An examination of index-calibration experiments: counting tigers at macroecological scales

Abstract

1. An index-calibration experiment involves rigorous estimation of animal abundance at a small scale to calibrate a less rigorously derived index of abundance. The efficacy of such index-calibration experiments has been a matter of much controversy. In this study, we develop theoretical models and test them with empirical data on large-scale index-calibration experiments on tigers Panthera tigris to advance our understanding of this controversy. 2. We propose two models that describe the sampling processes involved in typical index-calibration experiments. Using analytical derivations and some simulations, we evaluate the relative roles of these sampling parameters on the math formula R²(coefficient of determination) statistic – a common inferential tool used in such calibration experiments. 3. We make predictions about the math formula R² statistic using our theoretical derivations and estimates from large-scale occupancy surveys of tigers in India. We then compare our predictions with empirical estimates of two tiger sign index-calibration experiments (IC-Karanth and IC-Jhala). 4. Our theoretical models show that the math formula R² statistic increases when individual-specific detection probability is high and is constant, increases when the variance-to-mean ratio of abundance increases, increases when precision of abundance estimates improves and declines when mean abundance increases. All predictions about the two index-calibration experiments showed a poor performance of the math formula R² statistic (R² < 0·40). Inference from IC-Karanth was extremely poor (R² = 0.0004) and comparable to model predictions (P value = 0·0754). Anomalously (P value < 0·0001), inference from IC-Jhala was exceedingly high (R² = 0.95). 5. Our study shows that such direct index-calibration experiments using the math formula R² statistic yield poor inferences unless all the sampling process parameters lie within a limited range. Ignoring the consequence of the effect of these parameters during survey design could result in expenditure of huge resources with little gain in ecological inference. Analysis using joint likelihood models, with appropriate survey designs, may be more fruitful than clinging on to such composite, direct R²-based models.