Exposure through time

Fit one climatic reference

The analysis uses the six Bio-ORACLE variables and the continuous anchovy SDM suitability layer prepared in the Mediterranean example. The current realised climatic niche is fitted once. Its centre, climatic weighting matrix and empirical radial boundary are then held fixed across all four projections.

projection_years <- c(2030, 2050, 2070, 2090)

future_series <- list(
  ssp245_2030 = climate_2030,
  ssp245_2050 = climate_2050,
  ssp245_2070 = climate_2070,
  ssp245_2090 = climate_2090
)

# Project each period into the same fitted climatic niche.
series <- fit_climniche_series(
  current = current_climate,
  future = future_series,
  time = projection_years,
  scenario = "SSP2-4.5",
  occupied = anchovy_suitability,
  occupied_threshold = sdm_threshold,
  domain = mediterranean_sea_mask,
  sensitivity = predictor_sensitivity
)

The order of the future list must match time. Current and future rasters use the same variables, names, resolution and cell alignment.

Range-level exposure

The temporal summaries are derived from Niche Boundary Exceedance; they are not additional cell-level exposure metrics. Let \(E_{it}\) denote Niche Boundary Exceedance for cell \(i\) at time \(t\), \(B\) the fitted radial boundary distance and \(w_i\) the product of current SDM suitability and cell area. With boundary_exceedance_tolerance = 0,

\[ F_t = \frac{\sum_i w_i I(E_{it} > 0)} {\sum_i w_i} \]

is the Weighted Niche Boundary Exceedance Fraction,

\[ S_t = \frac{\sum_i w_i (E_{it}/B) I(E_{it} > 0)} {\sum_i w_i I(E_{it} > 0)} \]

is Conditional Relative Niche Boundary Exceedance, and

\[ M_t = \frac{\sum_i w_i (E_{it}/B) I(E_{it} > 0)} {\sum_i w_i} = F_t S_t \]

is Range Mean Relative Niche Boundary Exceedance. Here, \(I(\cdot)\) is the indicator function.

range_summary <- climniche_range_summary(
  series,
  scope = "current",
  area_weight = TRUE
)

subset(
  range_summary,
  select = c(
    time,
    exposed_fraction,
    conditional_relative_exceedance,
    range_wide_relative_exceedance
  )
)

extent_plot <- plot_climniche_time(
  series,
  metric = "exposed_fraction",
  scope = "current",
  area_weight = TRUE,
  show_models = FALSE
)

conditional_plot <- plot_climniche_time(
  series,
  metric = "conditional_relative_exceedance",
  scope = "current",
  area_weight = TRUE,
  show_models = FALSE
)

range_plot <- plot_climniche_time(
  series,
  metric = "range_wide_relative_exceedance",
  scope = "current",
  area_weight = TRUE,
  show_models = FALSE
)

patchwork::wrap_plots(
  extent_plot,
  conditional_plot,
  range_plot,
  nrow = 1
)

The suitability- and area-weighted fraction beyond the boundary increases from 7.7% in 2030 to 78.9% in 2090. Conditional Relative Niche Boundary Exceedance falls from 27.6% to 12.5% over the same period. This combination is consistent with the addition of cells with relatively small exceedance. Range Mean Relative Niche Boundary Exceedance rises from 2.1% to 9.9%.

Persistent Niche Boundary Exceedance

Here, persistence requires positive Niche Boundary Exceedance in at least two consecutive projections. The onset is the first sampled year in a qualifying run; it is not an interpolated date of boundary crossing.

departure <- climniche_departure(
  series,
  scope = "current",
  persistence = 2
)

rate <- climniche_change_rate(
  series,
  metric = "range_wide_relative_exceedance",
  scope = "current",
  area_weight = TRUE
)

onset_map <- plot_climniche_departure_map(
  series,
  metric = "first_persistent_departure",
  scope = "current",
  persistence = 2,
  scenario = "SSP2-4.5",
  study_region = mediterranean_boundary,
  degree_labels = "hemisphere"
)

time_weighted_map <- plot_climniche_departure_map(
  series,
  metric = "departure_time_fraction",
  scope = "current",
  persistence = 2,
  scenario = "SSP2-4.5",
  study_region = mediterranean_boundary,
  degree_labels = "hemisphere"
)

patchwork::wrap_plots(onset_map, time_weighted_map, nrow = 1)

Cells with persistent Niche Boundary Exceedance in at least two consecutive sampled projections account for 28.4% of the current reference after weighting by suitability and cell area. Median onset is 2070. The earliest persistent exceedance occurs mainly in the Aegean, while later onset extends through parts of the western and south-central Mediterranean. No sampled return below the boundary follows a persistent exceedance run in this four-period series.

The largest increase in Range Mean Relative Niche Boundary Exceedance occurs between 2070 and 2090:

Report

climniche_series_report() collects the fixed niche reference, projections, range summaries, temporal Niche Boundary Exceedance summaries and interval changes.

series_report <- climniche_series_report(
  series,
  species = "European anchovy",
  scope = "current",
  area_weight = TRUE,
  persistence = 2
)

series_report
write_climniche_series_report(
  series_report,
  "anchovy-exposure-through-time.md"
)