Introduction

Evolutionary constraints have been described with many different adjectives which leads to confusion (Antonovics and van Tienderen 1991). The problem also permeates to the classification of trade-offs. This is not a matter of employing different names for the same concepts but reflects an important overlapping among the concepts defined. Here, I propose a unified classification of evolutionary constraints and trade-offs. First, we briefly review some notions about components of fitness and adaptive landscapes, which are useful to understand how constraints and trade-offs limit the trajectories followed during evolution. All constraints are classified in two main types, depending on whether they restrict the phenotype-fitness or the genotype-phenotype relationship. The last type is, in turn, classified according to the level of biological organization to which the constraints belong. The classification of trade-offs simply follows from the classification of the constraints involved. We leave all the subtle problems relating to the experimental determination of trade-offs outside our scope. Trade-offs are illustrated with a reduced number of examples, used to clarify the main ideas behind each type. The mechanisms originating some fitness trade-offs are traced to the molecular level. A central issue is to show how a growth-variability trade-off, which operates at the level of metabolic fluxes, leads to the definition of a currency of fitness. The ways this currency is conditioned by evolutionary constraints are discussed.

Components of Fitness

Natural selection is one of the basic mechanisms of evolution. It requires that the organisms in a population show heritable phenotypic variation. The outcome of natural selection, acting on this variation, is that individuals with traits better suited for survival and reproduction in their environment will be more represented in the next generation. Therefore, to describe evolutionary processes, we need to define a measurable quantity that quantifies the ability of organisms to survive and reproduce in their environment. This quantity, called fitness, may be defined with respect to the phenotype or the genotype (Orr 2009). Here, we consider the first type of definition, because we focus on the constraints and trade-offs affecting phenotypic variation. Phenotypic variation may be conditioned by constraints in the phenotype-fitness relationship and the genotype-phenotype relationship, which we call selective and organizational constraints, respectively. These types of constraints are described below. A third type of phenotypic constraint, appearing when phenotypic variation is obtained in response to environmental changes, is not discussed here (Futuyma 2005).

Fitness may be estimated using the reproductive success, i.e. the number of descendants of an average female after one generation. In the case in which females reproduce once and then die (semelparous species), reproductive success may be simply calculated as the product of the probability of survival to reproductive age and the average number of offspring per survivor female. For those species in which females reproduce more than once (iteroparous species), the calculation is more complex but still depends on the two main components of fitness: survival and reproduction (Futuyma 2005). Note that reproduction needs growth, what is particularly clear for unicellular organisms where reproduction consists of growth and division and, therefore, the reproduction component of fitness could be better called growth/reproduction component. The two main components of fitness may be subdivided considering different stages of life history. For instance, survival may be divided into embryonic and adult survival, and reproduction into mating success and fecundity, but these subdivisions are somewhat arbitrary. In addition, subdivisions are not universal, e.g. mating success does not apply to asexual organisms. Descending in the trait hierarchy, life history traits are affected by behavioural (e.g. courtship), morphological (e.g. height), physiological (e.g. metabolic rate) and molecular (e.g. enzyme concentration) traits (Agrawal et al. 2010). Constraints and trade-offs operate on traits at the different levels of biological organization. Their effects propagate through the trait hierarchy, affecting life history traits and fitness.

Phenotypic Evolution in the Adaptive Landscape

The adaptive landscape is a representation to study phenotypic evolution in terms of the degree of adaptation of the various phenotypes in a population (Lande 1976; Arnold et al. 2001). It is a surface that relates average fitness to average trait values. It was introduced by Simpson (1953) to analyse phenotypic data in the fossil record.

The adaptive landscape for a single quantitative trait subject to selection may present three types of curves, representing three different modes of selection. Monotonic curves, increasing or decreasing, correspond to directional selection where one extreme phenotype is fittest (Fig. 1a), dome-shaped curves correspond to stabilizing selection where an intermediate phenotype is fittest (Fig. 1b) and U-shaped curves correspond to disruptive selection where two phenotypes are fitter than the intermediate between them (Fig. 1c) (Arnold et al. 2001). If the mean of a trait is situated some distance from the maximum of a dome-shaped adaptive landscape, the population initially experiences directional selection that will tend to pull the mean towards optimum fitness. Eventually equilibrium will be reached, although genetic drift can cause departures from upwards movement and equilibrium.

Fig. 1
figure 1

One-dimensional adaptive landscape. Three modes of selection: a directional, b stabilizing and c disruptive. The arrows show the directions of fitness improvement

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The relevant properties of the general multivariate case may be well illustrated with the case of two traits. The adaptive landscape represents all the possible combinations of the characters in a two-dimensional space. Each point in this space is the bivariate average value of the characters in the population. Fitness for each combination is given by elevation contours. To illustrate evolutionary dynamics in the adaptive landscape, we consider a stabilizing selection mode. In addition, we restrict to evolution under frequency-independent selection in a constant environment, so that the landscape presents a fixed topography. This is called a stationary adaptive landscape. For two continuously varying traits, the adaptive landscape can be represented by a hill-shaped surface, the optimum being represented by the crest of the hill. During evolution, the population tends to move uphill (Lande 1979). But, normally, the path does not follow the direction of greatest improvement in average fitness. Instead, the population will follow a curved trajectory determined by the starting point, the shape of the adaptive landscape and the genetic variation of the phenotypic characters in the population. Let us first consider the effect that the shape of the adaptive landscape has on the evolutionary trajectory. If the hill has circular contours, or elongated contours were the long axis is parallel to one of the axes of the two-dimensional space, there is no correlational selection, i.e. selection increasing the correlation between functionally related characters. On the other hand, elongated contours with long axes having a finite positive or negative slope impose positive or negative correlational selection, respectively. During evolution subject to correlational selection, trajectories tend to have a rapid initial phase along the short axis of the adaptive landscape and afterwards a slower phase along the long axis. In addition to these effects of the shape of the adaptive landscape, the distribution of the genetic variation of the phenotypic characters in the population can also greatly affect the trajectory. The relevant properties of the distribution are the extent of genetic variation of the traits and the genetic correlation among them. Genetic variation is necessary for the traits to evolve and if they are genetically correlated they will not evolve independently. For instance, if the adaptive landscape is circular (a case of no correlational selection), the trajectory will show a rapid initial phase in the direction of greater genetic variance and then a slower phase in the direction of lower genetic variance (Arnold et al. 2001).

Constraints on Phenotypic Variation

For all species, there are regions of the phenotype space that appear to be unreachable or, at least, difficult to approach by the trajectories followed during evolution. These regions correspond to traits that are absent (for example, lack of feathers in mammals) or to existing traits whose values are biased or limited. The constraints that condition the accessible phenotype space are called evolutionary constraints. For our purposes, it suffices to classify evolutionary constraints in two main categories: selective and organizational.

Selective constraints condition the shape of adaptive landscapes. They arise at the level of ecological processes. For example, the male guppy, a tropical fish, shows a colourful pattern of spots. Individuals with brighter spots have greater mating success but they are more susceptible to being captured by predators. The direction of evolution of male colouration depends on which selection pressure is stronger. These conflicting selection pressures lead to a dome-shaped adaptive landscape corresponding to stabilizing selection, favouring intermediate colouration (Endler 1980, 1983). Size-related traits may also be subject to stabilizing selection, for example, birth weight of humans (Karn and Penrose 1951) or embryo size in C. elegans (Farhadifar et al. 2015). However, some evolutionary trajectories of cell size in bacteria have been better explained as correlated responses to selection on other traits (Graña and Acerenza 2001). Selective constraints may also involve more than one trait. Brodie III (1992) found evidence that colour pattern and escape behaviour in the garter snake are selected simultaneously. The highest fitness was found for snakes that had striped patterns and made fewer reversals, or for those with spotted patterns that performed many reversals. Snakes with the other two possible patterns showed lower fitness. This type of selection, called correlational selection, acts to increase the correlation between the two functionally related characters, colour pattern and escape behaviour, constraining phenotypic variation. Importantly, the character correlation found is a consequence of selection only, because the characters show independent genetic variation. Other reported cases of traits subject to correlational selection leading to selective constraints are, for example, wing length and body mass of song sparrows (Schluter and Nychka 1994), phenology and floral morphology of orchids (Maad 2000) and pro- and anti-inflammatory effectors in the immune response (Guerreiro et al. 2012).

Organizational constraints are limitations on phenotypic variation caused by restrictions imposed by the composition, structure, kinetics and regulation of the organism. These are all the constraints that restrict the phenotype space generated by genotypic changes, including those that have been called genetic, functional and developmental constraints (Maynard Smith et al. 1985; Arnold 1992; Brakefield and Roskam 2006). Note that while selective constraints reduce the accessible phenotype space by limiting the persistence of phenotypic variants, organizational constraints do so by limiting the production of phenotypic variants. Next we describe some of the main types of organizational constraints, operating at the different levels of biological organization.

At the genome level, genes may be physically associated on the same chromosome. In this case, changes in allele frequencies at one locus may cause correlated changes at other loci with which that locus is linked. This association, called linkage disequilibrium, may constrain the patterns of phenotypic characters, even if linked genes independently affect each character. Recombination reduces the level of linkage disequilibrium, lowering the correlation between characters (Futuyma 2005). At the cellular processes level, the reactions are mediated by proteins. Mutations may change the structure of proteins, modifying their functions. As a result of mutations, enzymes may catalyse new biochemical reactions or may catalyse the same reaction with a different rate law (Ulusu 2015). In the first case, there are limitations in the new functions that can be achieved by mutation. For instance, there is no known enzymatic mechanism that can produce n-butanol by condensation of two molecules of ethanol, although this reaction is highly exergonic (Bar-Even et al. 2012). This constraint on the types of reactions that enzymes can catalyse is explained by the fact that enzyme catalysis is based on a limited number of reaction mechanisms. On the other hand, mutations that succeed to produce new enzyme functions may promote the synthesis of toxic compounds or hydrophobic intermediates that leak through the membrane, having deleterious effects on fitness. In the second case, i.e. mutants which catalyse the same reaction with a different rate law, there are several types of constraints that limit the effect that rate changes have on metabolite concentrations and fluxes. These may be classified in structural and kinetic constraints. The structure of a metabolic system consists on the network of component reactions and their stoichiometric coefficients. There are two types of structural constraints: concentration conservation and flux balance (Heinrich and Schuster 1996). The concentrations of certain metabolites are constrained by conservation relationships, for example, [ATP] + [ADP] = constant. These constraints operate at short-time scales, when synthesis and degradation of the conserved moiety is negligible (Hofmeyr et al. 1986). If the system reaches a stable steady state, the concentrations of intermediates take fixed values and the sum of the fluxes producing and consuming each metabolite are balanced. For instance, in a branch point with one input flux, J1, and two output fluxes, J2 and J3, the steady-state fluxes are constrained by the equation: J1 = J2 + J3. Note that while flux balance constraints apply to steady-state fluxes only, metabolite concentration constraints apply to transient regimes as well. Regarding kinetic constraints, the particular forms of the rate laws impose additional restrictions on the patterns of concentrations and fluxes that the metabolic system can display. For example, the structure of a metabolic network may show a certain maximum yield for the amount of a product that can be obtained from a unit amount of carbon source, but this yield may not be achieved in practice due to the particular kinetic properties of the reaction steps. If we focus at the whole cell level, the amount of protein that can be accommodated in the volume or membrane space of the cell is limited. These occupancy constraints impose upper limits to the concentrations of proteins that can be achieved and, therefore, to the increases in the enzyme concentrations that can be obtained by mutation. While, for many little represented enzymes, gene dose increase produces a proportional increase in the corresponding enzyme concentration, in the case that we increase the number of copies of all the genes (for example in diploid, triploid and tetraploid yeast) the volume shows a proportional compensatory increase and the total protein concentration remains essentially unchanged. Several studies have addressed the problem of assessing, quantitatively, the impact of structural, kinetic and occupancy constraints on the repertoire of responses that unicellular organisms can display (see for example, Kacser and Burns 1973; Reder 1988; Acerenza 1993, 1996a, b; Zhuang et al. 2011). At the organismal level, growth and development are conditioned by another type of organizational constraints, called developmental constraints. These constraints restrict morphogenetic evolution. Mutations that depart organisms from their normal development do so in a limited number of ways. For example, after 300 million years of evolution the vertebrate limb has become adapted to many different purposes (bat wing for flying, whale fin for swimming and human leg for walking) but the overall pattern of skeleton and muscles have varied very little. In particular, some patterns such as the middle digit being shorter than its neighbouring digits appear to be forbidden by morphogenetic construction rules (Holder 1983). More generally, development shows a remarkable robustness to mutations or environmental perturbations, property that has been called canalization (Waddington 1942, 1957). Constraints at the organismal level may be the consequence of constraints at the cellular level, described above, and constraints in the interaction between cells mediated by reaction–diffusion mechanisms (Oster and Murray 1989; Green and Sharpe 2015).

The description of organizational constraints was ordered according to the levels of organization of the organism. The effect of constraints at one level may spread to processes occurring at higher levels of the organism and at the population level. In addition, some evolutionary constraints, not included in organizational constraints, may take place at the level of populations only. Individuals or propagules moving from one population to another may change the genetic constitution of populations. This gene flow may act as a constraint, affecting evolutionary dynamics (Hoffmann 2014).

Fitness Trade-offs

The selective and organizational constraints, described in the previous section, may give rise to selective and organizational trade-offs. Selective trade-offs appear, for example, when there are conflicting selection pressures on one trait, leading to stabilizing selection. The patterns of spots of male guppies, described above, illustrate this type of trade-off. Brighter spots provide greater mating success but this advantageous character carries a disadvantage because it increases susceptibility to predation. The fitness trade-off arises due to the conflicting selection pressures, predation and sexual selection, on male colouration (Endler 1980, 1983; Kottler et al. 2013). As a consequence of organizational constraints, mutations produce correlated changes in phenotypic characters. When these correlated changes involve characters affecting fitness in opposing directions, we say that there is an organizational trade-off (Hoffmann 2014). Organizational trade-offs, normally, occur through antagonistic pleiotropy, where a single gene influences two traits, the effect on one of the traits increasing and the effect on the other decreasing fitness. The underlying mechanism is the effect of a gene on cellular processes that contribute to different traits (Keightley and Kacser 1987). The processes rely on the acquisition of a limiting resource that is allocated to traits which show opposing effects on fitness (van Noordwijk and de Jong 1986; King et al. 2010; Guillaume and Otto 2012).

We distinguish two main types of organizational trade-offs: life history and across environments. These are the ones that ultimately constrain fitness. There are, of course, other types of organizational trade-offs, which originate on constraints acting at lower levels of biological organization. An example is the trade-off between rate and yield of ATP production, found at the level of cellular processes in heterotrophic organisms (Pfeiffer et al. 2001; Hummert et al. 2014). Due to this constraint, a trade-off between growth rate and yield was theoretically predicted but could be experimentally tested only through a negative correlation within populations (Novak et al. 2006). Yet another example is the relationship between enzyme accuracy/specificity and speed/turnover (Tawfik 2014). Importantly, lower level organizational constraints and trade-offs are in the basis of the mechanisms explaining the two main organizational trade-offs: life history and across environments.

In life history trade-offs, the same mutations which have a beneficial effect in a component of fitness belonging to one stage of life history are harmful in a component of fitness of another stage (Zera and Harshman 2001; Sinervo and Svensson 1998). Here we focus on life history trade-offs linking the two main components of fitness: growth and survival. Most of the examples will refer to unicellular organisms, where life history trade-offs are more straightforwardly related to the lower level trade-offs which originate them. But, as we will see, some growth-survival trade-offs in multi-cellular organisms could also be associated to trade-offs operating at the cellular level.

As a consequence of occupancy constraints, cellular organisms face a trade-off in allocating total protein between the different types of proteins. This constraint at the whole cell level prevents different components of fitness from being maximized simultaneously, for example, survival requiring stress response proteins and growth requiring ribosomes (Nyström 2004). Theory predicts that protein allocation patterns fall on a low-dimensional surface, whose vertices are the patterns optimal for each fitness component (Shoval et al. 2012). This hypothesis was tested using E. coli gene expression. The activity of promoters was tracked as bacteria grew from exponential to stationary phase. During exponential phase, the number of cells appearing per unit time is proportional to present population size while, during stationary phase, growth is limited because of nutrient depletion and/or waste accumulation. At the beginning (exponential phase), expression is devoted mostly to growth genes and at the end (stationary phase) primarily to stress/survival genes (Shoval et al. 2012). As a consequence of the life history trade-off, maximization of fitness in the subsequent growth phases is achieved transferring protein, gradually, from the growth to the survival component. In another study (Haverkorn van Rijsewijk et al. 2011), growth of 91 transcriptional regulator mutants of E. coli was measured in exponential phase batch culture on glucose, its preferred substrate. None of the mutants clearly exhibited increased biomass productivity, indicating that in the original strain resources are allocated to the growth component of fitness. In contrast, several regulatory mutants of B. subtilis grown in glucose, also its preferred substrate, did have improved biomass productivity (Fischer and Sauer 2005). Most of these mutants were exclusively regulators of not-yet-activated adaptive responses, suggesting that B. subtilis protects itself against unpredictable environmental changes allocating resources to the survival component of fitness at the expense of the growth component. In changing environments which are to some extent predictable, microorganisms may evolve to adapt to the temporal order of stimuli (Mitchell et al. 2009, Mitchell and Pilpel 2011). A good example is gut E. coli (Brunke and Hube 2014). In this adaptive prediction, fitness is transferred from the growth to the survival component, just before increasing the survival component is required for survival. Finally, clonal bacterial populations (e.g. of E coli) may show heterogeneity in the allocation of resources to the growth and the survival components of fitness. This is produced by phenotypic switching between the normal state and a persistent state, characterized by slow growth and increased stress tolerance. Persister cells survive antibiotic treatment but, unlike resistant mutants, can spontaneously switch to fast growth when regrown in fresh medium, generating a population that is sensitive to the antibiotic (Balaban et al. 2004).

Antibiotic resistance is constrained by a growth-survival trade-off. When an antibiotic is present, bacteria may develop antibiotic resistance to increase survival. This adaptation transfers resources from the growth to the survival component of fitness and, as a consequence, resistant genotypes are less fit than susceptible genotypes in the absence of antibiotic. The trade-off may be overcome by evolving adaptations which mitigate the deleterious effects of resistance (Lenski 1998; Andersson 2014). Moreover, in some cases, a positive correlation between growth and antibiotic resistance may be found. For instance, it has been shown that mutations that improve growth in an E. coli strain with low-level resistance to fluoroquinolones could simultaneously select for increases in drug resistance even in the absence of further exposure to the antibiotic (Marcusson et al. 2009).

Another environmental challenge that can produce a fitness transfer from the growth to the survival component is hyperosmotic stress. After this type of stress, E. coli shows an adaptive response which restores the initial volume and shape, irrespective of medium osmolarity. After full recovery is achieved, the organism grows at a reduced rate, the resultant growth rate scaling with the magnitude of the shock (Pilizota and Shaevitz 2014).

At the cellular level, the balance between growth and the degree of stress resistance is not just passively controlled, being regulated in response to environmental changes by signalling pathways. In E. coli, stressful conditions induce extensive reprogramming of gene expression (Chang et al. 2002). Guanosine-tetraphosphate (ppGpp) controls this response by coordinating down-regulation of protein synthesis and induction of the stress response (Jin et al. 2012). This causes transient growth arrest. After a time lag, during which reprogramming of gene expression takes place, cells resume growth at a lower rate in the presence of a persistent stress (López-Maury et al. 2008).

Life history trade-offs relating the two main components of fitness, survival and growth, are found in multi-cellular organism. An example is the trade-off between larval survival and adult body weight in Drosophila melanogaster. Analysis of global gene expression indicates that this trade-off could be the result of resource allocation at the organismal level, the underlying cellular mechanism being an adaptive resource allocation to protein synthesis (favouring growth) and energy metabolism (favouring survival), regulated by the RAS signalling pathway (Bochdanovits and de Jong 2004). Note that the life history trade-off in D. melanogaster, at the organismal level, results from a protein allocation trade-off at the cellular level, which is of the same type as the life history trade-off in the transit of E. coli from exponential to stationary phase, described above. In plants, an important life history trade-off is the dilemma between growth and defence against pathogens and stress (Todesco et al. 2010). At the level of cellular processes, this defence response relies on multiple metabolic pathways. Large carbon fluxes into secondary (stress related) metabolism during the defence response compete with reactions in primary (growth related) metabolism determining the growth-survival trade-off at the plant level (Bolton 2009; Matyssek et al. 2012).

Energy dissipating process, which might seem to be a waste of resources, contribute to improve survival in fluctuating environments of both unicellular and multi-cellular organisms. For example, at the cellular level, membrane leak may increase regulatory capacity (and survival) at the cost of reducing the resources allocated for growth (Acerenza et al. 2011). In addition, it may contribute to important functions, such as thermoregulation and reducing the production of reactive oxygen species, in multi-cellular organisms (Brand et al. 1994; Rolfe and Brand 1997).

The other main type of organizational trade-off is the trade-off across environments. In this, the same mutations which are beneficial in one environment are detrimental in another. An example was obtained in a long-term evolution experiment (LTEE) with E. coli, growing in glucose minimal medium (Lenski and Travisano 1994). After the first 10,000 generations, a parallel decay in the use of sixteen carbon sources was found (Cooper and Lenski 2000). Average catabolic function decline was accompanied by a rapid fitness increase. The trade-off across environments occurs because the same mutations that improve fitness on glucose decrease fitness on other substrates. This trade-off was used to explain the parallel increase in cell volume and fitness during laboratory evolution and other rather puzzling features of E. coli physiology and evolution (Graña and Acerenza 2001; Acerenza and Graña 2006). Other trade-offs across environments have been found during temperature (Bennett and Lenski 2007, Futuyma and Bennett 2009) and pH (Hughes et al. 2007) adaptations. Mutation accumulation could give the same outcome as a trade-off across environments. In contrast to antagonistic pleiotropy, in mutation accumulation, the decay of unused functions become fixed by genetic drift, increase of fitness in one environment and loss of fitness in the other being caused by different mutations. Recent studies on populations from the LTEE with E. coli (Lenski and Travisano 1994), which have evolved during 50,000 generations, suggest that for these longer periods of evolution most of metabolic decline was driven by mutation accumulation and not by antagonistic pleiotropy (Leiby and Marx 2014).

Life history trade-offs and trade-offs across environments may be two sequels of the same phenomenon. Let us consider the first 10,000 generations of the LTEE (Lenski and Travisano 1994). The mutations that simultaneously improve fitness on glucose and decrease fitness on other substrates also simultaneously improve the growth component and decrease the survival component of fitness (Cooper and Lenski 2000; Graña and Acerenza 2001). Therefore, how we classify this trade-off depends on our point of view: along life history or across environments.

Growth-Variability Trade-off and the Currency of Fitness

The survival of microorganisms in changing environments depends on the repertoire of adaptive responses that metabolic fluxes can display. This adaptive capacity may be quantified determining flux variability in genome-scale metabolic reconstructions (Mahadevan and Schilling 2003). In a recent publication (San Román et al. 2014), we show that, from the three sources of flux variability (internal, external and growth), growth is the only significant source in E. coli. The amount of flux variability depends on the availability of limiting resources. For instance, flux variability is approximately proportional to glucose uptake and increases by a factor of five when going from anaerobic to aerobic conditions. For a fixed input of limiting resources, there is a linear trade-off between the value at which growth is set and flux variability (Fig. 2), which we have called growth-flexibility or growth-variability trade-off (San Román et al. 2014).

Fig. 2
figure 2

Growth-variability trade-off. Due to organizational constraints operating at the cellular processes level, the correlated changes of the phenotypic characters (growth rate and flux variability) occur in opposite directions

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The growth-variability trade-off is an organizational constraint, operating at the cellular processes level. It constrains the type of flux patterns that the metabolic network can display, restricting the paths that can be followed during evolution. Next, we illustrate how the growth-variability trade-off constrains evolutionary trajectories, using the adaptive landscape representation. The phenotypic characters are growth rate and flux variability. We assume that fitness is an increasing function of them. This phenotype-fitness relationship corresponds to directional selection, where higher phenotypes are fitter (see Fig. 1a). In Fig. 3a, the phenotype-fitness relationship is represented in a three-dimensional plot (for simplicity, we assumed that the traits affect fitness in a multiplicative way). The contours (dashed lines) join points on the surface that have the same fitness. Trajectories followed during evolution in the adaptive landscape would also be conditioned by constraints in the genotype-phenotype relationship. The growth-variability trade-off, represented in Fig. 3a by a plain line, is one of these constraints. In Fig. 3b, we give the corresponding two-dimensional contour plot, where the trade-off is represented by a straight line. In the case that the evolutionary process under study does not affect the growth-variability trade-off (e.g. the structure of the network and the input fluxes remain unchanged), the trajectories in phenotype space followed during evolution may not pass through the grey region in Fig. 3b.

Fig. 3
figure 3

Adaptive landscape representation of the growth-variability trade-off. a Three-dimensional plot and b contour plot of the adaptive landscape. Dashed lines join points of equal fitness and the plain line represents the growth-variability trade-off. Phenotypes in the grey region in (b) are forbidden by the growth-variability trade-off

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As a consequence of the growth-variability trade-off, the only way to increase flux variability is decreasing growth to suboptimal values. This increase in variability may be used to achieve adaptive responses in the face of environmental challenges. Therefore, being able to achieve a high maximum growth rate is advantageous in both constant and fluctuating environments. In constant environments, where fitness increases with growth rate, growth may be set at a near-maximum value. In fluctuating conditions, the greater the maximum growth that can be achieved, the greater is the remaining growth, after growth is reduced to increase flux variability for adaptations.

In the context of life history trade-offs, when the environment changes, some life history components of fitness must decrease so that other components can increase, to maximize fitness in the new conditions. For instance, if high energy consumption is needed in the new environment, growth may be reduced to virtually zero to obtain maximum ATP production. In this case, maximization of fitness in the new conditions requires increasing the survival component at the expense of the growth component. At the metabolic level, the intermediary in the transfer of fitness among the life history components is flux variability. Thus, flux variability could be considered as a currency of fitness. The cost of adaptation would be the amount of flux variability (currency), obtained from growth reduction, which has to be invested for survival in the new environment.

The growth-variability trade-off is a robust property. We have shown that genome-scale models of pathogenic E. coli strains and previous versions of the commensal E. coli K-12 MG1655 strain, including the core model (Palsson 2006) which consists on less than 3 % of the reactions of the latest and more comprehensive model (Orth et al. 2011), also fulfil the growth-variability linear trade-off (San Román et al. 2014).

Could the amount of fitness currency, sustaining the variety of metabolic responses, be increased during the course of evolution? Expansion of the repertoire of metabolic responses can be achieved by increasing the set of processes that the metabolic network can perform (Handorf et al. 2005). This type of increase in network size and complexity may have been particularly spectacular during adaptations to the introduction of O2 into the biosphere around 2.2 billion years ago (Raymond and Segre 2006). In present organisms, however, a comparable expansion in network size would probably need an increase in the amount of total protein challenging the fulfilment of occupancy constraints. Evolution of the kinetic properties of existing enzymes, in particular when increasing the number of interactions between metabolites and enzymes, may also increase the repertoire of metabolic responses. For instance, it may be shown that for every new allosteric site appearing during evolution the metabolic system gains one additional independent steady-state response (Acerenza 1993). This source of novel responses is limited (Acerenza 1996a). An obvious limitation is that the number of allosteric sites that an enzyme can accommodate in its surface is relatively small if we compare it with the number of potential allosteric effectors, which could in principle be equal to the number of metabolic intermediates (more than one thousand in E. coli). For a given reaction, the number of allosteric effectors could be increased replacing a single monomeric enzyme with a polymeric enzyme or with several isoenzymes but these solutions, which require new proteins, are also restricted by occupancy constraints. Another potential limitation to the increase in the number of allosteric interactions is associated with the stability of metabolic systems. Theoretical work suggests that, at least in some cases, the probability that the steady state is unstable increases with the number of interactions (Gardener and Ashby 1970; May 1972, 1974). According to this result, an increase in the number of allosteric interactions, which has a beneficial effect on the flexibility of metabolic responses, could be disadvantageous for the stability of the network. However, the instability of the steady state may not, necessarily, be a disadvantageous property. For instance, glycolysis in yeast presents a transition from a stable to an oscillatory regime when the uptake of glucose is increased (Goldbeter 1996). Although it is not clear if glycolytic oscillations are beneficial to the organism, at least, they are not deleterious because they would have been eliminated during evolution. On the other hand, the existence of division mutants which form filaments without visible sign of constriction and attaining sizes of several hundreds of micrometres (Lutkenhaus and Mukherjee 1996) suggests that in the absence of division, a steady state in cell volume may not exist. This hypothesis is in agreement with the behaviour of a theoretical model of E.coli, developed to explain the parallel increase in cell volume and fitness during experimental evolution and which was also able to predict many relevant properties of the physiology and evolution of growth rate and cell volume (Graña and Acerenza 2001). In the model, for the sets of parameter values giving the correct predictions, inevitably, the steady state of the model does not exist (what mathematically corresponds to negative steady-state concentrations or cell volume). These results imply that E.coli’s state need not be a stable steady state, not even being necessary that an unstable steady-state exists. Taken together, the arguments previously developed suggest that occupancy constraints are probably the main restrictions which limit the increase in the amount of fitness currency during evolution.

According to the law of requisite variety (Ashby 1956), the repertoire of responses needed for adaptation in a changing environment must have at least the same variety as the environmental changes. Due to constraints and trade-offs, the variety of responses needed may not be implemented simultaneously and everywhere. To compensate for this deficiency, organisms have evolved a more efficient strategy based on sophisticated regulatory mechanisms that turn on and off the adequate responses in the appropriate times and regions of space. At the metabolic level, the currency for switching between responses is flux variability. The ultimate effect of this strategy is fitness transfer among the different fitness components, seeking to maximize adaptation in an ever changing environment.