riverconn (version 0.3.31)

B_ij_fun: Calculates B_ij: the functional contribution to dispersal probability I_ij

Description

Calculates B_ij: the functional contribution to dispersal probability I_ij

Usage

B_ij_fun(
  graph,
  field_B = "length",
  dir_distance_type = "symmetric",
  disp_type = "exponential",
  param_u,
  param_d,
  param,
  param_l
)

Value

a square matrix of size length(V(graph)) containing B_ij values. The matrix is organized with "from" nodes on the columns and "to" nodes on the rows

Arguments

graph

an object of class igraph. Can be both directed or undirected.

field_B

the 'graph' edge attribute to be used to calculate the distance. Default is "length".

dir_distance_type

how directionality in B_ij calculations is dealt with: "symmetric" (i.e. undirected graph) or "asymmetric" (i.e. directed graph). See details.

disp_type

the formula used to calculate the probabilities in the B_ij matrix. Use "exponential" for exponential decay, "threshold" for setting a distance threshold, or "leptokurtic" for leptokurtic dispersal.

param_u

the upstream dispersal parameter. Must be a numeric value. Only used if dir_distance_type = "asymmetric". See details.

param_d

the downstream dispersal parameter. Must be a numeric value. Only used if dir_distance_type = "asymmetric". See details.

param

the dispersal parameter. Must be a numeric value. Only used if dir_distance_type = "symmetric". See details.

param_l

the parameters for the leptokurtic dispersal mode. Must be a numeric vector of the type c(sigma_stat, sigma_mob, p). See details below.

Details

dir_distance_type = "symmetric" is to be used when the directionality of the river network is not relevant. The distance between reaches midpoints is calculated for each couple of reaches. dir_distance_type = "asymmetric" is to be used when the directionality is relevant. The distance between reaches midpoints is calculated for each couple of reaches and splitted between 'upstream travelled' distance and 'downstream travelled' distance. When disp_type ="leptokurtic" is selected, symmetric dispersal is assumed.

The 'param_u', 'param_d', and 'param' values are interpreted differently based on the formula used to relate distance (d_ij) and probability (B_ij). When disp_type ="exponential", those values are used as the base of the exponential dispersal kernel: B_ij = param^d_ij. When disp_type ="threshold", those values are used to define the maximum dispersal length: B_ij = ifelse(d_ij < param, 1, 0).

When disp_type ="leptokurtic" is selected, a leptokurtic dispersal kernel is used to calculate B_ij. A leptokurtic dispersal kernel is a mixture of two zero-centered gaussian distributions with standard deviations sigma_stat (static part of the population), and sigma_mob (mobile part of the population). The probability of dispersal is calculated as: B_ij = p F(0, sigma_stat, d_ij) + (1-p) F(0, sigma_mob, d_ij) where F is the upper tail of the gaussian cumulative density function.

Examples

library(igraph)
g <- igraph::graph_from_literal(1-+2, 2-+5, 3-+4, 4-+5, 6-+7, 7-+10, 8-+9, 9-+10,
5-+11, 11-+12, 10-+13, 13-+12, 12-+14, 14-+15, 15-+16)
E(g)$id_dam <- c("1", NA, "2", "3", NA, "4", NA, "5", "6", NA,  NA, NA, NA, "7", NA)
E(g)$type <- ifelse(is.na(E(g)$id_dam), "joint", "dam")
V(g)$length <- c(1, 1, 2, 3, 4, 1, 5, 1, 7, 7, 3, 2, 4, 5, 6, 9)
V(g)$HSI <- c(0.2, 0.1, 0.3, 0.4, 0.5, 0.5, 0.5, 0.6, 0.7, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8)
V(g)$Id <- V(g)$name
E(g)$pass_u <- E(g)$pass_d <- ifelse(!is.na(E(g)$id_dam),0.1,NA)
dist_mat <- B_ij_fun(g, param = 0.9)