The Optimal Number of Surveys when Detectability Varies
Publication Date
December 19, 2014
Journal
PLOS ONE
Authors
Alana L. Moore, Michael A. Mc Carthy, Kirsten M. Parris & Joslin L. Moore
Volume
9
Issue
12
Pages
e115345
DOI
https://dx.plos.org/10.1371/journal.pone.0115345
Publisher URL
http://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0115345
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/25526514
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4272285
Europe PMC
http://europepmc.org/abstract/MED/25526514
Web of Science
000347186200023
Scopus
84919489143
Mendeley
http://www.mendeley.com/research/optimal-number-surveys-detectability-varies
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Mendeley | Further Information

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Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1849263"], "description"=>"<p>Abundance = 1 (µ = 0.67) in (a) &amp; (d), and abundance  = 3 (µ = 2.2) in (b) &amp; (d). The shaded area is the region such that the expected probability of failed detection is no more than 0.01 probability units away from the optimum. The correlation coefficient <i>r</i> = 0.3, fixed cost <i>c</i> = 1 hour and survey season length <i>T</i> = 90 days.</p>", "links"=>[], "tags"=>["detection rates result", "probability", "survey effort protocols", "undertaking field ecology", "detection rates", "survey design"], "article_id"=>1275520, "categories"=>["Ecology", "Science Policy", "Biological Sciences"], "users"=>["Alana L. Moore", "Michael A. McCarthy", "Kirsten M. Parris", "Joslin L. Moore"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0115345.g004", "stats"=>{"downloads"=>2, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Optimal_number_of_surveys_for_i_Litoria_pearsoniana_i_when_the_objective_is_to_maximize_the_expected_probability_of_detection_a_amp_b_and_maximize_the_probability_of_satisfying_a_prescribed_detection_rate_of_95_c_amp_d_/1275520", "title"=>"Optimal number of surveys for <i>Litoria pearsoniana</i> when the objective is to maximize the expected probability of detection (a &amp; b), and maximize the probability of satisfying a prescribed detection rate of 95% (c &amp; d).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-12-19 02:51:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/1849265"], "description"=>"<p>Multiple values are indicated by the bolder points; three values at the point (1,1) for <i>Atriplex</i> (c), and two values at point (1,2) for <i>Lomandra</i> (d). Search budget <i>B</i> is 5,10 and 15 minutes; travel time between quadrats <i>c</i> is 0.25, 0.5 and 1 minute. The diagonal line represents perfect correspondence.</p>", "links"=>[], "tags"=>["detection rates result", "probability", "survey effort protocols", "undertaking field ecology", "detection rates", "survey design"], "article_id"=>1275522, "categories"=>["Ecology", "Science Policy", "Biological Sciences"], "users"=>["Alana L. Moore", "Michael A. McCarthy", "Kirsten M. Parris", "Joslin L. Moore"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0115345.g005", "stats"=>{"downloads"=>1, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Predicted_versus_observed_optimal_number_of_quadrats_to_search_when_the_objective_is_to_maximize_the_expected_probability_of_detection_for_i_Atriplex_semibaccata_i_a_and_i_Lomandra_longifolia_i_b_the_objective_is_to_satisfy_a_required_probability_of_detec/1275522", "title"=>"Predicted versus observed optimal number of quadrats to search when: the objective is to maximize the expected probability of detection for <i>Atriplex semibaccata</i> (a) and <i>Lomandra longifolia</i> (b); the objective is to satisfy a required probabil", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-12-19 02:51:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/1849266"], "description"=>"<p>Summary of key results.</p>", "links"=>[], "tags"=>["detection rates result", "probability", "survey effort protocols", "undertaking field ecology", "detection rates", "survey design"], "article_id"=>1275523, "categories"=>["Ecology", "Science Policy", "Biological Sciences"], "users"=>["Alana L. Moore", "Michael A. McCarthy", "Kirsten M. Parris", "Joslin L. Moore"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0115345.t001", "stats"=>{"downloads"=>6, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Summary_of_key_results_/1275523", "title"=>"Summary of key results.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-12-19 02:51:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/1849268", "https://ndownloader.figshare.com/files/1849281", "https://ndownloader.figshare.com/files/1849280", "https://ndownloader.figshare.com/files/1849279", "https://ndownloader.figshare.com/files/1849278", "https://ndownloader.figshare.com/files/1849276", "https://ndownloader.figshare.com/files/1849275", "https://ndownloader.figshare.com/files/1849274", "https://ndownloader.figshare.com/files/1849273", "https://ndownloader.figshare.com/files/1849272", "https://ndownloader.figshare.com/files/1849271", "https://ndownloader.figshare.com/files/1849270", "https://ndownloader.figshare.com/files/1849269", "https://ndownloader.figshare.com/files/1849282"], "description"=>"<div><p>The survey of plant and animal populations is central to undertaking field ecology. However, detection is imperfect, so the absence of a species cannot be determined with certainty. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115345#s2\" target=\"_blank\">Methods</a> developed to account for imperfect detectability during surveys do not yet account for stochastic variation in detectability over time or space. When each survey entails a fixed cost that is not spent searching (e.g., time required to travel to the site), stochastic detection rates result in a trade-off between the number of surveys and the length of each survey when surveying a single site. We present a model that addresses this trade-off and use it to determine the number of surveys that: 1) maximizes the expected probability of detection over the entire survey period; and 2) is most likely to achieve a minimally-acceptable probability of detection. We illustrate the applicability of our approach using three practical examples (minimum survey effort protocols, number of frog surveys per season, and number of quadrats per site to detect a plant species) and test our model's predictions using data from experimental plant surveys. We find that when maximizing the expected probability of detection, the optimal survey design is most sensitive to the coefficient of variation in the rate of detection and the ratio of the search budget to the travel cost. When maximizing the likelihood of achieving a particular probability of detection, the optimal survey design is most sensitive to the required probability of detection, the expected number of detections if the budget were spent only on searching, and the expected number of detections that are missed due to travel costs. We find that accounting for stochasticity in detection rates is likely to be particularly important for designing surveys when detection rates are low. Our model provides a framework to do this.</p></div>", "links"=>[], "tags"=>["detection rates result", "probability", "survey effort protocols", "undertaking field ecology", "detection rates", "survey design"], "article_id"=>1275525, "categories"=>["Ecology", "Science Policy", "Biological Sciences"], "users"=>["Alana L. Moore", "Michael A. McCarthy", "Kirsten M. Parris", "Joslin L. Moore"], "doi"=>[nil, nil, nil, nil, nil, nil, nil, nil, nil, nil, nil, nil, nil, nil], "stats"=>{"downloads"=>11, "page_views"=>17, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/The_Optimal_Number_of_Surveys_when_Detectability_Varies/1275525", "title"=>"The Optimal Number of Surveys when Detectability Varies", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2014-12-19 02:51:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/1849255"], "description"=>"<p>The figures compare the exact solution with <i>c</i>′ = 0.5 (a) and approximate solution (b). For the approximate solution, dashed-line A corresponds to <i>Litoria pearsoniana</i> (θ = 2.45), dashed-line B corresponds <i>Atriplex semibaccata</i> (θ = 0.91) and dashed-line C corresponds <i>Lomandra longifolia</i> (θ = 0.87). Note that exact solution depends on the value of <i>B</i>, not just the ratio <i>B</i>/<i>c</i>, hence lines indicating the optimal number of surveys for the case studies are not shown on (a).</p>", "links"=>[], "tags"=>["detection rates result", "probability", "survey effort protocols", "undertaking field ecology", "detection rates", "survey design"], "article_id"=>1275512, "categories"=>["Ecology", "Science Policy", "Biological Sciences"], "users"=>["Alana L. Moore", "Michael A. McCarthy", "Kirsten M. Parris", "Joslin L. Moore"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0115345.g001", "stats"=>{"downloads"=>2, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Optimal_number_of_surveys_contours_when_maximizing_the_expected_probability_of_detection_as_a_function_of_the_budget_to_fixed_cost_ratio_i_B_i_i_c_i__i_B_i_i_c_i_and_the_coefficient_of_variation_/1275512", "title"=>"Optimal number of surveys (contours) when maximizing the expected probability of detection as a function of the budget to fixed-cost ratio <i>B</i>/<i>c</i> ( = <i>B</i>′/<i>c</i>′) and the coefficient of variation θ.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-12-19 02:51:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/1849256"], "description"=>"<p>Optimal number of surveys (contours) when maximizing the probability of achieving a prescribed detection rate as a function of the scaled budget <i>B</i>′ and the prescribed detection rate <i>Qc</i> for the exact solution, with θ = 1.5 and <i>c</i>′ = 0.5, (a) and the approximate solution, with <i>c</i>′ = 0.5 (b).</p>", "links"=>[], "tags"=>["detection rates result", "probability", "survey effort protocols", "undertaking field ecology", "detection rates", "survey design"], "article_id"=>1275513, "categories"=>["Ecology", "Science Policy", "Biological Sciences"], "users"=>["Alana L. Moore", "Michael A. McCarthy", "Kirsten M. Parris", "Joslin L. Moore"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0115345.g002", "stats"=>{"downloads"=>1, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Optimal_number_of_surveys_contours_when_maximizing_the_probability_of_achieving_a_prescribed_detection_rate_as_a_function_of_the_scaled_budget_i_B_i_and_the_prescribed_detection_rate_i_Qc_i_for_the_exact_solution_with__1_5_and_i_c_i__0_5_a_and_the_approxi/1275513", "title"=>"Optimal number of surveys (contours) when maximizing the probability of achieving a prescribed detection rate as a function of the scaled budget <i>B</i>′ and the prescribed detection rate <i>Qc</i> for the exact solution, with θ = 1.5 and <i>c</i>′ = 0.5", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-12-19 02:51:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/1849261"], "description"=>"<p>Likelihood that the failed-detection probability <i>Q</i> is less than the prescribed value <i>Qc</i> (b) as a function of the scaled budget <i>B</i>′, with θ = 1.5 and <i>c</i>′ = 0.5, when detection rate is assumed to be variable (solid lines) compared to when it is assumed to be constant (dashed line).</p>", "links"=>[], "tags"=>["detection rates result", "probability", "survey effort protocols", "undertaking field ecology", "detection rates", "survey design"], "article_id"=>1275518, "categories"=>["Ecology", "Science Policy", "Biological Sciences"], "users"=>["Alana L. Moore", "Michael A. McCarthy", "Kirsten M. Parris", "Joslin L. Moore"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0115345.g003", "stats"=>{"downloads"=>4, "page_views"=>15, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Expected_probability_of_detection_a_as_a_function_of_the_scaled_budget_i_B_i_with_i_c_i__0_5_when_detection_rate_is_assumed_to_be_variable_solid_line__1_5_compared_to_when_it_is_assumed_to_be_constant_dashed_line_/1275518", "title"=>"Expected probability of detection (a) as a function of the scaled budget <i>B</i>′, with <i>c</i>′ = 0.5, when detection rate is assumed to be variable (solid line, θ = 1.5) compared to when it is assumed to be constant (dashed line).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-12-19 02:51:06"}

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Relative Metric

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