On random conformity bias in cultural transmission of polychotomous traits.

Mathematical models of conformity and anti-conformity have commonly included a set of simplifying assumptions. For example, (1) there are m=2 cultural variants in the population, (2) naive individuals observe the cultural variants of n=3 adult "role models," and (3) individuals' levels of conformity or anti-conformity do not change over time. Three recent theoretical papers have shown that departures from each of these assumptions can produce new population dynamics. Here, we explore cases in which multiple, or all, of these assumptions are violated simultaneously: namely, in a population with m variants of a trait where conformity (or anti-conformity) occurs with respect to n role models, we study a model in which the conformity rates at each generation are random variables that are independent of the variant frequencies at that generation. For this model a class of symmetric constant equilibria exist, and it is possible that all of these equilibria are simultaneously stochastically locally stable. In such cases, the effect of initial conditions on subsequent evolutionary trajectories becomes very complicated.

Epidemiology, Pathophysiology, and Genetics of Primary Hyperparathyroidism.

In this narrative review, we present data gathered over four decades (1980-2020) on the epidemiology, pathophysiology and genetics of primary hyperparathyroidism (PHPT). PHPT is typically a disease of postmenopausal women, but its prevalence and incidence vary globally and depend on a number of factors, the most important being the availability to measure serum calcium and parathyroid hormone levels for screening. In the Western world, the change in presentation to asymptomatic PHPT is likely to occur, over time also, in Eastern regions. The selection of the population to be screened will, of course, affect the epidemiological data (ie, general practice as opposed to tertiary center). Parathyroid hormone has a pivotal role in regulating calcium homeostasis; small changes in extracellular Ca++ concentrations are detected by parathyroid cells, which express calcium-sensing receptors (CaSRs). Clonally dysregulated overgrowth of one or more parathyroid glands together with reduced expression of CaSRs is the most important pathophysiologic basis of PHPT. The spectrum of skeletal disease reflects different degrees of dysregulated bone remodeling. Intestinal calcium hyperabsorption together with increased bone resorption lead to increased filtered load of calcium that, in addition to other metabolic factors, predispose to the appearance of calcium-containing kidney stones. A genetic basis of PHPT can be identified in about 10% of all cases. These may occur as a part of multiple endocrine neoplasia syndromes (MEN1-MEN4), or the hyperparathyroidism jaw-tumor syndrome, or it may be caused by nonsyndromic isolated endocrinopathy, such as familial isolated PHPT and neonatal severe hyperparathyroidism. DNA testing may have value in: confirming the clinical diagnosis in a proband; eg, by distinguishing PHPT from familial hypocalciuric hypercalcemia (FHH). Mutation-specific carrier testing can be performed on a proband's relatives and identify where the proband is a mutation carrier, ruling out phenocopies that may confound the diagnosis; and potentially prevention via prenatal/preimplantation diagnosis. © 2022 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR).

Polychotomous traits and evolution under conformity.

Conformist and anticonformist transmission of dichotomous cultural traits (i.e., traits with two variants) have been studied both experimentally, in many species, and theoretically, with mathematical models. Signatures of types of conformity to polychotomous traits (with more than two variants; e.g., baby names and syllables in bird song) have been inferred from population-level data, but there are few models that include individual-level biases among more than two discrete variants. We generalize the standard dichotomous trait conformity model by Boyd and Richerson to incorporate [Formula: see text] role models and [Formula: see text] variants. Our analysis shows that in the case of [Formula: see text] role models, under anticonformity, the central polymorphic equilibrium [Formula: see text] is globally stable, whereas under conformity, if initially the frequencies of [Formula: see text] variants are all equal to the maximum variant frequency in the population, there is global convergence to an equilibrium in which the frequencies of these variants are all [Formula: see text] and all other variants are absent. With a general number n of role models, the same result holds with conformity, whereas under anticonformity, global convergence is not guaranteed, and there may be stable frequency cycles or chaos. If both conformity and anticonformity occur for different configurations of variants among the n role models, a variety of novel polymorphic equilibria may exist and be stable. Future empirical studies may use this formulation to directly quantify an individual's level of (anti)conformist bias to a polychotomous trait.

On randomly changing conformity bias in cultural transmission.

Humans and nonhuman animals display conformist as well as anticonformist biases in cultural transmission. Whereas many previous mathematical models have incorporated constant conformity coefficients, empirical research suggests that the extent of (anti)conformity in populations can change over time. We incorporate stochastic time-varying conformity coefficients into a widely used conformity model, which assumes a fixed number n of "role models" sampled by each individual. We also allow the number of role models to vary over time ([Formula: see text]). Under anticonformity, nonconvergence can occur in deterministic and stochastic models with different parameter values. Even if strong anticonformity may occur, if conformity or random copying (i.e., neither conformity nor anticonformity) is expected, there is convergence to one of the three equilibria seen in previous deterministic models of conformity. Moreover, this result is robust to stochastic variation in [Formula: see text] However, dynamic properties of these equilibria may be different from those in deterministic models. For example, with random conformity coefficients, all equilibria can be stochastically locally stable simultaneously. Finally, we study the effect of randomly changing weak selection. Allowing the level of conformity, the number of role models, and selection to vary stochastically may produce a more realistic representation of the wide range of group-level properties that can emerge under (anti)conformist biases. This promises to make interpretation of the effect of conformity on differences between populations, for example those connected by migration, rather difficult. Future research incorporating finite population sizes and migration would contribute added realism to these models.

Evolution of transmission modifiers under frequency-dependent selection and transmission in constant or fluctuating environments.

Although the Reduction Principle for rates of mutation, migration, and recombination has been proved for large populations under constant selection, the fate of modifiers of these evolutionary forces under frequency-dependent or fluctuating selection is, in general, less well understood. Here we study modifiers of transmission, which include modifiers of mutation and oblique cultural transmission, under frequency-dependent and cyclically fluctuating selection, and develop models for which the Reduction Principle fails. We show that whether increased rates of transmission can evolve from an equilibrium at which there is zero transmission (for example, no mutation) depends on the number of alleles among which transmission is occurring. In addition, properties of the null-transmission state are clarified.

Cultural evolution of conformity and anticonformity.

Conformist bias occurs when the probability of adopting a more common cultural variant in a population exceeds its frequency, and anticonformist bias occurs when the reverse is true. Conformist and anticonformist bias have been widely documented in humans, and conformist bias has also been observed in many nonhuman animals. Boyd and Richerson used models of conformist and anticonformist bias to explain the evolution of large-scale cooperation, and subsequent research has extended these models. We revisit Boyd and Richerson's original analysis and show that, with conformity based on more than three role models, the evolutionary dynamics can be more complex than previously assumed. For example, we show the presence of stable cycles and chaos under strong anticonformity and the presence of new equilibria when both conformity and anticonformity act at different variant frequencies, with and without selection. We also investigate the case of population subdivision with migration and find that the common claim that conformity can maintain between-group differences is not always true. Therefore, the effect of conformity on the evolution of cooperation by group selection may be more complicated than previously stated. Finally, using Feldman and Liberman's modifier approach, we investigate the conditions under which a rare modifier of the extent of conformity or the number of role models can invade a population. Understanding the dynamics of conformist- and anticonformist-biased transmission may have implications for research on human and nonhuman animal behavior, the evolution of cooperation, and frequency-dependent transmission in general.

The evolution of frequency-dependent cultural transmission.

In a model of vertical and oblique cultural transmission of a dichotomous trait, the rates of transmission of each form of the trait are functions of the trait frequency in the population. Sufficient conditions on these functions are derived for a stable trait polymorphism to exist. If the vertical transmission rates are monotone decreasing functions of the trait frequency, a complete global stability analysis is presented. It is also shown that a unique protected polymorphism can be globally stable even though the sufficient conditions are not met. The evolution of frequency-dependent transmission is modeled using modifier theory, and exact conditions are derived for a transmission modifier to invade a population at a stable polymorphism. Finally, the interaction between frequency-dependent selection and frequency-dependent transmission is explored.

Vertical and oblique cultural transmission fluctuating in time and in space.

Evolutionary models for a cultural trait under vertical and oblique cultural transmission are analyzed. For a dichotomous trait, both the fitnesses of the variants and their rates of transmission are allowed to vary. In one class of models, transmission fluctuates cyclically together with fitnesses, and conditions are derived for a cultural polymorphism. A second class of models has transmission and selection fluctuating randomly with possible covariance between them. A third class of models involves two populations with migration between them and with transmission rates and fitnesses different in the two populations. Numerical analysis leads to qualitative conditions on the transmission rates and fitnesses that allow protected polymorphisms. With symmetric migration analytical conditions for protected polymorphism are derived.

Generation of variation and a modified mean fitness principle: Necessity is the mother of genetic invention.

Generation of variation may be detrimental in well-adapted populations evolving under constant selection. In a constant environment, genetic modifiers that reduce the rate at which variation is generated by processes such as mutation and migration, succeed. However, departures from this reduction principle have been demonstrated. Here we analyze a general model of evolution under constant selection where the rate at which variation is generated depends on the individual. We find that if a modifier allele increases the rate at which individuals of below-average fitness generate variation, then it will increase in frequency and increase the population mean fitness. This principle applies to phenomena such as stress-induced mutagenesis and condition-dependent dispersal, and exemplifies "Necessity is the mother of genetic invention."

Evolution of vertical and oblique transmission under fluctuating selection.

The evolution and maintenance of social learning, in competition with individual learning, under fluctuating selection have been well-studied in the theory of cultural evolution. Here, we study competition between vertical and oblique cultural transmission of a dichotomous phenotype under constant, periodically cycling, and randomly fluctuating selection. Conditions are derived for the existence of a stable polymorphism in a periodically cycling selection regime. Under such a selection regime, the fate of a genetic modifier of the rate of vertical transmission depends on the length of the cycle and the strength of selection. In general, the evolutionarily stable rate of vertical transmission differs markedly from the rate that maximizes the geometric mean fitness of the population. The evolution of rules of transmission has dramatically different dynamics from the more frequently studied modifiers of recombination, mutation, or migration.

Unified reduction principle for the evolution of mutation, migration, and recombination.

Modifier-gene models for the evolution of genetic information transmission between generations of organisms exhibit the reduction principle: Selection favors reduction in the rate of variation production in populations near equilibrium under a balance of constant viability selection and variation production. Whereas this outcome has been proven for a variety of genetic models, it has not been proven in general for multiallelic genetic models of mutation, migration, and recombination modification with arbitrary linkage between the modifier and major genes under viability selection. We show that the reduction principle holds for all of these cases by developing a unifying mathematical framework that characterizes all of these evolutionary models.

Evolution of reduced mutation under frequency-dependent selection.

Most models for the evolution of mutation under frequency-dependent selection involve some form of host-parasite interaction. These generally involve cyclic dynamics under which mutation may increase. Here we show that the reduction principle for the evolution of mutation, which is generally true for frequency-independent selection, also holds under frequency-dependent selection on haploids and diploids that does not involve cyclic dynamics.

Management of Hypoparathyroidism: Present and Future.

CONTEXT: Conventional management of hypoparathyroidism has focused upon maintaining the serum calcium with oral calcium and active vitamin D, often requiring high doses and giving rise to concerns about long-term consequences including renal and brain calcifications. Replacement therapy with PTH has recently become available. This paper summarizes the results of the findings and recommendations of the Working Group on Management of Hypoparathyroidism. EVIDENCE ACQUISITION: Contributing authors reviewed the literature regarding physiology, pathophysiology, and nutritional aspects of hypoparathyroidism, management of acute hypocalcemia, clinical aspects of chronic management, and replacement therapy of hypoparathyroidism with PTH peptides. PubMed and other literature search engines were utilized. EVIDENCE SYNTHESIS: Under normal circumstances, interactions between PTH and active vitamin D along with the dynamics of calcium and phosphorus absorption, renal tubular handing of those ions, and skeletal responsiveness help to maintain calcium homeostasis and skeletal health. In the absence of PTH, the gastrointestinal tract, kidneys, and skeleton are all affected, leading to hypocalcemia, hyperphosphatemia, reduced bone remodeling, and an inability to conserve filtered calcium. Acute hypocalcemia can be a medical emergency presenting with neuromuscular irritability. The recent availability of recombinant human PTH (1-84) has given hope that management of hypoparathyroidism with the missing hormone in this disorder will provide better control and reduced needs for calcium and vitamin D. CONCLUSIONS: Hypoparathyroidism is associated with abnormal calcium and skeletal homeostasis. Control with calcium and active vitamin D can be a challenge. The availability of PTH (1-84) replacement therapy may usher new opportunities for better control with reduced supplementation requirements.

Evolution in changing environments: modifiers of mutation, recombination, and migration.

The production and maintenance of genetic and phenotypic diversity under temporally fluctuating selection and the signatures of environmental changes in the patterns of this variation have been important areas of focus in population genetics. On one hand, periods of constant selection pull the genetic makeup of populations toward local fitness optima. On the other, to cope with changes in the selection regime, populations may evolve mechanisms that create a diversity of genotypes. By tuning the rates at which variability is produced--such as the rates of recombination, mutation, or migration--populations may increase their long-term adaptability. Here we use theoretical models to gain insight into how the rates of these three evolutionary forces are shaped by fluctuating selection. We compare and contrast the evolution of recombination, mutation, and migration under similar patterns of environmental change and show that these three sources of phenotypic variation are surprisingly similar in their response to changing selection. We show that the shape, size, variance, and asymmetry of environmental fluctuation have different but predictable effects on evolutionary dynamics.

The evolution of phenotypic switching in subdivided populations.

Stochastic switching is an example of phenotypic bet hedging, where offspring can express a phenotype different from that of their parents. Phenotypic switching is well documented in viruses, yeast, and bacteria and has been extensively studied when the selection pressures vary through time. However, there has been little work on the evolution of phenotypic switching under both spatially and temporally fluctuating selection pressures. Here we use a population genetic model to explore the interaction of temporal and spatial variation in determining the evolutionary dynamics of phenotypic switching. We find that the stable switching rate is mainly determined by the rate of environmental change and the migration rate. This stable rate is also a decreasing function of the recombination rate, although this is a weaker effect than those of either the period of environmental change or the migration rate. This study highlights the interplay of spatial and temporal environmental variability, offering new insights into how migration can influence the evolution of phenotypic switching rates, mutation rates, or other sources of phenotypic variation.

Evolution with stochastic fitnesses: a role for recombination.

Phenotypic adaptation to fluctuating environments has been an important focus in the population genetic literature. Previous studies have shown that evolution under temporal variation is determined not only by expected fitness in a given generation, but also by the degree of variation in fitness over generations; in an uncertain environment, alleles that increase the geometric mean fitness can invade a randomly mating population at equilibrium. This geometric mean principle governs the evolutionary interplay of genes controlling mean phenotype and genes controlling phenotypic variation, such as genetic regulators of the epigenetic machinery. Thus, it establishes an important role for stochastic epigenetic variation in adaptation to fluctuating environments: by modifying the geometric mean fitness, variance-modifying genes can change the course of evolution and determine the long-term trajectory of the evolving system. The role of phenotypic variance has previously been studied in systems in which the only driving force is natural selection, and there is no recombination between mean- and variance-modifying genes. Here, we develop a population genetic model to investigate the effect of recombination between mean- and variance-modifiers of phenotype on the geometric mean principle under different environmental regimes and fitness landscapes. We show that interactions of recombination with stochastic epigenetic variation and environmental fluctuations can give rise to complex evolutionary dynamics that differ from those in systems with no recombination.

On the evolution of mutation in changing environments: recombination and phenotypic switching.

Phenotypic switching has been observed in laboratory studies of yeast and bacteria, in which the rate of such switching appears to adjust to match the frequency of environmental changes. Among possible mechanisms of switching are epigenetic influences on gene expression and variation in levels of methylation; thus environmental and/or genetic factors may contribute to the rate of switching. Most previous analyses of the evolution of phenotypic switching have compared exponential growth rates of noninteracting populations, and recombination has been ignored. Our genetic model of the evolution of switching rates is framed in terms of a mutation-modifying gene, environments that cause periodic changes in fitness, and recombination between the mutation modifier and the gene under selection. Exact results are obtained for all recombination rates and symmetric fitnesses that strongly generalize earlier results obtained under complete linkage and strong constraints on the relation between fitness and period of switching. Our analytical and numerical results suggest a general principle that recombination reduces the stable rate of switching in symmetric and asymmetric fitness regimes and when the period of switching is random. As the recombination rate increases, it becomes less likely that there is a stable nonzero rate of switching.

On the evolution of epistasis III: the haploid case with mutation.

Whether interaction between genes is better represented by synergistic or antagonistic epistasis has been a focus of experimental research in bacterial population genetics. Our previous research on evolution of modifiers of epistasis in diploid systems has indicated that the strength of positive or negative epistasis should increase provided linkage disequilibrium is maintained. Here we study a modifier of epistasis in fitness between two loci in a haploid system. Epistasis is modified in the neighborhood of a mutation-selection balance. We show that when linkage in the three-locus system is tight, an increase in the frequency of a modifier allele that induces either more negative or more positive epistasis is possible. Epistasis here can be measured on either an additive or multiplicative scale.

On the evolution of epistasis II: a generalized Wright-Kimura framework.

The evolution of fitness interactions between genes at two major loci is studied where the alleles at a third locus modify the epistatic interaction between the two major loci. The epistasis is defined by a parameter epsilon and a matrix structure that specifies the nature of the interactions. When epsilon=0 the two major loci have additive fitnesses, and when these are symmetric the interaction matrices studied here produce symmetric viabilities of the Wright [1952. The genetics of quantitative variability. In: Reeve, E.C.R., Waddington, C.H. (Eds.), Quantitative Inheritance. Her Majesty's Stationary Office, London]-Kimura [1956. A model of a genetic system which leads to closer linkage by natural selection. Evolution 10, 278-281] form. Two such interaction matrices are studied, for one of which epistasis as measured by |epsilon| always increases, and for the other it increases when the linkage between the major loci is tight enough and there is initial linkage disequilibrium. Increase of epistasis does not necessarily coincide with increase in equilibrium mean fitness.

Vitamin D-resistant diseases.

Hereditary vitamin D receptor defects (HVDRDs) is a more appropriate and precise title for an inborn error of metabolism commonly known as pseudo-vitamin D deficiency or vitamin D dependency, type II. It is a rare autosomal recessive disorder, approximately 70 kindreds were described, but its main importance is elucidating the physiology of vitamin D and calcium homeostasis in humans. Patients usually develop the clinical and biochemical aberrations, identical to vitamin D deficiency, but with high serum levels of calcitriol, within the first year of life (i.e., muscle weakness, bone pain, deformities, and fractures). Defective calcium gut absorption leads to hypocalcemia, secondary hyperparathyroidism, hypophosphatemia, and defective mineralization of newly formed bone matrix. The disease is not cured by vitamin D replacement therapy, although some patients respond to very high doses of vitamin D or its metabolites. Cells derived from patients, mainly cultured skin fibroblasts, were used to assess steps in calcitriol action from cellular uptake to bioresponse and to elucidate the molecular aberrations in the vitamin D receptor (VDR). Point mutations in the VDR gene were identified in every patient examined, and the same defect was observed in the obligatory heterozygotes. The functional characterization of the patient's VDR reflected the localization of the mutation (18 different ones described to date), thus providing vital information about the structure-function relationship in the human VDR and the essentiality of the VDR as the mediator of vitamin D action.