Chapter 5: Sampling for Age and Growth Estimation
L. E. Miranda and Michael E. Colvin
Sampling for age and growth estimation entails selecting a random sample from the population to estimate age and (or) growth metrics for the whole population. Age metrics of interest may include mean age, longevity, and age frequency; growth metrics may include mean length at age and parameters of growth curves. Various sources of bias and error directly or indirectly influence estimation of these metrics. Some obvious concerns include how to collect and select a sample to avoid bias and minimize error, how many samples are enough to bound estimates within acceptable error levels, and what metrics can be estimated with the least amount of error. Sample collection is limited by attributes and selectivity of the sampling gear and gear deployment strategy and further influenced by site selection and fish behavior. Different metrics may require different levels of sampling effort. Obtaining an adequate sample size is a key aspect of sampling because there is always a limit on the resources that can be invested in sampling. Awareness of the sample size required to estimate a metric within a desired level of confidence and with specific accuracy can avoid insufficient or excessive sampling, both of which result in misspent efforts.
Age and growth metrics are typically estimated with some degree of error (i.e., estimates based on samples deviate from true values). This deviation can be attributed to four general types of estimation errors, including natural variation, sampling bias, estimation bias, and sampling error (Figure 5.1). Errors derived from these four sources generally occur concurrently and may be hard or impossible to disentangle.
The four general types of error we distinguish have a diversity of sources. Natural variation originates from innate variation among individuals relative to longevity, growth trajectories, and mortality patterns. Natural variation is species-, population-, and water body-specific and cannot be reduced by the sampling design—it is always present. Although natural variation is arguably not error, it can cause estimation error. Sampling bias originates from choices such as how fish are collected, when and where, and with what collection gear, deployment method, and sampling design. Because of the diversity of gears, environments, species, and collection methodologies, sampling bias can often be a major component of error. Estimation bias originates from bias introduced by the type of structure used to age fish, the age-estimation protocol, the protocol applied to measure annuli, the age back-calculation model (if applied), the estimator selected to represent length at age, and the length-at-age model applied. Sampling error originates because only a sample of the population is examined, even when the sample is selected at random. Because a sample includes only a fraction of the population, statistics computed from the sample frequently differ from those computed from the entire population. Sampling error can be controlled by adjusting the sample collection design and the sample size.