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Mean predicted deviation (MPD)

Source: R/MPD.R
MPD.Rd

Metric to quantify the accuracy of predicted trajectories using PETRA-EDR.

Usage

MPD(x, pc_predicted = 1)

Arguments

x

Object of class PETRA returned by petra_edr() using return_args = T.

pc_predicted

Numeric value in the range 0-1, indicating the percentage of predicted states used to compute MPD.

Value

MPD() returns a numeric value quantifying the average dissimilarity between the target used to compute x and the trajectories predicted from the precedent and following states included in x. Note that the larger the value of MPD, the lower the accuracy of x.

Details

MDP estimates the accuracy of predicted trajectories (x) returned by petra_edr(). MDP is based on the assumption that only one trajectory passes by each target, and therefore, subsequent trajectories predicted from any point of x should contain the original states in the target.

\( MPD = \frac{\sum_{i=1}^{n}\sum_{j=1}^{m}d(x_i, \hat{Z}_j)}{n m} \)

where \(d(x_i, \hat{Z}_i)\) is the dissimilarity between the initial or final state \(x_i\) of the target and the predicted trajectory \(\hat{Z}_j\), defined as the minimum dissimilarity between \(x_i\) and the predicted states of \(\hat{Z}_j\); \(n\) is the number of states of the target; and \(m\) is the number of states of the trajectory predicted from the target (\(\hat{Z}_i\)).

pc_predicted values lower than 1 may reduce the computation time.

References

Sánchez-Pinillos M., Fortin, M-J., Messier, C., Kneeshaw, D. 2026. Forecasting ecological trajectories from ecological dynamic regimes to improve resilience analysis. Methods in Ecology and Evolution. doi:10.1111/2041-210x.70372

See also

petra_edr() for predicting ecological trajectories from EDRs.

plot.PETRA() for plotting predicted trajectories in an ordination space representing the state space of the EDR.

Author

Martina Sánchez-Pinillos

Examples

if (requireNamespace("vegan", quietly = TRUE)) {
  # Define state_var including the state variables for the states in the EDR and
  # the target
  EDR_var <- EDR_data$EDR1$abundance
  target_var <- data.frame(sp1 = 30, sp2 = 10, sp3 = 13, sp4 = 12, sp5 = 5, sp6 = 2,
                           sp7 = 6, sp8 = 3, sp9 = 7, sp10 = 8, sp11 = 2, sp12 = 3)
  state_var <- data.frame(rbind(EDR_var[, -c("EDR", "traj", "state")], target_var))

  # Compute PETRA-EDR
  petra <- petra_edr(state_var = state_var,
                     trajectories = c(EDR_var$traj, "target"),
                     states = as.integer(c(EDR_var$state, 0)),
                     targets = "target",
                     k = 5L,
                     minPts = 2L,
                     d_function = "vegan::vegdist",
                     d_args = list(x = state_var, method = "bray"),
                     return_args = TRUE,
                     direction = 2)

  # Calculate MPD
  MPD(x = petra)
}
#>     target 
#> 0.08324062