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Autozygosity is homozygosity by descent: the maternal and paternal copies in one individual derive from the same ancestral copy. Unlike ordinary homozygosity, it concerns the ancestry of chromosome copies rather than only their observed states. In a pedigree with one ancestral disease-allele copy and fully penetrant recessive inheritance, every affected individual is autozygous for that copy.

A founder is an individual whose parents are outside the recorded pedigree. The standard pedigree likelihood assigns unrelated founders independent genotype distributions based on population allele or haplotype frequencies. If founders are related, their joint prior must instead account for that relationship.

Why can two individually fair allele transmissions fail to be independent? Genetic loci on the same chromosome can travel together through meiosis. This tendency is genetic linkage; in an ordinary two-locus model, detectable genetic linkage means a recombination fraction below $1/2$. A genetic marker can therefore help track a neighboring genetic locus through a pedigree. See Clark, Douglas and Choi, Biology 2e: chromosomal theory and genetic linkage.

Take a diploid individual heterozygous at two genetic loci, with phase-known genotype $AB/ab$: one homologous chromosome carries alleles $A,B$, the other $a,b$. The parental haplotypes are $AB,ab$; the recombinant haplotypes are $Ab,aB$. Assume fair Mendelian segregation, equal probabilities within each reciprocal pair of gametes, and no allele-dependent differences in gamete recovery. If the recombination fraction is $r=0.2$, the gamete probabilities are $0.4,0.4,0.1,0.1$ in that order. Each genetic locus still transmits its two alleles equally, but $P(AB)=0.4$ exceeds $P(A)P(B)=0.25$: fairness at each genetic locus does not imply independence between genetic loci.

At $r=0$, only the parental haplotypes occur, each with probability $0.5$: this is complete genetic linkage. At $r=0.5$, all four haplotypes have probability $0.25$, giving independent assortment. A recombination fraction near $0.5$ alone cannot establish whether the genetic loci lie on different chromosomes or far apart on one chromosome.

Genetic linkage concerns joint transmission through meiosis. Linkage disequilibrium concerns haplotype frequencies in a population, while genetic association compares allele or genotype frequencies with a phenotype. These questions require different observations; pedigrees directly reveal co-transmission.

Genetics studies how genes are inherited, how their alleles vary, and how that variation contributes to phenotypes. Its central distinction is between an inherited description, the genotype, and what an organism actually expresses, the phenotype. Following alleles through a pedigree answers a family-level question; following allele frequencies through generations leads to population genetics and evolution.

The beauty of Mendelian segregation is that discrete inherited copies can generate predictable statistical patterns without making every offspring identical. A single genetic locus already connects meiosis, probability and observable variation. The Hardy-Weinberg principle then supplies a population baseline: it separates reshuffling inherited copies from processes such as natural selection that change their frequencies. These simple models are useful precisely because their assumptions can be stated and checked.

Haplotype estimation reconstructs which alleles share a chromosome from observed genotypes and other information, such as pedigrees. A doubly heterozygous genotype can be $AB/ab$ or $Ab/aB$; a phase-known genotype distinguishes them. Uncertainty in that reconstruction must propagate to estimated haplotype frequencies and linkage disequilibrium.

Nonparametric linkage analysis tests excess identity by descent among relatives with a shared phenotype, without specifying its complete penetrance model or disease-allele frequency. Its null still uses Mendelian segregation and the specified pedigree.

// Target: biology.bigb

The area for the pedigrees on page 7 is blank in the official Part III PDF and PostScript edition, and in the corresponding MPhil PDF and MPhil PostScript edition. All four copies have been checked visually. The family-specific calculations in Question 6 remain dependent on those unavailable drawings.

Genetic linkage analysis asks whether a genetic marker and a disease genetic locus cosegregate within families more often than would be expected under independent assortment. It uses pedigrees and Mendelian segregation to estimate the recombination fraction $\theta$, with evidence for linkage arising when the data favor $\theta <1/2$. Even when founders are in linkage equilibrium, linked loci can show familial cosegregation.

Genetic association analysis instead asks whether observed allele or genotype frequencies differ with disease status in a sampled population, often comparing cases with controls. It can detect a causal variant or a correlated genetic marker through linkage disequilibrium; population structure and selection can also create association. Linkage is about familial transmission; association is about population dependence. Neither an association alone nor a low family recombination estimate establishes that the marker itself causes disease.

To identify the unlabelled individuals in the original pedigree, call the three children of $A,B$ from left to right $U,V,W$. Then $G$ has parents $C,U$, $D$ has parents $V,W$, and $E,F$ have parents $G,D$. The three full siblings $U,V,W$ are noninbred because $A,B$ are unrelated noninbred founders in a pedigree. Their pairwise kinship coefficients areSince $D$ is the child of the sibling pair $V,W$, its inbreeding coefficient is

The full siblings $E,F$ have parents $G,D$. Since $G$ is noninbred, ${\varphi }_{GG}=1/2$, whereas ${\varphi }_{DD}=5/8$ and ${\varphi }_{GD}=1/8$. Applying the parental kinship coefficient recursion to both siblings givesThe familiar outbred-sibling value $1/4$ does not apply to this inbred pedigree.

A valid triangulation of an undirected graph adds exactly the two fill edgesTo verify it, eliminate the vertices in the order $P,Q,R,S,X,Y,B,D,F,M,A,C,U,V$. The first eight eliminations have neighboring vertices already joined. When $F$ is eliminated, its remaining neighbors are $A,M$, so add $AM$. When $M$ is eliminated, its remaining neighbors are $A,C$, so add $AC$. The remaining $A,C,U,V$ form a clique.

Thus this order is a perfect elimination ordering of the completed graph, which is a chordal graph. The fill edges are computational devices for genotype elimination; they do not add parent-child relationships to the pedigree.

Parametric linkage analysis specifies a disease-transmission model: the mode of inheritance, disease-allele frequency and penetrance of each genotype. Combining these with Mendelian segregation and the recombination fraction gives a pedigree likelihood. One can estimate the recombination fraction or compare a linked model, $\theta <1/2$, with the unlinked model, $\theta =1/2$, using a likelihood-ratio test or LOD score. Incomplete penetrance and unobserved genotypes are accommodated by summing over the possible underlying inheritance states.

Nonparametric linkage analysis instead tests whether relatives with the same disease phenotype share marker alleles identical by descent more often than expected from their pedigree. For example, affected-sib-pair analysis compares sharing among affected full siblings with its Mendelian null distribution. It avoids specifying a complete disease-penetrance model and disease-allele frequency. “Model-free” still assumes an inheritance model for the marker, correct family relationships and a justified treatment of genetic-study ascertainment; it does not mean assumption-free.

Assume a single disease allele $a$, complete penetrance of $aa$, no disease in $Aa$ or $AA$, and Hardy-Weinberg equilibrium in the outbred population. If its population frequency is $q$, the disease prevalence is $q^2=10^{-6}$, so $q=10^{-3}$.

For a child with inbreeding coefficient $F$, the two inherited copies are identical by descent with probability $F$. In that component there is just one ancestral allele draw, and it is $a$ with probability $q$. In the remaining component there are two independent ancestral draws, with probability $q^2$ of $aa$. Thus the inbreeding genotype frequencies giveUsing the first-cousin inbreeding coefficient $F=1/16$, the disease-risk ratio isThe absolute risk in this model is $6.34375\times 10^{-5}$. This calculation averages over the parental genotypes in first-cousin marriages before observing an affected child. It is not the risk conditional on both parents being known genetic carriers, and assumes the specified cousin relationship is independent of disease status rather than conditioning on a selected disease pedigree.

Suppose a disease-risk mutation first occurs on an ancestral haplotype. Descendants carrying the risk allele initially share that surrounding haplotype. Historical genetic recombination progressively replaces the flanks while retaining the disease allele, leaving linkage disequilibrium between the causal variant and some nearby genetic markers. A noncausal marker can therefore have different allele frequencies in affected individuals and suitably chosen controls. This is the basis of association mapping.

One first tests dense markers or multi-marker haplotypes for genetic association with the disease phenotype. Strongly correlated single-nucleotide polymorphisms can be represented by tag SNPs to locate an associated region efficiently. Within that region, denser genotyping and examination of disease-associated haplotypes locate historical recombination breakpoints: segments retained across independently recombined disease-bearing chromosomes are stronger candidates for containing the causal allele. Compare affected and unaffected carriers as well, since incomplete penetrance and other risk factors can prevent a perfect haplotype-disease correspondence.

Association mapping can achieve fine resolution because it uses recombination accumulated over many generations, rather than only the few observed meioses in a present-day linkage pedigree. Resolution depends on the local recombination history: a long region of strong LD may identify a disease-associated block while leaving many variants statistically indistinguishable. Additional informative haplotypes or populations with different LD can help separate them. Conversely, very weak LD requires closer marker spacing to avoid missing the causal region.

Population stratification must be controlled by ancestry-matched comparisons, statistical adjustment or an appropriate family-based association design, since ancestry can affect both disease frequency and marker frequency. A marker association alone establishes neither causality nor identity of the disease gene; nearby correlated variants must be distinguished by further genetic and functional evidence. Use LD to detect a disease-associated ancestral segment, then use historical recombinants to narrow the causal interval. The correlation between causal variants and their surrounding haplotypes, together with the value of representative markers, is illustrated in the HapMap study.

Genetic linkage analysis follows co-segregation of genetic marker and disease alleles within pedigrees. It estimates or tests a recombination fraction, with independent assortment at $\theta =1/2$ as the ordinary null. It can locate a disease genetic locus even when different families have different genetic marker alleles on their disease chromosomes.

Genetic association analysis tests whether allele or genotype frequencies differ with disease status. It can compare unrelated cases and controls, or compare transmitted and untransmitted parental alleles. A noncausal genetic marker can be associated through population linkage disequilibrium with a causal genetic locus. Association therefore concerns population-frequency relationships, whereas linkage concerns inheritance; population stratification can confound the former without producing genuine within-family linkage.

Family comparisons condition on the parental genotypes, so cases are compared with the alleles they could have inherited. This protects a transmission test from ordinary population stratification, avoids having to recruit unrelated controls matched for ancestry, and can resolve haplotypes and identify Mendelian inconsistencies. The same pedigree may also provide linkage information.

The costs are recruiting and genotyping relatives, missing or unavailable parents, and fewer informative comparisons because homozygous parents contribute no transmission contrast. These problems are especially important for late-onset disease. Related cases or multiple siblings also require an analysis accounting for dependence, and genotyping error or transmission distortion can mimic overtransmission. Population-based case/control studies are usually easier to assemble and can offer greater power per genotyped person, but need careful control of ancestry and other sources of confounding. Family sampling does not remove every form of ascertainment in a genetic study or observation bias.

Let $E_q$ be the event that all eight selected subjects carry two copies of the same specified ancestral copy $q$, and that no other generation-4 subject is autozygous at this genetic locus. The selected subjects occur in every sibship, so this event forces both generation-2 transmissions and all six relevant generation-3 transmissions. Applying the preceding conditional probabilities,Once all six parents carry $q$, their other copies come from the two unrelated outside pedigree founders, one on each side of the pedigree. A child not receiving two $q$ copies therefore cannot become autozygous for a different founding copy. This verifies the “only” condition, rather than merely excluding homozygosity for $q$.

For the event $E$ without specifying which of the original four copies is shared, the four alternatives $E_q$ are disjoint: a selected child cannot simultaneously have both its copies descended from two different ancestral copies. HenceAll selected individuals are then autozygous for the same copy and mutually 2-IBD. The distinction from the $3/4$ probability in the alternative interpretation of part (a) is precisely this disjointness.

Write $D$ for the disease observations and $M$ for the genetic marker observations. The LOD score for complete linkage isThe disease marginal cancels because the single-locus disease segregation law does not depend on the genetic marker–disease recombination fraction. The ten genetic markers form one nonrecombining haplotype; they do not supply ten independent copies of the pedigree's segregation evidence.

There is a distinction between identity by state and identity by descent. The reported observation that affected subjects all have $h/h$ establishes the former. An exact genetic marker likelihood requires pedigree founder haplotype frequencies, or the actual pedigree founder genotypes if conditioning on them. Here is an explicit expression using independent pedigree founder haplotypes, with frequency $p$ for the observed haplotype $h$, and linkage equilibrium between pedigree founder genetic marker and disease states. There are eight genetic marker copies in the four pedigree founders: the original couple and the two generation-2 outside spouses. For genetic marker inheritance configuration $v$, let $K(v)$ be the number of distinct pedigree founder copies ancestral to the sixteen chromosome copies in the eight selected subjects. Thenis the unlinked probability that all those copies have state $h$. At complete linkage the affected subjects all inherit the disease pedigree founder copy twice, and the probability that this copy has genetic marker state $h$ is $p$. Therefore

The denominator can be evaluated without an unspecified inheritance sum. Let $B_a=\left(\genfrac{}{}{0ex}{}{2}{a}\right)p^a(1-p{)}^{2-a}$ for $a=0,1,2$. If parental genetic marker genotypes contain $a,b$ copies of $h$, the child count distribution isFor a generation-2 couple defineFor a particular generation-3 parent with $j$ genetic marker copies, the chance it transmits $h$ to all its $r$ selected offspring is $(j/2{)}^r$, which explains each factor. Conditional on the original founding couple, its two generation-2 siblings and their independent outside spouses give independent left and right contributions. ThusExpanding givesIt satisfies $R(1)=1$, as it must for a monomorphic haplotype. This expression supplies a numerical LOD once $p$ is specified; the problem does not specify that frequency.

In the idealized limit where a matching rare haplotype identifies one ancestral copy, the leading coefficient is particularly simple. Dropping restrictions on the eight unaffected subjects, the probability that all selected subjects are autozygous for one common copy isAccordingly $R(p)/p\to 2^{-22}$ as $p\to 0$, and the affected-only IBD calculation gives $Z(0)=22{\log }_{10}2\simeq 6.623$.

If the genetic marker observations additionally establish the exact pattern $E$ of part (d), including that the eight unaffected subjects are not autozygous, its idealized IBD likelihood ratio is insteadThis latter value requires the additional negative genetic marker observations. It cannot be inferred merely from homozygosity in the affected subjects, and neither simplified IBD score is an exact identity-by-state likelihood for an unspecified common haplotype.

behavioural plasticity can slow inherited change by buffering selection, or accelerate it by permitting persistence and exposing organisms to new selection. There is no general ranking without specifying the trait, environment and timescale. The immediate adjustment of an individual's animal behaviour is a change in expression. evolution of that response requires a change in inherited properties of a biological population. A learned innovation spreading through cultural inheritance is another form of transmitted change, which should be distinguished from a change in allele frequencies.

A reaction norm makes this distinction explicit. Suppose a behavioural measurement in environment $E$ is $z=a+bE$, with inherited variation in baseline $a$ and responsiveness $b$. For illustration, let the favoured value be $E$, and let relative genotype fitness be:The first term penalizes mismatch; the second represents a possible cost of responsiveness. This is a deliberately simple model, not a claim that all animal behaviour has one optimum. Its phenotypic selection gradient on baseline, holding $b$ fixed, is:Immediately after a change to $E=1$, individuals with $a=0,b=1$ match the optimum and experience no mismatch selection on $a$; otherwise identical individuals with $b=0$ experience a gradient $2k$. Thus phenotypic buffering can reduce selection for inherited baseline change even when the response is highly beneficial. If $c>0$, selection on responsiveness can nevertheless persist. Buffering one dimension of the phenotype does not stop all evolution.

This impeding effect is biologically plausible when animals can avoid adverse conditions. Moving to a cooler microhabitat can reduce exposure to heat and therefore weaken selection on heat tolerance. Switching food can similarly reduce selection on digestive performance for an avoided resource. These are conditional mechanisms: the relevant evidence would be reduced differences in survival or reproduction among inherited physiological variants, rather than mere observation that animals move or switch foods. learning can also allow several inherited variants to reach similar behavioural performance, weakening selection among them. Such buffering may preserve genetic variation, which can become consequential after later environmental change; slow immediate change can therefore coexist with greater long-term evolutionary potential.

Acceleration begins with the demographic problem. An inherited advantage cannot spread in a lineage that disappears before it is expressed or transmitted. A flexible response can allow individuals to survive and reproduce after an environmental shift, providing time for subsequent inherited adaptation and possibly evolutionary rescue. This need not increase the selection coefficient of a particular variant. Increasing the number of surviving individuals or generations available for selection can matter even while the per-generation gradient becomes smaller. A comparison of change per generation and total adaptation over a fixed number of years can consequently give different answers.

behavioural plasticity can also change which environments impose selection. A newly learned foraging technique may expose animals to a new resource, making inherited differences in handling, digestion or sensory discrimination important. habitat preference can alter encounters with competitors and mates; repeated use of a new host can influence gene flow when mating occurs there. The host fidelity of Rhagoletis pomonella provides evidence that host-associated actions can constitute a premating barrier. It demonstrates a route from animal behaviour to evolutionary consequences, but does not by itself establish that the initiating host shift was a plastic response. ^[ref] Establishing that historical sequence is necessary before counting the case as plasticity-led evolution.

In the Baldwin effect, acquired adjustments change survival and the selection subsequently experienced by inherited variants. genetic accommodation can then refine the threshold, specificity or efficiency of an environmentally induced response. Its outcome may be greater phenotypic plasticity, a differently tuned response, or genetic assimilation, in which expression becomes less dependent on the original inducing condition. No step requires a learned action to be copied directly into DNA.

Experiments on spadefoot toad tadpoles provide relevant, though not exclusively behavioural, evidence. Populations that expressed the carnivore ecomorph more frequently showed refinement of associated resource-use performance and morphology under laboratory comparison. Such correspondence is predicted if recurrent induction exposes the expressed phenotype to selection. The comparison supports inherited refinement following environmental responsiveness, but contemporary populations are not a direct film of the ancestral transition, and their prior ecological histories could differ. ^[ref] Classic selection on heat-induced crossveinless wings in Drosophila melanogaster also showed that a previously induced phenotype could eventually appear without the inducing treatment. That is evidence for genetic assimilation, not direct evidence that behavioural innovations generally accelerate evolution. ^[ref]

The balance depends on cue reliability, environmental persistence and costs of phenotypic plasticity. A response based on a formerly reliable cue can become maladaptive after environmental change. A persistent new environment may favour a cheaper constitutive solution, whereas recurring variation can favour continued flexibility. Response delays, limited sensory discrimination and trade-offs between alternative activities can leave substantial residual selection. Conversely, sufficiently effective and inexpensive flexibility can remove much of the benefit of further inherited change. The availability of relevant genetic variation and its genetic covariance with other traits also constrain the response.

A decisive study would separate immediate adjustment from inherited divergence. Replicated populations could experience stable and fluctuating environments, with variation in access to a learned response or environmental cue. Descendants should then be assayed in a common garden experiment, both with and without that cue. Repeated measures estimate within-individual change; pedigrees or crosses estimate inherited reaction norm differences. Survival, reproduction, population persistence and changes in other traits must all be measured. Manipulating responsiveness requires controls for sensory damage, stress and general incapacity: disabling a neural process and then observing extinction would not isolate an evolutionary benefit of flexibility. Comparisons across species additionally require control for phylogenetic nonindependence and ecological opportunity.

The strongest conclusion is conditional: effective adjustment often weakens immediate selection on the buffered trait, while persistence, new ecological exposure and inherited refinement can increase cumulative evolutionary change. Those mechanisms can operate together within the same lineage; their relative importance is an empirical question rather than an intrinsic property of flexible animal behaviour.

Knowing the molecular basis of a behaviour is not a prerequisite for understanding its evolution or many of its evolutionary consequences. Evidence about transmission is essential for claims of inherited change, while detailed genetic architecture becomes essential for particular mechanistic predictions. The claim therefore depends on what is meant by a genetic basis and on the explanatory question being asked.

Tinbergen's four questions distinguish mechanism, development, adaptive significance and evolutionary history. Identifying a neural or molecular mechanism helps explain how a response is produced; it does not automatically show why a variant spread, whether it currently increases reproductive success, or whether the same mechanism generated the ancestral transition. Conversely, a well-supported evolutionary explanation can begin with experimentally demonstrated biological fitness consequences and transmission without a complete molecular account. These explanatory levels are complementary rather than substitutes. ^[ref]

The phrase genetic basis can refer to several different achievements: identifying inherited variation; estimating the number and effects of contributing genetic loci; finding a causal nucleotide change; or describing every gene required for development of the relevant sensory and motor systems. These are not equivalent. Many genes can be necessary for an animal to perform an action while none explains variation in that action within the studied population. Knocking out a broadly required neural gene and eliminating courtship does not identify an evolutionary substitution for a naturally varying mate preference.

quantitative genetics can predict a response without naming the causal molecular variants. Under the appropriate additive, generational and environmental assumptions, the multivariate breeder's equation gives:where $\mathbf{G}$ is the additive genetic covariance matrix and $\mathbf{\beta }$ the vector of phenotypic selection gradients. Behavioural measurements, pedigrees, repeated observations and reproductive success can therefore estimate whether and in what direction a response is expected. The covariances matter: selection favouring exploration can produce a correlated response in aggression or constrain the response when their biological fitness effects conflict. Naming an exploration-related gene would not replace this population-level information.

These estimates require strong controls. behavioural repeatability is consistency among observations of the same individual; it can reflect persistent environment as well as inherited differences and is not equivalent to heritability. Parent–offspring resemblance can also reflect teaching, maternal provisioning or shared habitat. cross-fostering, common garden experiments and appropriately structured breeding designs help separate these alternatives. heritability is conditional on the sampled population and environment, not a measure of immutability. A response measured in one environment may fail elsewhere because of genotype-environment interaction or altered selection. Thus ignorance of exact molecular variants is compatible with informative prediction, but ignorance of transmission and its confounders is not.

Molecular work adds power when it establishes a causal link to naturally occurring variation. In Drosophila melanogaster, rover and sitter food-search variants were connected to the foraging gene, which encodes a cGMP-dependent protein kinase. Mapping, enzyme activity and transgenic rescue linked the molecular difference to behavioural performance; comparable locomotion without food helped exclude a general activity explanation. ^[ref] This is much stronger than finding a statistical association between a gene and a behavioural score. Nevertheless, the experiment alone does not establish which ecological conditions historically maintained the polymorphism. That requires biological fitness comparisons across resources, densities and frequencies, with genetic-background controls.

genetic architecture is particularly informative when animal behaviour changes gene flow. In Heliconius melpomene and Heliconius cydno, mapping identified several major regions associated with male mating preferences; one lay close to the wing-pattern regulator Optix. Tight genetic linkage can help maintain associations between a mating cue and preference despite exchange between lineages. It does not establish pleiotropy, and courtship assays must distinguish attraction from the female's response and subsequent mating. ^[ref] Here molecular localization helps evaluate whether a proposed route to reproductive isolation is genetically feasible. A preference could still have been shown to reduce heterospecific mating before its contributing regions were mapped.

The influence of one individual's animal behaviour on another's development further complicates a simple own-genotype explanation. Maternal provisioning in Onthophagus taurus was studied using a breeding design that separated direct and maternal genetic contributions to offspring traits. ^[ref] An indirect genetic effect occurs when another individual's inherited properties alter the focal individual's phenotype. Such effects change the environment in which selection acts and can alter expected evolutionary responses. Identifying only the offspring's molecular variants would miss an important part of the causal system. Conversely, an observed maternal effect is not automatically a maternal genetic effect; provisioning can vary for environmental reasons.

Transmission need not follow genetic parentage. In wild great tits, experimenters trained demonstrators to use alternative puzzle-box techniques and followed the spread of the introduced variants. Persistent local traditions and preferential adoption of the common local technique supported social learning and conformist transmission. ^[ref] The experiment established a route of behavioural inheritance without identifying a molecular difference between the techniques' users. It did not prove that learning ability has no inherited basis, or that the new tradition changed allele frequencies. Rather, it shows why an account of behavioural change needs to identify the relevant transmission process instead of assuming it.

Even a learned response with no demonstrated inherited differences can influence subsequent evolution. A new resource use can alter selection on digestion; a socially learned mating signal can alter assortative mating; habitat choice can change contact with other populations. The immediate causal effect can be tested by manipulating the action or its social transmission and measuring biological fitness or exchange. To claim ensuing genetic adaptation, one must additionally show inherited change. To explain exactly which variants can respond, how quickly, and with what correlated effects, information about genetic architecture becomes increasingly valuable.

The most productive programme therefore combines behavioural intervention, transmission studies, biological fitness measurement and molecular analysis when it addresses an unresolved mechanism. Candidate variants should be tested across natural genetic backgrounds and environments, preferably with targeted perturbation and rescue; historical claims also need comparative or temporal evidence. Exact molecular knowledge is neither sufficient nor universally necessary: the necessary evidence is the evidence that connects the particular behavioural difference, its transmission and its measured evolutionary consequence.