Conclusions

Last updated

September 15, 2026

Olinger LK, Edmunds PJ, Levitan D, Smith TB, Lasker H, Feeley M, Mahoney L, Dahl A. Reproductive mode, but not rarity, influences population trajectories in corals. In Review 2026.

This page gathers the headline results of the study and pairs them with a tool to test the one choice they rest on. The figures below show the published analysis; open any program page for the full analysis and its updated version.

Highlight results

The integrated result

Figure 1: Coral cover by ranked taxonomic abundance (common versus rare) and reproductive mode (brooders versus broadcasters). (A,C,E) Abundance distributions ranked by mean percent cover during baseline periods (2001–2005 for TCRMP; 2001–2005 for VINPS; 1992–1996 for CSUN). (B,D,F) Temporal trends of log₁₀-transformed percent cover. Taxa are grouped and colored by commonness (common: top 90% of cumulative cover; rare: bottom 10%) and reproductive mode. Trend lines represent model-derived slopes ± robust standard errors. (A,B) TCRMP species-level data; (C,D) VINPS species-level data; (E,F) CSUN genus-level data.

Table 1 reports the model coefficients for all three programs, fit with HC3 robust standard errors (1).

Table 1: Linear model coefficients and robust standard errors from linear regression models predicting log₁₀-transformed percentage cover for three monitoring programs. Predictors include year (continuous), commonness category (rare vs. common), reproductive mode (brooder vs. broadcaster), and all two-way and three-way interaction terms. 'Common' is the reference level for commonness category, and 'Broadcaster' is the reference for reproductive mode. Models were fitted independently: TCRMP (species), VINPS (species), and CSUN (genus). Significant terms are denoted in bold.
Predictor TCRMP VINPS CSUN
Intercept 0.042 (0.039) 0.070 (0.054) 0.350 (0.081) ***
Year -0.019 (0.003) *** -0.010 (0.004) * -0.011 (0.004) **
Rarity -1.047 (0.056) *** -1.073 (0.078) *** -1.431 (0.118) ***
Repro. mode (brooder) -0.245 (0.055) *** -0.416 (0.079) *** -0.611 (0.097) ***
Year x Rarity -0.007 (0.005) 0.004 (0.006) -0.001 (0.006)
Year x Repro. mode 0.011 (0.004) * 0.027 (0.005) *** 0.019 (0.005) ***
Rarity x Repro. mode -0.339 (0.084) *** -0.035 (0.115) 0.463 (0.154) **
Year x Rarity x Repro. mode 0.009 (0.007) -0.023 (0.009) ** -0.016 (0.008) *

Test the rarity boundary

The rarity result rests on one choice: the boundary that separates common taxa from rare taxa along the ranked abundance distribution. Our paper sets the boundary of common species as those representing the top 90% of baseline cover.

Here we show that major patterns largely hold when move this boundary up or down the abundance distributions. Please try for yourself, and see how the primary statistics change.

#| '!! shinylive warning !!': |
#|   shinylive does not work in self-contained HTML documents.
#|   Please set `embed-resources: false` in your metadata.
#| standalone: true
#| viewerHeight: 760
#| viewerWidth: 1100

## file: app.R

library(shiny)
library(dplyr)

b64 <- paste(readLines("pre_b64.txt"), collapse = "")
pre <- unserialize(memDecompress(jsonlite::base64_dec(b64), "gzip"))

progs <- c("TCRMP", "VINPS", "CSUN")

palette_grp <- c(
  "Common.Broadcaster" = "#0072B2",
  "Rare.Broadcaster" = "#56B4E9",
  "Common.Brooder" = "#D55E00",
  "Rare.Brooder" = "#E69F00"
)

label_grp <- c(
  "Common.Broadcaster" = "Common broadcaster",
  "Rare.Broadcaster" = "Rare broadcaster",
  "Common.Brooder" = "Common brooder",
  "Rare.Brooder" = "Rare brooder"
)

term_labels <- c(
  "(Intercept)" = "Intercept",
  "yearind" = "Year",
  "categoryRare" = "Rarity",
  "Reproductive_modeBrooder" = "Repro. mode (Brooder)",
  "yearind:categoryRare" = "Year x Rarity",
  "yearind:Reproductive_modeBrooder" = "Year x Repro. mode",
  "categoryRare:Reproductive_modeBrooder" = "Rarity x Repro. mode",
  "yearind:categoryRare:Reproductive_modeBrooder" = "Year x Rarity x Repro. mode"
)

plot_sad <- function(prog, part) {
  d <- part$classification
  d <- d[order(prog$baseline$rank[match(d$taxon, prog$baseline$taxon)]), ]

  grp <- paste(d$commonness, d$Reproductive_mode, sep = ".")
  cols <- palette_grp[grp]
  cols[is.na(cols)] <- "grey70"

  op <- par(
    mar = c(3.2, 8.2, 2.2, 0.4),
    mgp = c(1.8, 0.5, 0),
    tcl = -0.25,
    cex.axis = 0.7,
    cex.lab = 0.8,
    cex.main = 0.88
  )
  on.exit(par(op))

  bp <- barplot(
    rev(d$meancov),
    horiz = TRUE,
    col = rev(cols),
    border = NA,
    names.arg = rev(d$taxon),
    las = 1,
    cex.names = 0.58,
    xlab = "Mean baseline abundance",
    main = sprintf("%d common / %d rare", part$n_common, prog$N - part$n_common)
  )

  nb <- nrow(d)

  if (part$n_common >= 1 && part$n_common < nb) {
    abline(
      h = mean(bp[c(nb - part$n_common, nb - part$n_common + 1)]),
      lty = 2,
      lwd = 1.5,
      col = "grey10"
    )
  }
}

plot_trend <- function(part) {
  d <- part$analysis

  grp <- paste(d$category, d$Reproductive_mode, sep = ".")
  cols <- palette_grp[grp]

  op <- par(
    mar = c(3.3, 3.2, 1.1, 0.3),
    mgp = c(1.8, 0.5, 0),
    tcl = -0.25,
    cex.axis = 0.72,
    cex.lab = 0.8
  )
  on.exit(par(op))

  plot(
    d$year,
    d$perccover,
    log = "y",
    pch = 21,
    cex = 0.68,
    bg = adjustcolor(cols, 0.32),
    col = "#00000055",
    xlab = "Year",
    ylab = "Abundance, log scale"
  )

  for (g in unique(grp)) {
    sub <- d[grp == g, ]

    if (nrow(sub) > 2) {
      m <- lm(log10(perccover) ~ year, sub)
      xs <- range(sub$year)
      ys <- 10^predict(m, data.frame(year = xs))
      lines(xs, ys, col = palette_grp[g], lwd = 1.7)
    }
  }

  legend(
    "topright",
    legend = label_grp[names(palette_grp)],
    col = palette_grp,
    lwd = 1.7,
    cex = 0.58,
    bty = "n",
    inset = 0.01
  )
}

part_of <- function(p, k) {
  pp <- pre[[p]]
  key <- as.character(min(max(round(k), min(pp$valid_k)), max(pp$valid_k)))
  pp$parts[[key]]
}

ui <- fluidPage(
  tags$style(HTML(
    "
    body {
      font-family: 'Space Grotesk', system-ui, sans-serif;
      font-size: 12px;
    }

    h4 {
      margin-top: 8px;
      margin-bottom: 6px;
    }

    h5 {
      margin-top: 10px;
      margin-bottom: 4px;
      font-size: 12px;
      font-weight: 700;
    }

    p {
      margin-bottom: 8px;
    }

    hr {
      margin-top: 10px;
      margin-bottom: 10px;
    }

    .form-group {
      margin-bottom: 4px;
    }

    .plot-pair {
      display: flex;
      flex-direction: row;
      align-items: flex-start;
      justify-content: flex-start;
      gap: 12px;
      width: 100%;
    }

    .plot-pane {
      min-width: 0;
      flex: 0 0 auto;
    }

    .sad-inner {
      width: 300px;
      max-width: 100%;
    }

    .trend-inner {
      width: 300px;
      max-width: 100%;
    }

    .sad-inner .shiny-plot-output {
      width: 460px !important;
      max-width: 100%;
    }

    .trend-inner .shiny-plot-output {
      width: 380px !important;
      max-width: 100%;
    }

    .pubtbl {
      border-collapse: collapse;
      font-size: 12px;
      margin: 4px 0;
    }

    .pubtbl th,
    .pubtbl td {
      border-bottom: 1px solid #ddd6ca;
      padding: 4px 8px;
      text-align: center;
      vertical-align: top;
    }

    .pubtbl td:first-child,
    .pubtbl th:first-child {
      text-align: left;
    }

    .pubtbl thead th {
      background: #0b2444;
      color: #fff;
      white-space: pre-line;
      font-weight: 600;
    }
    "
  )),

  #h4("Rare / common boundary explorer"),

  p(
    "Move each program's boundary. Taxa above the split are common, below are rare. "
  ),

  actionButton("reset", "Reset all to 90%"),

  tags$hr(),

  lapply(progs, function(p) {
    tagList(
      h5(sprintf("%s (%s)", p, pre[[p]]$taxon_level)),

      uiOutput(paste0("sl_", p)),

      tags$div(
        class = "plot-pair",

        tags$div(
          class = "plot-pane sad-pane",
          tags$div(
            class = "sad-inner",
            plotOutput(paste0("sad_", p), height = "300px", width = "300")
          )
        ),

        tags$div(
          class = "plot-pane trend-pane",
          tags$div(
            class = "trend-inner",
            plotOutput(paste0("trend_", p), height = "300px", width = "300px")
          )
        )
      ),

      tags$hr()
    )
  }),

  h5("Table 1, regenerated at the current boundaries"),
  uiOutput("table1"),

  h5("Supplemental: group-specific temporal slopes"),
  tableOutput("slopes")
)

server <- function(input, output, session) {
  po <- function(p) {
    part_of(p, input[[paste0("k_", p)]])
  }

  lapply(progs, function(p) {
    output[[paste0("sl_", p)]] <- renderUI({
      pp <- pre[[p]]

      sliderInput(
        paste0("k_", p),
        label = NULL,
        min = min(pp$valid_k),
        max = max(pp$valid_k),
        value = pp$k_paper,
        step = 1,
        width = "100%"
      )
    })

    output[[paste0("sad_", p)]] <- renderPlot({
      req(input[[paste0("k_", p)]])
      plot_sad(pre[[p]], po(p))
    })

    output[[paste0("trend_", p)]] <- renderPlot({
      req(input[[paste0("k_", p)]])
      plot_trend(po(p))
    })
  })

  observeEvent(input$reset, {
    for (p in progs) {
      updateSliderInput(session, paste0("k_", p), value = pre[[p]]$k_paper)
    }
  })

  output$table1 <- renderUI({
    req(input$k_TCRMP, input$k_VINPS, input$k_CSUN)

    parts <- lapply(progs, po)
    req(all(!vapply(parts, is.null, logical(1))))

    f2 <- function(x) {
      formatC(x, format = "f", digits = 2)
    }

    cell <- function(est, se, p) {
      st <- ifelse(
        p < 0.001,
        "***",
        ifelse(p < 0.01, "**", ifelse(p < 0.05, "*", ""))
      )

      pt <- ifelse(
        p < 0.001,
        "p<0.001",
        paste0("p=", formatC(p, format = "f", digits = 3))
      )

      HTML(paste0(f2(est), " (", f2(se), ")<br>", pt, st))
    }

    co1 <- parts[[1]]$coef

    body <- lapply(seq_len(nrow(co1)), function(i) {
      tags$tr(
        tags$td(term_labels[[co1$term[i]]]),
        lapply(seq_along(progs), function(j) {
          co <- parts[[j]]$coef
          sig <- co$p.value[i] < 0.05

          tags$td(
            style = if (sig) "font-weight:700" else "",
            cell(co$estimate[i], co$std.error[i], co$p.value[i])
          )
        })
      )
    })

    stat_labs <- c("Adj. R-squared", "Observations", "Residual SE", "df")

    stat_vals <- lapply(parts, function(pt) {
      fs <- pt$fit_stats

      c(
        formatC(fs$adj_r2, format = "f", digits = 3),
        fs$n,
        formatC(fs$rse, format = "f", digits = 3),
        fs$df
      )
    })

    stats <- lapply(seq_along(stat_labs), function(r) {
      tags$tr(
        tags$td(stat_labs[r]),
        lapply(stat_vals, function(v) tags$td(v[r]))
      )
    })

    tags$div(
      tags$table(
        class = "pubtbl",
        tags$thead(
          tags$tr(
            tags$th("Predictor"),
            lapply(progs, function(p) {
              tags$th(paste0(p, "\nEstimate (SE)\nP-value"))
            })
          )
        ),
        tags$tbody(body, stats)
      ),

      tags$p(
        style = "font-size:11px;color:#6d685e",
        "Table 1. Linear-model coefficients with HC3 robust standard errors. Dependent variable: ",
        "log10 percent cover. Significant terms (p<0.05) in bold."
      )
    )
  })

  output$slopes <- renderTable({
    req(input$k_TCRMP, input$k_VINPS, input$k_CSUN)

    do.call(
      rbind,
      lapply(progs, function(p) {
        po(p)$slopes %>%
          transmute(
            Program = p,
            Group,
            Slope = sprintf("%.4f", Slope),
            SE = sprintf("%.4f", SE),
            `Annual % change` = sprintf("%.2f", `Annual % change`),
            `P-value` = ifelse(
              `P-value` < 0.001,
              "< 0.001",
              sprintf("%.3f", `P-value`)
            )
          )
      })
    )
  },
  striped = TRUE,
  hover = TRUE,
  width = "100%")
}

shinyApp(ui, server)

## file: pre_b64.txt
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Brooders and broadcasters over time

Reproductive mode reshapes the community. Figure 2 follows the mean cover of broadcasters and brooders separately in each program, and tracks the brooder share of total coral cover. Broadcaster cover falls across all three programs while brooder cover holds steadier, so the brooder share of cover climbs over the record. In two programs it approaches the 50 percent parity line, meaning brooders may soon hold as much reef cover as broadcasters, a reversal of the historical dominance of broadcasting reef-builders.

Figure 2: Brooder versus broadcaster cover over time, all taxa (as published). (A) Mean cover per site for broadcasters (solid) and brooders (dashed) in each program. (B) Brooder proportion of total coral cover, with the dashed line marking 50 percent parity.

Occupancy versus local cover

Two taxa can lose the same amount of cover in different ways: one by disappearing from sites (a loss of site occupancy), another by thinning where it persists (a loss of local cover). Figure 3 separates the two. Each arrow runs from a taxon’s baseline site occupancy and local cover to its recent values. The taxa the manuscript names are colored by group and labeled; all other taxa are gray. Broadcasters tend to slide down and to the left (thinner and less widespread); several brooders hold or expand their occupancy.

Figure 3: Site occupancy (x) versus local cover (y), baseline to recent, per program (A TCRMP, B VINPS, C CSUN), as published. Site occupancy is the proportion of surveyed sites where the taxon was present; local cover is its mean percent cover at the sites and years where it was present. Labeled arrows, colored by group, are the taxa named in the manuscript; other taxa are shown in gray. Both axes are log scaled.

Download the data and code

The input datasets read in Step 1 of each analysis, and the full analysis code, are available for download here. Each dataset keeps its original file name; the cover and survey files are clipped to their analysis year range.

Analysis code:

Input data:

References

1.
A. Zeileis, Econometric computing with HC and HAC covariance matrix estimators. Journal of Statistical Software 11, 1–17.