Abstract. Robustness is the invariance of phenotypes in the face of perturbation. The robustness of phenotypes appears at various levels of biological organization, including gene expression, protein folding, metabolic flux, physiological homeostasis, development, and even organismal fitness. The mechanisms underlying robustness are diverse, ranging from thermodynamic stability at the RNA and protein level to behavior at the organismal level. Phenotypes can be robust either against heritable perturbations (e.g., mutations) or nonheritable perturbations (e.g., the weather). Here we primarily focus on the first kind of robustness-genetic robustness-and survey three growing avenues of research: (1) measuring genetic robustness in nature and in the laboratory; (2) understanding the evolution of genetic robustness; and (3) exploring the implications of genetic robustness for future evolution.

Epistasis for fitness means that the selective effect of a mutation is conditional on the genetic background in which it appears. Although epistasis is widely observed in nature, our understanding of its consequences for evolution by natural selection remains incomplete. In particular, much attention focuses only on its influence on the instantaneous rate of changes in frequency of selected alleles via epistatic contribution to the additive genetic variance for fitness. Thus, in this framework epistasis only has evolutionary importance if the interacting loci are simultaneously segregating in the population. However, the selective accessibility of mutational trajectories to high fitness genotypes may depend on the genetic background in which novel mutations appear, and this effect is independent of population polymorphism at other loci. Here we explore this second influence of epistasis on evolution by natural selection. We show that it is the consequence of a particular form of epistasis, which we designate sign epistasis. Sign epistasis means that the sign of the fitness effect of a mutation is under epistatic control; thus, such a mutation is beneficial on some genetic backgrounds and deleterious on others. Recent experimental innovations in microbial systems now permit assessment of the fitness effects of individual mutations on multiple genetic backgrounds. We review this literature and identify many examples of sign epistasis, and we suggest that the implications of these results may generalize to other organisms. These theoretical and empirical considerations imply that strong genetic constraint on the selective accessibility of trajectories to high fitness genotypes may exist and suggest specific areas of investigation for future research.

We demonstrate that in liquid cultures, defined in this study as a mass habitat, the outcome ofcompetition between Escherichia coli that produce an antibacterial toxin (colicin) and sensitive E. coli is frequency dependent; the colicinogenic bacteria are at an advantage only when fairly common (frequencies in excess of2 x 10-2). However, we also show that in a soft agar matrix, a structured habitat, the colicinogenic bacteria have an advantage even when initially rare (frequencies as low as 106). These contrasting outcomes are attributed to the colicinogenic bacteria's lower intrinsic growth rate relative to the sensitive bacteria and the different manner in which bacteria and resources are partitioned in the two types ofhabitats. Bacteria in a liquid culture exist as randomly distributed individuals and the killing of sensitive bacteria by the colicin augments the amount of resource available to the colicinogenic bacteria to an extent identical to that experienced by the surviving sensitive bacteria. On the other hand, the bacteria in a soft agar matrix exist as single-clone colonies. As the colicinogenic colonies release colicin, they kill neighboring sensitive bacteria and form an inhibition zone around themselves. By this action, they increase the concentration of resources around themselves and overcome their growth rate disadvantage. We suggest that structured habitats are more favorable for the evolution of colicinogenic bacteria.A number of phylogenetically distinct groups of bacteria produce toxic substances, known collectively as bacteriocins, that can kill members of the same or closely related species (1). The colicins, the most extensively studied class of bacteriocins, are produced by the bacterium Escherichia coli and other members of the family Enterobacteriaceae (for reviews see refs. 1-4). In general: (i) at any given time only a small fraction of the colicinogenic population actually produces colicin; (ii) the production ofthe colicin results in the death ofthe producing (induced) cells-i.e., lethal synthesis; (iii) colicinogenic bacteria not producing colicin are immune to the colicin released by the induced cells; and (iv) the characters ofcolicin production and immunity are determined by plasmid-borne genes. Colicin can kill sensitive bacteria by many varied mechanisms. For example, colicin K acts by deenergizing the cell membrane, colicin E2 inhibits DNA synthesis, whereas colicin E3 inhibits protein synthesis. In all cases, however, the killing action requires the initial adsorption of a colicin particle onto specific receptors present on the surface of sensitive bacteria. Multiple adsorptions per individual bacterium are possible, but a single hit is sufficient to kill. Sensitive bacteria, in turn, can mutate to resistance through the alteration or loss of the receptors. Resistance differs from the immunity ofcolicinogenic bacteria in that the latter results from the synthesis ofan intracellular inhibitor that neutralizes a colicin particle after it has adsorbed to a colicinogen...

In a recent article and monograph, May (1972May ( , 1973 has demonstrated that many of the models of predator-prey interactions used by ecologists have solutions specifying stable equilibrium points or stable limit cycles. These theoretical results are extremely significant. In the models considered by May, the interacting populations exist in homogeneous habitats. Consequently, it is not necessary to invoke spatial or temporal heterogeneities or nonattainment of equilibria to account for the coexistence of predators and their prey.The models studied by May are, however, nonspecific. The species growth and interactions are described simply as functions of their respective densities. The nature of the habitat, the relationships between the primary resources, and the growth of the prey populations are not specified. Neither is the form of the predation. Consequently the factors responsible for stabilizing the equilibria or limit cycles are described primarily in terms of the properties of the equations rather than in terms of the biology. As a result, this theory is of limited utility for predicting when there will be stable states of coexistence in a given predatorprey situation.Campbell (1961) studied the predator-prey association between bacteria and their viruses. His models were developed from a consideration of the biology of the interacting species, but were not very specific about the nature of the habitat and took no account of the relationship between prey growth and the availability of primary resources.In this investigation, we present models of this bacteriophage-bacteria interaction which are based on specific assumptions about the habitat, the use of primary resources, the population growth, and the nature of the interaction between predator and prey. We consider conditions for equilibria and demonstrate that on a priori grounds, stable states of coexistence are to be anticipated. We then compare the behavior of these models with that of experimental populations of Escherichia coli and its virulent virus T2. I. THEORETICAL CONSIDERATIONS The Basic ModelThe model developed here is an extension of that we used in a study of resource-limited population growth and competition on two trophic levels

The evolution of competitive interactions among viruses was studied in the RNA phage phi6 at high and low multiplicities of infection (that is, at high and low ratios of infecting phage to host cells). At high multiplicities, many phage infect and reproduce in the same host cell, whereas at low multiplicities the viruses reproduce mainly as clones. An unexpected result of this study was that phage grown at high rates of co-infection increased in fitness initially, but then evolved lowered fitness. Here we show that the fitness of the high-multiplicity phage relative to their ancestors generates a pay-off matrix conforming to the prisoner's dilemma strategy of game theory. In this strategy, defection (selfishness) evolves, despite the greater fitness pay-off that would result if all players were to cooperate. Viral cooperation and defection can be defined as, respectively, the manufacturing and sequestering of diffusible (shared) intracellular products. Because the low-multiplicity phage did not evolve lowered fitness, we attribute the evolution of selfishness to the lack of clonal structure and the mixing of unrelated genotypes at high multiplicity.