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Sensitivity Analysis of Ozkan's pTO Index (Islem 3 / Run 3)

Source: R/ozkan_pto_resample.R
ozkan_pto_sensitivity.Rd

Implements the sensitivity analysis procedure from Ozkan's Excel macro (Islem 3). Uses the jackknife results from Run 2 to apply species-specific inclusion probabilities: unhappy species get \(P = (S-1)/S\), happy species get a data-driven probability derived from Run 2 iteration results.

Usage

ozkan_pto_sensitivity(
  community,
  tax_tree,
  run2_result,
  n_iter = NULL,
  seed = NULL
)

Arguments

community

A named numeric vector of species abundances.

tax_tree

A data frame with taxonomic hierarchy.

run2_result

The result from ozkan_pto_resample().

n_iter

Number of iterations (default: same as Run 2).

seed

Optional random seed for reproducibility.

Value

A named list with components:

uTO_plus_max

Maximum uTO+ across Run 1, 2, and 3

TO_plus_max

Maximum TO+ across all runs

uTO_max

Maximum uTO across all runs

TO_max

Maximum TO across all runs

run3_uTO_plus_max

Maximum uTO+ from Run 3 only

run3_TO_plus_max

Maximum TO+ from Run 3 only

run3_uTO_max

Maximum uTO from Run 3 only

run3_TO_max

Maximum TO from Run 3 only

n_iter

Number of iterations performed

species_probs

Named numeric vector of inclusion probabilities

prob_happy

Probability used for happy species

prob_unhappy

Probability used for unhappy species

iteration_results

Data frame with all Run 3 iteration results

Details

The algorithm follows the Excel macro's Islem 3 logic:

For each species, the inclusion probability depends on its jackknife classification from Islem 1:

  • Unhappy species (AA = 0, non-contributing): Included with probability \((S-1)/S\), where S is total species count. In the Excel formula: IF(RANDBETWEEN(1, S) > 1, H2, 0).

  • Happy species (AA > 0, contributing): Included with probability derived from Run 2 results. In the Excel formula: IF(L25 >= RANDBETWEEN(0, K22), H2, 0), where L25 is a summary score from Run 2 and K22 is the iteration count.

The happy species probability is computed as: $$P_{happy} = \frac{\max(0, N_{positive} - S) + 1}{N_{iter} + 1}$$

where \(N_{positive}\) is the number of Run 2 iterations that produced a positive uTO+ value and S is the species count.

The maximum pTO across all three runs (Run 1, 2, 3) is the final result.

References

Ozkan, K. (2018). A new proposed measure for estimating taxonomic diversity. Turkish Journal of Forestry, 19(4), 336-346. DOI: 10.18182/tjf.441061

See also

ozkan_pto_resample() for Run 2, ozkan_pto_full() for the full pipeline.

Examples

comm <- c(sp1 = 4, sp2 = 2, sp3 = 3, sp4 = 1, sp5 = 2)
tax <- data.frame(
  Species = paste0("sp", 1:5),
  Genus   = c("G1", "G1", "G1", "G2", "G2"),
  Family  = c("F1", "F1", "F1", "F1", "F1"),
  stringsAsFactors = FALSE
)
set.seed(42)
run2 <- ozkan_pto_resample(comm, tax, n_iter = 101)
ozkan_pto_sensitivity(comm, tax, run2, n_iter = 101)
#> taxdiv -- Sensitivity Analysis (Run 3)
#> 
#>   Iterations: 101 
#>   P(happy):   0.7745 
#>   P(unhappy): 0.8 
#> 
#>   Overall maximum (across Run 1-2-3):
#>     uTO+ : 3.060705 
#>     TO+  : 3.753852 
#>     uTO  : 2.632978 
#>     TO   : 3.305854