A multispecies hierarchical model to integrate count and distance sampling data

Neil A. Gilbert, Caroline M. Blommel, Matthew T. Farr, David S. Green, Kay E. Holekamp, Elise F. Zipkin

Data/code DOI: To be added upon acceptance

Please contact the first author for questions about the code or data: Neil A. Gilbert (neil.allen.gilbert@gmail.com)

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Abstract

Integrated community models—an emerging framework in which multiple data sources for multiple species are analyzed simultaneously—offer opportunities to expand inferences beyond the single-species and single-data source approaches common in ecology. We developed a novel integrated community model that combines distance sampling and single-visit count data; within the model, information is shared among data sources (via a joint likelihood) and species (via a random effects structure) to estimate abundance patterns across a community. Parameters relating to abundance are shared between data sources, while the model specifies separate observation processes for each data source. Simulations demonstrated that the model provided unbiased estimates of abundance and detection parameters even when detection probabilities vary between the data types. Simulations also showed that the integrated community model tended to provide more accurate and more precise parameter estimates than alternative single-species and single-datastream models. We applied the model to datasets on 11 herbivore species from the Masai Mara National Reserve, Kenya, and found considerable interspecific variation in response to local wildlife management practices: five species showed higher abundances in a region with passive conservation enforcement (median across species: 4.5x higher), three species showed higher abundances in a region with active conservation enforcement (median: 3.9x higher), and the remaining three species showed no abundance differences between the two regions. Furthermore, the hierarchical structure of the model revealed that the community average of abundance was slightly higher (posterior mean: by 0.20 animals) in the region with active conservation enforcement, but this difference was not statistically significant. Future applications of this modeling framework should consider the circumstances under which data integration is appropriate given assumptions about shared abundance patterns between data sources.

Repository Directory

code: Contains code for preparing case study data, running case study model, and simulations

• case_study_analysis
  • herbivore_case_study_analaysis_v01.R Code to run case study model.
• data_processing
  • prepare_distance_sampling_data_v01.R Format case study distance sampling data.
  • prepare_count_data_v01.R Format case study count data.
• simulations
  • alternative_model_comparison Folder containing scripts to run simulations for alternative single datastream / single-species models.
    • community_count_v01.R Community count-only model.
    • community_distance_sampling_v01.R Community distance sampling-only model.
    • single_species_count_common_v01.R Single species (common) count only model.
    • single_species_distance_sampling_common_v01.R Single species (common) distance sampling only model.
    • single_species_integrated_common_v01.R Single species (common) integrated model.
    • single_species_count_rare_v01.R Single species (rare) count only model.
    • single_species_distance_sampling_rare_v01.R Single species (rare) distance sampling only model.
    • single_species_integrated_common_v01.R Single species (rare) integrated model.
  • main_simulation_v01.R Script to run the main simulation.

data: Contains data for case study

• Shapefiles Various shapefiles.

  • DS Shapefiles for distance sampling transects.
  • Transects Shapefiles for transects where count data was collected.
  • reserve Shapefile for reserve / management zone boundaries.

• Herbivore Utilization Complete.csv Unformatted distance sampling data.

• count_data_v01.RData - Formatted count data. This .RData file contains 1 object:

  • transect_data. A dataframe with the following columns:

    Variable name	Meaning
    transect	Transect name
    sp_name	Common name of species
    date	Date of survey
    sp	Species id
    site	Site (transect} id
    rep	Visit id
    count	Count of the total number of individuals of a species observed on a survey
    area	Area offset for transect
    region	Binary variable indicating Mara (0) or Talek (1) region

• distance_sampling_data_v01.RData Formatted distance sampling data. This .RData file contains 3 objects:

  • b. A scalar, the maximum distance to which animals are counted (1000 m).

  • mdpt. A vector, the distance (in m) to the midpoint of each distance bin from the transect line.

  • v. A scalar, the width (in m) of the distance bins.

  • final2. A dataframe with the following columns:

    Variable name	Meaning
    sp	Species id
    site	Site (transect) id
    rep	Visit id
    gs	Observed group size
    dclass	Distance class (1 through 40) of observed group
    ng	Observed number of groups for species x site x rep combo
    area	Area offset for transect
    region	Binary variable indicating Mara (0) or Talek (1) region
    date	Date of survey
    sp_name	Common name of species

• tblPreyCensus_2012to2014.csv Unformatted count data.

figures Contains figures, and code to create them.

• code_for_figures Folder with scripts to create figures.
  • figure_02.R Create Figure 2 (simulation - distribution of bias)
  • figure_03.R Create Figure 3 (simulation - boxplots comparing models)
  • figure_04.R Create Figure 4 (case study - region differences)
  • figure_s1_s2.R Plot simulated community example.
  • figure_s3.R Prior predictive check for scale parameter intercept
  • figure_s4.R Make study area map for case study
  • figure_s6.R Create Figure S6
  • figure_s7.R Create Figure S7
  • figure_s8_s9.R Create Figures S8 & S9
  • table_s2.R Create Table S2 (relative bias)
  • table_s3.R Create Table S3 (absolute bias)
  • table_s4.R Create Table S4 (precision)
  • table_s5.R Create Table S5 (convergence)
• figure_01.png Figure 1. Conceptual overview of model. (PNG)
• figure_01.pptx Figure 1. Conceptual overview of model. (PPT)
• figure_02.png Figure 2. Main simulation results.
• figure_03.png Figure 3. Simulation - comparison to alternative models.
• figure_04.png Figure 4. Case study results.
• figure_04.pptx Figure 4. Case study results. (PPT file for annotation)
• figure_s1.png Figure S1. Simulated covariate effect.
• figure_s2.png Figure S2. Simulated detection function.
• figure_s3.png Figure S3. Prior predictive check
• figure_s4.png Figure S4. Case study map.
• figure_s5.png Figure S5. Updated DAG for case study (PNG)
• figure_s5.pptx Figure S5. Updated DAG for case study (PPT)
• figure_s6.png Figure S6. Rank relative bias figure
• figure_s7.png Figure S7. Rank precision figure
• figure_s8.png Figure S8. Case study: transect-level density estimates (posterior mean).
• figure_s9.png Figure S9. Case study: transect-level density estimate uncertainty (posterior standard deviation).
• figures_s8_s9.pptx PPT file to annotate Figures S8 and S9

results Contains results files.

• herbivore_case_study_results_v01.RData Model output for Mara herbivores case study. This .RData contains 4 objects

  • constants. A list of constants used in Nimble model:

    Variable name	Meaning
    NSPECIES	Number of species
    NBINS	Number of distance bins (distance sampling data)
    NBINS_C	Number of distance bins for latent detection function for count data
    NDISTANCES	Number of distance observations
    NSURVEYS	Number of distance sampling surveys
    NCOUNTS	Number of count surveys
    SP_GS	Species index for the distance data
    SP_NG	Species index for the abundance data (distance sampling)
    SP_TC	Species index for the count data
    REGION_NG	Region index for the abundance data
    REGION_TC	Regon index for the count data
    REGION_GS	Region index for the distance data
    NREGION	Number of regions

  • data. A list of data used in the Nimble model:

    Variable name	Meaning
    MIDPOINT	Distance to the midpoint of each distance bin
    DCLASS	Observed distance class
    B_DS	Maximum distance to which animals are counted for distance sampling
    B_TC	Maximum distance to which animals are counted for counts
    V	Width of distance bins
    yN_DS	Observed count of animals (distance sampling
    yN_TC	Observed count of animals (counts)
    OFFSET_DS	Area offset for distance sampling transects
    OFFSET_TC	Area offset for count transects
    MASS	Body mass of each species

  • out. A list of the MCMC chains with the posterior samples for model parameters.

  • model.code. Code for the Nimble model.

• cc.RData Simulation results for community count-only model. This .RData contains one dataframe named cc, with the following variables:

  Variable name	Meaning
  model	Model identifier, here "cc" (for count community)
  simrep	Replicate simulation
  param	Name of parameter
  sp	Species identifier
  nobs	Total number of individuals for that species counted across sites
  truth	True value of parameter
  mean	Posterior mean of parameter estimate
  sd	Posterior standard deviation of parameter estimate
  2.5%	Lower bound of 95% credible interval for estimate
  97.5%	Upper bound of 95% credible interval for estimate
  Rhat	Convergence diagnostic for parameter

• dc.RData Simulation results for community distance-sampling-only model. This .RData contains one dataframe named dc, which has the same variable names as cc (see above)

• ic.RData Simulation results for community integrated model. This .RData contains one dataframe named ic, which has the same variable names as cc (see above)

• cs.RData Simulation results for single-species count-only model. This .RData contains one dataframe named cs, which has the same variable names as cc (see above)

• ds.RData Simulation results for single-species distance-sampling-only model. This .RData contains one dataframe named ds, which has the same variable names as cc (see above)

• is.RData Simulation results for single-species integrated model. This .RData contains one dataframe named is, which has the same variable names as cc (see above)