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Predicting Population Extirpation in the Cerulean Warbler

The Cerulean Warbler is exhibiting severe declines which, if they persist, will lead to the extirpation of this species over much of its range. In the animation below, we show a potential timeframe for this extirpation, projecting trends in the species abundance as determined in our earlier study of the species in the Prairie Hardwood Transition (Thogmartin et al. 2004). The peak predicted abundance in the Prairie Hardwood Transition occurs in southeastern Michigan, at Allegan State Game Area.

This animated projection is a deterministic assessment and does not recognize the uncertainty associated with the estimates of trend.

The U.S. Fish and Wildlife Service is considering listing the Cerulean Warbler under the Endangered Species Act. To help the U.S. Fish and Wildlife Service determine whether this listing is appropriate, we applied the best available science in estimating probabilities of extinction for this species. We employed a diffusion approximation approach to solving this problem, which accounts for uncertainty in the estimation of the population trend. Available methods for parameterizing a diffusion model include maximum likelihood methods (Dennis et al. 1991), these same methods but using a running sum transformation of the data (Holmes 2001), maximum likelihood methods employing a Kalman filter (Harvey 1989, Lindley 2003), slope methods (Holmes 2001, Holmes and Fagan 2002), and asymptotically unbiased estimators for random matrix products (Heyde and Cohen 1985). Holmes (2004) provides a thorough treatment of these methods.

Methods

The various diffusion models require a time series of population estimates to predict probability and time to extinction. However, for the Cerulean Warbler, absolute estimates of population size do not exist. Indices of relative abundance do however exist, as derived from modeling of population trends with Breeding Bird Survey data (Link and Sauer 2002, Sauer et al. 2003). Additionally, K. Rosenberg and P. Blancher, as part of the North American Landbird Conservation Plan, derived a continental estimate of Cerulean Warbler population size (Rich et al. 2004). These population size estimates are ostensibly relevant to the mid-point of the 1990s. The Bird Conservation Regions we examined included all regions for which there were at least five Breeding Bird Survey routes informing trend estimates. These included BCR29 (Piedmont, n = 7 survey routes), BCR28 (Appalachian Mountains, n = 143), BCR25 (West Gulf Coastal Plain / Ouachitas, n =5), BCR24 (Central Hardwoods, n = 35), BCR23 (Prairie Hardwood Transition, n = 15), BCR22 (Eastern Tallgrass Prairie, n = 9), and BCR13 ( Lower Great Lakes / St. Lawrence Plain, n = 19) (Figure 1). We also used the survey-wide estimate of trend resulting from 238 survey routes.

The Rosenberg and Blancher population size estimate was associated with the annual index of relative abundance for 1995. These estimates were extrapolated to the years 1966–1994 and 1996–2005 by multiplying the ratio of the relative abundance estimates (RA _t/RA 1995) by the population size estimate for 1995 (Table 1).

Results

Eight models and their diagnostics were calculated to derive point estimates for the regions and the entire survey (Table 2). Point estimates for the regional and survey-wide diffusion models suggested that Cerulean Warblers were declining across the survey by 3.1% per annum (Table 3). There was heterogeneity in this decline across the various Bird Conservation Regions, with the decline ranging from 1% per annum in BCR29 and 16.9% per annum in BCR25. This latter decline constitutes a population collapse, though we are reminded that it is derived from data collected at only five survey sites.

The majority of the posterior probability distribution of the survey-wide l is in the region l < 1 (Figure 2), indicating that the data give high support to long-term declining dynamics.  The probability that the population as a whole and at the level of the individual Bird Conservation Regions ever experiences a 90% decline within the next century is outlined in Figure 3.  There is approximately an 80% probability of a 90% decline within 80 years for the species (the survey-wide estimate).  The probability of a 90% decline occurs within the next couple decades for the population in BCRs 22 and 25, whereas BCRs 13, 24, and 28 do not begin to exhibit a 90% decline for 5 decades.  In the core of the species range, BCR28, there was approximately a 50% probability of a 90% decline within 80 years.  All of the Bird Conservation Regions except for BCR29 exhibit a substantial probability of a 90% decline within the next century; all but BCR28 and 29 exhibited >90% probability of a 90% decline within the century.  

Literature Cited

Dennis, B., P. L. Munholland, and J. M. Scott. 1991. Estimation of growth and extinction parameters for endangered species. Ecological Monographs 61:115–143.

Harvey, A. C. 1989. Forecasting, structural time series models and the Kalman filter. Cambridge University Press, Cambridge, UK.

Heyde, C. C., and J. E. Cohen. 1985. Confidence intervals for demographic projections based on products of random matrices. Theoretical Population Biology 27:120–153.

Holmes, E. E. 2001. Estimating risks in declining populations with poor data. Proceedings of the National Academy of Sciences ( USA) 98:5072–5077.

Holmes, E. E. 2004. Beyond theory to application and evaluation: diffusion approximations for population viability analysis. Ecological Applications 14:1272–1292.

Holmes, E. E., and W. F. Fagan. 2002. Validating population viability analysis for corrupted data sets. Ecology 83:2379–2386.

Lindley, S. T. 2003. Estimation of population growth and extinction parameters from noisy data. Ecological Applications 13:806–813.

Link, W. A., and J. R. Sauer. 2002. A hierarchical model of population change with application to Cerulean Warblers. Ecology 83:2832 –2840.

Rich, T. D., C. J. Beardmore, H. Berlanga, P. J. Blancher, M. S. W. Bradstreet, G. S. Butcher, D. W. Demarest, E. H. Dunn, W. C. Hunter, E. E. Iñigo-Elias, J. A. Kennedy, A. M. Martell, A. O. Panjabi, D. N. Pashley, K. V. Rosenberg, C. M. Rustay, J. S. Wendt, T. C. Will. 2004. Partners in Flight North American Landbird Conservation Plan. Cornell Lab of Ornithology. Ithaca, NY. Partners in Flight website. URL: <http://www.partnersinflight.org/cont_plan/> (VERSION: March 2005).

Sauer, J. R., J. E. Fallon, and R. Johnson. 2003. Use of North American Breeding Bird Survey data to estimate population change for bird conservation regions. Journal of Wildlife Management 67:372–389.

Thogmartin, W. E., J. R. Sauer, and M. G. Knutson. 2004. A hierarchical spatial model of avian abundance with application to Cerulean Warblers. Ecological Applications 14:1766–1779.

Tables and Figures

• Table 1. Reconstructed time series of regional abundance for the Cerulean Warbler in the United States.
  
  
• Table 2. Basic diagnostics for estimating parameters and risk metrics from regional time series of Cerulean Warbler abundance using the Dennis-Holmes method.
  
  
• Table 3. Point estimates for the diffusion approximation of regional predictions of Cerulean Warbler population change.
  
  
• Figure 1. Bird Conservation Regions for which the probability of extinction was predicted for Cerulean Warblers.
  
  
• Figure 2. Posterior probability distribution of, the population rate of change, as estimated for the Cerulean Warbler using a diffusion approximation for Breeding Bird Survey-derived estimates of population abundance for the period 1996–2005.
  
  
• Figure 3. Expected total probability of 90% decline within the next century.