Overcoming limitations of modelling rare species by using ensembles of small models

1. Species distribution models (SDMs) have become a standard tool in ecology and applied conservation biology. Modelling rare and threatened species is particularly important for conservation purposes. However, modelling rare species is difficult because the combination of few occurrences and many predictor variables easily leads to model overfitting. A new strategy using ensembles of small models was recently developed in an attempt to overcome this limitation of rare species modelling and has been tested successfully for only a single species so far. Here, we aim to test the approach more comprehensively on a large number of species including a transferability assessment. 2. For each species numerous small (here bivariate) models were calibrated, evaluated and averaged to an ensemble weighted by AUC scores. These 'ensembles of small models' (ESMs) were compared to standard Species Distribution Models (SDMs) using three commonly used modelling techniques (GLM, GBM, Maxent) and their ensemble prediction. We tested 107 rare and under-sampled plant species of conservation concern in Switzerland. 3. We show that ESMs performed significantly better than standard SDMs. The rarer the species, the more pronounced the effects were. ESMs were also superior to standard SDMs and their ensemble when they were independently evaluated using a transferability assessment. 4. By averaging simple small models to an ensemble, ESMs avoid overfitting without losing explanatory power through reducing the number of predictor variables. They further improve the reliability of species distribution models, especially for rare species, and thus help to overcome limitations of modelling rare species.

Fibroblast growth factor-23 (FGF-23) levels differ across populations by degree of industrialization.

CONTEXT: Compensatory increases in FGF23 with increasing phosphate intake may adversely impact health. However, population and clinical studies examining the link between phosphate intake and FGF23 levels have focused mainly on populations living in highly industrialized societies in which phosphate exposure may be homogenous. OBJECTIVE: Contrast dietary phosphate intake, urinary measures of phosphate excretion and FGF23 levels across populations that differ by level of industrialization. DESIGN: Cross-sectional analysis of three populations Setting: Maywood, IL, U.S., Mah|fe Island, Seychelles, and Kumasi, Ghana Participants: Adults with African ancestry aged 25-45 years Main Outcome: Fibroblast growth factor 23 (FGF23) levels Results: The mean age was 35.1 (6.3) years and 47.9% were male. Mean phosphate intake and fractional excretion of phosphate were significantly higher in the U.S. vs. Ghana while no significant difference in phosphate intake or fractional excretion of phosphate was noted between U.S. and Seychelles for men or women. Overall, median FGF23 values were 57.41 RU/ml (IQR 43.42, 75.09) in U.S., 42.49 RU/ml (IQR 33.06, 55.39) in Seychelles and 33.32 RU/ml (IQR 24.83, 47.36) in Ghana. In the pooled sample, FGF23 levels were significantly and positively correlated with dietary phosphate intake (r=0.11; P < 0.001), and the fractional excretion of phosphate (r=0.13; P < 0.001) but not with plasma phosphate levels (-0.001; P = 0.8). Dietary phosphate intake was significantly and positively associated with the fractional excretion of phosphate (r=0.23; P < 0.001). CONCLUSION: The distribution of FGF23 levels in a given population may be influenced by the level of industrialization, likely due to differences in access to foods preserved with phosphate additives.