater than the null hypothesis of 50%; one-sided binomial test P < 0.0001). However, the r/K relationships from a small bottleneck size were shallower than the relationships with the large bottleneck (Wilcoxon nonparametric, small vs. large bottleneck for ancestral and evolved clones, P < 0.0001 and P= 0.0024, respectively; Fig. 7).


We isolated single yeast clones from eight replicate populations cryopreserved at regular intervals throughout 5000 generations of selection in a glucose-limited environment (Zeyl et al. 2003), and measured aspects of their life history in a galactose-limited environment. Selection in the glucose-limited environment included a bottleneck to 1% of the maximal population size followed by approximately 6.6 doublings, whereas in the galactose-limited environment a bottleneck size of 40% was followed by approximately 1.3 doublings (this was done to maintain a large effective population size on microwell plates). The correlated response in galactose to selection in glucose was generally positive for growth rate r and negative for yield K, although two of eight lines diverged from this pattern over the last 2000 generations of selection (Fig. 3C, G). Next, we selected the glucose-adapted clones on galactose for approximately 120 generations, which caused growth rate on galactose to accelerate and yield to decline. The magnitude of the growth rate acceleration was best predicted by the ancestral growth rate, with slow growers responding more than faster ones, in general (Figs. 5, 6). As a result, the correlation between r and K among clones within each line became shallower after selection on galactose, mainly because selection decreased variation among clones in both traits. This is clear evidence that r and K evolved, first during selection on glucose, and then during selection on galactose. It is less clear that the relationship between r and K evolved.

One explanation for the negative relationship between r and K is that it costs energy to accelerate the metabolic reactions that generate cellular energy, so that mutations that accelerate growth must reduce yield (Pfeiffer et al. 2001; Maclean 2008). A negative genetic correlation (or trade-off) between r and K should emerge from the thermodynamics principle of conservation of energy, which could apply in our system if the genotypes we selected were well-enough adapted to the selective conditions that further adaptation in growth rate must come at the cost of deterioration in yield (Novak et al. 2006; Fairbairn and Roff 2007). In yeast, the fast–slow strategies may correspond to the proportion of sugar that is fermented versus respired (Piškur et al. 2006; Hong et al. 2011). Fermentation is a fast but inefficient process because glycolysis (the energy-yielding path during fermentation) generates about 10 times less ATP than oxidative phosphorylation per molecule of glucose (Voet and Voet 2004).

Our results suggest that the negative correlation between r and K is environmental, K being negatively correlated with r even among replicates of the same clone. In fact, the slope of the r/K relationship is very similar whether it is taken among replicate assays or among clones within a line (Fig. 7). Our previous analyses accounted for density-dependent growth by fitting a logistic model to the population growth curves; however, this model does not account for possible environmental effects on r and K. The large volume of day-old culture transferred in our protocol for selection on galactose (80 μl into 120 μl of fresh medium) was not the only cause of the environmental correlation. Indeed, supplementary assays showed that the r/K relationships among replicate assays were also negative with a bottleneck of approximately 1.5%, although the slopes were slightly shallower than with the large dilution ratio (Fig. 7).

The nature of the environmental correlation between r and K is not known. Two mechanisms seem plausible: (1) chance variation in N0 impacts resource competition; stronger resource competition lowers r, and low r is associated with a higher respiration:fermentation ratio, which increases K; (2) other factors such as day-to-day variation in the growth medium or incubation conditions may influence the respiration:fermentation ratio and thus change both r and K directly. More importantly, both of these scenarios rely on the respiration:fermentation ratio, which is central to the thermodynamic model outlined above. Although we found little evidence for a genetic correlation between r and K, it remains likely that the thermodynamic principles outlined above are responsible for the negative environmental correlation we observed.

We did find two pieces of evidence for a genetic effect on the relationship between r and K. First, the r/K relationship diverged among lines as correlated responses to selection on glucose (Figs. 3, 4A). Here, the thermodynamic trade-off between rate and yield would predict a negative correlation between the average growth rate within a line and the slope of the r/K relationship, which is expected to become more negative as the population adapts and moves closer to the metabolic trade-off line (Novak et al. 2006). However, the relationship we observed has a positive slope if one outlying selection line is excluded (line B; slope ± SE = 10 ± 4, F1,5= 5.2, P= 0.07), the opposite pattern of what we would expect under the thermodynamic model. Second, the slopes of the r/K relationship among clones within each line before selection on galactose are steeper than both the within-line slopes after selection on galactose (paired t-test, t= 2.6, df = 7, P= 0.035) and the nonheritable slopes within each clone before selection on galactose (unequal variance ANOVA, F1,12.4= 4.0, P= 0.07; Fig. 7). Thus, the population of clones prior to selection on galactose has a slightly lower K for a given r in comparison to the population of clones evolved on galactose. This also indicates that the evolved clones, which grow faster on galactose than their ancestors (Figs. 5, 6), do not suffer more from density-dependence than do their respective ancestors. Again, this pattern is contrary to the prediction of the thermodynamic model. Given that we selected on galactose at high population densities (N0 > K/2), one may have expected the growth rate of evolved clones to become less sensitive to population density. The fact that this did not happen suggests that mutations that accelerated growth were more beneficial than mutations that decreased sensitivity to density-dependent effects, at least over the short-term selection on galactose.

It is not clear, however, that the thermodynamic model can be tested with growth curves alone. One might think that a stronger test would require comparing growth rate among clones at a similar initial density, that is, imposing soft selection. But this approach may not be more useful than hard selection (our protocol) because fast-growing genotypes would still experience density effects (lower resources and higher concentration of metabolic wastes) earlier in the growth cycle than slow growers, potentially also resulting in an environmental correlation. Instead, each clone changes its environment in a different way, and therefore it seems impossible to discriminate genetic differences in life-history traits from differences in how each strain responds to the changes it makes to its own environment. Environmental correlations should therefore be the null hypothesis for studies like ours, especially when yield can directly influence growth rate as in batch cultures. Of course, the thermodynamic trade-off is a necessity of cell metabolism, so it must apply in some situations, for example, to the fermenter and respirer specialists of S. cerevisiae used by Maclean and Gudelj (2006; Maclean 2008).

Two aspects of our research are not impacted by the fact that the negative relationship between r and K that we observed is likely not caused by a genetic trade-off: (1) the pattern of the correlated response of life-history traits in galactose after selection in glucose (Fig. 3), and (2) the effect of r on Δr, the response of r to selection on galactose.

Models of the evolution of specialization often assume that traits weakly or negatively correlated with fitness in the current environment will decline monotonically during selection (Cooper and Lenski 2000; Cooper et al. 2001; Elena 2002; Kassen 2002; Legros and Koella 2010; Ellis and Cooper 2010). Further, these studies suggest that early rapid adaptation to new conditions coincides with the bulk of the loss of adaptation to alternative conditions. The analogous relationship is expected for positive correlated responses to selection (Travisano et al. 1995b; Ostrowski et al. 2005; Jasmin and Kassen 2007). Despite the typical (Elena and Lenski 2003) hyperbolic increase of competitive fitness during selection in glucose (Fig. 2), five of eight populations showed a steady linear increase in the correlated response (here growth rate in galactose) whereas the other three lines showed a hyperbolic, a negative quadratic, or no change through time (Fig. 3). Thus, contrary to the antagonistic pleiotropy model, all lines showed a steady rate of correlated response in galactose despite their strongly decelerating rate of adaptation on glucose. This result could be taken as support for the mutation accumulation theory of specialization, which attributes correlated responses to selection to random mutations that are nearly neutral in the selective environment (Travisano 1997; Cooper and Lenski 2000; Maclean and Bell 2002). However, our results are also consistent with adaptive mutations having fitness effects of varying size, but similar pleiotropic effect sizes (see Ostrowski et al. 2005 for a similar result). Other studies that report more than a few time-points for changes in traits not under direct selection in long-term replicate selection lines have found a similar lack of correspondence between direct and correlated responses to selection (Maughan et al. 2006; Meyer et al. 2010). This suggests that the temporal association between direct and correlated responses may not be as common and homogeneous as early studies suggested.

Glucose-adapted clones that grew slowly on galactose improved more than initially faster clones, suggesting that mutations of larger effect on growth rate were available to slow growers, and that more resources were available to beneficial mutants that were competing against slow growers. Assuming that growth rate strongly correlates with fitness in galactose (Figs. 5, 6), the negative correlation between r and Δr suggests that the response to selection increases as genotypes move farther from the adaptive optimum. Both geometric models of adaptation (Fisher 1930; Burch and Chao 1999; see also Maynard Smith 1976) and quantitative genetics theory (Lande 1979) predict this pattern, which has often been observed in experimental evolution (Travisano et al. 1995a; Bull et al. 2000; Silander et al. 2007; Schoustra et al. 2009; Barrick et al. 2010; Gifford et al. 2011). Most of these studies tested for this relationship using compensatory adaptation to the cost of carrying an allele of resistance to an antibiotic or a parasite (Lenski 1988; Moore et al. 2000 and Reynolds 2000 in E. coli; Poon and Chao 2005; Barrick et al. 2010; Hall et al. 2010; Maclean et al. 2010) and we confirmed the pattern in a more general context (see also Moore and Woods 2006). A negative relationship between initial fitness and rate of adaptation suggests that there is a single maximal growth rate achievable for an organism in a given environment; whereas, if epistasis for fitness was ubiquitous among mutations, different genotypes would have access to different adaptive peaks and the negative relationship between r and Δr would be weak or inexistent (Burch and Chao 2000; Rokyta et al. 2009; De Visser et al. 2011). Nevertheless, the relationship between r and Δr did diverge among replicate glucose lines (lines C, F, and G have a shallower slope than the five other lines), possibly because the lines diverged in r and did not sample the same region of the rr relationship. However, this divergence was not strong enough to change the sign of the relationship, such that even over 5000 generations of selection in a glucose-limited environment, the growth rate in galactose was overall a good predictor of the response to selection on galactose. The negative correlation between fitness and the rate of adaptation that we observed here and that is so common in experimental evolution studies suggests that a general rule is emerging. It would be interesting to find cases where it does not hold.

Finally, we emphasize the paucity of evidence for genetic correlations between r and K in our results. Instead, much of the phenotypic variation among clones was driven by an environmental correlation between r and K. On the other hand, we obtained strong evidence that r was heritable and evolved by natural selection. Therefore, it is the relationship between r and K that generally showed a lack of heritability. Defining traits is often an issue in studies of multivariate evolution (Wagner and Zhang 2011) and we demonstrated above that such an issue exists even for life-history traits in controlled environments. We hope our results will help designing future tests of life-history trade-offs.

Associate Editor: I. Gordo


We thank J. B. Kelley and the work-study students in our lab for their help in the laboratory. C. Devaux commented a previous version of the manuscript, T. M. Anderson helped with statistics. We also thank two anonymous reviewers. JNJ was supported in part by the Fonds Québécois sur la Recherche et les Technologies (FQRNT), and the research was supported by National Science Foundation (NSF) grant no. 0820969 to CZ.