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Count PVA in Excel 08

# Count PVA in Excel 08 - Count-Based Density-Independent PVA...

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Count-Based, Density-Independent PVA in Excel This document describes how to use Microsoft Excel to perform the density independent, count-based PVA (Dennis et al., Ch. 3 of Morris and Doak). The example dataset used is the Yellowstone grizzly population used in Morris and Doak Ch. 3. Estimate μ and σ 2 Enter the data Set up the data in a sensible tabular format, with census index, census time, and census value. Plot the data to get a sense of whether the model makes sense. In this case, it looks like both μ and σ 2 may be increasing through time. However, apart from the early decline, the data do not look inconsistent with exponential growth. Estimate r Calculate λ i = N i+1 /N i and r i = log( λ i ).

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Estimate μ and σ 2 directly If the censuses occur at yearly intervals, as they do for the grizzlies, then μ can be estimated as the mean of r and σ 2 can be estimated as the variance of r. Their confidence intervals can be calculated using the t and inverse χ 2 distributions, respectively.
Estimate μ and σ 2 from regression If the censuses occur at irregular intervals, construct two new variables, x i and y i . Now regress y on x, forcing the intercept through zero. Regression, along with a variety of other statistical tests, is found under Tools->Data Analysis. If the latter is not on your tools menu (it will be near the bottom) go to Tools->Add-Ins and add the Analysis Tool- Pak. μ is estimated from the slope of the regression, and σ 2 is the residual mean squares. The confidence interval of mu can be calculated automatically by the regression, but the CI of σ 2 still has to be calculated using the inverse χ 2 distribution.

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