Modeling observation error and its effects in a random walk/extinction model.
This paper examines the consequences of observation errors for the "random walk with drift", a model that incorporates density independence and is frequently used in population viability analysis. Exact expressions are given for biases in estimates of the mean, variance and growth parameters under very general models for the observation errors. For other quantities, such as the finite rate of increase, and probabilities about population size in the future we provide and evaluate approximate expressions. These expressions explain the biases induced by observation error without relying exclusively on simulations, and also suggest ways to correct for observation error. A secondary contribution is a careful discussion of observation error models, presented in terms of either log-abundance or abundance. This discussion recognizes that the bias and variance in observation errors may change over time, the result of changing sampling effort or dependence on the underlying population being sampled.
Department of Mathematics and Statistics and Graduate Program in Organismic and Evolutionary Biology Lederle Graduate Research Tower, University of Massachusetts, Amherst MA, 01003-9305, USA. johnpb@math.umass.edu
John P
JP
Buonaccorsi
John
J
Staudenmayer
Maximo
M
Carreras
D000704:Analysis of Variance; D015982:Bias; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D053476:Extinction, Biological; D020342:Finite Element Analysis; D040961:Genetic Drift; D005828:Genetics, Population; D016014:Linear Models; D008957:Models, Genetic; D019370:Observation; D011156:Population Density; D011157:Population Dynamics; D011336:Probability; D015203:Reproducibility of Results; D013269:Stochastic Processes; D013997:Time Factors