A Review of Envelope Models

Great Gerbils (Rhombomys opimus) in Central Asia Are Spreading to Higher Latitudes and Altitudes

The great gerbil (Rhombomys opimus) is a gregarious rodent in Central Asia and is one of the major pests found in desert forest and grassland areas. The distribution changes and migration routes of R. opimus in Central Asia under climate change remain unexplored. This study employed multi-model ensemble, correlation analysis, jackknife method, and minimum cumulative resistance (MCR) model to simulate the potential habitat of R. opimus under current and future (2030 and 2050) climate scenarios and estimate its possible migration routes. The results indicate that the ensemble model integrating Random Forest (RF), Gradient Boosting Machine (GBM), and Maximum Entropy Model (MaxEnt) performed best within the present climate context. The model predicted the potential distribution of R. opimus in Central Asia with an area under the curve (AUC) of 0.986 and a True Skill Statistic (TSS) of 0.899, demonstrating excellent statistical accuracy and spatial performance. Under future climate scenarios, northern Xinjiang and southeastern Kazakhstan will remain the core areas of R. opimus distribution. However, the optimal habitat region will expand relative to the current one. This expansion will increase with the rising CO2 emission levels and over time, potentially enlarging the suitable area by up to 39.49 × 104 km2. In terms of spatial distribution, the suitable habitat for R. opimus is shifting toward higher latitudes and elevations. For specific migration routes, R. opimus tends to favor paths through farmland and grassland. This study can provide guidance for managing and controlling R. opimus under future climate change scenarios.

Reducing subspace models for large-scale covariance regression

We develop an envelope model for joint mean and covariance regression in the large p, small n setting. In contrast to existing envelope methods, which improve mean estimates by incorporating estimates of the covariance structure, we focus on identifying covariance heterogeneity by incorporating information about mean-level differences. We use a Monte Carlo EM algorithm to identify a low-dimensional subspace that explains differences in both means and covariances as a function of covariates, and then use MCMC to estimate the posterior uncertainty conditional on the inferred low-dimensional subspace. We demonstrate the utility of our model on a motivating application on the metabolomics of aging. We also provide R code that can be used to develop and test other generalizations of the response envelope model.