# Formule de lincertitude relative dating

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Lincertituds have aided in establishing continental and regional species prioritization and planning Potter et al. PIF lincertigude estimates are also increasingly being used to assess the impacts of Formyle sources of anthropogenic avian mortality Johnson et Formule de lincertitude relative dating. Because of the importance of population size estimation for assessing species risk and mortality impacts, PIF has committed to improve and revise the approach and, to the extent possible, address critiques and suggestions that have datihg raised Thogmartin et al.

A key suggestion for improving the usefulness of the population size estimates llincertitude to incorporate an explicit measure of uncertainty Thogmartin et al. We present a modification to the Lincertirude approach to estimating population sizes for landbirds breeding in the cating United States U. This modification allows for the relatvie of uncertainty underlying the raw data and the other model parameters to be numerically presented lincertituee the final estimate. Specifically, lincertitjde use a Monte Carlo simulation to propagate limcertitude arising from the individual components of the estimation process through to the final estimation of total population size.

The result is a distribution of population size estimates for re species in each geographic region, which Forjule be subsequently described by standard descriptive statistics mean, median, quantiles rather than as a single point estimate. In addition to incorporating uncertainty, we rating refine the PIF population estimation approach to include an update to the time-of-day adjustment factor Blancher et al. Formule de lincertitude relative dating we briefly describe the PIF approach to Fomule size estimation for additional details see Rosenberg and BlancherBlancher et al. The PIF approach relies on a series of logical assumptions for extrapolating survey-level counts to total abundance within defined geographic regions.

The approach is based on a series of adjustment factors applied to mean bird counts observed along BBS routes. Each adjustment factor is meant to adjust the mean count for the approximate proportion of birds that are missed relative to those that are observed, as well as the amount of area on average that is effectively surveyed along a BBS route. The PIF approach to estimating the population size within each defined geographic area is based on the following equation: The divisor on a, The three constants: CD and CP are both categorical and derived through a process of literature review, data review, and expert opinion Blancher et al.

CD, the detection-distance adjustment, is used to modify the presumed BBS sampling radius, m, for each species based on habitat, behavior, and song characteristics. CP, the pair adjustment, is used to modify the estimate based on the assumption that detection of some species may be biased toward only one member of a breeding pair. CT, the time-of-day adjustment, is used to modify the estimate due to variable detection probability throughout the survey period. CT is derived through an analysis of stop-level BBS data available from to the present and estimates the ratio of the average count at the peak-detection stop to the mean count across all stops based on polynomial smoothing models Blancher et al.

Digital species range maps Ridgely et al. The PIF approach to estimating population sizes does not incorporate variance or uncertainty into the estimate. Rather, PIF reports categorical data quality ratings based on variation among BBS routes in each region but does not measure or report variation or uncertainty within the BBS route-level counts or in any of the adjustment factors. Our method largely adheres to the PIF approach as described above but incorporates uncertainty in the regional BBS count estimates as well as the individual adjustment factors, and propagates that uncertainty through to the final population size estimates.

Mean BBS route count There are two sources of variance in the number of birds counted along BBS routes that we accounted for in the population size calculation for each species in each region: To account for within-route variation, we calculated the mean and variance of total counts for each species along each route within a region for runs meeting acceptable standards for time of day and weather conditions as determined by the BBS; Pardieck et al. We used the mean and variance to define a discrete distribution for each route to sample from.

If the variance was greater than the mean count data overdispersedwe used a negative binomial distribution using the method of moment matching; Hobbs and Hooten If the variance was not greater than the mean we sampled from a Poisson distribution. For routes with only a single run in the last 10 years, we sampled from a Poisson distribution around the observed count.

For each route in each lincertiture, we drew 10 random values from either a negative binomial datinv Poisson distribution around the mean count for that route, regardless of how many times a route was actually run in the past 10 years. This was done to avoid weighting routes by the number of runs conducted. For each iteration of the population size calculation, we pooled the simulated observations for all routes within a region and calculated the mean to determine the mean route-level count for the linxertitude. To account for between-route variation, lincegtitude used a bootstrap approach to linceftitude routes to represent a region.

Relativr each iteration, we Formjle selected, with replacement, a set of routes equal in size to the total number of routes within each region. Because the sampling was done with replacement, a route may have been selected more than once or not at all for a given iteration. Time-of-day adjustment For many species, detectability can vary by time of day with daily cycles in activity level, i. The time-of-day adjustment assumes that birds are present at a constant rate throughout the period of a BBS survey typically from 30 minutes before sunrise until roughly 4 hours after sunrisebut the probability of detection varies with daily bird activity. The proportion of birds present, but not detected, is therefore proportional to the peak count over the mean count across BBS stops.

We revised the time-of-day adjustment for each species by adding additional years of data and using generalized additive models rather than polynomials for the smoothed models. We used all available BBS stop-level data for each species stop data are available from the BBS going back to Our generalized additive models relate the time of day, i. Additional details describing how we fit the smoothed time-of-day models are available in Appendix 1. We used the fitted curves to calculate a distribution for the time-of-day adjustment statistic by sampling from the distribution of the fitted curve at each stop.

### Relative lincertitude Formule dating de

The time-of-day adjustment was estimated as the maximum divided by the mean across stops. The result of this adjustment is that extrapolated population estimates are based on the counts lkncertitude birds during their lincertiude time of detection, reducing underestimates due to undetected individuals. Alternative approaches to accommodate an empirical estimate of detection probability are feasible for some species, but these approaches remain beyond the scope of the current improvements to the PIF approach employed here. Pair adjustment PIF assigns a pair adjustment multiplier to the PS calculation to account for the probability that for some species, one member of a breeding pair, e.

For those species, it is assumed that for every bird recorded at the peak time of day, there may be a second bird present that was not recorded. Therefore, the pair adjustment parameter should theoretically not be less than 1 both sexes equally likely to be detected nor greater than 2 only one member of a pair detected.

PIF assigned each species to liincertitude of five categories 1. To assign these categories, PIF reviewed available evidence related to observational sex-bias. We maintained these categorical linceftitude but incorporated uncertainty in lincertiitude assignments by replacing them with truncated normal distributions. The means of the distributions were equal to the previously assigned PIF pair adjustment values and truncated at 1. Detection-distance adjustment The PIF approach to estimating population sizes is particularly sensitive to the detection-distance adjustment Thogmartin et al. Comparisons with field tests of detection distances suggest that the assigned detection-distance categories for the PIF population size calculation may be too large for many species Confer et al.

The PIF approach assigns each species to one of seven detection-distance categories based on a combination of published maximum detection distances see Rosenberg and Blancher and references thereinexpert opinion, and by comparing relative distances across species in regional point count surveys that included detection distances Blancher et al.

Downtown, there is much day between the PIF termites and our present fines Fig. Processed qualified leads for more-scale conservative data.

We still lack an empirically based approach that can be applied systematically df species to estimate detection distances. We assigned the sampling distribution in this manner so that the distribution would 1 include the previously assigned detection-distance adjustment, 2 be broad enough to encompass the uncertainty of this parameter, and 3 partly account for recent empirical estimates of detection distance suggesting that the assigned PIF detection-distance categories may be generally overestimated see Matsuoka et al. For the present study, we focus on the species for which the BBS is the sole or major contributing data source. The remaining species for which PIF reports population size estimates rely on non-BBS data sources, such as species-specific surveys, that were deemed more reliable than BBS for those species Blancher et al.

To incorporate uncertainty into the PIF process, we employed a Monte Carlo approach to estimate population size distributions by randomly sampling from each variable or nonfixed model component linertitude to calculating the population size estimate. The components of rlative model that were variable were either species-specific pair adjustment, relwtive adjustment, time-of-day adjustment or species-by-region specific mean route-level Relagive count. Fixed model components were treated as known without error range adjustment, region area. Population size distributions were derived by making iterations of the calculation for each species in each region by making independent random draws from each Formule de lincertitude relative dating component.

We did not model any correlation between model parameters. Lincertitjde 2 includes R scripts and for downloading and processing BBS count data, code and accompanying parameter files for running the Monte Carlo population Forjule estimation, lincertjtude summary output data of population size estimates with uncertainty ranges. Aside from the changes noted here, the PIF population size estimation is as described previously eelative the PIF database and handbooks Blancher et al. Using our refined methods, Fkrmule BBS data from towe estimate 6. Of those species for which our new estimate range does ed include daitng PIF North American estimate, Population size uncertainty The mean standardized interquantile distance linceftitude species for the combined North American population rwlative was 0.

This estimation excludes physio-political regions where population size estimates were licnertitude on non-BBS sources. The size of the standardized interquantile distance was strongly influenced by the number of BBS routes used in the analysis, with fewer routes analyzed leading to larger uncertainty bounds Fig. We found that the PIF data quality scores 5 color-coded rating categories ranging from good to poor quality; Blancher et al. Dsting the uncertainty ranges with the PIF quality ratings showed increasing uncertainty with increasingly poorer quality ratings. We also found greater variation in the uncertainty widths with increasingly poorer PIF data quality ratings Fig.

We found In general, species with smaller estimated populations within North America were more likely to have larger standardized interquantile rleative and were, therefore, also more likely to have uncertainty in the assignment lindertitude a PS score Table 2. Our analysis would result in 20 species being assigned a different PS score relative to scores based on the PIF population size database, though only nine of those species would not include the PIF score within the uncertainty bounds of the new analysis. Components of uncertainty Of the four model components serving as sources of uncertainty, interquartile variance was largest for the distance adjustment mean of 0.

Variance in the distance relatjve, pair adjustment, and time-of-day adjustment was consistent across all population size categories Table 2. These estimates are an important component of the PIF species assessment but have also been used for other conservation planning and assessment purposes. We present Formuke methods for characterizing and expressin