Movement Ecology

Table 1 Simulation findings comparing the azimuthal telemetry model (ATM) with the average of the component-wise azimuth intersections (simple) and Lenth (1981) maximum likelihood estimator (Lenth, sigloc) and M-estimators (Andrews, Huber)

From: Accounting for location uncertainty in azimuthal telemetry data improves ecological inference

		κ=100						κ=25
		Simple	sigloc	Lenth	Huber	Andrews	ATM	Simple	sigloc	Lenth	Huber	Andrews	ATM
Encircle design comparison:
n_θ=3	\(n_{\hat {\boldsymbol {\mu }}}\)	600	597	600	600	600	600	600	581	598	600	600	600
	d_0.5 (m)	22.4	20.8	20.5	20.4	20.4	21.0	45.3	43.6	42.7	42.8	43.5	42.8
	Coverage	–	0.430	0.432	0.432	0.433	0.888	–	0.422	0.425	0.423	0.435	0.858
n_θ=4	\(n_{\hat {\boldsymbol {\mu }}}\)	600	539	600	600	600	600	600	470	592	595	599	600
	d_0.5 (m)	9.9	9.3	8.7	8.7	8.8	8.7	19.2	19.6	17.5	17.6	17.4	17.5
	Coverage	–	0.575	0.592	0.585	0.592	0.923	–	0.553	0.542	0.538	0.541	0.917
Random design comparison:
n_θ=3	\(n_{\hat {\boldsymbol {\mu }}}\)	600	533	595	593	593	600	600	439	564	561	566	600
	d_0.5 (m)	32.6	32.2	25.1	25.1	25.3	25.0	62.9	75.1	54.2	53.4	53.7	55.6
	Coverage	–	0.403	0.418	0.417	0.417	0.883	–	0.328	0.348	0.348	0.352	0.850
n_θ=4	\(n_{\hat {\boldsymbol {\mu }}}\)	600	454	594	594	598	600	600	367	573	573	579	600
	d_0.5 (m)	14.2	13.0	9.9	10.0	9.9	10.0	25.3	34.0	19.5	19.6	20.0	20.3
	Coverage	–	0.559	0.581	0.567	0.572	0.920	–	0.526	0.560	0.550	0.556	0.912
Road design comparison:
n_θ=3	\(n_{\hat {\boldsymbol {\mu }}}\)	600	499	593	593	597	600	600	409	573	571	576	600
	d_0.5 (m)	56.7	44.4	39.0	39.0	38.5	40.5	95.5	110.4	85.1	84.6	83.9	86.4
	Coverage	–	0.397	0.418	0.418	0.412	0.877	–	0.296	0.316	0.310	0.312	0.822
n_θ=4	\(n_{\hat {\boldsymbol {\mu }}}\)	600	443	600	600	600	600	600	316	592	593	595	600
	d_0.5 (m)	53.8	33.4	26.9	27.7	28.1	26.5	90.3	83.5	54.6	54.8	55.2	55.8
	Coverage	–	0.580	0.618	0.595	0.588	0.923	–	0.487	0.561	0.543	0.545	0.883

‘sigloc’ implements Lenth’s maximum likelihood estimator via an alternative algorithm than suggested by Lenth (1981)
Notes: Random, encircle, and road indicate different telemetry study designs. κ is the concentration parameter of the von Mises distribution and controls the amount of azimuthal uncertainty; larger values indicate higher precision. We use κ=100 as moderate uncertainty and a κ=25 for high uncertainty. n_θ indicates the number of observer locations used for each spatial animal location. \(n_{\boldsymbol {\hat {\mu }}}\) is the number of animal spatial location estimates that were appropriately estimated; we simulated a total of 600 locations per scenario. d_0.5 is the median of the Euclidean distance between the estimated animal location and true location (\(d(\hat {\boldsymbol {\mu }},\boldsymbol {\mu })\)). Coverage is defined as the number of 95% isopleths that contained the true μ out of the total \(n_{\hat {\boldsymbol {\mu }}}\)

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ISSN: 2051-3933

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