Biogeography And Migration

Biogeographic analysis reconstructs discrete region states and derives bounded transition, chronology, and migration-event records. Bijux exposes region probabilities, rates, constraints, sampling-bias diagnostics, time-stratified matrices, tree-set stability, exclusions, and report packages as separate review surfaces.

flowchart LR
    inputs["Rooted tree or tree set<br/>taxa · regions · times"]
    model["State model<br/>root · rates · constraints"]
    nodes["Node region<br/>probabilities"]
    branches["Branch transitions<br/>certainty · chronology"]
    population["Tree-set events<br/>stability · exclusions"]
    claim["Bounded migration<br/>conclusion"]

    inputs --> model --> nodes --> branches --> population --> claim

Separate State, Opportunity, And Process

A migration claim crosses three inferential layers. Collapsing them produces the common error of reading reconstructed changes as observed movement rates.

Layer	Governing evidence	Defensible claim	Claim that remains unsupported
state	admitted tip regions, state vocabulary, node probabilities	a region is conditionally preferred at a node	an ancestor was observed in that region
opportunity	dated branches, occupied source states, allowed routes, time strata	a transition could contribute under the model	every route was equally available or sampled
process	rate parameterization, exposure, constraints, fitted model	transition intensity under the declared process	an empirical movement frequency independent of the model
event summary	parent/child uncertainty, branch identity, event rule	a branch satisfies the declared reconstructed-event rule	a witnessed dispersal event or causal mechanism

The opportunity population is especially important. Counts must not be compared across regions, time bins, or tree sets unless eligible branches, exposure, exclusions, and failed reconstructions remain visible.

Choose The Biogeographic Contract

Question	Public surface	Record that controls interpretation
Which region states and transitions follow from one model?	summarize_geographic_state_model	state order, root treatment, rate rows, node probabilities, exclusions
Which transitions remain possible under geographic constraints?	summarize_constrained_geographic_model	allowed-transition policy, constrained and unconstrained fits, unsupported claims
Does uneven regional sampling alter the reconstruction?	summarize_geographic_sampling_bias	sampling counts, node and transition sensitivity, exclusions
Do transition opportunities change through time?	summarize_time_stratified_geographic_transitions	time-bin definitions, branch overlap, matrix identity, unsupported branches
Which dated events are reconstructed?	summarize_biogeographic_transition_chronology	node ages, event time, bin assignment, temporal uncertainty
How stable are events across trees?	summarize_geographic_migration_event_tree_set	admitted tree population, per-tree events, failures, event aggregation rule

summarize_geographic_migration_events creates an event ledger for one tree. It does not observe migration directly.

Preserve Region And Transition Identity

Region labels are model states, not decorative map text. Retain their order, normalization, spatial definition, missing-state policy, and any transition allowlist. For every rate or event, identify source region, target region, branch, parent and child node, descendant taxa, support class, and whether the transition was admissible.

A forbidden transition must remain visible as an unsupported claim or failed model condition. Silently removing it changes both the candidate process and the event denominator.

Time Stratification Changes The Model

Time bins define different transition opportunity regimes. Record bin boundaries, time units, inclusivity rules, branch overlap, and which transition matrix applies to each interval. A branch that crosses a boundary cannot be assigned by label proximity alone.

Chronology inherits uncertainty from topology, branch times, calibrations, state reconstruction, and bin definition. Similar event ages from different time trees are not equivalent until those inputs align.

Separate Count, Rate, And Stability

Quantity	Denominator	Common overclaim
event count	admitted branches or events on one reconstruction	more events means higher migration propensity
transition rate	model exposure under the declared state process	rate is an observed movement frequency
tree-set frequency	admitted trees with a structurally corresponding event	frequency is posterior probability without a posterior sampling contract
region count	admitted tips, nodes, or observations named by the record	count represents unbiased geographic prevalence

Keep tree-level events and tree-set summaries together. Failed or incompatible trees remain in the population record even when they cannot contribute an event row.

Sampling Bias And Constraints Are First-Class

Sampling concentration can change region probabilities and apparent transition support. Constraint policies can prevent biologically or geographically impossible transitions but can also force probability into the remaining paths. Review unconstrained and constrained fits, boundary states, unsupported claims, and bias-sensitive nodes before interpreting a favored route.

Publication Packet

Retain the tree or tree-set identity, region table and vocabulary, model and root policy, rate and transition rows, node probabilities, sampling counts, constraint revision, time bins, event ledger, tree-set denominator, exclusions, warnings, and report inventory. build_biogeography_report_package assembles projections from these records; it does not replace them.

Refuse a migration conclusion when region identity is ambiguous, required taxa are missing without policy, node or branch identity cannot be reconciled, time units are unknown, the selected transition is forbidden, or tree/model sensitivity reverses the conclusion.