Percolation on fitness landscapes: effects of correlation, phenotype, and incompatibilities

We study how correlations in the random fitness assignment may affect the structure of fitness landscapes, in three classes of fitness models. The first is a phenotype space in which individuals are characterized by a large number n of continuously varying traits. In a simple model of random fitness assignment, viable phenotypes are likely to form a giant connected cluster percolating throughout the phenotype space provided the viability probability is larger than 1/2(n). The second model explicitly describes genotype-to-phenotype and phenotype-to-fitness maps, allows for neutrality at both phenotype and fitness levels, and results in a fitness landscape with tunable correlation length. Here, phenotypic neutrality and correlation between fitnesses can reduce the percolation threshold, and correlations at the point of phase transition between local and global are most conducive to the formation of the giant cluster. In the third class of models, particular combinations of alleles or values of phenotypic characters are "incompatible" in the sense that the resulting genotypes or phenotypes have zero fitness. This setting can be viewed as a generalization of the canonical Bateson-Dobzhansky-Muller model of speciation and is related to K-SAT problems, prominent in computer science. We analyze the conditions for the existence of viable genotypes, their number, as well as the structure and the number of connected clusters of viable genotypes. We show that analysis based on expected values can easily lead to wrong conclusions, especially when fitness correlations are strong. We focus on pairwise incompatibilities between diallelic loci, but we also address multiple alleles, complex incompatibilities, and continuous phenotype spaces. In the case of diallelic loci, the number of clusters is stochastically bounded and each cluster contains a very large sub-cube. Finally, we demonstrate that the discrete NK model shares some signature properties of models with high correlations.     

Simon-Ando decomposability and fitness landscapes

In this paper, we investigate fitness landscapes (under point mutation and recombination) from the standpoint of whether the induced evolutionary dynamics have a “fast-slow” time scale associated with the differences in relaxation time between local quasi-equilibria and the global equilibrium. This dynamical hevavior has been formally described in the econometrics literature in terms of the spectral properties of the appropriate operator matrices by Simon and Ando (Econometrica 29 (1961) 111), and we use the relations they derive to ask which fitness functions and mutation/recombination operators satisfy these properties. It turns out that quite a wide range of landscapes satisfy the condition (at least trivially) under point mutation given a sufficiently low mutation rate, while the property appears to be difficult to satisfy under genetic recombination. In spite of the fact that Simon-Ando decomposability can be realized over fairly wide range of parameters, it imposes a number of restriction on which landscape partitionings are possible. For these reasons, the Simon-Ando formalism does not appear to be applicable to other forms of decomposition and aggregation of variables that are important in evolutionary systems.     

Degeneracy: A design principle for achieving robustness and evolvability

Robustness, the insensitivity of some of a biological system's functionalities to a set of distinct conditions, is intimately linked to fitness. Recent studies suggest that it may also play a vital role in enabling the evolution of species. Increasing robustness, so is proposed, can lead to the emergence of evolvability if evolution proceeds over a neutral network that extends far throughout the fitness landscape. Here, we show that the design principles used to achieve robustness dramatically influence whether robustness leads to evolvability. In simulation experiments, we find that purely redundant systems have remarkably low evolvability while degenerate, i.e. partially redundant, systems tend to be orders of magnitude more evolvable. Surprisingly, the magnitude of observed variation in evolvability can neither be explained by differences in the size nor the topology of the neutral networks. This suggests that degeneracy, a ubiquitous characteristic in biological systems, may be an important enabler of natural evolution. More generally, our study provides valuable new clues about the origin of innovations in complex adaptive systems.     

Evolutionary Landscapes for the Acquisition of New Ligand Recognition by RNA Aptamers

The evolution of ligand specificity underlies many important problems in biology, from the appearance of drug resistant pathogens to the re-engineering of substrate specificity in enzymes. In studying biomolecules, however, the contributions of macromolecular sequence to binding specificity can be obscured by other selection pressures critical to bioactivity. Evolution of ligand specificity in vitro—unconstrained by confounding biological factors—is addressed here using variants of three flavin-binding RNA aptamers. Mutagenized pools based on the three aptamers were combined and allowed to compete during in vitro selection for GMP-binding activity. The sequences of the resulting selection isolates were diverse, even though most were derived from the same flavin-binding parent. Individual GMP aptamers differed from the parental flavin aptamers by 7 to 26 mutations (20 to 57% overall change). Acquisition of GMP recognition coincided with the loss of FAD (flavin-adenine dinucleotide) recognition in all isolates, despite the absence of a counter-selection to remove FAD-binding RNAs. To examine more precisely the proximity of these two activities within a defined sequence space, the complete set of all intermediate sequences between an FAD-binding aptamer and a GMP-binding aptamer were synthesized and assayed for activity. For this set of sequences, we observe a portion of a neutral network for FAD-binding function separated from GMP-binding function by a distance of three mutations. Furthermore, enzymatic probing of these aptamers revealed gross structural remodeling of the RNA coincident with the switch in ligand recognition. The capacity for neutral drift along an FAD-binding network in such close approach to RNAs with GMP-binding activity illustrates the degree of phenotypic buffering available to a set of closely related RNA sequences—defined as the sets functional tolerance for point mutations—and supports neutral evolutionary theory by demonstrating the facility with which a new phenotype becomes accessible as that buffering threshold is crossed.     

Random field models for fitness landscapes

 In many cases fitness landscapes are obtained as particular instances of random fields by randomly assigning a large number of parameters. Models of this type are often characterized reasonably well by their covariance matrices. We characterize isotropic random fields on finite graphs in terms of their Fourier series expansions and investigate the relation between the covariance matrix of the random field model and the correlation structure of the individual landscapes constructed from this random field. Correlation measures are a good characteristic of “rugged landscapes” models as they are closely related to quantities like the number of local optima or the length of adaptive walks. Our formalism suggests to approximate landscape with known autocorrelation function by a random field model that has the same correlation structure. Received: 10 November 1995 / Revised version: 19 February 1996     

Fitting protein-folding free energy landscape for a certain conformation to an NK fitness landscape

The NK fitness landscape is a mathematical landscape model with a parameter k that governs the degree of ruggedness of the landscape. We presented a procedure to fit a given landscape to the NK fitness landscape by introducing the “apparent k-value” k_app. In this paper, we defined the protein free energy (ΔG) landscape in amino acid sequence space, where ΔG is the folding free energy from a random coil to a “certain conformation”. Applying this landscape to our fitting procedure, we examined the statistical properties of the landscape. For calculation of a conformation energy, amino acid residues are represented by points, and interaction energies among amino acid residues are given as (1+K)-body interactions, that is, an unit of interacting (1+K) residues cooperatively contribute a single energy value to the conformational energy. Our results suggest that the apparent k-value of the free energy landscape is k_app≈K, and that the number of possible interactions among residues is unrelated to the k_app value. This leads to the inference that k_app takes values about 1-3 in real landscapes, if nature adopts two-body ∼four-body interaction energies.     

A further note on the estimation of a fitness function from two samples taken from a popolation

A modification is proposed for the moments method for estimating a fitness function that was discussed in an earlier paper (Manly , 1976b). This modification ensures that fitness estimates are always positive. The theory has been worked out for a fitness function of any number of variables and a computer program has been written to carry out the iterative calculations needed for estimation.     

On the notion of fitness,or: The selfish ancestor

We introduce a concept of fitness of a lineage as the number of descendents weighted by their degree of relatedness with the ancestor of the lineage and propose this as a scheme for analyzing altruistic behavior.     

Wolbachia属共生菌及其对节肢动物宿主适合度的影响

Wolbachia是广泛分布于节肢动物体生殖组织内呈母质遗传的一类共生细菌。近30多年来,大量的研究主要集中于Wolbachia对宿主生殖方式的调控方面;近年来的研究发现,Wolbachia对节肢动物宿主的适合度具有不同程度的影响。现对Wolbachia的宿主分布、存在部位及其对节肢动物宿主种群适合度的影响等方面进行了综述,探讨了Wolbachia在该领域的研究意义和潜在的应用价值。     

Genetic distance and species formation in evolving populations

Summary We compare the behavior of the genetic distance between individuals in evolving populations for three stochastic models.In the first model reproduction is asexual and the distribution of genetic distances reflects the genealogical tree of the population. This distribution fluctuates greatly in time, even for very large populations.In the second model reproduction is sexual with random mating allowed between any pair of individuals. In this case, the population becomes homogeneous and the genetic distance between pairs of individuals has small fluctuations which vanish in the limit of an infinitely large population.In the third model reproduction is still sexual but instead of random mating, mating only occurs between individuals which are genetically similar to each other. In that case, the population splits spontaneously into species which are in reproductive isolation from one another and one observes a steady state with a continual appearance and extinction of species in the population. We discuss this model in relation to the biological theory of speciation and isolating mechanisms.We also point out similarities between these three models of evolving populations and the theory of disordered systems in physics. Offprint requests to: P.G. Higgs     

Landscape dynamics and their effect on the functional connectivity of a Mediterranean landscape in Chile

Land use and cover changes have been identified as a major factor contributing to shape landscape structure and biodiversity patterns, particulary in areas with a long history of human occupation and habitat fragmentation, such as the Mediterranean landscapes. However, the existing studies on landscape change indicators for Mediterranean areas have mostly focused in Europe, while for other Mediterranean zones, and especially for South America, there is a serious lack of knowledge concerning the impact of landscape dynamics on ecological processes. Further research on this topic is urgently needed, given the high biodiversity levels and the rapidly increasing rates of human modification in the Mediterranean landscapes of South America. For this purpose, we investigated the dynamics of a landscape in the semiarid region of the Mediterranean zone of Chile, and measured the effect of those dynamics on functional connectivity, during a period of about four decades (1975–2011). Landscape connectivity indicators were extracted from a series of Landsat images. The Equivalent Connnected Area index (ECA) was used as indicator of connectivity trends, and was evaluated for three representative distances of seed dispersal in the study area (150 m, 500 m and 1000 m). In addition, the patches that most contribute to maintain the present connectivity, and their roles as connectivity providers, were identified through a set of commensurable indicators: betweenness centrality and the fractions (intra, flux connector) of the Integral Index of Connectivity. We found that these indicators were useful to detect and summarize a number of previously unreported trends in these Mediterranean landscapes. First, population growth and economic development were compatible with an increase in functional connectivity for forest habitats, mainly because the abandonment of marginal agricultural lands and their subsequent conversion to espinals (Acacia caven) triggered vegetation succession towards secondary forests. Second, increased forest connectivity was not associated to a decrease in the characteristic heterogeneity of Mediterranean landscapes. Third, many patches of espinal, despite being commonly regarded as of poor conservation value, were crucial to promote connectivity by acting as stepping stones among other patches with higher habitat quality. The approach here presented provides a combined assessment of landscape structure, function and change that should be valuable and applicable to deliver operational indicators in dynamic landscapes in South America and other Mediterranean regions.     

Extinction debt and the role of static and dynamical fragmentation on biodiversity

The mass-extinction events caused by human-driven habitat loss are a current concern in conservation science. However, the observed number of extinctions is considerably smaller than predicted. The overestimation of extinction rates comes from the time-delay which depends on the species sensitivity to habitat changes. The standard method of predicting the effect of habitat loss on biodiversity is to use the species–area relationship and progressively following it backwards to smaller areas. The difference between the actual number of species and the one provided by the backwards species–area relationship is dubbed extinction debt. Previous studies in general adopt a static view for the spatial distribution of species. Nonetheless, a precise understanding of the problem urges us to adopt a dynamic framework to this issue since the time between disturbances of the landscape plays an active role in influencing the strength of the extinction debt. In this context, here we address two distinct approaches for this question: a static and a dynamic view of fragmentation. In the former we quantify the extinction debt in a quenched spatial distribution of species, whereas in the latter the community is let to evolve between disturbance events of the landscape. Here we show that the size of the extinction debt depends on the pattern of the fragmentation. It is found that random distributions of destroyed habitats provide larger extinction debts than those obtained for contiguous areas of fragmentation. Furthermore, in the dynamic approach it is observed that dispersal can lead to unexpected outcomes such as lower biodiversity levels than ones inferred from the backwards species–area relationship.     

Fame,fortune, and fitness at the Academy Awards

People across many societies routinely participate in physical or intellectual competitions in the absence of immediate substantial monetary or other apparent material rewards. But increased fame and social status associated with awards, such as the “Oscars”, need not be necessarily and solely a cultural construct unrelated to natural selection. Rather, prizes might be badges of honor if they are also honest indicators of evolutionary fitness. Analyses of reported reproductive success data, from a survey of well-known female and male actors, followed previously reported patterns of biological fitness in this sample of a human population. In addition, the numbers of Academy Awards received for acting were positively associated with reported numbers of biological children for both genders. The association of increased fitness with more awards received was statistically consistent even when considering that this subset of the population conformed to the Bateman effect in human reproduction: male actors had a more positive correlation than females between cumulative numbers of married partners and overall numbers of children. Honest signals of reproductive quality that are displayed by both sexes are expected to occur in humans and other species with costly biparental care and mutual mate choice.     

Impact of drug resistance on fitness of Mycobacterium tuberculosis strains of the W-Beijing genotype

Mycobacterium tuberculosis strains of the W-Beijing genotype became a common cause of tuberculosis during the past years and they are often associated with drug resistance. The biological factors facilitating the selection and wide dissemination of these strains are not known. To determine how acquisition of drug resistance affected growth of strains of the W-Beijing genotype, the growth of 55 M. tuberculosis isolates were studied using the BBL MGIT Mycobacteria Growth Indicator Tube and the BACTEC MGIT 960 System. Susceptible strains of non-Beijing genotypes were found to be the most fit strains. Drug-resistant strains of non-Beijing genotypes were more likely to grow slower than susceptible strains (P=0.001). Drug-resistant strains of the W-Beijing genotype had two tendencies of growth: some of them showed reduced growth compared to susceptible strains, while others did not show loss of fitness measured as growth.     

Pruning the tree of life: k-core percolation as selection mechanism

We propose a model for evolution aiming to reproduce statistical features of fossil data, in particular the distributions of extinction events, the distribution of species per genus and the distribution of lifetimes, all of which are known to be of power-law type. The model incorporates both species-species interactions and ancestral relationships. The main novelty of this work is to show the feasibility of k-core percolation as a selection mechanism. We give theoretical predictions for the observable distributions, confirm their validity by computer simulation and compare with fossil data. A key feature of the proposed model is a co-evolving fitness landscape determined by the topology of the underlying species interactions, ecological niches emerge naturally. The predicted distributions are independent of the rate of speciation, i.e. whether one adopts an gradualist or punctuated view of evolution.     

Evolutionary dynamics, epistatic interactions, and biological information

We investigate a definition of biological information that connects population genetics with the tools of information theory by focusing on the distribution of genotypes found in a population. Previous research has treated loci as non-interacting by making specific approximations in the calculation of information-theoretic quantities. We expand earlier mathematical forms to include epistasis, or interactions between mutations at all pairs of loci. Application of our improved measure of biological information to evolution on two-locus, two-allele fitness landscapes demonstrates that mutual information between loci reflects epistatic interaction of mutations. Finally, we consider four-locus, two-allele fitness landscapes with modular structure. As modular interactions are inherently epistatic, we demonstrate that our refined approximation provides insight into the underlying structure of these non-trivial fitness landscapes.     

Tests for host-associated fitness trade-offs in the milkweed-oleander aphid

The milkweed-oleander aphid, Aphis nerii (Boyer de Fonscolombe) (Homoptera: Aphididae), feeds on different milkweed species in northern California than in Puerto Rico. The hosts vary, primarily between regions, for both identity and quantity of cardenolides that the aphid sequesters for its own defense. In tests for hostassociated fitness trade-offs only one case was found in which host plant and fitness corresponded, but the effect was not significant. However, power to detect fitness trade-offs was limited and the possibility of considerable differences in fitness on a particular host for aphids from different hosts cannot be excluded. On Californian host species, among which migration is common, generalized host use could result from selection for general-purpose genotypes. However, this explanation cannot apply to generalized host use of Californian and Puerto Rican milkweeds because the regions are isolated by distance. A cardenolide sequestration mechanism that is free of substantial energy costs could provide the basis for fitness homeostasis on variable host plants that makes trade-offs unlikely even on hosts from different regions.     

Remotely sensed landscape heterogeneity as a rapid tool for assessing local biodiversity value in a highly modified New Zealand landscape

The widespread conversion of natural habitats to agricultural land has created a need to integrate intensively managed landscapes into conservation management priorities. However, there are no clearly defined methods for assessing the conservation value of managed landscapes at the local scale. We used remotely sensed landscape heterogeneity as a rapid practical tool for the assessment of local biodiversity value within a predominantly agricultural landscape in Canterbury, New Zealand. Bird diversity was highly significantly correlated with landscape heterogeneity, distance from rivers and the Christchurch central business district, altitude and average annual household income, indicating that remotely sensed landscape heterogeneity is a good predictor of local biodiversity patterns. We discuss the advantages and limitations of using geographic information systems to determine local areas of high conservation value.