Natasha B. Kotliar, Patricia L. Kennedy, and Kimberly Ferree. 2007. Avifaunal responses to fire in southwestern montane forests along a burn severity gradient. Ecological Applications 17:491–507.

Appendix B. Calculation of detection probabilities.

Pre-fire detection probabilities

Nine transects sampled in 1988 and 1990 were used to calculate pre-fire detection probabilities (Table B1), which were assigned to 1986–1987 data because detection distances were not recorded during those years. Pre-fire detection probabilities varied significantly by sampling period (P < 0.05) and could not be pooled, thus densities were calculated by sampling period separately.

Post-fire detection probabilities

The 13 post-fire transects (Table A1 in Appendix A) and 49 after-only plots were pooled to calculate detection probabilities for most species. We also used data from 40 plots collected post-fire (2001–2002) at the Pumpkin fire (burned in 2000) in Arizona (Kotliar, unpublishished data); after-only sampling protocols were the same at the Pumpkin fire and cover types and overall burn severity patterns were similar at both burns (Kotliar et al. 2003). Collectively, the three data sources provided a sufficient number of observations (> 40 per species as recommended by Buckland et al. 2001) to estimate detection probabilities for 15 species (before-after) and 21 species (after-only). Post-fire data were truncated at 50 or 75 m improving model fit for most species (Buckland et al. 2001; Table B1).

We tested for differences in detection probabilities among the 10 observers using quantitative and qualitative methods. Because sample sizes were generally too low to stratify detection probabilities by observer; the probability density functions were examined for any unusual patterns. We eliminated data from one observer who consistently underestimated distances, especially in the first interval (0–10 m), as this violated a critical assumption of distance sampling (Buckland et al. 2001). Data from the remaining observers were pooled to generate detection probabilities for each species.

We also evaluated whether detection probabilities could be pooled across the three post-fire data sets: before-after and after-only at Cerro Grande and Pumpkin fires (hereafter “pooled post-fire data”) to increase precision (Table B1). Pooling was not required for Cordilleran Flycatcher, Warbling Vireo, White-breasted Nuthatch, House Wren, Hermit Thrush, Yellow-rumped Warbler, and Dark-eyed Junco (only included in the after-only analysis), because these species had sufficient sample sizes to calculate detection probabilities using after-only Cerro Grande data. For Mourning Dove and Western Tanager, there were sufficient detections to compare detection probabilities generated from models based on single data sets as compared to models based on pooled post-fire data; all ∆ AICc were < 2.0, indicating detection probabilities estimated with the single data sets were not different from the model based on pooled data sets, thus, detection probabilities were generated using the pooled-post fire data (Table B1).

The remaining 13 species had insufficient detections in the before-after data set to reliably compare with the pooled post-fire data. Nine of these 13 species had sufficient detections to use ∆ AICc values to compare detection probabilities estimated from after-only models (Cerro Grande and Pumpkin data sets separately) with models based on pooled after-only data. All ∆ AICc were < 2.0 suggesting detection probabilities generated from either model did not differ (Table B1). Steller’s Jay, Pygmy Nuthatch, Virginia’s Warbler, and Spotted Towhee did not have sufficient detections in one or both data sets to calculate a reliable ∆ AICc for the pooled after-only data. Consequently, we evaluated the potential for pooling by the degree of overlap in 95% confidence intervals estimated from all three data sets; for these four species, the confidence intervals overlapped and detection probabilities changed by < 8%, so the pooled post-fire data set was used to estimate detection probabilities (Table B1).

To determine if burn severity level influenced species detectability, we estimated separate detection functions for high-severity (i.e., canopy consumed by fire) versus unburned, low-, and moderate-severity areas (i.e., live or dead needles largely retained on trees). Ten species had sufficient sample sizes in high-severity areas (> 40 detections) to test for detection differences (Table B2). Five additional species analyzed by both designs (before-after and after-only), and five species analyzed by after-only were pooled together for one analysis (see “pooled species”; Table B2). Because ∆ AICc was < 2.0 for the comparison of detection probabilities for intact canopy vs. consumed canopy (Table B2), data were pooled across burn severity levels for estimating detection probabilities.

LITERATURE CITED

Buckland, S. T., D. R. Anderson, K. P. Burnham, J. L. Laake, D. L. Borchers, and L. Thomas. 2001. Introduction to distance sampling. Estimating abundance of biological populations. Oxford University Press, London, UK.

Kotliar, N. B., S. L. Haire, and C. H. Key. 2003. Lessons from the fires of 2000: Post-fire heterogeneity in ponderosa pine forests. Pages 277–279 in P. Omi and L. Joyce, editors. Fire, fuel treatments, and ecological restoration: USDA Forest Service Conference proceedings April 16–18, 2002, Fort Collins, CO. RMRS-P-29. Rocky Mountain Forest and Range Experiment Station, Fort Collins, Colorado, USA.

TABLE B1. Post-fire detection probabilities (95% confidence intervals) estimated in Program DISTANCE. ∆ AICc < 2.0 was used to evaluate pooling in two ways (1): pooling across all post-fire data sets [before-after (Cerro Grande fire) and after-only data (Cerro Grande and Pumpkin fires)] and (2) pooling across both after-only data sets.

† See Appendix C for scientific names.

‡ Total number of detections after truncation.

§ Comparison of detection probabilities generated from models based on single data sets as compared to models based on pooled post-fire data.

|| Comparison of detection probabilities generated from models based on after-only, single data sets as compared to models based on pooled after-only data..

¶ Species were not analyzed in the before-after data set. Thus, detection probabilities were estimated with after-only Cerro Grande data.

# Due to limited sample sizes, ∆ AICc was not calculated (indicated by dashed lines); pooling was based on overlapping confidence intervals between pooled post-fire data sets and pooled after-only data sets.

†† Truncated at 50 m.

‡‡ Truncated at 75 m.

TABLE B2. An evaluation of the effect of burn severity on post-fire detection probabilities (95% confidence intervals) estimated using Program DISTANCE. Detection probabilities based on pooled post-fire samples from before-after data (Cerro Grande) and after-only data (Cerro Grande and Pumpkin fires).

† See Appendix C for scientific names.

‡ Comparison of detection probabilities generated from models based on all post-fire high-severity data as compared to detection probabilities generated from models based on all post-fire data collected at unburned, low-, and moderate-severity locations.

§ Species detected infrequently at high severity points (before-after and after-only) were pooled (Mountain Chickadee, Pygmy Nuthatch, Virginia’s Warbler, Spotted Towhee, Chipping Sparrow).

|| Species detected infrequently at high severity plots (after-only) were pooled (Cordilleran Flycatcher, Warbling Vireo, Hermit Thrush, White-breasted Nuthatch, Dark-eyed Junco).