  The Mayfield method of estimating nest success:
a mathematical analysis.

### The Mayfield method

Ornithologists are interested in measuring the nest success of breeding birds. In 1961 Mayfield developed a method for estimating the daily survival rate. When estimating the daily survival rate, one can estimate the hatch rate as a measure for the nest success.
I wrote an article which gives you insight in the mathematical behaviour of the Mayfield method. The article is visualized with many graphs. So ornithologists who are not familiar with mathematics can understand the headlines of the article. ### Abstract

We find from literature that little is known of the statistical behaviour of the Mayfield method and its use is mainly ground on experiences and simulations.
This article provides the mathematical framework for the Mayfield method. The concept of observation interval plays a central role in the statistical model. During this interval we observe a clutch. At the end of each observation interval we decide if the clutch is destroyed or not.
In terms of the statistical model we define two Mayfield estimators:

• F = 1 - B/A
• G = A/(A+B)

In the article we investigate two variants of each estimator. The main results are:

• We show that the Mayfield estimator has approximately a normal distribution.
• We give equations for the expectation and variance.
• We analyse the behaviour of the Mayfield estimator and we compare the various variants.
• We also give the exact probability distribution of the Mayfield estimator and equations to calculate the exact expectation and variance.

It turns out that the Mayfield estimator has a bias: on average the result has a bias with regard to the real daily survival rate. Mostly the bias is negligible. Especially for small daily survival rates the bias can have a significant influence on the estimate.
The Mayfield method aims to estimate the nest success or hatch rate. For each Mayfield variant we define an estimator for the hatch rate. These estimators also have approximately a normal distribution. The bias of the daily survival rate implies a bias for estimating the hatch rate. The bias is largest if the hatch rate is small. We present an alternative estimator for the daily survival rate and for the hatch rate. This estimator has approximately a normal distribution. The benefit with regard to the Mayfield estimator is that this estimator is (asymptotically) unbiased. We find that this alternative estimator performs better than the Mayfield estimator.

### Keywords

Mayfield method, estimator, daily survival rate, nesting success, hatch rate, breeding bird, reproduction, sample size, survivorship, central limit theorem, probability distribution, expectation, variance, bias, confidence interval, statistics.