Fixation dynamics of beneficial alleles in prokaryotic polyploid chromosomes and plasmids

Theoretical population genetics has been mostly developed for sexually reproducing diploid and for monoploid (haploid) organisms, focusing on eukaryotes. The evolution of bacteria and archaea is often studied by models for the allele dynamics in monoploid populations. However, many prokaryotic organisms harbor multicopy replicons -- chromosomes and plasmids -- and theory for the allele dynamics in populations of polyploid prokaryotes remains lacking. Here we present a population genetics model for replicons with multiple copies in the cell. Using this model, we characterize the fixation process of a dominant beneficial mutation at two levels: the phenotype and the genotype. Our results show that, depending on the mode of replication and segregation, the fixation time of mutant phenotypes may precede the genotypic fixation time by many generations; we term this time interval the heterozygosity window. We furthermore derive concise analytical expressions for the occurrence and length of the heterozygosity window, showing that it emerges if the copy number is high and selection strong. Replicon ploidy thus allows for the maintenance of genetic variation following phenotypic adaptation and consequently for reversibility in adaptation to fluctuating environmental conditions.

Transient analyses of population dynamics using matrix projection models

The bulk of theoretical population biology has focused on long-term, asymptotic population dynamics for which tractable analytical solutions can be derived for particular questions. Following suit, the vast majority of empirical studies have focused on the established parameters provided by theory, such as the asymptotic population growth rate associated with a stable stage structure. But ‘there is nothing permanent [in natural environments] except change’ (Heraclitus), and thus there are good reasons to expect nonstable stage structures in real populations. The urgency of global change is indeed prompting increasing popularity of studying the transient dynamics caused by nonstable stage structures that occur before asymptotic dynamics are reached. This chapter provides an introduction to the concepts and analysis of transient dynamics using matrix projection models and ample examples.

Molecular Systems Predict Equilibrium Distributions of Phenotype Diversity Available for Selection

Two long-standing challenges in theoretical population genetics and evolution are predicting the distribution of phenotype diversity generated by mutation and available for selection and determining the interaction of mutation, selection, and drift to characterize evolutionary equilibria and dynamics. More fundamental for enabling such predictions is the current inability to causally link population genetic parameters, selection and mutation, to the underlying molecular parameters, kinetic and thermodynamic. Such predictions would also have implications for understanding cryptic genetic variation and the role of phenotypic robustness. Here we provide a new theoretical framework for addressing these challenges. It is built on Systems Design Space methods that relate system phenotypes to genetically-determined parameters and environmentally-determined variables. These methods, based on the foundation of biochemical kinetics and the deconstruction of complex systems into rigorously defined biochemical phenotypes, provide several innovations that automate (1) enumeration of the phenotypic repertoire without knowledge of kinetic parameter values, (2) representation of phenotypic regions and their relationships in a System Design Space, and (3) prediction of values for kinetic parameters, concentrations, fluxes and global tolerances for each phenotype. We now show that these methods also automate prediction of phenotype-specific mutation rate constants and equilibrium distributions of phenotype diversity in populations undergoing steady-state exponential growth. We introduce this theoretical framework in the context of a case study involving a small molecular system, a primordial circadian clock, compare and contrast this framework with other approaches in theoretical population genetics, and discuss experimental challenges for testing predictions.

Personalized Biometrics of Physical Pain Agree with Psychophysics by Participants with Sensory over Responsivity

The study of pain requires a balance between subjective methods that rely on self-reports and complementary objective biometrics that ascertain physical signals associated with subjective accounts. There are at present no objective scales that enable the personalized assessment of pain, as most work involving electrophysiology rely on summary statistics from a priori theoretical population assumptions. Along these lines, recent work has provided evidence of differences in pain sensations between participants with Sensory Over Responsivity (SOR) and controls. While these analyses are useful to understand pain across groups, there remains a need to quantify individual differences more precisely in a personalized manner. Here we offer new methods to characterize pain using the moment-by-moment standardized fluctuations in EEG brain activity centrally reflecting the person’s experiencing temperature-based stimulation at the periphery. This type of gross data is often disregarded as noise, yet here we show its utility to characterize the lingering sensation of discomfort raising to the level of pain, individually, for each participant. We show fundamental differences between the SOR group in relation to controls and provide an objective account of pain congruent with the subjective self-reported data. This offers the potential to build a standardized scale useful to profile pain levels in a personalized manner across the general population.

Personalized Biometrics of Physical Pain Agree with Its Psychological Perception by Participants with Sensory Over Responsivity

The study of pain requires a balance between subjective methods that rely on self-reports and complementary objective biometrics that ascertain physical signals associated with subjective accounts. There are at present no objective scales that enable the personalized assessment of pain, as most work involving electrophysiology rely on summary statistics from a priori theoretical population assumptions. Along these lines, recent work has provided evidence of differences in pain sensations between participants with Sensory Over Responsivity (SOR) and controls. While these analyses are useful to understand pain across groups, there remains a need to quantify individual differences more precisely in a personalized manner. Here we offer new methods to characterize pain using the moment-by-moment standardized fluctuations in EEG brain activity centrally reflecting the person’s experiencing temperature-based stimulation at the periphery. This type of gross data is often disregarded as noise, yet here we show its utility to characterize the lingering sensation of discomfort raising to the level of pain, individually, for each participant. We show fundamental differences between the SOR group in relation to controls and provide an objective account of pain congruent with the subjective self-reported data. This offers the potential to build a standardized scale useful to profile pain levels in a personalized manner across the general population.

Sometimes hidden but always there: the assumptions underlying genetic inference of demographic histories

Demographic processes directly affect patterns of genetic variation within contemporary populations as well as future generations, allowing for demographic inference from patterns of both present-day and past genetic variation. Advances in laboratory procedures, sequencing and genotyping technologies in the past decades have resulted in massive increases in high-quality genome-wide genetic data from present-day populations and allowed retrieval of genetic data from archaeological material, also known as ancient DNA. This has resulted in an explosion of work exploring past changes in population size, structure, continuity and movement. However, as genetic processes are highly stochastic, patterns of genetic variation only indirectly reflect demographic histories. As a result, past demographic processes need to be reconstructed using an inferential approach. This usually involves comparing observed patterns of variation with model expectations from theoretical population genetics. A large number of approaches have been developed based on different population genetic models that each come with assumptions about the data and underlying demography. In this article I review some of the key models and assumptions underlying the most commonly used approaches for past demographic inference and their consequences for our ability to link the inferred demographic processes to the archaeological and climate records. This article is part of the theme issue ‘Cross-disciplinary approaches to prehistoric demography’.

Radar observability of near-Earth objects using EISCAT 3D

Radar observations can be used to obtain accurate orbital elements for near-Earth objects (NEOs) as a result of the very accurate range and range rate measureables. These observations allow the prediction of NEO orbits further into the future and also provide more information about the properties of the NEO population. This study evaluates the observability of NEOs with the EISCAT 3D 233 MHz 5 MW high-power, large-aperture radar, which is currently under construction. Three different populations are considered, namely NEOs passing by the Earth with a size distribution extrapolated from fireball statistics, catalogued NEOs detected with ground-based optical telescopes and temporarily captured NEOs, i.e. mini-moons. Two types of observation schemes are evaluated, namely the serendipitous discovery of unknown NEOs passing the radar beam and the post-discovery tracking of NEOs using a priori orbital elements. The results indicate that 60–1200 objects per year, with diameters D>0.01 m, can be discovered. Assuming the current NEO discovery rate, approximately 20 objects per year can be tracked post-discovery near the closest approach to Earth. Only a marginally smaller number of tracking opportunities are also possible for the existing EISCAT ultra-high frequency (UHF) system. The mini-moon study, which used a theoretical population model, orbital propagation, and a model for radar scanning, indicates that approximately seven objects per year can be discovered using 8 %–16 % of the total radar time. If all mini-moons had known orbits, approximately 80–160 objects per year could be tracked using a priori orbital elements. The results of this study indicate that it is feasible to perform routine NEO post-discovery tracking observations using both the existing EISCAT UHF radar and the upcoming EISCAT 3D radar. Most detectable objects are within 1 lunar distance (LD) of the radar. Such observations would complement the capabilities of the more powerful planetary radars that typically observe objects further away from Earth. It is also plausible that EISCAT 3D could be used as a novel type of an instrument for NEO discovery, assuming that a sufficiently large amount of radar time can be used. This could be achieved, for example by time-sharing with ionospheric and space-debris-observing modes.

Rich Bifurcation Structure of Prey–Predator Model Induced by the Allee Effect in the Growth of Generalist Predator

Prey–predator models are building blocks for many food-chain and food-web models in theoretical population biology. These models can be divided into two groups depending on the nature of predators, namely, specialist predator and generalist predator. Generalist predators can survive in the absence of prey but specialist predators go to extinction. Prey–predator models with specialist predator and Allee effect in prey growth have been investigated by several researchers and various types of interesting dynamics have been reported. In this paper, we consider a prey–predator model with generalist predator subject to Allee effect in predator’s growth rate. In general, a prey–predator system with saturating functional response can be destabilized due to the increase of the carrying capacity of prey which is known as paradox of enrichment. In our model with Allee effect in predator growth, we have shown that increase in carrying capacity of prey helps the populations to survive in a coexistence steady state. The considered model is capable of producing bistable dynamics for a reasonable range of parameter values. The complete dynamics of the system are quite rich and all possible local and global bifurcations are studied to understand the dynamics of the model. Analytical results are verified with numerical examples and successive bifurcations are identified with the help of bifurcation diagrams.

Radar observability of near-Earth objects using EISCAT 3D

Radar observations can be used to obtain accurate orbital elements for near-Earth objects (NEOs) as a result of the very accurate range and range-rate measureables. These observations allow predicting NEO orbits further into the future, and also provide more information about the properties of the NEO population. This study evaluates the observability of NEOs with the EISCAT 3D high-power large-aperture radar, which is currently under construction. Three different populations are considered: NEOs passing by the Earth with a size distribution extrapolated from fireball statistics, catalogued NEOs detected with ground-based optical telescopes, and temporarily-captured NEOs, i.e., minimoons. Two types of observation schemes are evaluated: serendipitous discovery of unknown NEOs passing the radar beam, and post-discovery tracking of NEOs using a priori orbital elements. The results indicate that 60–1200 objects per year with diameters D > 0.01 m can be discovered. Assuming the current NEO discovery rate, approximately 20 objects per year can be tracked post-discovery near closest approach. Only a marginally smaller number of tracking opportunities are also possible for the existing EISCAT UHF system. The minimoon study, which used a theoretical population model, orbital propagation, and a model for radar scanning, indicates that approximately 7 objects per year can be discovered using 8–16 % of the total radar time. If all minimoons had known orbits, approximately 80–160 objects per year could be tracked using a priori orbital elements. The results of this study indicate that it is feasible to perform routine NEO post-discovery tracking observations using both the existing EISCAT UHF radar and the upcoming EISCAT 3D radar. Most detectable objects are within 1 LD distance of the radar. Such observations would complement the capabilities of the more powerful planetary radars that typically observe objects further away from Earth. It is also plausible that EISCAT 3D could be used as a novel type of an instrument for NEO discovery, assuming a sufficiently large amount of radar time can be used. This could be achieved, e.g., by time-sharing with ionospheric and space debris observing modes.