Dataset Information

Error and bias in size estimates of whale sharks: implications for understanding demography.

ABSTRACT: Body size and age at maturity are indicative of the vulnerability of a species to extinction. However, they are both difficult to estimate for large animals that cannot be restrained for measurement. For very large species such as whale sharks, body size is commonly estimated visually, potentially resulting in the addition of errors and bias. Here, we investigate the errors and bias associated with total lengths of whale sharks estimated visually by comparing them with measurements collected using a stereo-video camera system at Ningaloo Reef, Western Australia. Using linear mixed-effects models, we found that visual lengths were biased towards underestimation with increasing size of the shark. When using the stereo-video camera, the number of larger individuals that were possibly mature (or close to maturity) that were detected increased by approximately 10%. Mean lengths calculated by each method were, however, comparable (5.002?±?1.194 and 6.128?±?1.609?m, s.d.), confirming that the population at Ningaloo is mostly composed of immature sharks based on published lengths at maturity. We then collated data sets of total lengths sampled from aggregations of whale sharks worldwide between 1995 and 2013. Except for locations in the East Pacific where large females have been reported, these aggregations also largely consisted of juveniles (mean lengths less than 7?m). Sightings of the largest individuals were limited and occurred mostly prior to 2006. This result highlights the urgent need to locate and quantify the numbers of mature male and female whale sharks in order to ascertain the conservation status and ensure persistence of the species.

SUBMITTER: Sequeira AM

PROVIDER: S-EPMC4821267 | biostudies-literature | 2016 Mar

REPOSITORIES: biostudies-literature

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Error and bias in size estimates of whale sharks: implications for understanding demography.

Sequeira Ana M M AM Thums Michele M Brooks Kim K Meekan Mark G MG

Royal Society open science 20160323 3

Body size and age at maturity are indicative of the vulnerability of a species to extinction. However, they are both difficult to estimate for large animals that cannot be restrained for measurement. For very large species such as whale sharks, body size is commonly estimated visually, potentially resulting in the addition of errors and bias. Here, we investigate the errors and bias associated with total lengths of whale sharks estimated visually by comparing them with measurements collected usi ...[more]

PMID: 27069656

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Project description:BackgroundEstimates of under-5 mortality at the national level for countries without high-quality vital registration systems are routinely derived from birth history data in censuses and surveys. Subnational or stratified analyses of under-5 mortality could also be valuable, but the usefulness of under-5 mortality estimates derived from birth histories from relatively small samples of women is not known. We aim to assess the magnitude and direction of error that can be expected for estimates derived from birth histories with small samples of women using various analysis methods.MethodsWe perform a data-based simulation study using Demographic and Health Surveys. Surveys are treated as populations with known under-5 mortality, and samples of women are drawn from each population to mimic surveys with small sample sizes. A variety of methods for analyzing complete birth histories and one method for analyzing summary birth histories are used on these samples, and the results are compared to corresponding true under-5 mortality. We quantify the expected magnitude and direction of error by calculating the mean error, mean relative error, mean absolute error, and mean absolute relative error.ResultsAll methods are prone to high levels of error at the smallest sample size with no method performing better than 73% error on average when the sample contains 10 women. There is a high degree of variation in performance between the methods at each sample size, with methods that contain considerable pooling of information generally performing better overall. Additional stratified analyses suggest that performance varies for most methods according to the true level of mortality and the time prior to survey. This is particularly true of the summary birth history method as well as complete birth history methods that contain considerable pooling of information across time.ConclusionsPerformance of all birth history analysis methods is extremely poor when used on very small samples of women, both in terms of magnitude of expected error and bias in the estimates. Even with larger samples there is no clear best method to choose for analyzing birth history data. The methods that perform best overall are the same methods where performance is noticeably different at different levels of mortality and lengths of time prior to survey. At the same time, methods that perform more uniformly across levels of mortality and lengths of time prior to survey also tend to be among the worst performing overall.

Project description:The Mahalanobis distance is a statistical technique that has been used in statistics and data science for data classification and outlier detection, and in ecology to quantify species-environment relationships in habitat and ecological niche models. Mahalanobis distances are based on the location and scatter of a multivariate normal distribution, and can measure how distant any point in space is from the centre of this kind of distribution. Three different methods for calculating the multivariate location and scatter are commonly used: the sample mean and variance-covariance, the minimum covariance determinant, and the minimum volume ellipsoid. The minimum covariance determinant and minimum volume ellipsoid were developed to be robust to outliers by minimising the multivariate location and scatter for a subset of the full sample, with the proportion of the full sample forming the subset being controlled by a user-defined parameter. This outlier robustness means the minimum covariance determinant and the minimum volume ellipsoid are highly relevant for ecological niche analyses, which are usually based on natural history observations that are likely to contain errors. However, natural history observations will also contain extreme bias, to which the minimum covariance determinant and the minimum volume ellipsoid will also be sensitive. To provide guidance for selecting and parameterising a multivariate location and scatter method, a series of virtual ecological niche modelling experiments were conducted to demonstrate the performance of each multivariate location and scatter method under different levels of sample size, errors, and bias. The results show that there is no optimal modelling approach, and that choices need to be made based on the individual data and question. The sample mean and variance-covariance method will perform best on very small sample sizes if the data are free of error and bias. At larger sample sizes the minimum covariance determinant and minimum volume ellipsoid methods perform as well or better, but only if they are appropriately parameterised. Modellers who are more concerned about the prevalence of errors should retain a smaller proportion of the full data set, while modellers more concerned about the prevalence of bias should retain a larger proportion of the full data set. I conclude that Mahalanobis distances are a useful niche modelling technique, but only for questions relating to the fundamental niche of a species where the assumption of multivariate normality is reasonable. Users of the minimum covariance determinant and minimum volume ellipsoid methods must also clearly report their parameterisations so that the results can be interpreted correctly.

Dataset Information

Error and bias in size estimates of whale sharks: implications for understanding demography.

Publications

Error and bias in size estimates of whale sharks: implications for understanding demography.

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