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Phylogenetic estimation of diversity-dependent biogeographic rates using deep learning

Albert C. SoewongsonoiD, Michael J. LandisiD

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Abstract

Ecological theory predicts that local species richness can influence biogeographic rates of speciation, extinction, and dispersal. For instance, increasing the number of competing species within a region may cause local speciation and dispersal rates to decrease but local extinction rates to increase, inducing a carrying capacity for local species richness. In this article, we introduce a fully generative, event-based phylogenetic diversification model, called DDGeoSSE, that allows diversity-dependent effects of local species richness to modulate biogeographic rates of diversification and range evolution. DDGeoSSE can accommodate and test a variety of alternative diversification scenarios that involve positive, negative, and neutral interactions among sympatric species for speciation, extinction, and dispersal. We derive mathematical and statistical properties of biogeographic outcomes generated by this model, such as the carrying capacity for a clade at equilibrium, which we validate through simulation. Because diversity-dependent phylogenetic models typically do not have tractable likelihood functions, we use deep learning with \texttt{phyddle} to perform parameter inference and model selection. Separately applying DDGeoSSE to Caribbean \textit{Anolis} lizards and cloud forest-dwelling \textit{Viburnum} plants, we find evidence that local species richness plays a significant role in shaping diversification dynamics for both clades.

In-depth summary

Claude Opus 5.5 · xhigh effort · 8 Nov 2026 · from the full text of version 2 (15 Oct 2026) · CC BY 4.0

DDGeoSSE, a GeoSSE extension in which local species richness modulates speciation, extinction and dispersal, is fit with phyddle neural networks that detect diversity dependence in Anolis and Viburnum.

Diversification models mostly let species richness grow exponentially, while the few diversity-dependent biogeographic models (the Rabosky-Glor MuSSE variant, DAISIE) restrict widespread ranges and tie speciation, extinction and dispersal to one carrying capacity. DDGeoSSE gives each process its own effect of actual local species counts, lets equilibrium diversity emerge rather than be a parameter, and sidesteps its intractable likelihood with deep learning.

Key results

  1. ShownOn simulated test data, per-process classifiers can tell whether diversity dependence acts on within-region speciation, extinction or inbound dispersal, with limited confusion between processes.

    Three classifiers (one per process) trained on 400,000 simulations (8 submodels × 50,000), each replicated in 8 networks. Present effects detected 81% to 87% (speciation), 78% to 86% (extinction), 83% to 87% (dispersal); absent effects 73% to 81%, 76% to 83%, 74% to 80%. Support was 74% to 89% where truly present vs 9% to 38% where absent. · Deep learning method for parameter inference and…; Parameter estimation and model selection for…

  2. ShownOn held-out submodel 7 simulations, every parameter's 80% conformalized prediction interval (CPI) reached its target coverage, but diversity-dependent effect parameters are less precise than base rates, and the extinction effect e^D is the least precise across submodels.

    Submodel 7 test set: every parameter reached the 80% target coverage (Fig. 5). Base rates ρw, ρe, ρd, ρb had tighter intervals than w^D, e^D, d^(D,dest). e^D was least precise in all submodels with diversity-dependent extinction (Supp. Figs. S8, S11, S12). The authors say changing architectures or training did not improve it (results not shown). · Parameter estimation and model selection for…; Discussion

  3. SuggestedCaribbean Anolis is best fit by diversity dependence on within-region speciation, extinction and inbound dispersal (submodel 7). Oreinotinus Viburnum is best fit by dependence on within-region speciation and inbound dispersal but not extinction (submodel 6).

    Anolis (158 species, 5 Caribbean regions): slightly lower support for dispersal; predicted net diversification faster on smaller islands; within-region speciation and inbound dispersal highest in Jamaica, lowest in Cuba and the Caymans. Oreinotinus (38 species, 5 merged regions): weaker dispersal than speciation support. Estimates agreed across independently trained networks. · Model selection: Anolis tree; Model selection: Viburnum tree; Discussion

  4. ShownIn 3-region simulations, diversity dependence on speciation, extinction and dispersal each leaves a distinct combination of tree-shape, branching-time and range-size statistics, and a stronger effect on any process lowers extant species numbers.

    49,950 extant-only trees, 50 per grid point (w^D, d^(D,dest) in [−2, 0]; e^D in [0, 2]). Stronger w^D: larger ranges, more global (Colless) imbalance, more local balance, γ < 0. Stronger e^D: smaller ranges, sharply higher global imbalance, γ > 0. Stronger d^(D,dest): smaller ranges, slight global imbalance, branching nearer the tips. · Tree statistics for trees simulated under…; Tree and range statistics under DDGeoSSE

  5. ShownLocal equilibrium diversity, defined by balancing incoming and outgoing rates per region, follows from the model rather than being a parameter of it, and the derived values match stochastic simulations.

    Three parameter sets were tested: one fully unconstrained (solved numerically, Lemma 1) and two constrained (solved analytically, Lemmas 2 and 3). Each predicted around 19 extant species per region, and mean per-region trajectories over 100 replicates in a 3-region system converged to that level (Fig. 3). The simulator also matched diversitree on GeoSSE tree statistics (Supp. Figs. S32, S33). · Local equilibrium diversity; Deep learning method for parameter inference and…; Figure legends

Methods, data and reproducibility

DDGeoSSE scales each GeoSSE base rate (within- and between-region speciation, extinction, dispersal) by a factor of the log local species count, with a separate effect parameter per process. Trees simulated in Julia under eight submodels were used to train phyddle neural networks for parameter estimation (conformalized intervals) and per-process model selection, then applied to two clades.

  • Simulated extant-only trees and tip ranges for training, under 8 DDGeoSSE submodels with 5 regions and 10 to 300 extant tips · n = 50,000 per submodel (400,000 combined)
  • Simulated 3-region trees for exploring tree and range statistics over a grid of diversity-dependent effects · n = 49,950 trees; 6,200 weak-effect examples
  • Misspecification test sets simulated with relative area size (variants of Submodels 1 to 7) · n = 2,500 simulations per submodel
  • Caribbean Anolis phylogeny and ranges, reduced from Poe et al. (2017) and recoded to 5 island regions · Anolis lizards · n = 158 species
  • Oreinotinus time tree and ranges from Donoghue et al. (2022), pruned and merged from 10 to 5 montane regions · Viburnum (Oreinotinus clade) plants · n = 38 species
Methods & tools
DDGeoSSE, phyddle, Julia (custom simulator), diversitree, treestats, PyTorch, Dendropy
Assay conditions & compute
phyddle analyses ran on a Dell Precision 7920 server: 112 CPU cores (2 Intel CPUs), 2 Nvidia RTX A4000 GPUs, 128 GB RAM. Simulator runtime by number of regions is benchmarked in Supp. Fig. S31.
Reproducibility gaps
The text gives no software versions or environment files. The authors say the phyddle configuration files and simulator scripts are in the Supplementary Information. Network training times are not reported.
Limitations (6)
  • The extinction effect e^D is estimated poorly. The authors advise reading empirical values only as e^D > 0, although the classifiers detect its presence or absence well. · stated by the authors
  • Networks trained without relative area size were applied to data simulated with it. CPI coverage fell to 64 to 70% for some parameters, and between 2% and 20.4% of samples per submodel were out of distribution. This was the only misspecification tested. · stated by the authors
  • The trained networks assume five regions, complete taxon sampling and rate differences driven only by species counts. Other settings need new simulations and training, and bias from incomplete sampling has not been assessed. · stated by the authors
  • The Viburnum tree had to be pruned to 38 species and merged into 5 regions, and its branch lengths were stretched 7-fold to match the training tree ages. Its treeness (0.43) lies outside the simulated range [0.64, 0.90], and the small tree may explain the weaker dispersal signal. · stated by the authors
  • Inference accuracy is evaluated only on data simulated from the DDGeoSSE submodels themselves. The Rabosky-Glor MuSSE variant and DAISIE are not fit to the same empirical data for comparison. · noted in this summary
  • Each empirical conclusion rests on a single fixed phylogeny per clade (158 and 38 species), with no analysis of phylogenetic uncertainty. Beyond the networks, the only support is qualitative agreement with earlier studies (Poe et al. 2017; Rabosky and Glor 2010; Donoghue et al. 2022). · noted in this summary

Read this if you study diversity-dependent diversification or island biogeography and want a simulator plus trained phyddle networks to test whether speciation, extinction or dispersal responds to local richness.

Citations
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