# Calculate the reactivity of a community after disturbance `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 $B$ . ```r reactivity(B) ``` ## 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. ## Returns 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. ## 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 $B$ : $H(B) = \frac{x^{\mathsf{T}} B\, x}{x^{\mathsf{T}} x}$ . ## Examples ```r library(MARSS) # 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) ``` ## 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()`

reactivity function