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Mixture models for distance sampling detection functions.

Miller DL, Thomas L - PLoS ONE (2015)

Bottom Line: We also re-analyze four previously problematic real-world case studies.We find mixtures outperform K+A methods in many cases, particularly spiked line transect data (i.e., where detectability drops rapidly at small distances) and larger sample sizes.We recommend that current standard model selection methods for distance sampling detection functions are extended to include mixture models in the candidate set.

View Article: PubMed Central - PubMed

Affiliation: Centre for Research into Ecological and Environmental Modelling, and School of Mathematics and Statistics, University of St Andrews, St Andrews, Scotland, United Kingdom.

ABSTRACT
We present a new class of models for the detection function in distance sampling surveys of wildlife populations, based on finite mixtures of simple parametric key functions such as the half-normal. The models share many of the features of the widely-used "key function plus series adjustment" (K+A) formulation: they are flexible, produce plausible shapes with a small number of parameters, allow incorporation of covariates in addition to distance and can be fitted using maximum likelihood. One important advantage over the K+A approach is that the mixtures are automatically monotonic non-increasing and non-negative, so constrained optimization is not required to ensure distance sampling assumptions are honoured. We compare the mixture formulation to the K+A approach using simulations to evaluate its applicability in a wide set of challenging situations. We also re-analyze four previously problematic real-world case studies. We find mixtures outperform K+A methods in many cases, particularly spiked line transect data (i.e., where detectability drops rapidly at small distances) and larger sample sizes. We recommend that current standard model selection methods for distance sampling detection functions are extended to include mixture models in the candidate set.

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Plots of the mixture model detection functions fit to the British Columbia marine mammal data.In each case the best mixture model by AIC was a 2-point mixture. Dashed lines show the mixture components.
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pone.0118726.g004: Plots of the mixture model detection functions fit to the British Columbia marine mammal data.In each case the best mixture model by AIC was a 2-point mixture. Dashed lines show the mixture components.

Mentions: Results are summarised in Table 1 and detection functions for the AIC-best models are shown in Fig. 4. In each case mixture models were two component models. For harbour seal, the mixture model had a lower AIC than for the K+A model reported in Williams and Thomas [20]. The mixture model P̂a is approximately 20% lower, implying that the previous estimate of N̂ may have been an underestimate (as Pa decreases, 1/Pa increases in the Horvitz-Thompson estimator giving a larger estimate of abundance). For harbour porpoise, the mixture model AIC is almost 1.5 points higher than the K+A model, which was a hazard-rate with no adjustments. Hence, the model likelihoods are very similar, but the penalty due to the 2-point mixture having an additional parameter prevents it from being selected. The P̂a from the two models are very close. Lastly, for humpback whales, the mixture model AIC is almost 3 points higher than the K+A model—however, one advantage of the mixture model is that the fitted function is monotone (Fig. 4) while the K+A function is not (Fig. 1). Again, the estimated P̂as are very similar.


Mixture models for distance sampling detection functions.

Miller DL, Thomas L - PLoS ONE (2015)

Plots of the mixture model detection functions fit to the British Columbia marine mammal data.In each case the best mixture model by AIC was a 2-point mixture. Dashed lines show the mixture components.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4368789&req=5

pone.0118726.g004: Plots of the mixture model detection functions fit to the British Columbia marine mammal data.In each case the best mixture model by AIC was a 2-point mixture. Dashed lines show the mixture components.
Mentions: Results are summarised in Table 1 and detection functions for the AIC-best models are shown in Fig. 4. In each case mixture models were two component models. For harbour seal, the mixture model had a lower AIC than for the K+A model reported in Williams and Thomas [20]. The mixture model P̂a is approximately 20% lower, implying that the previous estimate of N̂ may have been an underestimate (as Pa decreases, 1/Pa increases in the Horvitz-Thompson estimator giving a larger estimate of abundance). For harbour porpoise, the mixture model AIC is almost 1.5 points higher than the K+A model, which was a hazard-rate with no adjustments. Hence, the model likelihoods are very similar, but the penalty due to the 2-point mixture having an additional parameter prevents it from being selected. The P̂a from the two models are very close. Lastly, for humpback whales, the mixture model AIC is almost 3 points higher than the K+A model—however, one advantage of the mixture model is that the fitted function is monotone (Fig. 4) while the K+A function is not (Fig. 1). Again, the estimated P̂as are very similar.

Bottom Line: We also re-analyze four previously problematic real-world case studies.We find mixtures outperform K+A methods in many cases, particularly spiked line transect data (i.e., where detectability drops rapidly at small distances) and larger sample sizes.We recommend that current standard model selection methods for distance sampling detection functions are extended to include mixture models in the candidate set.

View Article: PubMed Central - PubMed

Affiliation: Centre for Research into Ecological and Environmental Modelling, and School of Mathematics and Statistics, University of St Andrews, St Andrews, Scotland, United Kingdom.

ABSTRACT
We present a new class of models for the detection function in distance sampling surveys of wildlife populations, based on finite mixtures of simple parametric key functions such as the half-normal. The models share many of the features of the widely-used "key function plus series adjustment" (K+A) formulation: they are flexible, produce plausible shapes with a small number of parameters, allow incorporation of covariates in addition to distance and can be fitted using maximum likelihood. One important advantage over the K+A approach is that the mixtures are automatically monotonic non-increasing and non-negative, so constrained optimization is not required to ensure distance sampling assumptions are honoured. We compare the mixture formulation to the K+A approach using simulations to evaluate its applicability in a wide set of challenging situations. We also re-analyze four previously problematic real-world case studies. We find mixtures outperform K+A methods in many cases, particularly spiked line transect data (i.e., where detectability drops rapidly at small distances) and larger sample sizes. We recommend that current standard model selection methods for distance sampling detection functions are extended to include mixture models in the candidate set.

Show MeSH