The influence of inequality on the standard of living: Worldwide anthropometric evidence from the 19th and 20th centuries

We provide empirical evidence on the existence of the Pigou–Dalton principle. The latter indicates that aggregate welfare is – ceteris paribus – maximized when incomes of all individuals are equalized (and therefore marginal utility from income is as well). Using anthropometric panel data on 101 countries during the 19th and 20th centuries, we determine that there is a systematic negative and concave relationship between height inequality and average height. The robustness of this relationship is tested by means of several robustness checks, including two instrument variable regressions. These findings help to elucidate the impact of economic inequality on welfare.     

Robustness and evolvability: a paradox resolved

Understanding the relationship between robustness and evolvability is key to understand how living things can withstand mutations, while producing ample variation that leads to evolutionary innovations. Mutational robustness and evolvability, a system's ability to produce heritable variation, harbour a paradoxical tension. On one hand, high robustness implies low production of heritable phenotypic variation. On the other hand, both experimental and computational analyses of neutral networks indicate that robustness enhances evolvability. I here resolve this tension using RNA genotypes and their secondary structure phenotypes as a study system. To resolve the tension, one must distinguish between robustness of a genotype and a phenotype. I confirm that genotype (sequence) robustness and evolvability share an antagonistic relationship. In stark contrast, phenotype (structure) robustness promotes structure evolvability. A consequence is that finite populations of sequences with a robust phenotype can access large amounts of phenotypic variation while spreading through a neutral network. Population-level processes and phenotypes rather than individual sequences are key to understand the relationship between robustness and evolvability. My observations may apply to other genetic systems where many connected genotypes produce the same phenotypes.     

Evolution of robustness to noise and mutation in gene expression dynamics

Phenotype of biological systems needs to be robust against mutation in order to sustain themselves between generations. On the other hand, phenotype of an individual also needs to be robust against fluctuations of both internal and external origins that are encountered during growth and development. Is there a relationship between these two types of robustness, one during a single generation and the other during evolution? Could stochasticity in gene expression have any relevance to the evolution of these types of robustness? Robustness can be defined by the sharpness of the distribution of phenotype; the variance of phenotype distribution due to genetic variation gives a measure of 'genetic robustness', while that of isogenic individuals gives a measure of 'developmental robustness'. Through simulations of a simple stochastic gene expression network that undergoes mutation and selection, we show that in order for the network to acquire both types of robustness, the phenotypic variance induced by mutations must be smaller than that observed in an isogenic population. As the latter originates from noise in gene expression, this signifies that the genetic robustness evolves only when the noise strength in gene expression is larger than some threshold. In such a case, the two variances decrease throughout the evolutionary time course, indicating increase in robustness. The results reveal how noise that cells encounter during growth and development shapes networks' robustness to stochasticity in gene expression, which in turn shapes networks' robustness to mutation. The necessary condition for evolution of robustness, as well as the relationship between genetic and developmental robustness, is derived quantitatively through the variance of phenotypic fluctuations, which are directly measurable experimentally.     

Architecture-Dependent Robustness and Bistability in a Class of Genetic Circuits

Understanding the relationship between genotype and phenotype is a challenge in systems biology. An interesting yet related issue is why a particular circuit topology is present in a cell when the same function can supposedly be obtained from an alternative architecture. Here we analyzed two topologically equivalent genetic circuits of coupled positive and negative feedback loops, named NAT and ALT circuits, respectively. The computational search for the oscillation volume of the entire biologically reasonable parameter region through large-scale random samplings shows that the NAT circuit exhibits a distinctly larger fraction of the oscillatory region than the ALT circuit. Such a global robustness difference between two circuits is supplemented by analyzing local robustness, including robustness to parameter perturbations and to molecular noise. In addition, detailed dynamical analysis shows that the molecular noise of both circuits can induce transient switching of the different mechanism between a stable steady state and a stable limit cycle. Our investigation on robustness and dynamics through examples provides insights into the relationship between network architecture and its function.     

Connectance indicates the robustness of food webs when subjected to species loss

Many ecologists are concerned that biodiversity loss from human impact on natural ecosystems could compromise ecosystem stability. A relationship between diversity and stability was proposed by MacArthur [MacArthur, R.H., 1955. Fluctuation of animal populations and a measure of community stability. Ecology 36, 533–536.]. Current thinking (for example, McCann, K., 2000. The diversity–stability debate. Nature 405, 228–233.) acknowledges that interaction pattern among species, rather than species richness per se, is one element of this relationship. Dunne et al. [Dunne, J.A., Williams, R.J., Martinez, N.D., 2002a. Network structure and biodiversity loss in food webs: robustness increases with connectance. Ecol. Lett. 5, 558–567.] showed that the robustness of 16 food webs is correlated with their connectance. Connectance is one measure of interaction pattern. Robustness relates to the maintenance of network integrity and so has consequences for stability; the loss of integrity must have ecosystem-wide implications. This paper tests the hypothesis that changes in a food web's connectance indicate changes in its robustness. It concludes that any change in connectance with species loss, but especially large, negative changes, constitutes a decrease in robustness. Estimation of the change in connectance could support interpretation of monitoring data on species composition, acting as an indicator of food web robustness and, indirectly, of ecosystem stability. It could assist managers to understand the implications of biodiversity loss caused by human intervention in ecosystems, and could assist either choice of intervention or amelioration of impacts.     

Distributed robustness versus redundancy as causes of mutational robustness

A biological system is robust to mutations if it continues to function after genetic changes in its parts. Such robustness is pervasive on different levels of biological organization, from macromolecules to genetic networks and whole organisms. I here ask which of two possible causes of such robustness are more important on a genome-wide scale, for systems whose parts are genes, such as metabolic and genetic networks. The first of the two causes is redundancy of a system's parts: A gene may be dispensable if the genome contains redundant, back-up copies of the gene. The second cause, distributed robustness, is more poorly understood. It emerges from the distributed nature of many biological systems, where many (and different) parts contribute to system functions. I will here discuss evidence suggesting that distributed robustness is equally or more important for mutational robustness than gene redundancy. This evidence comes from the functional divergence of redundant genes, as well as from large-scale gene deletion studies. I also ask whether one can quantify the extent to which redundancy or distributed robustness contribute to mutational robustness.     

Histone Variant HTZ1 Shows Extensive Epistasis with,but Does Not Increase Robustness to,New Mutations

Biological systems produce phenotypes that appear to be robust to perturbation by mutations and environmental variation. Prior studies identified genes that, when impaired, reveal previously cryptic genetic variation. This result is typically interpreted as evidence that the disrupted gene normally increases robustness to mutations, as such robustness would allow cryptic variants to accumulate. However, revelation of cryptic genetic variation is not necessarily evidence that a mutationally robust state has been made less robust. Demonstrating a difference in robustness requires comparing the ability of each state (with the gene perturbed or intact) to suppress the effects of new mutations. Previous studies used strains in which the existing genetic variation had been filtered by selection. Here, we use mutation accumulation (MA) lines that have experienced minimal selection, to test the ability of histone H2A.Z (HTZ1) to increase robustness to mutations in the yeast Saccharomyces cerevisiae. HTZ1, a regulator of chromatin structure and gene expression, represents a class of genes implicated in mutational robustness. It had previously been shown to increase robustness of yeast cell morphology to fluctuations in the external or internal microenvironment. We measured morphological variation within and among 79 MA lines with and without HTZ1. Analysis of within-line variation confirms that HTZ1 increases microenvironmental robustness. Analysis of between-line variation shows the morphological effects of eliminating HTZ1 to be highly dependent on the line, which implies that HTZ1 interacts with mutations that have accumulated in the lines. However, lines without HTZ1 are, as a group, not more phenotypically diverse than lines with HTZ1 present. The presence of HTZ1, therefore, does not confer greater robustness to mutations than its absence. Our results provide experimental evidence that revelation of cryptic genetic variation cannot be assumed to be caused by loss of robustness, and therefore force reevaluation of prior claims based on that assumption.     

Financial hardship and obesity

There is a substantial correlation between household debt and health. Individuals with less healthy lifestyles are more likely to hold debt, yet there is little evidence as to whether this is merely a correlation or if financial hardship actually causes obesity. In this paper, we use data from the National Longitudinal Survey of Adolescent Health to test whether financial hardship affects body weight. We divide our sample into two groups: men and women, explore two different types of financial hardship: holding credit card debt and having trouble paying bills, and three outcomes: overweight, obese and body mass index (BMI). We use a variety of econometric techniques: Ordinary Least Squares, Propensity Score Matching, Sibling Fixed Effects, and Instrumental Variables to investigate the relationship that exists between financial hardship and body weight. In addition, we conduct several robustness checks. Although our OLS and PSM results indicate a correlation between financial hardship and body weight these results appear to be largely driven by unobservables. Our IV results suggest that there is no causal relationship between credit card debt and overweight or obesity for either men or women. However, we find suggestive evidence that having trouble paying bills may be a cause of obesity for women.     

Revisiting Robustness and Evolvability: Evolution in Weighted Genotype Spaces

Robustness and evolvability are highly intertwined properties of biological systems. The relationship between these properties determines how biological systems are able to withstand mutations and show variation in response to them. Computational studies have explored the relationship between these two properties using neutral networks of RNA sequences (genotype) and their secondary structures (phenotype) as a model system. However, these studies have assumed every mutation to a sequence to be equally likely; the differences in the likelihood of the occurrence of various mutations, and the consequence of probabilistic nature of the mutations in such a system have previously been ignored. Associating probabilities to mutations essentially results in the weighting of genotype space. We here perform a comparative analysis of weighted and unweighted neutral networks of RNA sequences, and subsequently explore the relationship between robustness and evolvability. We show that assuming an equal likelihood for all mutations (as in an unweighted network), underestimates robustness and overestimates evolvability of a system. In spite of discarding this assumption, we observe that a negative correlation between sequence (genotype) robustness and sequence evolvability persists, and also that structure (phenotype) robustness promotes structure evolvability, as observed in earlier studies using unweighted networks. We also study the effects of base composition bias on robustness and evolvability. Particularly, we explore the association between robustness and evolvability in a sequence space that is AU-rich – sequences with an AU content of 80% or higher, compared to a normal (unbiased) sequence space. We find that evolvability of both sequences and structures in an AU-rich space is lesser compared to the normal space, and robustness higher. We also observe that AU-rich populations evolving on neutral networks of phenotypes, can access less phenotypic variation compared to normal populations evolving on neutral networks.     

Mutational robustness and geometrical form in protein structures

Theoretical studies of RNA and lattice protein models suggest that mutationally robust or the so-called designable phenotypes tend to have special geometric features such as being more compact and more geometrically regular. Such geometrical forms have been also linked to speed of folding and stability properties that may also assist in promoting mutational robustness. Here we test these theoretical predictions on a non-redundant collection of 2,660 experimentally determined structures from the PDB (Protein Data Bank) and CATH (Class Architecture Topology Homologous superfamily) database. We first developed an index summarizing the geometrical regularity of the structures and then used this index to show that the statistical pattern of empirical data is consistent with the theoretical predictions relating geometry to mutational robustness. Mutationally robust proteins tend to be more symmetric and compact. But, the relationship between compactness and robustness cannot be explained simply by the geometrical packing of individual amino acids in proteins; rather, it is the property of the whole system that is related to the statistical characteristics of the folding landscape. Finally, we hypothesize that a triplet relationship between mutational robustness, stability and form is a general properties of objects that optimize real-valued relationships between sequences and discrete structures.     

The effect of mutational robustness on the evolvability of multicellular organisms and eukaryotic cells

Canalization involves mutational robustness, the lack of phenotypic change as a result of genetic mutations. Given the large divergence in phenotype across species, understanding the relationship between high robustness and evolvability has been of interest to both theorists and experimentalists. Although canalization was originally proposed in the context of multicellular organisms, the effect of multicellularity and other classes of hierarchical organization on evolvability has not been considered by theoreticians. We address this issue using a Boolean population model with explicit representation of an environment in which individuals with explicit genotype and a hierarchical phenotype representing multicellularity evolve. Robustness is described by a single real number between zero and one which emerges from the genotype–phenotype map. We find that high robustness is favoured in constant environments, and lower robustness is favoured after environmental change. Multicellularity and hierarchical organization severely constrain robustness: peak evolvability occurs at an absolute level of robustness of about 0.99 compared with values of about 0.5 in a classical neutral network model. These constraints result in a sharp peak of evolvability in which the maximum is set by the fact that the fixation of adaptive mutations becomes more improbable as robustness decreases. When robustness is put under genetic control, robustness levels leading to maximum evolvability are selected for, but maximal relative fitness appears to require recombination.     

Geometric robustness theory and biological networks

We provide a geometric framework for investigating the robustness of information flows over biological networks. We use information measures to quantify the impact of knockout perturbations on simple networks. Robustness has two components, a measure of the causal contribution of a node or nodes, and a measure of the change or exclusion dependence, of the network following node removal. Causality is measured as statistical contribution of a node to network function, wheras exclusion dependence measures a distance between unperturbed network and reconfigured network function. We explore the role that redundancy plays in increasing robustness, and how redundacy can be exploited through error-correcting codes implemented by networks. We provide examples of the robustness measure when applied to familiar boolean functions such as the AND, OR and XOR functions. We discuss the relationship between robustness measures and related measures of complexity and how robustness always implies a minimal level of complexity.     

A Nonadaptive Origin of a Beneficial Trait: In Silico Selection for Free Energy of Folding Leads to the Neutral Emergence of Mutational Robustness in Single Domain Proteins

Proteins are regarded as being robust to the deleterious effects of mutations. Here, the neutral emergence of mutational robustness in a population of single domain proteins is explored using computer simulations. A pairwise contact model was used to calculate the ΔG of folding (ΔG _folding) using the three dimensional protein structure of leech eglin C. A random amino acid sequence with low mutational robustness, defined as the average ΔΔG resulting from a point mutation (ΔΔG _average), was threaded onto the structure. A population of 1,000 threaded sequences was evolved under selection for stability, using an upper and lower energy threshold. Under these conditions, mutational robustness increased over time in the most common sequence in the population. In contrast, when the wild type sequence was used it did not show an increase in robustness. This implies that the emergence of mutational robustness is sequence specific and that wild type sequences may be close to maximal robustness. In addition, an inverse relationship between ??G _average and protein stability is shown, resulting partly from a larger average effect of point mutations in more stable proteins. The emergence of mutational robustness was also observed in the Escherichia coli colE1 Rop and human CD59 proteins, implying that the property may be common in single domain proteins under certain simulation conditions. The results indicate that at least a portion of mutational robustness in small globular proteins might have arisen by a process of neutral emergence, and could be an example of a beneficial trait that has not been directly selected for, termed a “pseudaptation.”     

Evolution under Fluctuating Environments Explains Observed Robustness in Metabolic Networks

A high level of robustness against gene deletion is observed in many organisms. However, it is still not clear which biochemical features underline this robustness and how these are acquired during evolution. One hypothesis, specific to metabolic networks, is that robustness emerges as a byproduct of selection for biomass production in different environments. To test this hypothesis we performed evolutionary simulations of metabolic networks under stable and fluctuating environments. We find that networks evolved under the latter scenario can better tolerate single gene deletion in specific environments. Such robustness is underlined by an increased number of independent fluxes and multifunctional enzymes in the evolved networks. Observed robustness in networks evolved under fluctuating environments was “apparent,” in the sense that it decreased significantly as we tested effects of gene deletions under all environments experienced during evolution. Furthermore, when we continued evolution of these networks under a stable environment, we found that any robustness they had acquired was completely lost. These findings provide evidence that evolution under fluctuating environments can account for the observed robustness in metabolic networks. Further, they suggest that organisms living under stable environments should display lower robustness in their metabolic networks, and that robustness should decrease upon switching to more stable environments.     

Why nestedness in mutualistic networks?

We investigate the relationship between the nested organization of mutualistic systems and their robustness against the extinction of species. We establish that a nested pattern of contacts is the best possible one as far as robustness is concerned, but only when the least linked species have the greater probability of becoming extinct. We introduce a coefficient that provides a quantitative measure of the robustness of a mutualistic system.     

Ensemble Modeling for Robustness Analysis in engineering non-native metabolic pathways

Metabolic pathways in cells must be sufficiently robust to tolerate fluctuations in expression levels and changes in environmental conditions. Perturbations in expression levels may lead to system failure due to the disappearance of a stable steady state. Increasing evidence has suggested that biological networks have evolved such that they are intrinsically robust in their network structure. In this article, we presented Ensemble Modeling for Robustness Analysis (EMRA), which combines a continuation method with the Ensemble Modeling approach, for investigating the robustness issue of non-native pathways. EMRA investigates a large ensemble of reference models with different parameters, and determines the effects of parameter drifting until a bifurcation point, beyond which a stable steady state disappears and system failure occurs. A pathway is considered to have high bifurcational robustness if the probability of system failure is low in the ensemble. To demonstrate the utility of EMRA, we investigate the bifurcational robustness of two synthetic central metabolic pathways that achieve carbon conservation: non-oxidative glycolysis and reverse glyoxylate cycle. With EMRA, we determined the probability of system failure of each design and demonstrated that alternative designs of these pathways indeed display varying degrees of bifurcational robustness. Furthermore, we demonstrated that target selection for flux improvement should consider the trade-offs between robustness and performance.     

Conservation of the segmented germband stage: robustness or pleiotropy?

Gene expression patterns of the segment polarity genes in the extended and segmented germband stage are remarkably conserved among insects. To explain the conservation of these stages, two hypotheses have been proposed. One hypothesis states that the conservation reflects a high interactivity between modules, so that mutations would have several pleiotropic effects in other parts of the body, resulting in stabilizing selection against mutational variation. The other hypothesis states that the conservation is caused by robustness of the segment polarity network against mutational changes. When evaluating the empirical evidence for these hypotheses, we found strong support for pleiotropy and little evidence supporting robustness of the segment polarity network. This points to a key role for stabilizing selection in the conservation of these stages. Finally, we discuss the implications for robustness of organizers and long-term conservation in general.     

Linking structural variability in long bone diaphyses to habitual behaviors: foragers from the southern African Later Stone Age and the Andaman Islands

The cross-sectional distribution of cortical bone in long bone diaphyses is highly responsive to mechanical loading during life, yet the relationship between systemic and localized influences on skeletal structure remains unclear. This study investigates postcranial robustness throughout the body among adults from two groups of foragers with different patterns and modes of mobility, to determine whether there is evidence for upper vs. lower body localization of skeletal robustness. The samples used for this comparison are from the southern African Later Stone Age (LSA; n = 65, male = 33, female = 28) dating from ca. 10,000 to 2,000 B.P., and 19th century indigenous Andaman Islanders (AI; n = 36, male = 17, female = 16). The LSA were highly mobile foragers who did not exploit offshore marine resources. In contrast, the AI had tightly constrained terrestrial, but significant marine, mobility. Geometric properties of cortical bone distribution in the diaphyses of the clavicle, humerus, femur, tibia, and first metatarsal are compared between the samples, providing a representation of skeletal robustness throughout the body. Multivariate ANOVA shows the AI to have significantly stronger clavicles and humeri, while the LSA femora, tibiae, and first metatarsals are stronger than those of the AI. These patterns, in which upper and lower limbs show biomechanical properties that are consistent with habitual behaviors, suggest localized osteogenic response. Although postcranial robustness appears to be correlated with overall limb function, the results suggest that more proximal elements within the limb may be more responsive to mechanical loading.     

Are Nested Networks More Robust to Disturbance? A Test Using Epiphyte-Tree,Comensalistic Networks

Recent research on ecological networks suggests that mutualistic networks are more nested than antagonistic ones and, as a result, they are more robust against chains of extinctions caused by disturbances. We evaluate whether mutualistic networks are more nested than comensalistic and antagonistic networks, and whether highly nested, host-epiphyte comensalistic networks fit the prediction of high robustness against disturbance. A review of 59 networks including mutualistic, antagonistic and comensalistic relationships showed that comensalistic networks are significantly more nested than antagonistic and mutualistic networks, which did not differ between themselves. Epiphyte-host networks from old-growth forests differed from those from disturbed forest in several topological parameters based on both qualitative and quantitative matrices. Network robustness increased with network size, but the slope of this relationship varied with nestedness and connectance. Our results indicate that interaction networks show complex responses to disturbances, which influence their topology and indirectly affect their robustness against species extinctions.