PCM2: Primate PGLS And Signal¶

PCM2 evaluates how phylogenetic covariance changes regression, model comparison, signal diagnostics, and ancestral inference on the prepared primate data. Baseline GLS and phylogenetically corrected models remain in one comparison chain so changes in coefficients and fit can be attributed.

flowchart LR
    data["Shared primate<br/>traits and taxa"]
    gls["Baseline GLS"]
    transformed["Transformed-tree<br/>covariance"]
    pgls["Pagel-λ PGLS"]
    modes["Evolutionary<br/>mode fits"]
    diagnostics["Residual, signal,<br/>ancestral diagnostics"]

    data --> gls
    data --> transformed --> pgls
    pgls --> modes --> diagnostics
    gls --> diagnostics

The Covariance Question In One View¶

Dimension	PCM2 contract
scientific object	the PCM1 primate population evaluated through independent GLS, tree-transformed covariance, Pagel-λ PGLS, evolutionary modes, residual diagnostics, and ancestral models
central idea	changing residual covariance can change coefficients, uncertainty, likelihood, diagnostics, and ancestral estimates even when response and taxa remain fixed
evidence role	tests which conclusions survive the move from independent errors to phylogenetically structured dependence and which discrepancies remain model-specific
present conclusion	bundle manifests record 3 `matched`, 6 `matched_with_tolerance`, and 1 `not_comparable`; the broader scalar ledger still retains 12 `mismatch_unexplained` observations
downstream role	supplies the covariance and model-comparison discipline that PCM3 must extend when categorical coding and interactions change the design matrix
forbidden inference	favorable claim-scoped bundles do not make PCM2 uniformly matching, interchangeable with the reference ecosystem, or biologically causal

PCM2 is deliberately a two-ledger study. The claim ledger says whether each bounded bundle closes; the scalar ledger preserves wider numerical debt. A reader needs both before summarizing correspondence.

Separate The Four Sentences PCM2 Can Produce¶

One table of coefficients can tempt a reader into one omnibus conclusion. PCM2 instead supports or limits four different sentences:

Sentence type	Example	Required comparison
within-model correspondence	R and Bijux baseline GLS slopes correspond	same population, design, covariance, likelihood, and coefficient key across implementations
within-model correspondence	R and Bijux Pagel-λ PGLS slopes correspond within tolerance	same fitted phylogenetic covariance contract across implementations
cross-model scientific contrast	the slope is smaller under PGLS than under independent GLS	accepted fits within one interpretation chain, with covariance as the deliberate change
model adequacy or sensitivity	residual behavior or evolutionary-mode results qualify the preferred interpretation	named diagnostics, candidate models, failures, and complete denominator

The first two are parity statements. The third is a scientific model comparison. The fourth determines whether either model supports the intended interpretation. Combining values across rows and columns—for example R GLS against Bijux PGLS—changes both implementation and model and isolates neither.

Scientific Questions¶

How do coefficient estimates and residual structure change after phylogenetic covariance is introduced?
Does estimating or transforming the covariance improve fit under a declared comparison rule?
Are signal, evolutionary-mode, and ancestral results mutually consistent for the same taxa and response definition?

PGLS changes the residual covariance model. It does not simply add a “phylogenetic correction” flag to ordinary regression, and it does not make the fitted relationship causal.

Independence Is Also A Model¶

Baseline GLS assumes that, after accounting for the predictors, one species' residual contains no information about another's. PGLS replaces that identity covariance with a tree-derived covariance whose strength is estimated or declared. The observations and printed formula can stay fixed while the effective weighting, uncertainty, likelihood, and coefficient estimates all change.

PCM2 uses that controlled change to ask whether the social-group-size association is sensitive to shared ancestry. The smaller PGLS slope is not a “phylogeny removed” coefficient; it is the coefficient under a different residual dependence model for the same governed population.

Keep Cross-Implementation And Cross-Model Contrasts Orthogonal¶

PCM2 contains two comparison axes. They answer different questions and use different denominators.

Axis	Comparison	Quantity held fixed	Conclusion available
implementation correspondence	R baseline GLS versus Bijux baseline GLS	population, formula, independent covariance, likelihood convention	whether two implementations reproduce the registered baseline result
implementation correspondence	R Pagel-λ PGLS versus Bijux Pagel-λ PGLS	population, formula, tree covariance parameterization, likelihood convention	whether two implementations reproduce the registered phylogenetic fit
scientific model contrast	baseline GLS versus Pagel-λ PGLS within an accepted implementation record	population and mean design	how the estimate changes when residual covariance changes
scientific model contrast	Brownian, OU, early-burst, and other registered modes	population, response, and declared comparison basis	how candidate evolutionary models differ when their identities are aligned

The fall in the social-group-size slope from roughly 3.59 to 1.66 is a cross-model scientific contrast. The close R–Bijux values within each model are correspondence observations. Subtracting the R baseline slope from the Bijux PGLS slope would cross both axes and would not isolate either question.

What PCM2 Adds Beyond PCM1¶

PCM1 established the admitted primate population and a signal/ancestral comparison. PCM2 keeps that population fixed while changing the model layer. This lets the study ask whether a result changes because covariance changed, rather than because different taxa or traits entered the fit.

Analytical move	New question	Evidence required
independent GLS → Pagel-λ PGLS	how do coefficients and uncertainty change when residual covariance follows the tree?	same response/design population, covariance identity, fitted λ, coefficients, likelihood, residual diagnostics
source tree → transformed trees	how do OU or time-dependent branch transformations change evolutionary-mode fits?	parent tree, transform convention and direction, parameters, branch totals, fitted objectives
fitted modes → likelihood-ratio tests	does a more complex registered mode improve fit under the declared comparison?	same observations and likelihood convention, nesting, degrees of freedom, optimizer state, statistic
fitted process → ancestral estimates	how do conditional node values change under Brownian or early-burst assumptions?	model and tree revision, clade-keyed node identity, estimates, uncertainty, complete node denominator
model family → intercept sweep	can the source `corBlomberg` likelihood surface be reproduced?	aligned execution and observations that are currently absent

The study therefore contributes more than a list of coefficients. It exposes which conclusions remain stable under a covariance change and where transform, residual, ancestral, or coverage semantics still disagree.

Evidence Decomposition¶

Bundle	Evaluated surface	Manifest verdict
`evidence-001`	reload semantics	`matched`
`evidence-002`	baseline GLS	`matched`
`evidence-003`	Pagel-λ regression	`matched_with_tolerance`
`evidence-004`	phylogenetic signal	`matched_with_tolerance`
`evidence-005`	residual diagnostics	`matched_with_tolerance`
`evidence-006`	transformed tree	`matched`
`evidence-007`	evolutionary mode fits	`matched_with_tolerance`
`evidence-008`	likelihood-ratio comparison	`matched_with_tolerance`
`evidence-009`	ancestral modes	`matched_with_tolerance` for named node identities
`evidence-010`	intercept sweep	`not_comparable`; required observations are absent

The final row prevents a mostly aligned bundle ledger from being summarized as unqualified end-to-end parity.

These verdicts are claim-scoped. They coexist with the aggregate scalar table's 12 mismatch_unexplained rows because the scalar table compares a broader set of observations than several focused bundle claims. The bundle ledger and scalar ledger answer different questions; neither may be used to erase the other.

Comparison Dependency Graph¶

flowchart LR
    population["evidence-001<br/>shared workspace population"]
    gls["evidence-002<br/>baseline GLS"]
    lambda["evidence-003<br/>Pagel-λ PGLS"]
    signal["evidence-004<br/>signal"]
    residuals["evidence-005<br/>residual diagnostics"]
    transforms["evidence-006<br/>tree transforms"]
    modes["evidence-007<br/>mode fits"]
    lrt["evidence-008<br/>likelihood ratios"]
    ancestral["evidence-009<br/>ancestral modes"]
    sweep["evidence-010<br/>intercept sweep"]

    population --> gls --> lambda
    population --> signal
    lambda --> residuals
    population --> transforms --> modes --> lrt
    modes --> ancestral
    modes --> sweep

Each downstream claim must retain the exact upstream artifact identities it consumed. A favorable baseline or PGLS bundle does not repair a transformed-tree or early-burst mismatch, and a named-node ancestral tolerance does not close the non-comparable intercept sweep.

Bundle And Scalar Verdicts¶

The ten bundle manifests currently record 3 matched, 6 matched_with_tolerance, and 1 not_comparable. The observation ledger is not uniformly passing: the generated scalar parity table associated with evidence-001 retains 12 mismatch_unexplained rows involving ancestral, early-burst, likelihood-ratio, transformed-tree, and residual quantities.

Those rows are registered scientific debt even though evidence-001 itself has a matched manifest verdict for the narrower workspace-reload contract. Therefore, quote the claim identifier and ledger level. Do not summarize PCM2 as clean parity from the bundle counts alone.

Governed Findings¶

The claim-scoped result files expose the scientific changes that the bundle headlines summarize:

Fit or test	Bijux observation	Reference relationship
baseline GLS social-group-size slope	3.591156	agrees with the registered R baseline within numerical precision
baseline GLS R²	0.257170	agrees with the registered R baseline
baseline GLS log likelihood	−456.310147	agrees under the registered likelihood convention
Pagel-λ PGLS estimated λ	0.768657	agrees with the R estimate to less than 10⁻⁶
Pagel-λ PGLS social-group-size slope	1.662147	agrees with the registered R coefficient within tolerance
Pagel-λ PGLS log likelihood	−444.069148	agrees with the registered R result within tolerance
longevity signal λ	0.802734	agrees with the registered R signal fit
λ=0 likelihood-ratio statistic	41.030419	agrees with the registered R test

The slope change from 3.591156 in baseline GLS to 1.662147 under the fitted phylogenetic covariance is the substantive comparison. It shows why model identity must accompany a coefficient; it does not, by itself, establish that either model is causal or biologically sufficient.

Unexplained Observation Inventory¶

The aggregate scalar ledger retains all 12 non-matches:

Surface	Rows	Recorded discrepancy
transformed trees	4	exact branch-length totals disagree, including reversed early- and late-burst totals
early-burst fit	2	rate change differs by 10.6718757865625; log likelihood differs by 15.170304341821
Brownian versus early-burst LRT	1	statistic differs by 30.340684573422
ancestral reconstruction	4	Brownian and early-burst estimate vectors fail the registered exact rule
estimated-λ residual diagnostic	1	absolute residual–fitted correlation differs by 0.095590314522858

These observations remain mismatch_unexplained even where a neighboring bundle has a favorable verdict for a narrower claim. The early-burst mismatch, for example, prevents the continuous-mode material from being cited as uniform numerical correspondence despite aligned Brownian and OU observations.

Inspect the scalar-parity-table.json for row identifiers, values, tolerances, and comparison kinds.

Cite PCM2 Without Flattening It¶

Statement	Records that must travel together
baseline versus Pagel-λ slope change	`evidence-002` and `evidence-003` model identities, coefficients, covariance, diagnostics, verdicts
signal result	`evidence-004` statistic, null rule, reference observation, tolerance, verdict
evolutionary-mode comparison	`evidence-006` through `evidence-008` plus the unresolved transformed-tree, early-burst, and LRT rows
ancestral estimate	`evidence-009` named-node identity, model, interval/tolerance, and tree revision
PCM2-wide conclusion	all ten bundle verdicts plus the 12 `mismatch_unexplained` scalar rows and open intercept-sweep boundary

The first four statements can be narrower than the whole study. The last one cannot be constructed by counting favorable bundle manifests while omitting the scalar mismatch ledger or evidence-010.

Reconstruct The Two-Ledger Decision¶

Read the relevant bundle manifest.json to identify the exact claim and its current verdict.
Follow its input manifest and freshness locators to the registered primate derivatives, reference result, and owned PCM2 runtime definition.
For a PCM2-wide statement, inspect evidence-001/results/scalar-parity-table.json and retain all 12 unexplained mismatches in the denominator.
Read evidence-010 separately: not_comparable means the required intercept-sweep observations are not available under a registered comparison contract.
Cite a favorable focused claim only at its own scope. Do not promote it to evolutionary-mode, ancestral, or study-wide equivalence.

This route explains an apparent contradiction without weakening either record: a narrow registered claim can match while broader retained observations still disagree.

Inputs And Provenance¶

The dossier contains the source workspace and tree plus governed reference_primate.csv and reference_trimmed_primatetree.nwk derivatives. See the dataset catalog, provenance record, and runtime mapping.

Model Comparison Discipline¶

Likelihood-ratio conclusions require nested, comparably fitted models and a declared degrees-of-freedom convention. Information-criterion comparisons answer a different question. Residual diagnostics qualify both baseline and phylogenetic fits; a better scalar score does not excuse a broken residual contract.

The baseline and Pagel-λ residual summaries use different residual scales in some fields across implementations. The aggregate ledger therefore preserves the residual diagnostic mismatch instead of treating matching coefficients and likelihoods as proof that every diagnostic definition is equivalent.

Review Priorities¶

Verify shared taxa and response transformation across every fit.
Inspect the covariance/tree transformation rather than only its fitted parameter.
Compare coefficients, likelihoods, and diagnostics together.
Preserve the scalar mismatch_unexplained rows in PCM2-wide summaries.
Keep evidence-009 bounded to its named-node tolerance contract.
Keep the evidence-010 verdict as not_comparable while its intercept-sweep resolution work remains open.

Detailed analysis is divided between model comparisons and PGLS and signal diagnostics and open boundaries. Continue to PCM3 for categorical predictors and interactions.