Proportional stochastic generalized Lotka–Volterra model with an application to learning microbial community structures
Why this work is in the frame
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Bibliographic record
Abstract
Inferring microbial community structure based on temporal metagenomics data is an important goal in microbiome studies. The deterministic generalized Lotka–Volterra (GLV) differential equations have been commonly used to model the dynamics of microbial taxa. However, these approaches fail to take random environmental fluctuations into account and usually ignore the compositional nature of relative abundance data, which may deteriorate the estimates. In this article, we consider the microbial dynamics in terms of relative abundances by introducing a reference taxon, and propose a new proportional stochastic GLV (pSGLV) differential equation model, where the random perturbations of Brownian motion in this model can naturally account for the external environmental effects on the microbial community . We establish conditions and show some mathematical properties of the solutions including general existence and uniqueness, stochastic ultimate boundedness, stochastic permanence, the existence of stationary distribution, and ergodicity property. We further develop approximate maximum likelihood estimators (AMLEs) based on discrete observations and systematically investigate the consistency and asymptotic normality of the proposed estimators. At last, numerical simulations support our theoretical findings and our method is demonstrated through an application to the well-known “moving picture” temporal microbial dataset.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it