Claddis (version 0.7.0)

calculate_gmax: Calculate the maximum possible tree length, gmax, under parsimony

Description

Given a costmatrix and number of tips, calculates the longest possible tree length under maximum parsimony.

Usage

calculate_gmax(costmatrix, n_taxa, allow_zeroes = FALSE)

Value

A numeric indicating the maximum possible cost, gmax.

Arguments

costmatrix

An object of class costMatrix.

n_taxa

The number of taxa (ree tips) to consider.

allow_zeroes

Logical indicating whether some states are allowed to be assigned zero tips. Defaults to FALSE (recommended). Note that if the number of states exceeds the number of tips then allow_zeroes = TRUE is forced.

Author

Graeme T. Lloyd and Jen Hoyal Cuthill

Details

The concept of gmax was introduced by Hoyal Cuthill et al. (2010) and in the strictest sense represents the integer state frequency that maximizes g with the restriction that every state is sampled at least once. This function is intended to relax that slightly using the allow_zeroes option and indeed this is not possible in rare cases such as either high levels of missing data or gap-weighted (Thiele 1993) characters where it is possible for the number of states to exceed the (effective) number of tips. For a more detailed description of the problem and implemented solution(s) see Hoyal Cuthill and Lloyd (in press).

References

Hoyal Cuthill, J. F. and Lloyd, G. T., in press. Measuring homoplasy I: comprehensive measures of maximum and minimum cost under parsimony across discrete cost matrix character types. Cladistics, bold, .

Hoyal Cuthill, J. F., Braddy, S. J. and Donoghue, P. C. J., 2010. A formula for maximum possible steps in multistate characters: isolating matrix parameter effects on measures of evolutionary convergence. Cladistics, 26, 98-102.

Thiele, K.. 1993. The Holy Grail of the perfect character: the cladistic treatment of morphometric data. Cladistics, 9, 275-304.

See Also

calculate_g

Examples

# Create a Type I character costmatrix:
constant_costmatrix <- make_costmatrix(
  min_state = 0,
  max_state = 0,
  character_type = "unordered"
)

# Calculate gmax for ten tips:
calculate_gmax(
  costmatrix = constant_costmatrix,
  n_taxa = 10
)

# Create a Type II character costmatrix:
binary_symmetric_costmatrix <- make_costmatrix(
  min_state = 0,
  max_state = 1,
  character_type = "unordered"
)

# Calculate gmax for ten tips:
calculate_gmax(
  costmatrix = binary_symmetric_costmatrix,
  n_taxa = 10
)

# Create a Type III character costmatrix:
unordered_costmatrix <- make_costmatrix(
  min_state = 0,
  max_state = 2,
  character_type = "unordered"
)

# Calculate gmax for ten tips:
calculate_gmax(
  costmatrix = unordered_costmatrix,
  n_taxa = 10
)

# Create a Type IV character costmatrix:
linear_ordered_costmatrix <- make_costmatrix(
  min_state = 0,
  max_state = 2,
  character_type = "ordered"
)

# Calculate gmax for ten tips:
calculate_gmax(
  costmatrix = linear_ordered_costmatrix,
  n_taxa = 10
)

# Create a Type V character costmatrix:
nonlinear_ordered_costmatrix <- convert_adjacency_matrix_to_costmatrix(
  adjacency_matrix = matrix(
    data = c(
      0, 1, 0, 0,
      1, 0, 1, 1,
      0, 1, 0, 0,
      0, 1, 0, 0
    ),
    nrow = 4,
    dimnames = list(0:3, 0:3)
  )
)

# Calculate gmax for ten tips:
calculate_gmax(
  costmatrix = nonlinear_ordered_costmatrix,
  n_taxa = 10
)


# Create a Type VI character costmatrix:
binary_irreversible_costmatrix <- make_costmatrix(
  min_state = 0,
  max_state = 1,
  character_type = "irreversible"
)

# Calculate gmax for ten tips:
calculate_gmax(
  costmatrix = binary_irreversible_costmatrix,
  n_taxa = 10
)

# Create a Type VII character costmatrix:
multistate_irreversible_costmatrix <- make_costmatrix(
  min_state = 0,
  max_state = 2,
  character_type = "irreversible"
)

# Calculate gmax for ten tips:
calculate_gmax(
  costmatrix = multistate_irreversible_costmatrix,
  n_taxa = 10
)

#' # Create a Type VIII character costmatrix:
binary_dollo_costmatrix <- make_costmatrix(
  min_state = 0,
  max_state = 1,
  character_type = "dollo"
)

# Calculate gmax for ten tips:
calculate_gmax(
  costmatrix = binary_dollo_costmatrix,
  n_taxa = 10
)

# Create a Type IX character costmatrix:
multistate_dollo_costmatrix <- make_costmatrix(
  min_state = 0,
  max_state = 2,
  character_type = "dollo"
)

# Calculate gmax for ten tips:
calculate_gmax(
  costmatrix = multistate_dollo_costmatrix,
  n_taxa = 10
)

# Create a Type X character costmatrix:
multistate_symmetric_costmatrix <- make_costmatrix(
  min_state = 0,
  max_state = 5,
  character_type = "ordered"
)
multistate_symmetric_costmatrix$type <- "custom"
multistate_symmetric_costmatrix$costmatrix <- matrix(
  data = c(
    0, 1, 2, 3, 2, 3,
    1, 0, 3, 2, 1, 2,
    2, 3, 0, 3, 2, 1,
    3, 2, 3, 0, 1, 2,
    2, 1, 2, 1, 0, 1,
    3, 2, 1, 2, 1, 0
  ),
  nrow = multistate_symmetric_costmatrix$size,
  ncol = multistate_symmetric_costmatrix$size,
  byrow = TRUE,
  dimnames = list(
    multistate_symmetric_costmatrix$single_states,
    multistate_symmetric_costmatrix$single_states
  )
)

# Calculate gmax for ten tips:
calculate_gmax(
  costmatrix = multistate_symmetric_costmatrix,
  n_taxa = 10
)

# Create a Type XI character costmatrix:
binary_asymmetric_costmatrix <- make_costmatrix(
  min_state = 0,
  max_state = 1,
  character_type = "ordered"
)
binary_asymmetric_costmatrix$type <- "custom"
binary_asymmetric_costmatrix$costmatrix <- matrix(
  data = c(
    0, 1,
    10, 0
  ),
  nrow = binary_asymmetric_costmatrix$size,
  ncol = binary_asymmetric_costmatrix$size,
  byrow = TRUE,
  dimnames = list(
    binary_asymmetric_costmatrix$single_states,
    binary_asymmetric_costmatrix$single_states
  )
)
binary_asymmetric_costmatrix$symmetry <- "Asymmetric"

# Calculate gmax for ten tips:
calculate_gmax(
  costmatrix = binary_asymmetric_costmatrix,
  n_taxa = 10
)

# Create a Type XII character costmatrix:
multistate_asymmetric_costmatrix <- make_costmatrix(
  min_state = 0,
  max_state = 2,
  character_type = "ordered"
)
multistate_asymmetric_costmatrix$type <- "custom"
multistate_asymmetric_costmatrix$costmatrix <- matrix(
  data = c(
    0, 1, 1,
    1, 0, 1,
    10, 10, 0
  ),
  nrow = multistate_asymmetric_costmatrix$size,
  ncol = multistate_asymmetric_costmatrix$size,
  byrow = TRUE,
  dimnames = list(
    multistate_asymmetric_costmatrix$single_states,
    multistate_asymmetric_costmatrix$single_states
  )
)
multistate_asymmetric_costmatrix$symmetry <- "Asymmetric"

# Calculate gmax for ten tips:
calculate_gmax(
  costmatrix = multistate_asymmetric_costmatrix,
  n_taxa = 10
)