141 lines
4.8 KiB
R
141 lines
4.8 KiB
R
####################
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# Global Constants #
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####################
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# age at which birds in captivity begin breeding (become adults)
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captive_begin_breeding <- 7
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# age at which birds in the wild begin breeding (become adults)
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wild_begin_breeding <- 8
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# if the captive population exceeds this amount, then the entire year one
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# population will be released
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max_in_captivity <- 150
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# carrying capacity in the wild
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wild_carrying_capacity <- 400
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# percentage of children which will make it to year 1 in captivity,
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# per mating pair
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captive_productivity_rate <- 0.9
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# percentage of children which will make it to year 1 in captivity,
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# per mating pair (with double clutching)
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captive_productivity_rate_dc <- 1.8
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# percentage of children which will make it to year 1, per mating pair
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wild_productivity_rate <- 0.3729
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################################
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# Global Simulation Parameters #
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################################
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# number of years to simulate
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simulation_years <- 50
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######################
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# Derived Parameters #
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######################
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# rate at which captive immature birds will become adults
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# an approximation which assumes an equal distribution of immature bird ages
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captive_immature_to_adult_rate <- 1 / (captive_begin_breeding - 2)
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# rate at which wild immature birds will become adults
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# an approximation which assumes an equal distribution of immature bird ages
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wild_immature_to_adult_rate <- 1 / (wild_begin_breeding - 2)
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# Simulates the Condor population over time using the given parameters.
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# * `rd1` - death rate of year one birds
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# * `rdI` - death rate of immature birds
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# * `rdA` - death rate of adult birds
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simulate_condor_population <- function(rd1, rdI, rdA) {
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# captive population groups
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c_Y0 <- c(30)
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c_Y1 <- c(30)
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c_I <- c(30)
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c_A <- c(30)
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# wild population groups
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w_Y0 <- c(100)
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w_Y1 <- c(100)
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w_I <- c(100)
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w_A <- c(100)
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years <- seq(1, simulation_years)
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for (t in 2:simulation_years) {
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# model captive population changes (year 1, immature, and adult)
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c_Y1[t] <- c_Y0[t - 1] - # last year's population
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rd1 * c_Y0[t - 1] # outflow to deaths
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c_I[t] <- c_I[t - 1] - # last year's population
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rdI * c_I[t - 1] - # outflow to deaths
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captive_immature_to_adult_rate * c_I[t - 1] + # outflow to adult
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c_Y1[t - 1] # inflow from year 1
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c_A[t] <- c_A[t - 1] - # last year's population
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rdA * c_A[t - 1] + # outflow to deaths
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captive_immature_to_adult_rate * c_I[t - 1] # inflow from immature
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# model new births in captive population
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c_Y0[t] <- captive_productivity_rate * (c_A[t] / 2)
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# sum of all population groups
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last_captive_population <- c_Y0[t - 1] + c_Y1[t - 1] + c_I[t - 1] + c_A[t - 1]
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released_to_wild <- if (last_captive_population > max_in_captivity) {
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c_Y1[t]
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} else {
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0.8 * c_Y1[t]
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}
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# subtract the released birds from the captive year one population
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c_Y1[t] <- c_Y1[t] - released_to_wild
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# carrying capacity death rate
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last_wild_population <- w_Y0[t - 1] + w_Y1[t - 1] + c_I[t - 1] + c_A[t - 1]
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approx_wild_growth_rate <- (wild_productivity_rate * (w_A[t - 1] / 2) + released_to_wild) / last_wild_population
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rd_carrying <- approx_wild_growth_rate * (last_wild_population / wild_carrying_capacity) # r * P / M
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w_Y1[t] <- (w_Y0[t - 1] + # inflow from year zero
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released_to_wild) * # inflow from captive
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(1 - rd1) * # outflow to deaths (death rate)
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(1 - rd_carrying) # outflow to deaths (carrying capacity)
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w_I[t] <- w_I[t - 1] + # last year's population
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w_Y1[t - 1] - # inflow from year one
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w_I[t - 1] * wild_immature_to_adult_rate - # outflow to adult
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w_I[t - 1] * rdI - # outflow to deaths (death rate)
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w_I[t - 1] * rd_carrying # outflow to deaths (carrying capacity)
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w_A[t] <- w_A[t - 1] + # last year's population
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w_I[t - 1] * wild_immature_to_adult_rate - # inflow from immature
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w_A[t - 1] * rdA - # outflow to deaths (death rate)
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w_A[t - 1] * rd_carrying # outflow to deaths (carrying capacity)
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w_Y0[t] <- wild_productivity_rate * (w_A[t] / 2) *
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(1 - rd_carrying) # deaths due to carrying capacity
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}
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captive_population <- c_Y0 + c_Y1 + c_I + c_A
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plot(
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years,
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c_Y0,
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ylim = c(0, 150),
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col = "red",
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main = "Condor Population in Captivity",
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xlab = "Time (years)",
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ylab = "Population"
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)
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points(years, c_Y1, col = "orange")
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points(years, c_I, col = "darkgreen")
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points(years, c_A, col = "blue")
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points(years, captive_population)
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wild_population <- w_Y0 + w_Y1 + w_I + w_A
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plot(
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years,
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w_Y0,
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ylim = c(0, wild_carrying_capacity + 100),
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col = "red",
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main = "Condor Population in the Wild",
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xlab = "Time (years)",
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ylab = "Population"
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)
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points(years, w_Y1, col = "orange")
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points(years, w_I, col = "darkgreen")
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points(years, w_A, col = "blue")
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points(years, wild_population)
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}
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