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To infer time-varying population trajectories under known historical constraints, the authors formulate the bounded coalescent as an inhomogeneous point process and develop both an exact simulation algorithm and a continuous-time MCMC posterior sampler. This addresses a key limitation in standard coalescent frameworks, which lack efficient inference tools when the time to the most recent common ancestor is bounded by a known cutoff, such as an epidemic introduction event or experimental lineage-tracing window. Across empirical simulations and SARS-CoV-2 genomic data, the approach eliminates the need for likelihood grid discretization and reduces parameter estimation error across non-rapidly fluctuating demographic histories.
Conditioning genealogical trees on hard temporal bounds cuts parameter estimation error in dynamic populations without the steep computational penalty of rejection sampling or cumulative hazard inversion.
The coalescent is a central framework in population genetics for modelling the ancestral relationships among sampled individuals through a genealogy, represented as a rooted and ranked binary tree. In this model, lineages coalesce at a rate inversely proportional to the effective population size, a time-varying quantity of primary interest. The bounded coalescent conditions genealogies on the time to the most recent common ancestor being bounded above by a fixed time. This model is useful in various contexts, such as phylodynamics of infectious diseases with known introduction times and single-cell lineage tracing in synthetic barcoding experiments. To our knowledge, there is no existing tool that infers variable effective population size trajectories under the bounded coalescent. We view estimation under the bounded coalescent as equivalent to estimation of the intensity function of an inhomogeneous point process. We provide an efficient algorithm for coalescent simulation under the bounded coalescent using point process methods, retaining the exactness of naive rejection sampling while substantially reducing computational cost and avoiding repeated numerical inversion of the bounded cumulative hazard. We then develop a Markov chain Monte Carlo procedure for posterior inference of effective population size trajectories that avoids discretization of the likelihood integrals. In simulations, conditioning on the bound reduces the median sum of squared errors in two of three settings, with less favourable results in the most rapidly varying setting. We illustrate the method using severe acute respiratory syndrome coronavirus 2 sequence data from Washington State.