estar (version 1.0-1)

reactivity: Calculate the reactivity of a community after disturbance

Description

reactitvity calculates reactivity \(R_a\) as the initial rate of return to equilibrium (Downing et al. 2020). Following Neubert et al. (1996), it is calculated as the largest eigenvalue of the Hermitian part of the community matrix \(B\) .

Usage

reactivity(B)

Value

A single numeric value, the reactivity value. If \(R_a > 0\)

, the perturbation grows, i.e., the system is initially destabilised. If \(R_a < 0\)

0 the perturbation doesn’t grow and the system isn’t initially destabilised.

Arguments

B

a matrix, containing the interactions between the species or functional groups in the community. Can be calculated with extractB from the fitted MARSS object.

Details

\(R_a = \lambda_{\mathrm{dom}}\!\left( H(B) \right)\) where \(\lambda_{\mathrm{dom}}\) is the dominant eigenvalue, and \(H(B)\) is the Rayleigh quotient of \(B\) : \(H(B) = \frac{x^{\mathsf{T}} B\, x}{x^{\mathsf{T}} x}\) .

References

Neubert, M. G., & Caswell, H. (1997). Alternatives to Resilience for Measuring the Responses of Ecological Systems to Perturbations. Ecology, 78(3), 653–665.

Downing, A. L., Jackson, C., Plunkett, C., Lockhart, J. A., Schlater, S. M., & Leibold, M. A. (2020). Temporal stability vs. Community matrix measures of stability and the role of weak interactions. Ecology Letters, 23(10), 1468–1478. tools:::Rd_expr_doi("10.1111/ele.13538")

See Also

extractB()

Examples

library(MARSS)

# \donttest{
  # smaller dataset for example:
  # 3 functional groups and two insecticide concentrations besides control
  data_df <- subset(
    aquacomm_fgps,
    treat %in% c(0.0, 0.9, 6) &
      time >= 1 & time <= 28,
    select = c(time, treat, repli, herb, carn, detr)
  )

  # estimate z-score transformation and replace zeros with NA
  data_df[, c("herb", "carn", "detr")] <- lapply(data_df[, c("herb", "carn", "detr")],
                                                 MARSS::zscore)
  data_df[, c("herb", "carn", "detr")] <- lapply(data_df[, c("herb", "carn", "detr")],
                                                 function(x) replace(x, x == 0, NA))

  # reshape data from wide to long format
  data_z_ldf <- reshape(
    data_df,
    varying = list(c("herb", "carn", "detr")),
    v.names = "abund_z",
    timevar = "fgp",
    times = c("herb", "carn", "detr"),
    direction = "long",
    idvar = c("time", "treat", "repli")
  )

  data_z_ldf <- data_z_ldf[order(data_z_ldf$time, data_z_ldf$treat, data_z_ldf$fgp), ]

  # summarize mean and sd
  data_z_summldf <- aggregate(abund_z ~ time + treat + fgp, data_z_ldf, function(x)
    c(mean = mean(x, na.rm = TRUE), sd = sd(x, na.rm = TRUE)))
  data_z_summldf <- do.call(data.frame, data_z_summldf)
  names(data_z_summldf)[4:5] <- c("abundz_mu", "abundz_sd")

  # split dataframe per functional groups
  # into list to apply the MARSS model more easily
  split_data_z <- split(data_z_summldf[, c("time", "fgp", "abundz_mu")], data_z_summldf$treat)

  reshape_to_wide <- function(df) {
    df_wide <- reshape(df,
                       idvar = "fgp",
                       timevar = "time",
                       direction = "wide")
    rownames(df_wide) <- df_wide$fgp
    df_wide <- df_wide[, -1]  # Remove the 'fgp' column
    as.matrix(df_wide)
  }

  data_z_summls <- lapply(split_data_z, reshape_to_wide)

  # fit MARSS models
  data.marssls <- list(
    MARSS(
      data_z_summls[[1]],
      model = list(
        B = "unconstrained",
        U = "zero",
        A = "zero",
        Z = "identity",
        Q = "diagonal and equal",
        R = matrix(0, 3, 3),
        tinitx = 1
      ),
      method = "BFGS"
    ),
    MARSS(
      data_z_summls[[2]],
      model = list(
        B = "unconstrained",
        U = "zero",
        A = "zero",
        Z = "identity",
        Q = "diagonal and equal",
        R = matrix(0, 3, 3),
        tinitx = 1
      ),
      method = "BFGS"
    ),
    MARSS(
      data_z_summls[[3]],
      model = list(
        B = "unconstrained",
        U = "zero",
        A = "zero",
        Z = "identity",
        Q = "diagonal and equal",
        R = matrix(0, 3, 3),
        tinitx = 1
      ),
      method = "BFGS"
    )
  )

  # identify experiments
  names(data.marssls) <- paste0("Conc. = ", c("0", "0.9", "44"), " micro g/L")

  # extract community matrices (B)
  data.Bls <- data.marssls |>
    lapply(extractB,
           states_names = c("Herbivores", "Carnivores", "Detrivores"))

  # calculate reactivity for each of the B matrices
  purrr::map(data.Bls, reactivity)

# }