Effects of sampling error and temporal correlations in population growth on process variance estimators |
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Authors: | David F Staples Mark L Taper Brian Dennis Robert J Boik |
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Institution: | 1. Department of Ecology, 310 Lewis Hall, Montana State University, Bozeman, MT, 59717-5065, USA 2. Minnesota Department of Natural Resources, 5463-C West Broadway, Forest Lake, MN, 55025-8824, USA 3. Department of Fish and Wildlife Resources, University of Idaho, Moscow, ID, 83844-1103, USA 4. Department of Statistics, University of Idaho, Moscow, ID, 83844-1103, USA 5. Department of Mathematical Sciences, Montana State University, Bozeman, MT, 59717-2400, USA
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Abstract: | Estimates of a population’s growth rate and process variance from time-series data are often used to calculate risk metrics
such as the probability of quasi-extinction, but temporal correlations in the data from sampling error, intrinsic population
factors, or environmental conditions can bias process variance estimators and detrimentally affect risk predictions. It has
been claimed (McNamara and Harding, Ecol Lett 7:16–20, 2004) that estimates of the long-term variance that incorporate observed
temporal correlations in population growth are unaffected by sampling error; however, no estimation procedures were proposed
for time-series data. We develop a suite of such long-term variance estimators, and use simulated data with temporally autocorrelated
population growth and sampling error to evaluate their performance. In some cases, we get nearly unbiased long-term variance
estimates despite ignoring sampling error, but the utility of these estimators is questionable because of large estimation
uncertainty and difficulties in estimating correlation structure in practice. Process variance estimators that ignored temporal
correlations generally gave more precise estimates of the variability in population growth and of the probability of quasi-extinction.
We also found that the estimation of probability of quasi-extinction was greatly improved when quasi-extinction thresholds
were set relatively close to population levels. Because of precision concerns, we recommend using simple models for risk estimates
despite potential biases, and limiting inference to quantifying relative risk; e.g., changes in risk over time for a single
population or comparative risk among populations. |
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