Ignoring Imperfect Detection in Biological Surveys Is Dangerous: A Response to ‘Fitting and Interpreting Occupancy Models'
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{"title"=>"Ignoring imperfect detection in biological surveys is dangerous: A response to 'fitting and interpreting occupancy models'", "type"=>"journal", "authors"=>[{"first_name"=>"Gurutzeta", "last_name"=>"Guillera-Arroita", "scopus_author_id"=>"36056611300"}, {"first_name"=>"José J.", "last_name"=>"Lahoz-Monfort", "scopus_author_id"=>"36056786800"}, {"first_name"=>"Darryl I.", "last_name"=>"MacKenzie", "scopus_author_id"=>"56123975300"}, {"first_name"=>"Brendan A.", "last_name"=>"Wintle", "scopus_author_id"=>"6507286963"}, {"first_name"=>"Michael A.", "last_name"=>"McCarthy", "scopus_author_id"=>"7402061574"}], "year"=>2014, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "scopus"=>"2-s2.0-84905017777", "pui"=>"373645947", "doi"=>"10.1371/journal.pone.0099571", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "sgr"=>"84905017777", "pmid"=>"25075615"}, "id"=>"7d74d94b-4968-3a2a-867d-75c7d80b1194", "abstract"=>"In a recent paper, Welsh, Lindenmayer and Donnelly (WLD) question the usefulness of models that estimate species occupancy while accounting for detectability. WLD claim that these models are difficult to fit and argue that disregarding detectability can be better than trying to adjust for it. We think that this conclusion and subsequent recommendations are not well founded and may negatively impact the quality of statistical inference in ecology and related management decisions. Here we respond to WLD's claims, evaluating in detail their arguments, using simulations and/or theory to support our points. In particular, WLD argue that both disregarding and accounting for imperfect detection lead to the same estimator performance regardless of sample size when detectability is a function of abundance. We show that this, the key result of their paper, only holds for cases of extreme heterogeneity like the single scenario they considered. Our results illustrate the dangers of disregarding imperfect detection. When ignored, occupancy and detection are confounded: the same naïve occupancy estimates can be obtained for very different true levels of occupancy so the size of the bias is unknowable. Hierarchical occupancy models separate occupancy and detection, and imprecise estimates simply indicate that more data are required for robust inference about the system in question. As for any statistical method, when underlying assumptions of simple hierarchical models are violated, their reliability is reduced. Resorting in those instances where hierarchical occupancy models do no perform well to the naïve occupancy estimator does not provide a satisfactory solution. The aim should instead be to achieve better estimation, by minimizing the effect of these issues during design, data collection and analysis, ensuring that the right amount of data is collected and model assumptions are met, considering model extensions where appropriate.", "link"=>"http://www.mendeley.com/research/ignoring-imperfect-detection-biological-surveys-dangerous-response-fitting-interpreting-occupancy-mo", "reader_count"=>231, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>8, "Librarian"=>1, "Researcher"=>59, "Student > Doctoral Student"=>18, "Student > Ph. D. Student"=>59, "Student > Postgraduate"=>9, "Student > Master"=>43, "Other"=>13, "Student > Bachelor"=>15, "Lecturer"=>1, "Professor"=>4}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>8, "Librarian"=>1, "Researcher"=>59, "Student > Doctoral Student"=>18, "Student > Ph. D. Student"=>59, "Student > Postgraduate"=>9, "Student > Master"=>43, "Other"=>13, "Student > Bachelor"=>15, "Lecturer"=>1, "Professor"=>4}, "reader_count_by_subject_area"=>{"Unspecified"=>6, "Environmental Science"=>65, "Biochemistry, Genetics and Molecular Biology"=>1, "Mathematics"=>1, "Agricultural and Biological Sciences"=>153, "Medicine and Dentistry"=>1, "Business, Management and Accounting"=>1, "Social Sciences"=>1, "Computer Science"=>2}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Social Sciences"=>{"Social Sciences"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>153}, "Computer Science"=>{"Computer Science"=>2}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>6}, "Environmental Science"=>{"Environmental Science"=>65}}, "reader_count_by_country"=>{"United States"=>14, "Japan"=>2, "United Kingdom"=>2, "Switzerland"=>1, "Portugal"=>2, "Spain"=>2, "India"=>1, "Canada"=>1, "Belgium"=>1, "Brazil"=>5, "Italy"=>6, "South Africa"=>1, "Australia"=>1, "Germany"=>1}, "group_count"=>2}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1614875"], "description"=>"<p>In (a) results obtained by <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099571#pone.0099571-Welsh1\" target=\"_blank\">[14]</a>, in (b) results obtained in this study. In both cases estimates were categorized as 0 or 1 based on thresholds 0.0001 and 0.9999 respectively. Sample size <i>S</i> = 55 sites and <i>K</i> = 2 replicate surveys. Model fitted .</p>", "links"=>[], "tags"=>["biogeography", "Computational biology", "Population modeling", "ecology", "Ecological metrics", "Population ecology", "Spatial and landscape ecology", "Population biology", "Veterinary science", "Animal types", "wildlife", "Computerized simulations", "mathematics", "Statistics (mathematics)", "Statistical methods", "estimation", "fitting", "hierarchical", "occupancy", "simulated"], "article_id"=>1122272, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Gurutzeta Guillera-Arroita", "José J. Lahoz-Monfort", "Darryl I. MacKenzie", "Brendan A. Wintle", "Michael A. McCarthy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0099571.t002", "stats"=>{"downloads"=>3, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Counts_of_different_estimation_results_obtained_when_fitting_hierarchical_occupancy_models_to_simulated_data_from_Scenario_A1_/1122272", "title"=>"Counts of different estimation results obtained when fitting hierarchical occupancy models to simulated data from Scenario A1.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-07-30 03:04:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1614857"], "description"=>"<p>For details in figure arrangement see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099571#pone-0099571-g002\" target=\"_blank\">Figure 2</a>; here the true occupancy was 0.8. In this example the hierarchical model clearly outperforms the naïve model, which is greatly biased. A comparison of the estimates for <i>K</i> = 2 illustrates with those in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099571#pone-0099571-g002\" target=\"_blank\">Figure 2</a> illustrates how the naïve model can produce the same estimates for very different scenarios.</p>", "links"=>[], "tags"=>["biogeography", "Computational biology", "Population modeling", "ecology", "Ecological metrics", "Population ecology", "Spatial and landscape ecology", "Population biology", "Veterinary science", "Animal types", "wildlife", "Computerized simulations", "mathematics", "Statistics (mathematics)", "Statistical methods", "fitting", "hierarchical", "occupancy", "5000", "sets", "a2", "55"], "article_id"=>1122253, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Gurutzeta Guillera-Arroita", "José J. Lahoz-Monfort", "Darryl I. MacKenzie", "Brendan A. Wintle", "Michael A. McCarthy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0099571.g003", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulation_results_of_fitting_hierarchical_and_na_239_ve_occupancy_models_to_5000_data_sets_from_Scenario_A2_with_55_sites_/1122253", "title"=>"Simulation results of fitting hierarchical and naïve occupancy models to 5000 data sets from Scenario A2 with 55 sites.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:04:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1614873"], "description"=>"<p>Simulations were run for a range of sample sizes, with <i>S</i> sites and <i>K</i> replicate surveys per site (5000 simulations per case). When , the naïve model was fitted to the data resulting from collapsing the detection/non-detection history into a single record per site (1 if species detected at least once, 0 otherwise). In the majority of these cases the performance of the hierarchical model was either comparable or considerably superior to that of the naïve model. A ratio <1 indicates that the MSE of the hierarchical model is smaller than in the naïve model.</p>", "links"=>[], "tags"=>["biogeography", "Computational biology", "Population modeling", "ecology", "Ecological metrics", "Population ecology", "Spatial and landscape ecology", "Population biology", "Veterinary science", "Animal types", "wildlife", "Computerized simulations", "mathematics", "Statistics (mathematics)", "Statistical methods", "occupancy", "estimator", "simulations", "a1", "a2"], "article_id"=>1122270, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Gurutzeta Guillera-Arroita", "José J. Lahoz-Monfort", "Darryl I. MacKenzie", "Brendan A. Wintle", "Michael A. McCarthy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0099571.t003", "stats"=>{"downloads"=>4, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mean_square_error_MSE_for_the_occupancy_estimator_in_the_hierarchical_na_ve_models_and_their_ratio_obtained_from_simulations_of_a_Scenario_A1_and_b_Scenario_A2_see_Table_1_for_details_/1122270", "title"=>"Mean square error (MSE) for the occupancy estimator in the hierarchical/naïve models, and their ratio, obtained from simulations of (a) Scenario A1 and (b) Scenario A2 (see Table 1 for details).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-07-30 03:04:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1614900", "https://ndownloader.figshare.com/files/1614902", "https://ndownloader.figshare.com/files/1614903", "https://ndownloader.figshare.com/files/1614904"], "description"=>"<div><p>In a recent paper, Welsh, Lindenmayer and Donnelly (WLD) question the usefulness of models that estimate species occupancy while accounting for detectability. WLD claim that these models are difficult to fit and argue that disregarding detectability can be better than trying to adjust for it. We think that this conclusion and subsequent recommendations are not well founded and may negatively impact the quality of statistical inference in ecology and related management decisions. Here we respond to WLD's claims, evaluating in detail their arguments, using simulations and/or theory to support our points. In particular, WLD argue that both disregarding and accounting for imperfect detection lead to the same estimator performance regardless of sample size when detectability is a function of abundance. We show that this, the key result of their paper, only holds for cases of extreme heterogeneity like the single scenario they considered. Our results illustrate the dangers of disregarding imperfect detection. When ignored, occupancy and detection are confounded: the same naïve occupancy estimates can be obtained for very different true levels of occupancy so the size of the bias is unknowable. Hierarchical occupancy models separate occupancy and detection, and imprecise estimates simply indicate that more data are required for robust inference about the system in question. As for any statistical method, when underlying assumptions of simple hierarchical models are violated, their reliability is reduced. Resorting in those instances where hierarchical occupancy models do no perform well to the naïve occupancy estimator does not provide a satisfactory solution. The aim should instead be to achieve better estimation, by minimizing the effect of these issues during design, data collection and analysis, ensuring that the right amount of data is collected and model assumptions are met, considering model extensions where appropriate.</p></div>", "links"=>[], "tags"=>["biogeography", "Computational biology", "Population modeling", "ecology", "Ecological metrics", "Population ecology", "Spatial and landscape ecology", "Population biology", "Veterinary science", "Animal types", "wildlife", "Computerized simulations", "mathematics", "Statistics (mathematics)", "Statistical methods", "imperfect", "detection", "surveys", "interpreting", "occupancy"], "article_id"=>1122298, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Gurutzeta Guillera-Arroita", "José J. Lahoz-Monfort", "Darryl I. MacKenzie", "Brendan A. Wintle", "Michael A. McCarthy"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0099571.s001", "https://dx.doi.org/10.1371/journal.pone.0099571.s002", "https://dx.doi.org/10.1371/journal.pone.0099571.s003", "https://dx.doi.org/10.1371/journal.pone.0099571.s004"], "stats"=>{"downloads"=>4, "page_views"=>29, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Ignoring_Imperfect_Detection_in_Biological_Surveys_Is_Dangerous_A_Response_to_8216_Fitting_and_Interpreting_Occupancy_Models_/1122298", "title"=>"Ignoring Imperfect Detection in Biological Surveys Is Dangerous: A Response to ‘Fitting and Interpreting Occupancy Models'", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2014-07-30 03:04:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1614869"], "description"=>"<p>In the data-generating model, occupancy is constant and detectability at each site is drawn from a single distribution . In the fitted model both occupancy and detectability are assumed constant across sites (i.e. heterogeneity is not modelled). Heterogeneity is expressed in the x-axis as the coefficient of variation of the distribution (CV). Black thick lines represent the hierarchical model and red thin lines the naïve model (solid lines for <i>K</i> = 2 and dashed lines for <i>K</i> = 5; horizontal grey lines correspond to a naïve model where <i>K</i> = 1). In extreme heterogeneity conditions (high CV such that detectability switches between 0 and 1) both models lead to the same bias. For more realistic scenarios, where heterogeneity is still substantial, the hierarchical model has lower asymptotic bias. The hierarchical model is asymptotically unbiased in the absence of heterogeneity (i.e. CV = 0). Plots in the lower row (A–C) illustrate the heterogeneity in detectability represented by three different CVs when mean detectability is 0.33. Note that the relative asymptotic bias is independent of occupancy probability.</p>", "links"=>[], "tags"=>["biogeography", "Computational biology", "Population modeling", "ecology", "Ecological metrics", "Population ecology", "Spatial and landscape ecology", "Population biology", "Veterinary science", "Animal types", "wildlife", "Computerized simulations", "mathematics", "Statistics (mathematics)", "Statistical methods", "hierarchical", "occupancy", "estimators", "heterogeneity"], "article_id"=>1122266, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Gurutzeta Guillera-Arroita", "José J. Lahoz-Monfort", "Darryl I. MacKenzie", "Brendan A. Wintle", "Michael A. McCarthy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0099571.g006", "stats"=>{"downloads"=>2, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Asymptotic_bias_of_the_na_239_ve_and_hierarchical_occupancy_estimators_as_a_function_of_heterogeneity_in_detectability_/1122266", "title"=>"Asymptotic bias of the naïve and hierarchical occupancy estimators as a function of heterogeneity in detectability.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:04:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1614850"], "description"=>"<p>The first three columns correspond to the hierarchical model: in column 1 estimates of occupancy probability (‘psi-hat’), in column 2 estimates of the conditional single-survey detection probability (‘p-hat’) and in column 3 estimates of the unconditional detection probability after <i>K</i> surveys (‘pdet-hat’). Column 4 presents the estimates for the naïve model that assumes perfect detection. Rows represent increasing number of replicate surveys per site, from <i>K</i> = 1 to <i>K</i> = 5. Where the naïve model was fitted to data collapsed to a single record per site (1 if species detected at least once, 0 otherwise). In this particular scenario (also presented by <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099571#pone.0099571-Welsh1\" target=\"_blank\">[14]</a>) the imprecision in the hierarchical model is large compared to the bias in the naïve model. The true occupancy was 0.4, and the true detection probability increased with the value of the x-variable. In each figure a solid line represents true values. For reference, in columns 3 and 4 a dashed line represents the true occupancy probability.</p>", "links"=>[], "tags"=>["biogeography", "Computational biology", "Population modeling", "ecology", "Ecological metrics", "Population ecology", "Spatial and landscape ecology", "Population biology", "Veterinary science", "Animal types", "wildlife", "Computerized simulations", "mathematics", "Statistics (mathematics)", "Statistical methods", "fitting", "hierarchical", "occupancy", "5000", "sets", "a1", "55"], "article_id"=>1122247, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Gurutzeta Guillera-Arroita", "José J. Lahoz-Monfort", "Darryl I. MacKenzie", "Brendan A. Wintle", "Michael A. McCarthy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0099571.g002", "stats"=>{"downloads"=>4, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulation_results_of_fitting_hierarchical_and_na_239_ve_occupancy_models_to_5000_data_sets_from_Scenario_A1_with_55_sites_/1122247", "title"=>"Simulation results of fitting hierarchical and naïve occupancy models to 5000 data sets from Scenario A1 with 55 sites.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:04:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1614846"], "description"=>"<p>This example corresponds to a constant hierarchical occupancy model and a data set where <i>S</i> = 200 sites, <i>K</i> = 2 replicate visits, <i>S<sub>d</sub></i> = 80 sites with detection and <i>d<sub>T</sub></i> = 134 detections. P1 is located at { = 0.416,  = 0.806} and P2 at { = 1,  = 0.335}.</p>", "links"=>[], "tags"=>["biogeography", "Computational biology", "Population modeling", "ecology", "Ecological metrics", "Population ecology", "Spatial and landscape ecology", "Population biology", "Veterinary science", "Animal types", "wildlife", "Computerized simulations", "mathematics", "Statistics (mathematics)", "Statistical methods", "displaying", "maximum-likelihood", "saddle"], "article_id"=>1122243, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Gurutzeta Guillera-Arroita", "José J. Lahoz-Monfort", "Darryl I. MacKenzie", "Brendan A. Wintle", "Michael A. McCarthy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0099571.g001", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Log_likelihood_surface_displaying_the_maximum_likelihood_estimate_P1_and_a_saddle_point_at_the_boundary_P2_/1122243", "title"=>"Log-likelihood surface displaying the maximum-likelihood estimate (P1) and a saddle point at the boundary (P2).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:04:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1614860"], "description"=>"<p>Lines correspond to (solid), (dashed) and (dotted). Panel (a) displays the probability density functions (pdf) for the distributions used by WLD (Scenario B1) and panel (b) for the distributions used in our Scenarios B2 and B3. The distribution that WLD used for has considerable mass for detectability very close to zero: . Panels (c-d) display the pdf of the probability of detecting the species in at least one of <i>K</i> surveys () at sites (from darker to lighter, lines correspond to ).</p>", "links"=>[], "tags"=>["biogeography", "Computational biology", "Population modeling", "ecology", "Ecological metrics", "Population ecology", "Spatial and landscape ecology", "Population biology", "Veterinary science", "Animal types", "wildlife", "Computerized simulations", "mathematics", "Statistics (mathematics)", "Statistical methods", "distributions", "detectability", "scenarios", "covariate"], "article_id"=>1122257, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Gurutzeta Guillera-Arroita", "José J. Lahoz-Monfort", "Darryl I. MacKenzie", "Brendan A. Wintle", "Michael A. McCarthy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0099571.g004", "stats"=>{"downloads"=>3, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Beta_distributions_used_to_generate_detectability_in_the_8220_abundance_8221_scenarios_for_the_different_covariate_categories_/1122257", "title"=>"Beta distributions used to generate detectability in the “abundance” scenarios for the different covariate categories.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:04:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1614871"], "description"=>"<p>For all scenarios we tested all the combinations of the following sampling sizes: sites and replicate surveys per site. The beta distributions below are plotted in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099571#pone-0099571-g004\" target=\"_blank\">Figure 4</a>.</p>", "links"=>[], "tags"=>["biogeography", "Computational biology", "Population modeling", "ecology", "Ecological metrics", "Population ecology", "Spatial and landscape ecology", "Population biology", "Veterinary science", "Animal types", "wildlife", "Computerized simulations", "mathematics", "Statistics (mathematics)", "Statistical methods", "scenarios", "asterisk", "tested"], "article_id"=>1122268, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Gurutzeta Guillera-Arroita", "José J. Lahoz-Monfort", "Darryl I. MacKenzie", "Brendan A. Wintle", "Michael A. McCarthy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0099571.t001", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulated_scenarios_marked_with_asterisk_those_also_tested_by_WLD_/1122268", "title"=>"Simulated scenarios (marked with asterisk * those also tested by WLD).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-07-30 03:04:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1614863"], "description"=>"<p>For details in figure arrangement see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099571#pone-0099571-g002\" target=\"_blank\">Figure 2</a>. This example shows that, even if detectability is heterogeneous, the hierarchical model has smaller bias and that this bias is reduced with the sample size.</p>", "links"=>[], "tags"=>["biogeography", "Computational biology", "Population modeling", "ecology", "Ecological metrics", "Population ecology", "Spatial and landscape ecology", "Population biology", "Veterinary science", "Animal types", "wildlife", "Computerized simulations", "mathematics", "Statistics (mathematics)", "Statistical methods", "fitting", "hierarchical", "occupancy", "5000", "sets", "b2", "165"], "article_id"=>1122259, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Gurutzeta Guillera-Arroita", "José J. Lahoz-Monfort", "Darryl I. MacKenzie", "Brendan A. Wintle", "Michael A. McCarthy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0099571.g005", "stats"=>{"downloads"=>1, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulation_results_of_fitting_hierarchical_and_na_239_ve_occupancy_models_to_5000_data_sets_from_Scenario_B2_with_165_sites_/1122259", "title"=>"Simulation results of fitting hierarchical and naïve occupancy models to 5000 data sets from Scenario B2 with 165 sites.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:04:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1614877"], "description"=>"<p>Simulations were run for a range of sample sizes, with <i>S</i> sites and <i>K</i> replicate surveys per site (5000 simulations per case). When , the naïve model was fitted to the data resulting from collapsing the detection/non-detection history into a single record per site (1 if species detected at least once, 0 otherwise). The hierarchical model outperforms the naïve model, being clearly superior in the third example.</p>", "links"=>[], "tags"=>["biogeography", "Computational biology", "Population modeling", "ecology", "Ecological metrics", "Population ecology", "Spatial and landscape ecology", "Population biology", "Veterinary science", "Animal types", "wildlife", "Computerized simulations", "mathematics", "Statistics (mathematics)", "Statistical methods", "occupancy", "estimator", "simulations", "b1", "b2"], "article_id"=>1122273, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Gurutzeta Guillera-Arroita", "José J. Lahoz-Monfort", "Darryl I. MacKenzie", "Brendan A. Wintle", "Michael A. McCarthy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0099571.t004", "stats"=>{"downloads"=>2, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mean_square_error_MSE_for_the_occupancy_estimator_in_the_hierarchical_na_ve_models_and_their_ratio_obtained_from_simulations_of_three_abundance_scenarios_a_Scenario_B1_from_14_b_Scenario_B2_and_c_Scenario_B3_/1122273", "title"=>"Mean square error (MSE) for the occupancy estimator in the hierarchical/naïve models, and their ratio, obtained from simulations of three “abundance” scenarios: (a) Scenario B1 from [14], (b) Scenario B2 and (c) Scenario B3.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-07-30 03:04:28"}

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Relative Metric

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