We have characterized the fitness of individual mutations as well as genetic interactions between mutations that arose during experimental evolution of yeast under glucose limitation. Our exhaustive analysis of single mutation fitness determined that only one to two mutations per adaptive clone individually result in a fitness gain, regardless of the total number of mutations in an adaptive clone (). The remaining mutations' effects are consistent with the null hypothesis of neutrality. Our data also show that, given an additive model, the identified singly adaptive mutations are sufficient to explain the fitness of adaptive clones M1–M3 and M5, and in one case (M4), there is evidence for negative epistasis between mutations (). The effect of negative epistasis may act like the idea of diminishing returns – adaptive mutations of large individual effect result in a smaller fitness effect when they occur together. The idea of diminishing returns of adaptation over time in a constant environment is further supported by data from long-term E. coli
evolution experiments, where the rate of fitness improvement was initially fast but quickly decreased over time and then remained low 
. Perhaps this decrease in the adaptive value of accumulated mutations is due to a maximum intrinsic fitness for a particular environment. This makes intuitive sense in the light of the mutations in our study having high relative fitness coefficients (1.1 to 1.45), which when combined under an additive model would result in extremely large fitness coefficients. This non-specific, negative epistasis-like phenomenon is further exemplified by the interactions between non-co-existing adaptive mutations (). Thus, it is possible that the pervasive negative epistasis observed is genetically promiscuous and not a result of the specific interactions between the two mutations, and any two mutations with large enough fitness increases will display such interactions. To our knowledge, this phenomenon has not been addressed in the literature, and there is as yet no distinction between true negative epistasis between specific sets of alleles and a non-specific, negative epistasis-like phenomenon due to a fitness upper bound, even though both scenarios would be classified as negative epistasis by its mathematical definition.
We have also determined that reciprocal sign epistasis between mutations in MTH1
constrains adaptation, which causes these two mutations to be mutually exclusive during the evolution experiment, a result that is consistent with data from an independent glucose-limited yeast evolution experiment 
. This constraint can be represented in an empirical fitness landscape, which maps out the mutational evolutionary trajectories available for natural selection, and our data make possible the construction of this landscape using direct fitness effects of combinations of mutations. Reciprocal sign epistasis between the adaptive mutations in MTH1
can be represented as a simple two-locus fitness landscape (Figure S5
). Here, the mth1
mutation is at a local optimum, as the only mutational steps available lead to a decrease in fitness, and it is not the fittest genotype on the landscape ( and Figure S4
). The HXT6/7
amplification mutation is the fittest genotype and is therefore the global optimum for this landscape. A consequence of this landscape is that lineages with an adaptive mutation in MTH1
are stuck on a local adaptive peak and may not be able to reach the higher fitness peak where the HXT6/7
amplification mutation lies. This is the likely reason why the mth1
mutations remain mutually exclusive for the duration the experiment.
The issue of how populations move from one peak to another in nature (the “peak shift” problem) has been disputed since Wright conceived of the fitness landscape metaphor 
. Furthermore, the existence of multi-peaked fitness landscapes themselves has recently been questioned at the theoretical level due to their immense multidimensionality causing neutral ridges connecting genotypes of high fitness on the landscape (the holey landscape model) 
. These ridges thereby eliminate the classical peak shift problem, and there is some experimental support for such ridges (e.g. 
). Since the adaptive mutations in mth1
remain mutually exclusive in our experiment, even after sampling several clones in different lineages, this supports the argument of an adaptive valley on the fitness landscape rather than a ridge connecting the two peaks. Alternatively, a ridge connecting the two peaks might be long and circuitous, and our experiment was not performed for sufficient evolutionary time for neutral evolution on a fitness ridge to occur. This is likely the case in 
, where an unresolved potentiating mutation is thought to have occurred 20,000 generations into the evolution experiment, allowing an innovative phenotype to evolve. In either case, the constraint is such that it would be difficult to adapt from one peak to the other.
In reality, all possible genotypes are present on a fitness landscape. In our case, while it is impossible to experimentally test all combinations of all possible mutations in conjunction with the mth1/(HXT6/7)
double mutant to prove that this portion of the fitness landscape does indeed have two peaks 
, the large population size of the culture (2×109
) means that a large spectrum of mutations should be sampled by natural selection often (~107
new SNP mutations per generation, based on the previously measured mutation rate 
). This suggests that natural selection may be rejecting the double mutant in myriad genomic contexts. Determining whether further evolution of an mth1
single mutant strain ever results in an HXT6/7
amplification mutation will shed additional light on the feasibility of adaptation from one peak to the other. If the HXT6/7
amplification can indeed appear on the mth1
background in such an evolution experiment, this would suggest that a compensatory mutation or mutations provide a fitness ridge between the peaks. While observing how an evolution experiment proceeds cannot indisputably prove the shape of the fitness landscape, it can inform the most relevant and repeated paths of adaptation.
It has been understood for quite some time that epistasis is a fundamental component of adaptation 
, but only have recent technological developments facilitated the discovery and testing of individual nucleotide changes and how they interact with one another to create function and fitness 
. We speculate that for the reciprocal sign epistasis between mth1
, the fitness defect may be caused by an overabundance of hexose transporter proteins in the cell, due to the fact that both individual mutations act to increase hexose transporter transcription 
. It is possible that the devotion of too many resources to the production of hexose transporters may take resources away from other essential functions. For example, the secretion machinery by which hexose transporters are localized to the plasma membrane may be overwhelmed by their overabundance. Alternatively, the large number of hexose transporters may take up space on the membrane's surface, preventing other transporters from being correctly localized or negatively impacting the fluidity of the membrane. Another scenario is that the overabundant hexose transporters may aggregate and form plaques in the cell due to their 12 hydrophobic trans-membrane domains. Understanding the mechanism of the reciprocal sign epistasis between mth1
will be important for understanding the underpinnings of molecular fitness landscapes and is worthy of further investigation.
The rugged mth1
) fitness landscape has far-reaching evolutionary implications. In the Dobzhansky-Muller model of postzygotic reproductive isolation, two species are separated from each other by a pair of genomic loci that interact negatively to create a hybrid organism that is of lower fitness compared to its parents 
. This model bears striking similarity to the epistatic interaction we see between mth1
amplification (also see 
). In our case, if two lineages became fixed for the mth1
mutations, the low fitness of hybrid double mutant offspring may lead the two lineages on a path to reproductive isolation, though in contrast to a typical D-M pair, clones containing the individual mutations are more fit than wild-type clones. This is in contrast to a recent finding of a D-M pair between two strains of S. cerevisiae
that were experimentally adapted to different environmental conditions 
. In this case, the two mutations were adaptive in the conditions in which they evolved, but maladaptive when made to co-occur in one of the conditions, which is the traditional way in which D-M pairs are thought to arise.
Mutually exclusive mutations are also known to exist in cancers 
. Of specific relevance is the recent observation that mutually exclusive mutations in the Ras pathway are individually adaptive under limiting glucose in colorectal cells, an environmental condition believed to be relevant to cancers in vivo 
. Intriguingly, these mutations lead to an increased expression of the glucose transporter GLUT1 resulting in increased glucose uptake by cancer cells 
. These results from human cancers closely parallel the mutations we see in the glucose sensing and Ras/cAMP pathways, which lead to an increase expression of the hexose transporters. Thus, human cancers and yeast may respond to the same selective pressures by mutating the same pathways, and these parallels beg the thought that reciprocal sign epistasis might be the mechanism by which these cancer mutations are mutually exclusive.