Statistical methods to correct for observation error in a density‐independent population model

Abstract

Abstract. The problem of observation error in assessing the dynamics of populations over time has received increasing attention of late. Of particular interest has been a densityindependent dynamic model, which allows a trend and is commonly employed in population viability analysis (PVA). Most of the recent work in this area has focused on assessing the impact of the observation error and on finding corrected estimators, primarily under normal models with the observation errors assumed to have a constant variance. This paper provides a comprehensive overview of statistical methods for this problem and evaluates them through simulations. This includes the development and assessment of simple and practical ways to obtain standard errors and confidence intervals for the basic parameters in the model and functions of them, such as the intrinsic rate of increase or the probability of eventual extinction. We allow for unequally spaced data and possibly changing observation error variances, and we also discuss how to employ standard errors that often accompany the estimated abundances. Both likelihood techniques under normality and methods allowing non-normal observation errors are discussed, and we describe how the various likelihoodbased techniques can be implement using standard mixed-model software, such as PROC MIXED in SAS. The projection technique we use to handle functions of the basic parameters is also valuable when there is no observation error. The methods are motivated and illustrated using data for grizzly bears, Whooping Cranes, California Condors, and Puerto Rican Parrots. We present a simulation experiment to evaluate the performance of the some of the methods.

Analysis of ecological time series with ARMA(p,q) models

“…As with other studies, we found that measurement error contaminating data sets introduces bias for parameter estimation and model selection (Shenk et al 1998, Staudenmayer and Buonaccorsi 2005, Dennis et al 2006, Buonaccorsi and Staudenmayer 2009). While measurement error can be explicitly incorporated into models for estimation (Bell andWilcox 1993, Staudenmayer andBuonaccorsi 2005), we found that using the simpler approach of fitting ARMA( p,p) models worked reasonably well to estimate the AR coefficients of the model with little excess bias.…”

“…Second, we address the issue of measurement error. Measurement error may contaminate time-series data, generating lags in the MA component of a fitted model and causing bias in the coefficient estimates (Shenk et al 1998, Ives et al 2003, Staples 2004, Staudenmayer and Buonaccorsi 2005, Dennis et al 2006, Buonaccorsi and Staudenmayer 2009). Here, we investigate two approaches to incorporating measurement error into ARMA models.…”

A Scheme for Evaluating Feral Horse Management Strategies

“…There is a large recent literature concerned with various error terms in population models ( [18,[28][29][30] provide examples). Much of the literature on biases is concerned with decreasing populations, rather than with the growth curves considered here, and it seems that there is little agreement yet on terms and methodology.…”

Re‐Evaluating Evidence for Past Population Trends and Predicted Dynamics of Yellowstone Grizzly Bears

“…The second of these two data sets is one of the most commonly used examples in the literature on count‐based population viability analysis (e.g., Dennis et al . ; Dennis & Taper ; Morris & Doak ; Lindley ; Buonaccorsi & Staudenmayer ).…”

“…In particular, we re-examine the use of two data sets at the core of the arguments about the population's status, past and present: demographic rate estimates from 1983 to 2001, and relative density estimates from 1973 to the present. The second of these two data sets is one of the most commonly used examples in the literature on count-based population viability analysis (e.g., Dennis et al 1991;Dennis & Taper 1994;Morris & Doak 2002;Lindley 2003;Buonaccorsi & Staudenmayer 2009).…”