Maximum mutational robustness in genotype-phenotype maps follows a self-similar blancmange-like curve.

Phenotype robustness, defined as the average mutational robustness of all the genotypes that map to a given phenotype, plays a key role in facilitating neutral exploration of novel phenotypic variation by an evolving population. By applying results from coding theory, we prove that the maximum phenotype robustness occurs when genotypes are organized as bricklayer's graphs, so-called because they resemble the way in which a bricklayer would fill in a Hamming graph. The value of the maximal robustness is given by a fractal continuous everywhere but differentiable nowhere sums-of-digits function from number theory. Interestingly, genotype-phenotype maps for RNA secondary structure and the hydrophobic-polar (HP) model for protein folding can exhibit phenotype robustness that exactly attains this upper bound. By exploiting properties of the sums-of-digits function, we prove a lower bound on the deviation of the maximum robustness of phenotypes with multiple neutral components from the bricklayer's graph bound, and show that RNA secondary structure phenotypes obey this bound. Finally, we show how robustness changes when phenotypes are coarse-grained and derive a formula and associated bounds for the transition probabilities between such phenotypes.

The structure of genotype-phenotype maps makes fitness landscapes navigable.

Fitness landscapes are often described in terms of 'peaks' and 'valleys', indicating an intuitive low-dimensional landscape of the kind encountered in everyday experience. The space of genotypes, however, is extremely high dimensional, which results in counter-intuitive structural properties of genotype-phenotype maps. Here we show that these properties, such as the presence of pervasive neutral networks, make fitness landscapes navigable. For three biologically realistic genotype-phenotype map models-RNA secondary structure, protein tertiary structure and protein complexes-we find that, even under random fitness assignment, fitness maxima can be reached from almost any other phenotype without passing through fitness valleys. This in turn indicates that true fitness valleys are very rare. By considering evolutionary simulations between pairs of real examples of functional RNA sequences, we show that accessible paths are also likely to be used under evolutionary dynamics. Our findings have broad implications for the prediction of natural evolutionary outcomes and for directed evolution.

Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution.

SignificanceWhy does evolution favor symmetric structures when they only represent a minute subset of all possible forms? Just as monkeys randomly typing into a computer language will preferentially produce outputs that can be generated by shorter algorithms, so the coding theorem from algorithmic information theory predicts that random mutations, when decoded by the process of development, preferentially produce phenotypes with shorter algorithmic descriptions. Since symmetric structures need less information to encode, they are much more likely to appear as potential variation. Combined with an arrival-of-the-frequent mechanism, this algorithmic bias predicts a much higher prevalence of low-complexity (high-symmetry) phenotypes than follows from natural selection alone and also explains patterns observed in protein complexes, RNA secondary structures, and a gene regulatory network.

Changes in neonatal admissions, care processes and outcomes in England and Wales during the COVID-19 pandemic: a whole population cohort study.

OBJECTIVES: The COVID-19 pandemic instigated multiple societal and healthcare interventions with potential to affect perinatal practice. We evaluated population-level changes in preterm and full-term admissions to neonatal units, care processes and outcomes. DESIGN: Observational cohort study using the UK National Neonatal Research Database. SETTING: England and Wales. PARTICIPANTS: Admissions to National Health Service neonatal units from 2012 to 2020. MAIN OUTCOME MEASURES: Admissions by gestational age, ethnicity and Index of Multiple Deprivation, and key care processes and outcomes. METHODS: We calculated differences in numbers and rates between April and June 2020 (spring), the first 3 months of national lockdown (COVID-19 period), and December 2019-February 2020 (winter), prior to introduction of mitigation measures, and compared them with the corresponding differences in the previous 7 years. We considered the COVID-19 period highly unusual if the spring-winter difference was smaller or larger than all previous corresponding differences, and calculated the level of confidence in this conclusion. RESULTS: Marked fluctuations occurred in all measures over the 8 years with several highly unusual changes during the COVID-19 period. Total admissions fell, having risen over all previous years (COVID-19 difference: -1492; previous 7-year difference range: +100, +1617; p<0.001); full-term black admissions rose (+66; -64, +35; p<0.001) whereas Asian (-137; -14, +101; p<0.001) and white (-319; -235, +643: p<0.001) admissions fell. Transfers to higher and lower designation neonatal units increased (+129; -4, +88; p<0.001) and decreased (-47; -25, +12; p<0.001), respectively. Total preterm admissions decreased (-350; -26, +479; p<0.001). The fall in extremely preterm admissions was most marked in the two lowest socioeconomic quintiles. CONCLUSIONS: Our findings indicate substantial changes occurred in care pathways and clinical thresholds, with disproportionate effects on black ethnic groups, during the immediate COVID-19 period, and raise the intriguing possibility that non-healthcare interventions may reduce extremely preterm births.

Birthweight and patterns of postnatal weight gain in very and extremely preterm babies in England and Wales, 2008-19: a cohort study.

BACKGROUND: Intrauterine and postnatal weight are widely regarded as biomarkers of fetal and neonatal wellbeing, but optimal weight gain following preterm birth is unknown. We aimed to describe changes over time in birthweight and postnatal weight gain in very and extremely preterm babies, in relation to major morbidity and healthy survival. METHODS: In this cohort study, we used whole-population data from the UK National Neonatal Research Database for infants below 32 weeks gestation admitted to neonatal units in England and Wales between Jan 1, 2008, and Dec 31, 2019. We used non-linear Gaussian process to estimate monthly trends, and Bayesian multilevel regression to estimate unadjusted and adjusted coefficients. We evaluated birthweight; weight change from birth to 14 days; weight at 36 weeks postmenstrual age; associated Z scores; and longitudinal weights for babies surviving to 36 weeks postmenstrual age with and without major morbidities. We adjusted birthweight for antenatal, perinatal, and demographic variables. We additionally adjusted change in weight at 14 days and weight at 36 weeks postmenstrual age, and their Z scores, for postnatal variables. FINDINGS: The cohort comprised 90 817 infants. Over the 12-year period, mean differences adjusted for antenatal, perinatal, demographic, and postnatal variables were 0 g (95% compatibility interval -7 to 7) for birthweight (-0·01 [-0·05 to 0·03] for change in associated Z score); 39 g (26 to 51) for change in weight from birth to 14 days (0·14 [0·08 to 0·19] for change in associated Z score); and 105 g (81 to 128) for weight at 36 weeks postmenstrual age (0·27 [0·21 to 0·33] for change in associated Z score). Greater weight at 36 weeks postmenstrual age was robust to additional adjustment for enteral nutritional intake. In babies surviving without major morbidity, weight velocity in all gestational age groups stabilised at around 34 weeks postmenstrual age at 16-25 g per day along parallel percentile lines. INTERPRETATION: The birthweight of very and extremely preterm babies has remained stable over 12 years. Early postnatal weight loss has decreased, and subsequent weight gain has increased, but weight at 36 weeks postmenstrual age is consistently below birth percentile. In babies without major morbidity, weight velocity follows a consistent trajectory, offering opportunity to construct novel preterm growth curves despite lack of knowledge of optimal postnatal weight gain. FUNDING: UK Medical Research Council.

Identification of variation in nutritional practice in neonatal units in England and association with clinical outcomes using agnostic machine learning.

We used agnostic, unsupervised machine learning to cluster a large clinical database of information on infants admitted to neonatal units in England. Our aim was to obtain insights into nutritional practice, an area of central importance in newborn care, utilising the UK National Neonatal Research Database (NNRD). We performed clustering on time-series data of daily nutritional intakes for very preterm infants born at a gestational age less than 32 weeks (n = 45,679) over a six-year period. This revealed 46 nutritional clusters heterogeneous in size, showing common interpretable clinical practices alongside rarer approaches. Nutritional clusters with similar admission profiles revealed associations between nutritional practice, geographical location and outcomes. We show how nutritional subgroups may be regarded as distinct interventions and tested for associations with measurable outcomes. We illustrate the potential for identifying relationships between nutritional practice and outcomes with two examples, discharge weight and bronchopulmonary dysplasia (BPD). We identify the well-known effect of formula milk on greater discharge weight as well as support for the plausible, but insufficiently evidenced view that human milk is protective against BPD. Our framework highlights the potential of agnostic machine learning approaches to deliver clinical practice insights and generate hypotheses using routine data.

Understanding learner behaviour in online courses with Bayesian modelling and time series characterisation.

The intrinsic temporality of learning demands the adoption of methodologies capable of exploiting time-series information. In this study we leverage the sequence data framework and show how data-driven analysis of temporal sequences of task completion in online courses can be used to characterise personal and group learners' behaviors, and to identify critical tasks and course sessions in a given course design. We also introduce a recently developed probabilistic Bayesian model to learn sequential behaviours of students and predict student performance. The application of our data-driven sequence-based analyses to data from learners undertaking an on-line Business Management course reveals distinct behaviors within the cohort of learners, identifying learners or groups of learners that deviate from the nominal order expected in the course. Using course grades a posteriori, we explore differences in behavior between high and low performing learners. We find that high performing learners follow the progression between weekly sessions more regularly than low performing learners, yet within each weekly session high performing learners are less tied to the nominal task order. We then model the sequences of high and low performance students using the probablistic Bayesian model and show that we can learn engagement behaviors associated with performance. We also show that the data sequence framework can be used for task-centric analysis; we identify critical junctures and differences among types of tasks within the course design. We find that non-rote learning tasks, such as interactive tasks or discussion posts, are correlated with higher performance. We discuss the application of such analytical techniques as an aid to course design, intervention, and student supervision.

HyperTraPS: Inferring Probabilistic Patterns of Trait Acquisition in Evolutionary and Disease Progression Pathways.

The explosion of data throughout the biomedical sciences provides unprecedented opportunities to learn about the dynamics of evolution and disease progression, but harnessing these large and diverse datasets remains challenging. Here, we describe a highly generalizable statistical platform to infer the dynamic pathways by which many, potentially interacting, traits are acquired or lost over time. We use HyperTraPS (hypercubic transition path sampling) to efficiently learn progression pathways from cross-sectional, longitudinal, or phylogenetically linked data, readily distinguishing multiple competing pathways, and identifying the most parsimonious mechanisms underlying given observations. This Bayesian approach allows inclusion of prior knowledge, quantifies uncertainty in pathway structure, and allows predictions, such as which symptom a patient will acquire next. We provide visualization tools for intuitive assessment of multiple, variable pathways. We apply the method to ovarian cancer progression and the evolution of multidrug resistance in tuberculosis, demonstrating its power to reveal previously undetected dynamic pathways.

Precision identification of high-risk phenotypes and progression pathways in severe malaria without requiring longitudinal data.

More than 400,000 deaths from severe malaria (SM) are reported every year, mainly in African children. The diversity of clinical presentations associated with SM indicates important differences in disease pathogenesis that require specific treatment, and this clinical heterogeneity of SM remains poorly understood. Here, we apply tools from machine learning and model-based inference to harness large-scale data and dissect the heterogeneity in patterns of clinical features associated with SM in 2904 Gambian children admitted to hospital with malaria. This quantitative analysis reveals features predicting the severity of individual patient outcomes, and the dynamic pathways of SM progression, notably inferred without requiring longitudinal observations. Bayesian inference of these pathways allows us assign quantitative mortality risks to individual patients. By independently surveying expert practitioners, we show that this data-driven approach agrees with and expands the current state of knowledge on malaria progression, while simultaneously providing a data-supported framework for predicting clinical risk.

Genetic Correlations Greatly Increase Mutational Robustness and Can Both Reduce and Enhance Evolvability.

Mutational neighbourhoods in genotype-phenotype (GP) maps are widely believed to be more likely to share characteristics than expected from random chance. Such genetic correlations should strongly influence evolutionary dynamics. We explore and quantify these intuitions by comparing three GP maps-a model for RNA secondary structure, the HP model for protein tertiary structure, and the Polyomino model for protein quaternary structure-to a simple random null model that maintains the number of genotypes mapping to each phenotype, but assigns genotypes randomly. The mutational neighbourhood of a genotype in these GP maps is much more likely to contain genotypes mapping to the same phenotype than in the random null model. Such neutral correlations can be quantified by the robustness to mutations, which can be many orders of magnitude larger than that of the null model, and crucially, above the critical threshold for the formation of large neutral networks of mutationally connected genotypes which enhance the capacity for the exploration of phenotypic novelty. Thus neutral correlations increase evolvability. We also study non-neutral correlations: Compared to the null model, i) If a particular (non-neutral) phenotype is found once in the 1-mutation neighbourhood of a genotype, then the chance of finding that phenotype multiple times in this neighbourhood is larger than expected; ii) If two genotypes are connected by a single neutral mutation, then their respective non-neutral 1-mutation neighbourhoods are more likely to be similar; iii) If a genotype maps to a folding or self-assembling phenotype, then its non-neutral neighbours are less likely to be a potentially deleterious non-folding or non-assembling phenotype. Non-neutral correlations of type i) and ii) reduce the rate at which new phenotypes can be found by neutral exploration, and so may diminish evolvability, while non-neutral correlations of type iii) may instead facilitate evolutionary exploration and so increase evolvability.

A tractable genotype-phenotype map modelling the self-assembly of protein quaternary structure.

The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here, we introduce a rich, intuitive and biologically realistic genotype-phenotype (GP) map that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly of polyomino structures on a two-dimensional lattice and exhibits a number of properties: redundancy (genotypes vastly outnumber phenotypes), phenotype bias (genotypic redundancy varies greatly between phenotypes), genotype component disconnectivity (phenotypes consist of disconnected mutational networks) and shape space covering (most phenotypes can be reached in a small number of mutations). We also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability. Although our GP map describes the assembly of disconnected objects, it shares many properties with other popular GP maps for connected units, such as models for RNA secondary structure or the hydrophobic-polar (HP) lattice model for protein tertiary structure. The remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic GP maps.

The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks.

We investigate how scale-free (SF) and Erdos-Rényi (ER) topologies affect the interplay between evolvability and robustness of model gene regulatory networks with Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006) we find that networks with SF(in) topologies, that is SF topology for incoming nodes and ER topology for outgoing nodes, are significantly more evolvable towards specific oscillatory targets than networks with ER topology for both incoming and outgoing nodes. Similar results are found for networks with SF(both) and SF(out) topologies. The functionality of the SF(out) topology, which most closely resembles the structure of biological gene networks (Babu et al., 2004), is compared to the ER topology in further detail through an extension to multiple target outputs, with either an oscillatory or a non-oscillatory nature. For multiple oscillatory targets of the same length, the differences between SF(out) and ER networks are enhanced, but for non-oscillatory targets both types of networks show fairly similar evolvability. We find that SF networks generate oscillations much more easily than ER networks do, and this may explain why SF networks are more evolvable than ER networks are for oscillatory phenotypes. In spite of their greater evolvability, we find that networks with SF(out) topologies are also more robust to mutations (mutational robustness) than ER networks. Furthermore, the SF(out) topologies are more robust to changes in initial conditions (environmental robustness). For both topologies, we find that once a population of networks has reached the target state, further neutral evolution can lead to an increase in both the mutational robustness and the environmental robustness to changes in initial conditions.