1 Introduction

This vignette is based upon a vignette by Erix Rexstad at the CREEM, St Andrews University1. The underlying data for the analysis presented is part of an ongoing survey within the Naboisho conservancy within the greater Mara ecosystem, and is led by Professor Stewart Thompson2. The project uses distance sampling techniques to record observations across 9 different transects within the conservancy. The overall aim of the project is to provide an evidence based approach for the ecological outcomes of conservancy partnerships between indigenous land owners and private investors.

1.1 Distance sampling

Distance sampling 3 is a statistical method that can be used for estimating population densities and abundance. Typically an observer traverses a straightline (a transecrt) that is randomly loated within the study area. On observing a species of interest, the distance from the observer to the observed species is recorded (r), as well as the angle of detection (\(\theta\)) to the transect line. The distance between the species detected and the transect line may then be calculatd as \(d = r \sin \theta\).

Once a number of detections have been made along a transect, the set of distance data, \(d\), can be used to estimate a detection function. This describes the probability of detecting a given species at a given distance. In effect, the detection models the detectability or species distribution across the landscape for a given habitat, and so helps to account for species that were undetected when the observer traversed the transect(s) in question. A key assumption is that all species at zero distance (on the transect) are detected; that is, detectability at zero distance has probabiliy 1.

Species density, \(D\), within a given survey area, \(A\), may then be determined as:

\(D= n/(P.A)\)

Where \(n\) = number of species detected, and \(P\) is the average probability of detecting a species within width w of a transect line.

1.2 Multi-species surveys

The Naboisho data is an example of a multi-species survey. Multispecies wildlife monitoring across large geographical regions is important for effective conservation planning in response to expected impacts from climate change and land use. This does mean the procesing of the data set is more complicated than it might be for a single species survey, as multiple detection functions must be calculated. The naboisho survey comprises observations from ten woodland and plains transects over four years of field work. Plains and woddlands transect types are known as strata. Different stratum exhibit different detectability functions, sowe need to fit specific detection functions accordingly.

Species observed within the Naboisho conservancy are typical of a large savannah ecosystem and includes large carnoves and ungulates. Some of the species observed, such as Dik Dik or Lion, are quite rare. As such there is often insufficient detections to fit a detection function from data for a rare species. But it is often true that the presence of rare species is a function of more common species. As such we can exploit this correlation an treat Species as a covariate in modelling the detection function. This vignette sets out to demonstrate how we can estimate abundance and density across a multi-species survey, useing the Distance package.

# Load some libraries to get started
library(Distance)
library(tidyverse)
library(lubridate)
library(dplyr)
library(ggplot2)
library(kableExtra)

# Clear environment and set working directory
rm(list = ls())  
wd = "/Users/anthony/Documents/GitHub/ComputationalEcology/data_analysis_files/"
setwd(wd)

# Load underlying survey data
clean_obs <- read.csv("clean_obs.csv", stringsAsFactors = F)

# Set units of measure
convunit <- convert_units("meter", "kilometer", "square kilometre")

2 Clean the data

Before we can proceed with our distance sampling analysis, we load all observations from the Naboisho surveys, from 2017 to 2019. This is a multi-species survey comprising:

  • Nine different transects
  • Two habitat types: woodland and plains
  • Transect are typically driven throughout the year, several times a month
# Remove rows with no species or transect data
clean_obs <- clean_obs %>%
  # Remove observations with no species field
  filter(Species != "") %>%      
  # Data that is classified as woodlands and plains
  filter(Woodland != "" & Plains == "" | Woodland == "" & Plains != "") 
  
# Reformat
data_clean <- clean_obs %>%
  # Create a column to indicate Region type
  mutate(Region.Label = case_when(
    Plains == "" ~ "Woodland",
    Plains != "" ~ "Plains")) %>%
  # Create a single column for all transect names
  mutate(Transect = case_when(
    Region.Label == "Woodland" ~ as.character(Woodland),
    Region.Label == "Plains"   ~ as.character(Plains))) %>%
  # Add in region area for each observation stratum
  mutate(Area = case_when(
    Region.Label == "Woodland" ~ as.numeric(165.763),         
    Region.Label == "Plains"   ~ as.numeric(36.579))) %>% 
  # Create a new column for the date
  mutate(Year = lubridate::dmy(as.character(Date)) %>% lubridate::year()) %>%
  # Add a new column for the month of the year
  mutate(Month = lubridate::month(as.character(Date), label= T, abbr = T)) %>%
  # Drop columns we dont need anymore
  dplyr::select(-c("Woodland","Plains")) %>%
    # Rename the Transect column to Sample.Label
  rename(Sample.Label = Transect) %>%
  # Drop any rows with NA
  drop_na()

# Plot

3 Analysis periods

We want to generate a detection function and ultimately a density estimate for each species by:

  • Year
  • Month
  • Habitat type

In order to capture all the necessary permutations we can use expand.grid to do this as follows:

# Generate all combinations to execute species estimates
ds_params <- expand.grid(Region.Label = c("Plains","Woodland"),
                      Year = c(2017, 2018),
                      Month = c("Jan","Feb","Mar","Apr","May","Jun","Jul","Aug","Sep","Oct","Nov","Dec")) 

# Make the factor levels on month variable the same in ds_params and data_clean
data_clean <- data_clean %>%
  mutate(Month = factor(Month, ordered = FALSE, levels = levels(ds_params$Month)))

# Take a look at the data structure
head(ds_params)
##   Region.Label Year Month
## 1       Plains 2017   Jan
## 2     Woodland 2017   Jan
## 3       Plains 2018   Jan
## 4     Woodland 2018   Jan
## 5       Plains 2017   Feb
## 6     Woodland 2017   Feb

3.1 Generating datasets for analysis

We can now use ds_params together with the purrr::map function to subset our data set of all observations to create a subset for each row within ds_params.

# Create all data set permutations for ddf calc
ds_data <- pmap_df(
  # Paramters for subsetting the data
  ds_params,
  # Filter the dataset by ds_params
  ~dplyr::filter(
    # Data to subset
    data_clean,
    #  By strata, Year and Month
    Region.Label == ..1,
    Year         == ..2,
    Month        == ..3)) %>%
  # Add effort column
  group_by(Sample.Label) %>%
  # Each transect is 2km
  mutate(Effort = length(unique(Date)) * 2) %>%
  ungroup() %>%
  # Nest the output data
  group_by(Region.Label,Year,Month) %>% nest()

4 Species detectability

# Generate a distance model for each dataset
ds_data <- ds_data %>%
  mutate(
    model = map(
      data, 
      # Catch model failures
      possibly(
        ~ds(
          # Call distance function
          data = as.data.frame(.) ,
          # Use a half-normal fit
          key="hn",
          # Convert to correct UoM
          convert.units = convunit,
          # Use species observed as covariate
          formula = ~Species),
        # Retrun NULL if fit fails
        otherwise = NULL)))

5 Species abundance

Now we can calculate the abundance of individual species within the overall dataset, for each calculation period. Density estimates for each species can be produced by using the dht2 function that contains the argument strat_formula used to specific the levels of stratum-specific estimates requested.

# Function to generate species abundance
# The function stratifies by species
dht2_poss <- function (.x, .y) {
    dht2(
      ddf = .y,
      flatfile = as.data.frame(.x),
      strat_formula = ~Species, 
      convert_units = convunit,
      stratification = "object")
}
                     
# Generate species specific abundance estiamtes
ds_data <- ds_data %>%
  mutate(abun_model = map2(
    # Given underlying data set by month/strate
    .x = data, 
    # And distance model
    .y = model,
    # Catch failed dht2 fits
    possibly(~dht2_poss(.x,.y), 
             # Return NULL if failure
             otherwise = NULL)))

6 Results

The results of the modelling can be seen below across all months.

# Create a table of results that we're interested in
tab <- ds_data %>% unnest(abun_model) %>%
  dplyr::select(Year, Month, Region.Label, Species, Abundance, LCI, UCI) %>%
  # group by Year, Month and strata
  group_by(Year, Month, Region.Label) %>%
  # Sort the data
  arrange(Year, Month) %>%
  # Set precision on doubles
  mutate_if(is.double, format, digits=2, scientific = FALSE) %>%
  # Calculate species densities
  mutate(Density = case_when(
    Region.Label == "Woodland" ~ as.numeric(Abundance) / 165.763,
    Region.Label == "Plains"   ~ as.numeric(Abundance) / 36.579
  ))

# Foramt the table using Kable Extra
kableExtra::kable(tab, align = "c", col.names = c("","", names(tab)[3:8])) %>%
  kable_styling(full_width = F, font_size = 10) %>%
  column_spec(1, bold = T) %>%
  collapse_rows(columns = 1:3, valign = "top") %>%
  scroll_box(width = "800px", height = "500px")
Region.Label Species Abundance LCI UCI Density
2017 May Plains Coke Hartebeest 1.42 0.002926 692 0.0388201
Grant Gazelle 1.43 0.256135 8 0.0390935
Impala 1.07 0.063089 18 0.0292518
Thomson Gazelle 10.76 2.075677 56 0.2941579
Topi 0.19 0.000099 353 0.0051942
Warthog 1.03 0.064431 16 0.0281582
Wildebeest 17.89 6.080585 53 0.4890784
Zebra 8.51 0.433942 167 0.2326471
Total 42.30 0.759108 2357 1.1564012
Woodland Buffalo 8.5 1.4410 50 0.0512780
Coke Hartebeest 1.9 0.0266 132 0.0114621
Dik Dik 3.8 0.0024 5788 0.0229243
Eland 5.2 0.7500 36 0.0313701
Giraffe 11.7 2.4942 55 0.0705827
Grant Gazelle 14.6 3.5558 60 0.0880776
Impala 143.1 64.2687 318 0.8632807
Thomson Gazelle 55.7 19.7066 158 0.3360219
Topi 22.8 8.4712 61 0.1375458
Warthog 9.2 2.8206 30 0.0555009
Waterbuck 9.0 0.0059 13611 0.0542944
Wildebeest 266.6 142.6757 498 1.6083203
Zebra 98.5 61.5690 158 0.5942219
Total 650.5 6.5752 64349 3.9242774
Jun Plains Coke Hartebeest 0.301 0.015839 5.7 0.0082288
Eland 1.323 0.326853 5.4 0.0361683
Elephant 0.838 0.150382 4.7 0.0229093
Giraffe 1.339 0.373061 4.8 0.0366057
Grant Gazelle 9.837 3.941190 24.6 0.2689248
Impala 21.987 8.201572 58.9 0.6010826
Thomson Gazelle 297.147 199.801877 441.9 8.1234315
Topi 3.140 1.101653 8.9 0.0858416
Warthog 7.855 1.924018 32.1 0.2147407
Waterbuck 0.056 0.000026 121.4 0.0015309
Wildebeest 169.963 87.004711 332.0 4.6464638
Zebra 13.813 2.952501 64.6 0.3776210
Total 527.598 316.585189 879.3 14.4235217
Woodland Coke Hartebeest 11.4 2.56 51 0.0687729
Dik Dik 41.4 11.42 150 0.2497542
Eland 11.6 2.72 49 0.0699794
Elephant 32.3 9.71 107 0.1948565
Giraffe 8.6 2.29 32 0.0518813
Grant Gazelle 193.0 48.43 769 1.1643129
Impala 500.5 248.30 1009 3.0193710
Thomson Gazelle 614.8 241.53 1565 3.7089097
Topi 98.2 50.45 191 0.5924121
Warthog 71.2 23.85 212 0.4295289
Waterbuck 3.7 0.25 55 0.0223210
Wildebeest 370.2 148.84 921 2.2333090
Zebra 131.9 72.22 241 0.7957144
Total 2088.8 1451.03 3007 12.6011233
Jul Plains Buffalo 0.27 0.00181 40.9 0.0073813
Coke Hartebeest 0.66 0.04028 10.8 0.0180431
Elephant 0.21 0.00014 323.3 0.0057410
Giraffe 0.43 0.13071 1.4 0.0117554
Grant Gazelle 18.93 5.53653 64.7 0.5175100
Impala 44.46 13.93227 141.9 1.2154515
Thomson Gazelle 419.21 201.85385 870.6 11.4604008
Topi 5.35 1.72633 16.6 0.1462588
Warthog 5.72 0.97506 33.6 0.1563739
Wildebeest 821.37 363.52020 1855.9 22.4546871
Zebra 11.88 3.34981 42.1 0.3247765
Total 1328.49 716.64911 2462.7 36.3183794
Woodland Buffalo 15.73 1.88462 131 0.0948945
Bushbuck 0.49 0.00034 713 0.0029560
Coke Hartebeest 7.06 2.12996 23 0.0425909
Dik Dik 25.32 7.40618 87 0.1527482
Elephant 8.76 1.09730 70 0.0528465
Giraffe 21.30 5.54129 82 0.1284967
Grant Gazelle 143.00 45.18466 453 0.8626774
Impala 658.48 390.95644 1109 3.9724185
Thomson Gazelle 934.94 343.41110 2545 5.6402213
Topi 159.31 87.78145 289 0.9610709
Warthog 81.73 30.83437 217 0.4930533
Waterbuck 3.09 0.24349 39 0.0186411
Wildebeest 5640.56 2321.33361 13706 34.0278591
Zebra 133.88 79.87869 224 0.8076591
Total 7833.66 4035.99393 15205 47.2581939
Aug Plains Buffalo 0.042 0.0040 0.45 0.0011482
Dik Dik 0.225 0.0002 255.67 0.0061511
Eland 0.251 0.0770 0.82 0.0068619
Giraffe 0.949 0.2507 3.59 0.0259438
Grant Gazelle 17.357 6.3965 47.10 0.4745072
Impala 13.455 3.2196 56.23 0.3678340
Thomson Gazelle 547.998 300.2003 1000.34 14.9812187
Topi 3.368 1.1399 9.95 0.0920747
Warthog 5.920 1.4410 24.32 0.1618415
Waterbuck 0.485 0.0523 4.50 0.0132590
Wildebeest 511.071 214.0062 1220.49 13.9717051
Zebra 3.499 0.6274 19.52 0.0956560
Total 1104.621 667.7175 1827.40 30.1982285
Woodland Buffalo 23.0 3.91870 135 0.1387523
Coke Hartebeest 3.3 0.76172 14 0.0199079
Dik Dik 26.0 11.64351 58 0.1568504
Eland 3.1 0.60245 16 0.0187014
Elephant 1.4 0.00062 2956 0.0084458
Giraffe 36.3 13.36400 98 0.2189873
Grant Gazelle 80.5 26.86481 241 0.4856331
Impala 780.4 422.30000 1442 4.7079264
Thomson Gazelle 669.9 248.01353 1810 4.0413120
Topi 121.4 66.74747 221 0.7323709
Warthog 39.8 14.20787 112 0.2401018
Waterbuck 3.7 0.44200 30 0.0223210
Wildebeest 2209.3 1210.30397 4033 13.3280648
Zebra 200.8 90.92731 444 1.2113680
Total 4198.9 1201.41836 14675 25.3307433
Sep Plains Coke Hartebeest 0.15 0.014436 1.6 0.0041007
Eland 0.52 0.000378 719.4 0.0142158
Elephant 0.20 0.000067 594.0 0.0054676
Giraffe 2.04 0.584343 7.1 0.0557697
Grant Gazelle 11.03 2.013946 60.4 0.3015391
Impala 15.26 3.297355 70.6 0.4171793
Thomson Gazelle 342.03 181.737375 643.7 9.3504470
Topi 1.54 0.286831 8.3 0.0421007
Warthog 5.28 2.096047 13.3 0.1443451
Waterbuck 0.29 0.000200 406.2 0.0079280
Wildebeest 926.30 478.985494 1791.3 25.3232729
Zebra 9.07 2.012428 40.8 0.2479565
Total 1313.71 354.407629 4869.6 35.9143224
Oct Buffalo 1.41 0.00635 311.4 0.0385467
Bushbuck 0.19 0.00012 283.1 0.0051942
Coke Hartebeest 1.52 0.16265 14.1 0.0415539
Eland 0.14 0.00857 2.3 0.0038273
Giraffe 1.53 0.37130 6.3 0.0418273
Grant Gazelle 10.15 3.48218 29.6 0.2774816
Impala 21.17 4.32153 103.7 0.5787474
Thomson Gazelle 215.29 112.86730 410.6 5.8856174
Topi 4.25 1.08340 16.7 0.1161869
Warthog 4.22 1.00355 17.8 0.1153667
Waterbuck 2.69 0.27546 26.3 0.0735395
Wildebeest 217.67 74.22225 638.4 5.9506821
Zebra 25.46 6.78972 95.5 0.6960278
Total 505.68 213.61928 1197.0 13.8243254
Nov Woodland Buffalo 60 9.1 388 0.3619626
Coke Hartebeest 12 1.7 79 0.0723925
Dik Dik 39 14.5 104 0.2352757
Elephant 30 3.2 285 0.1809813
Giraffe 21 9.8 44 0.1266869
Grant Gazelle 46 16.8 125 0.2775046
Impala 557 311.8 993 3.3602191
Thomson Gazelle 236 132.1 420 1.4237194
Topi 89 27.9 281 0.5369111
Warthog 31 15.9 61 0.1870140
Wildebeest 616 238.5 1594 3.7161490
Zebra 57 28.4 115 0.3438644
Total 1792 1234.2 2603 10.8106152
Dec Plains Grant Gazelle 4.6 0.90 23.3 0.1257552
Impala 8.5 1.79 40.5 0.2323738
Thomson Gazelle 105.9 61.73 181.6 2.8951037
Topi 1.3 0.34 5.3 0.0355395
Warthog 1.1 0.31 4.1 0.0300719
Wildebeest 30.8 13.46 70.3 0.8420132
Zebra 12.4 1.87 81.7 0.3389923
Total 164.6 100.59 269.2 4.4998496
Woodland Eland 5.8 0.011 2986 0.0349897
Giraffe 5.9 1.561 22 0.0355930
Grant Gazelle 36.0 4.527 287 0.2171775
Impala 56.1 13.552 232 0.3384350
Thomson Gazelle 144.8 32.988 635 0.8735363
Topi 6.8 1.743 27 0.0410224
Warthog 19.5 3.268 116 0.1176378
Wildebeest 456.8 74.609 2797 2.7557416
Zebra 114.1 22.030 591 0.6883321
Total 845.8 161.063 4442 5.1024656
2018 Jan Plains Buffalo 0.12 0.00775 2.0 0.0032806
Coke Hartebeest 1.52 0.19443 11.9 0.0415539
Eland 1.23 0.29578 5.1 0.0336259
Elephant 0.73 0.00053 1010.2 0.0199568
Giraffe 1.13 0.15949 7.9 0.0308920
Grant Gazelle 5.46 0.92706 32.1 0.1492660
Impala 8.21 1.59786 42.2 0.2244457
Thomson Gazelle 150.11 87.21074 258.4 4.1037207
Topi 5.41 2.05534 14.3 0.1478991
Warthog 3.33 0.67840 16.4 0.0910358
Waterbuck 0.36 0.06817 1.9 0.0098417
Wildebeest 165.14 59.81151 456.0 4.5146122
Zebra 67.33 21.36548 212.2 1.8406736
Total 410.08 45.23083 3718.0 11.2108040
Woodland Buffalo 2.18 0.00812 588 0.0131513
Coke Hartebeest 12.59 1.75264 90 0.0759518
Eland 22.95 6.17283 85 0.1384507
Elephant 0.73 0.00043 1247 0.0044039
Giraffe 6.17 1.55605 24 0.0372218
Grant Gazelle 24.24 9.43435 62 0.1462329
Impala 197.26 117.15744 332 1.1900122
Thomson Gazelle 209.05 146.33831 299 1.2611379
Topi 80.18 21.07400 305 0.4837026
Warthog 13.28 4.90291 36 0.0801144
Wildebeest 1037.74 469.39728 2294 6.2603838
Zebra 497.88 307.29468 807 3.0035653
Total 2104.26 848.73799 5217 12.6943890
Feb Plains Buffalo 0.40 0.0417 3.8 0.0109352
Coke Hartebeest 0.18 0.0180 1.7 0.0049209
Eland 0.31 0.0386 2.5 0.0084748
Elephant 0.18 0.0035 8.9 0.0049209
Giraffe 1.10 0.3865 3.1 0.0300719
Grant Gazelle 6.44 1.4986 27.6 0.1760573
Impala 2.14 0.7236 6.3 0.0585035
Thomson Gazelle 194.06 103.0994 365.3 5.3052298
Topi 2.50 0.6445 9.7 0.0683452
Warthog 3.55 0.6128 20.6 0.0970502
Wildebeest 155.54 80.0845 302.1 4.2521665
Zebra 57.33 19.0111 172.9 1.5672927
Total 423.72 289.9813 619.1 11.5836956
Woodland Buffalo 0.63 0.00243 164 0.0038006
Coke Hartebeest 8.20 1.89731 35 0.0494682
Dik Dik 4.25 0.00280 6470 0.0256390
Eland 7.81 0.91502 67 0.0471155
Elephant 1.78 0.27386 12 0.0107382
Giraffe 26.59 15.26123 46 0.1604097
Grant Gazelle 17.16 6.28149 47 0.1035213
Impala 175.54 110.06694 280 1.0589818
Thomson Gazelle 290.64 127.50598 662 1.7533466
Topi 47.14 22.37977 99 0.2843819
Warthog 25.69 10.44469 63 0.1549803
Waterbuck 0.90 0.00059 1366 0.0054294
Wildebeest 450.31 291.89776 695 2.7165893
Zebra 159.19 108.31922 234 0.9603470
Total 1215.84 48.43059 30523 7.3348093
Mar Plains Coke Hartebeest 1.02 0.003671 285.7 0.0278849
Eland 2.83 0.511795 15.7 0.0773668
Elephant 0.16 0.000093 277.9 0.0043741
Giraffe 2.79 1.000169 7.8 0.0762733
Grant Gazelle 7.27 2.226675 23.7 0.1987479
Impala 6.91 1.940804 24.6 0.1889062
Thomson Gazelle 208.09 143.101384 302.6 5.6887832
Topi 5.85 2.007677 17.0 0.1599278
Warthog 4.33 0.652959 28.7 0.1183739
Waterbuck 0.48 0.000276 825.0 0.0131223
Wildebeest 129.92 69.077201 244.3 3.5517647
Zebra 33.28 10.711163 103.4 0.9098116
Total 402.92 41.189130 3941.5 11.0150633
Woodland Buffalo 1.7 0.0058 528 0.0102556
Coke Hartebeest 4.3 0.4833 39 0.0259407
Dik Dik 11.6 0.0073 18287 0.0699794
Eland 17.3 4.2932 70 0.1043659
Elephant 2.2 0.3429 14 0.0132720
Giraffe 20.7 8.5062 50 0.1248771
Grant Gazelle 18.4 5.4568 62 0.1110019
Impala 267.6 128.9005 555 1.6143530
Thomson Gazelle 154.3 38.4791 619 0.9308471
Topi 32.3 11.6658 90 0.1948565
Warthog 50.8 18.4211 140 0.3064616
Waterbuck 1.9 0.0012 2926 0.0114621
Wildebeest 442.7 206.9760 947 2.6706804
Zebra 377.4 189.3910 752 2.2767445
Total 1403.2 22.0045 89476 8.4650978
Apr Plains Coke Hartebeest 1.442 0.1370 15.18 0.0394215
Eland 5.908 1.2663 27.57 0.1615134
Giraffe 2.875 0.5979 13.82 0.0785970
Grant Gazelle 6.173 1.8458 20.64 0.1687580
Hippo 0.045 0.0037 0.53 0.0012302
Impala 1.532 0.3251 7.22 0.0418820
Thomson Gazelle 211.111 119.0249 374.44 5.7713716
Topi 6.502 2.0463 20.66 0.1777523
Warthog 4.658 0.7724 28.09 0.1273408
Wildebeest 158.553 37.7807 665.39 4.3345362
Zebra 38.119 9.2930 156.36 1.0421007
Total 436.918 255.3561 747.57 11.9445037
May Coke Hartebeest 13.969 0.0439 4442.24 0.3818858
Eland 10.153 1.8244 56.50 0.2775636
Giraffe 2.538 0.3851 16.73 0.0693841
Grant Gazelle 5.844 0.9023 37.85 0.1597638
Hippo 0.081 0.0068 0.98 0.0022144
Impala 1.949 0.3730 10.18 0.0532819
Thomson Gazelle 248.342 46.7673 1318.73 6.7891960
Topi 8.758 1.9194 39.96 0.2394270
Warthog 1.027 0.2579 4.09 0.0280762
Waterbuck 0.797 0.0725 8.75 0.0217885
Wildebeest 79.138 11.0618 566.17 2.1634818
Zebra 50.599 9.7219 263.35 1.3832800
Total 423.195 28.0239 6390.75 11.5693431
Woodland Buffalo 106.01 0.3288 34173.2 0.6395275
Coke Hartebeest 4.21 0.0026 6776.8 0.0253977
Dik Dik 1.85 0.0012 2981.4 0.0111605
Eland 64.02 10.4132 393.5 0.3862141
Elephant 35.88 5.6519 227.8 0.2164536
Giraffe 25.06 2.6973 232.8 0.1511797
Grant Gazelle 51.04 14.4629 180.1 0.3079095
Impala 328.79 103.1533 1048.0 1.9834945
Thomson Gazelle 347.81 60.4674 2000.6 2.0982366
Topi 86.17 24.4839 303.3 0.5198386
Warthog 49.10 8.8164 273.4 0.2962060
Waterbuck 0.39 0.0162 9.5 0.0023528
Wildebeest 247.10 43.3984 1406.9 1.4906825
Zebra 558.93 133.6994 2336.6 3.3718622
Total 1906.35 54.0039 67294.4 11.5004555
Jun Plains Buffalo 6.437 0.025173 1645.9 0.1759753
Coke Hartebeest 2.106 0.343727 12.9 0.0575740
Eland 6.062 1.047547 35.1 0.1657235
Giraffe 0.855 0.285084 2.6 0.0233741
Grant Gazelle 5.173 1.035372 25.8 0.1414199
Impala 4.546 1.093700 18.9 0.1242790
Thomson Gazelle 95.618 34.291794 266.6 2.6140135
Topi 6.741 1.389153 32.7 0.1842861
Warthog 2.235 0.613667 8.1 0.0611006
Waterbuck 0.092 0.000061 137.7 0.0025151
Wildebeest 224.286 94.904502 530.0 6.1315509
Zebra 66.738 20.320763 219.2 1.8244895
Total 420.889 101.296119 1748.8 11.5063014
Woodland Coke Hartebeest 7.7 0.6893 86 0.0464519
Dik Dik 4.1 0.0024 7031 0.0247341
Eland 11.6 1.3559 99 0.0699794
Giraffe 7.4 2.1948 25 0.0446420
Grant Gazelle 30.0 3.2587 277 0.1809813
Impala 188.9 45.6962 781 1.1395788
Thomson Gazelle 145.3 23.0246 917 0.8765527
Topi 33.8 8.5297 134 0.2039056
Warthog 33.2 9.0406 122 0.2002860
Waterbuck 6.6 0.0039 11288 0.0398159
Wildebeest 100.9 19.5338 521 0.6087004
Zebra 98.3 24.0565 401 0.5930153
Total 667.9 7.2055 61904 4.0292466
Jul Plains Coke Hartebeest 2.09 0.288 15.1 0.0571366
Eland 2.07 0.405 10.6 0.0565898
Elephant 0.49 0.046 5.2 0.0133957
Giraffe 1.99 0.794 5.0 0.0544028
Grant Gazelle 16.82 10.013 28.2 0.4598267
Impala 31.80 9.816 103.0 0.8693513
Thomson Gazelle 332.46 199.841 553.1 9.0888215
Topi 17.14 5.143 57.2 0.4685749
Warthog 8.75 2.701 28.3 0.2392083
Wildebeest 358.25 183.193 700.6 9.7938708
Zebra 14.40 4.890 42.4 0.3936685
Total 786.26 558.865 1106.2 21.4948468
Woodland Coke Hartebeest 6.3 0.22 182.5 0.0380061
Dik Dik 13.4 2.02 89.2 0.0808383
Eland 16.2 5.58 47.0 0.0977299
Elephant 19.7 2.88 134.9 0.1188444
Giraffe 21.4 7.19 63.8 0.1291000
Grant Gazelle 59.4 11.65 302.8 0.3583429
Hippo 1.4 0.30 6.5 0.0084458
Impala 552.3 196.46 1552.7 3.3318654
Thomson Gazelle 587.4 107.42 3212.6 3.5436135
Topi 89.1 39.83 199.2 0.5375144
Warthog 133.7 21.07 849.2 0.8065732
Waterbuck 1.8 0.27 12.3 0.0108589
Wildebeest 831.2 197.77 3493.2 5.0143880
Zebra 224.8 97.46 518.4 1.3561531
Total 2558.2 1414.59 4626.3 15.4328771
Aug Plains Coke Hartebeest 3.14 0.3207 30.8 0.0858416
Eland 0.15 0.0001 226.0 0.0041007
Giraffe 0.79 0.1678 3.7 0.0215971
Grant Gazelle 10.79 4.7796 24.3 0.2949780
Impala 30.17 4.0284 226.0 0.8247902
Thomson Gazelle 142.71 69.9103 291.3 3.9014188
Topi 12.02 2.7676 52.2 0.3286038
Warthog 7.32 2.7107 19.8 0.2001148
Waterbuck 0.30 0.0260 3.6 0.0082014
Wildebeest 67.55 41.2648 110.6 1.8466880
Zebra 7.79 1.6451 36.9 0.2129637
Total 282.75 100.6180 794.5 7.7298450
Woodland Buffalo 23.12 0.09990 5351 0.1394762
Coke Hartebeest 3.09 0.75910 13 0.0186411
Dik Dik 12.64 1.10501 145 0.0762534
Elephant 4.27 0.61245 30 0.0257597
Giraffe 11.24 3.08850 41 0.0678077
Grant Gazelle 77.58 32.67266 184 0.4680176
Impala 380.85 186.66920 777 2.2975574
Thomson Gazelle 606.88 104.61860 3520 3.6611307
Topi 54.25 20.33305 145 0.3272745
Warthog 138.25 21.97862 870 0.8340221
Waterbuck 0.43 0.00023 792 0.0025941
Wildebeest 808.46 183.57225 3560 4.8772042
Zebra 115.75 34.00295 394 0.6982861
Total 2236.81 753.78549 6638 13.4940246
Sep Plains Coke Hartebeest 1.61 0.1854 13.9 0.0440143
Eland 6.49 0.0046 9119.8 0.1774242
Elephant 2.16 0.4205 11.1 0.0590503
Giraffe 1.60 0.4855 5.3 0.0437409
Grant Gazelle 12.24 5.6252 26.6 0.3346182
Impala 17.27 4.9042 60.8 0.4721288
Thomson Gazelle 160.66 68.0573 379.3 4.3921376
Topi 7.01 2.0117 24.4 0.1916400
Warthog 7.76 1.2293 49.0 0.2121436
Waterbuck 0.42 0.0383 4.6 0.0114820
Wildebeest 232.95 144.8555 374.6 6.3684081
Zebra 2.15 0.3029 15.2 0.0587769
Total 452.31 5.3110 38520.2 12.3652916
Woodland Buffalo 15.30 0.05451 4294 0.0923005
Coke Hartebeest 6.31 0.00407 9791 0.0380664
Dik Dik 30.87 0.02000 47648 0.1862297
Elephant 3.23 0.49672 21 0.0194857
Giraffe 66.23 14.03638 313 0.3995463
Grant Gazelle 101.62 22.77361 453 0.6130439
Impala 287.98 117.11826 708 1.7372996
Thomson Gazelle 471.97 97.11509 2294 2.8472578
Topi 22.68 8.33838 62 0.1368218
Warthog 75.17 17.91734 315 0.4534788
Waterbuck 0.46 0.00025 860 0.0027750
Wildebeest 1251.44 185.34991 8449 7.5495738
Zebra 42.50 7.78338 232 0.2563901
Total 2375.76 25.77806 218955 14.3322696
Oct Plains Coke Hartebeest 0.74 0.05823 9.3 0.0202302
Dik Dik 0.17 0.00010 291.2 0.0046475
Elephant 0.20 0.01885 2.1 0.0054676
Giraffe 1.14 0.16418 7.9 0.0311654
Grant Gazelle 7.77 1.46560 41.2 0.2124170
Impala 8.22 1.12728 60.0 0.2247191
Thomson Gazelle 112.73 52.03783 244.2 3.0818229
Topi 4.93 0.95555 25.5 0.1347768
Warthog 5.40 0.86781 33.7 0.1476257
Waterbuck 0.80 0.00054 1194.9 0.0218705
Wildebeest 136.58 76.05936 245.3 3.7338364
Zebra 8.02 1.48904 43.1 0.2192515
Total 286.71 15.44755 5321.3 7.8381038
Woodland Coke Hartebeest 4.9 0.68 36 0.0295603
Dik Dik 15.4 0.01 22828 0.0929037
Eland 11.6 3.84 35 0.0699794
Elephant 25.4 7.18 90 0.1532308
Giraffe 42.4 16.65 108 0.2557869
Grant Gazelle 37.7 7.40 192 0.2274331
Impala 393.8 189.60 818 2.3756809
Thomson Gazelle 824.2 176.83 3842 4.9721590
Topi 37.5 13.35 105 0.2262266
Warthog 94.7 25.14 356 0.5712976
Wildebeest 885.3 155.53 5039 5.3407576
Zebra 62.0 20.25 190 0.3740280
Total 2434.9 56.11 105659 14.6890440
Nov Plains Buffalo 0.76 0.00281 205.8 0.0207769
Coke Hartebeest 2.74 0.23254 32.4 0.0749064
Eland 0.58 0.00036 929.8 0.0158561
Giraffe 1.79 0.42553 7.6 0.0489352
Grant Gazelle 12.04 2.64563 54.8 0.3291506
Impala 5.20 0.62348 43.3 0.1421581
Thomson Gazelle 93.57 53.69510 163.0 2.5580251
Topi 8.13 0.86165 76.8 0.2222587
Warthog 5.07 0.54932 46.8 0.1386041
Wildebeest 189.48 41.53341 864.4 5.1800213
Zebra 5.31 0.85241 33.1 0.1451653
Total 324.68 25.93311 4064.9 8.8761311
Woodland Coke Hartebeest 17.3 2.37 126 0.1043659
Eland 4.1 0.67 25 0.0247341
Giraffe 22.5 5.97 84 0.1357360
Grant Gazelle 65.2 30.36 140 0.3933326
Impala 441.1 216.47 899 2.6610281
Thomson Gazelle 774.5 142.40 4213 4.6723334
Topi 48.3 12.25 190 0.2913799
Warthog 78.1 23.90 255 0.4711546
Wildebeest 626.2 151.67 2585 3.7776826
Zebra 65.3 27.71 154 0.3939359
Total 2142.4 1111.92 4128 12.9244765
Dec Plains Coke Hartebeest 0.28 0.039 2.0 0.0076547
Eland 1.21 0.114 12.8 0.0330791
Giraffe 1.02 0.190 5.4 0.0278849
Grant Gazelle 5.40 1.376 21.2 0.1476257
Impala 4.89 0.971 24.6 0.1336833
Thomson Gazelle 96.05 34.942 264.0 2.6258236
Topi 5.21 0.651 41.7 0.1424314
Warthog 2.95 0.428 20.3 0.0806474
Waterbuck 0.30 0.028 3.2 0.0082014
Wildebeest 30.54 15.285 61.0 0.8349053
Zebra 27.11 4.561 161.2 0.7411356
Total 174.95 97.530 313.8 4.7827989
Woodland Coke Hartebeest 36.1 5.0584 257.9 0.2177808
Eland 8.2 0.0048 13956.2 0.0494682
Giraffe 1.6 0.3487 6.9 0.0096523
Grant Gazelle 30.4 10.1485 90.9 0.1833944
Impala 188.3 83.3346 425.4 1.1359592
Thomson Gazelle 200.9 40.6377 993.6 1.2119713
Topi 21.0 6.7784 65.0 0.1266869
Warthog 54.6 12.4715 238.8 0.3293859
Wildebeest 4453.5 1546.8427 12822.2 26.8666711
Zebra 36.2 8.5357 153.1 0.2183841
Total 5030.7 405.1145 62471.8 30.3487509

7 References

  1. Covariate modeling with rare species, Rexstad, E. http://examples.distancesampling.org/Distance-spec-covar/species-covariate-distill.html↩

  2. Spatial Ecology and Landuse Unit, Oxford Brookes University. https://www.brookes.ac.uk/bms/research/groups/evolution-ecology-environment-and-conservation/conservation-ecology/spatial-ecology-and-landuse-unit-selu/↩

  3. Introduction to Distance Sampling, Centre for Research into Ecological and Environmental Modelling http://workshops.distancesampling.org/standrews-2019/intro/lectures/BlockA-introDS.pdf↩