Biology

The network of chemical reactions that maintains a living system, supplies energy and builds or processes its material. Gas emissions can arise as primary metabolic byproducts or secondary metabolic byproducts, with different implications for an atmospheric biosignature gas.

Conversion of light energy into chemical energy used to build biological material. Oxygenic photosynthesis uses water as an electron donor and releases molecular oxygen; other forms do not necessarily produce oxygen. Its atmospheric oxygen source is a major component of the modern terrestrial atmospheric biosignature gas interpretation.

A compound released through specialized functions such as signaling, defense or stress adaptation rather than the core reactions needed for energy and biomass. Dimethyl sulfide and chloromethane are examples discussed as atmospheric biosignatures. Their specialized origins may improve specificity while lowering the global emission flux.

A product released by reactions needed for energy acquisition, growth or biomass construction. Methane from energy-yielding microbial reactions and molecular oxygen from oxygenic photosynthesis are examples. Abiotic chemistry can make some of the same molecules, so production mechanism and environmental abundance matter.

A phylogenetic tree describes ancestral relationships. In a probabilistic graphical model on a rooted tree, latent variables at ancestral vertices are inferred from observations at leaves using belief propagation.

The Felsenstein pruning algorithm computes a site likelihood function by sum-product belief propagation from leaves to root. For a finite-state Markov kernel $K$, the subtree likelihood function obeys $L_v(a)={\prod }_{w\text{ child of }v}{\sum }_{b}K(a,b)L_w(b)$, with observed-state indicators at leaves. Summing against the root probability distribution gives the site likelihood function. An outward pass gives edge posterior probabilities and expected transition counts for the expectation-maximization algorithm.

Calcium has roles in cell signalling and skeletal structure. Dietary calcium intake and serum calcium are distinct quantities: physiological regulation means a change in one need not correspond to an equivalent change in the other.

Serum calcium is the concentration of calcium in blood serum. It can be an exposure in an observational study or Mendelian randomization, but genetically changing it need not reproduce the effect of changing dietary calcium intake.

Hypercalcaemia is an abnormally elevated serum calcium concentration. A diagnosis in medical records depends on testing and diagnostic practice, which can introduce selection bias into an observational study.

Calcium intake is the amount of calcium consumed, including food and supplements. It is an exposure that can be changed by an intervention, and should not be identified automatically with serum calcium in a causal inference analysis.

Genetics studies heredity and variation in organisms.

Population stratification is systematic variation in allele frequencies between subpopulations. If those subpopulations also differ in outcome causes, genetic variant associations can exhibit confounding, violating instrumental-variable independence in Mendelian randomization.

For two alleles $A,B$ sampled independently with frequencies $1-\theta$ and $\theta$, the genotype probabilities under Hardy-Weinberg equilibrium are

From genotype counts in $n$ independent diploid individuals, the unbiased and maximum-likelihood estimator of the frequency of allele $B$ isIt is the sample proportion among the $2n$ sampled alleles, so it is consistent and

A genetic variant is a heritable difference in a DNA sequence relative to a chosen reference. Genetic variants can be used as instrumental variables in Mendelian randomization when the required causal assumptions are credible.

Quantitative genetics studies how genetic and environmental variation contribute to continuously varying traits.

A genetic risk score combines allele counts from several genetic variants, usually using specified weights. In Mendelian randomization it can act as a combined instrumental variable for an exposure; interpretation still requires instrument relevance, instrumental-variable independence, and the exclusion restriction.

Heritability is the fraction of phenotypic variance in a specified population and environment attributed to genetic variation. It is a population parameter, not the genetic fraction of one individual's trait.

A twin study compares trait resemblance between twins with different degrees of genetic relatedness to separate genetic and environmental variance components.

Monozygotic twins develop from one zygote and are modeled as sharing essentially all additive genetic variation.

Dizygotic twins develop from two zygotes and, absent assortative mating and other complications, share one half of additive genetic variation on average.

The ACE model decomposes trait variation into additive genetic effects $A$, common environmental effects $C$, and unique environmental effects $E$.

Falconer's formula estimates narrow-sense heritability from monozygotic and dizygotic twin correlations:It relies on equal relevant environments and a dizygotic additive-genetic correlation of one half.

Assortative mating is nonrandom mating in which partners are more or less similar than random pairs for a trait or correlated characteristic. Positive assortment can increase genetic similarity among siblings.

Migraine is a neurological disorder that can be an outcome in a clinical trial or an observational study. Its statistical association with an exposure does not alone establish a causal effect.

A chronic disease persists over an extended period. A continuous-time multi-state model can represent its progression through severity states, but long duration alone does not imply irreversible progression or justify ignoring state misclassification.