In gauravsk/ecoevoapps: Simulate Dynamics of Ecology/Evolution Models

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knitr::opts_chunk$set(echo = TRUE)
library(tidyr)
library(ggplot2)
library(deSolve)
library(ecoevoapps)
library(patchwork)
library(latex2exp)
theme_set(ecoevoapps::theme_apps())

Ayrık üstel büyüme

$N_{t+1} = \lambda N_t$

sidebarLayout(
  sidebarPanel(
    # User defined lambda -------
    sliderInput("lambda", label = "Population growth rate (lambda):",
                min = 0.01, max = 2, value = 1.2, step = .01),
    # User defined N0 -------
    numericInput("N0", label = "Initial population size (N0)",
                min = 1, max = 100, value = 1),
    # User defined time ---------
    numericInput("time", label = "Number of time steps to project",
                min = 1, max = 1000, value = 30)
    ),

  # Panel of plots -----
  mainPanel(
    renderPlot({plots_to_print()}, width = 450, height = 450)
  )
)

# Generate trajectories for sp 1 --------

exponential_pop_df <- reactive({
  run_discrete_exponential_model(N0 = input$N0, lambda = input$lambda, time = input$time)
})


# Make plot -----------
trajaectory_plot <- reactive({
  plot_discrete_population_growth(exponential_pop_df()) +
    ylab(latex2exp::TeX("Population size at time $t$ ($N_t$)")) +
    labs(caption = latex2exp::TeX(paste0("Parameter values: $\\lambda = $", input$lambda)),
         title = "Population growth with the discrete exponential model")
})

# Make a list of plots  ----
plots_to_print <- reactive({trajaectory_plot()})

Ayrık lojsitik büyüme {.tabset}

Popülasyonun anlık nüfusuna dayalı büyüme gösteren popülasyon modellerini inceleyelim. Aşağıda, popülasyon büyümesinin popülasyon nüfusu yükseldikçe azaldığı popülasyonun dinamiklerini inceleyen temel modelleri sunuyoruz.

Standard ayrık lojistik modeli

Lojistik büyümeyi ayrık büyüme gösteren bir popülasyonda modellemenin yöntemlerinden biri lojistik haritayı kullanmaktır. Bu harita klasik, sürekli lojistik denkleminin ayrık zaman analogudur:

$$N_{t+1} = r_dN_t\left(1-\frac{N_t}{K}\right)$$

Bu formülasyon Robert May’in 1979 yılında yayınlanan klasik makalesi "Simple mathematical models with very complicated dynamics"’nde calışılmıştır. Bu makalede May, modelin kaotik dinamiklere yol açabileceğini göstermiştir.

sidebarLayout(
  sidebarPanel(
    # User defined lambda -------
    sliderInput("rd_dl", label = "Population growth rate (rd):",
                min = 0.01, max = 4.5, value = 1.05, step = .01),
    # User defined N0 -------
    numericInput("N0_dl", label = "Initial population size (N0)",
                min = 1, max = 100, value = 1),
    # User defined carrying capacity (K) ----------    
    numericInput("K_dl", label = "Carrying capacity (K)",
                 min = 1, max = 1000, value = 100),
    # User defined time ---------
    numericInput("time_dl", label = "Number of time steps to project",
                min = 1, max = 1000, value = 30)

    ),

  # Panel of plots -----
  mainPanel(
    renderPlot({plots_to_print_dl()}, width = 450, height = 800)
  )
)

# Get user defined parameters for discrete logistic  ------

params_dl <- reactive({c(rd = input$rd_dl, K = input$K_dl)})
dl_df <- reactive({
  run_discrete_logistic_model(N0 = input$N0_dl,
                                       params = params_dl(),
                                       time = input$time_dl)


})
# Generate trajectories for discrete logistic --------
trajaectory_plot_dl <- reactive({
  plot_discrete_population_growth(dl_df()) +
    labs(title = "Population growth with the discrete logistic model")
})

# cobweb for standard discrete logistic model -----
cobweb_dl <- reactive({
  plot_discrete_population_cobweb(dl_df(),
                                  params_vec = params_dl(),
                                  model_type = "discrete_logistic")
})

# Make plot caption ----
plot_caption_dl <- reactive({
    latex2exp::TeX(paste0("Parameter values: $r_d = $", input$rd_dl, "; K = ", input$K_dl))
})
# Make a list of plots  ----
plots_to_print_dl <- reactive({{trajaectory_plot_dl()/cobweb_dl()} + 
    labs(caption = plot_caption_dl())})

Ricker modeli

Ayrık büyüme gösteren, taşıma kapasitesine sahip bir popülasyonu modellemenin bir başka yolu da Ricker modelidir. Orjinal olarak 1954 yılında yayınlanan makalede tanımlanan bu model balık çiftliklerinin popülasyon dinamikleri icin yazılmıştır.

$$N_{t+1} = N_t e^{(r (1 - N_t/K))}$$

sidebarLayout(
  sidebarPanel(
    # User defined lambda -------
    sliderInput("r_ricker", label = "Population growth rate (r):",
                min = 0.01, max = 3, value = 1.01, step = .01),
    # User defined N0 -------
    numericInput("N0_ricker", label = "Initial population size (N0)",
                min = 1, max = 100, value = 1),
    # User defined carrying capacity (K) ----------    
    numericInput("K_ricker", label = "Carrying capacity (K)",
                 min = 1, max = 1000, value = 100),
    # User defined time ---------
    numericInput("time_ricker", label = "Number of time steps to project",
                min = 1, max = 1000, value = 30, step = 5)

    ),

  # Panel of plots -----
  mainPanel(
    renderPlot({plots_to_print_ricker()}, width = 450, height = 800)
  )
)
params_ricker <- reactive({c(rd = input$r_ricker, K = input$K_ricker)})

ricker_df <- reactive({
  run_ricker_model(N0 = input$N0_ricker,
                                 params = params_ricker(),
                                 time = input$time_ricker)
})
# Generate trajectories for discrete logistic --------
trajaectory_plot_ricker <- reactive({
  plot_discrete_population_growth(ricker_df()) +
    labs(title = "Population growth with the Ricker model")
})

# cobweb plot for ricker model -----
cobweb_ricker <- reactive({
    plot_discrete_population_cobweb(ricker_df(),
                                  params_vec = params_ricker(),
                                  model_type = "ricker")
})

# Make plot caption ----
plot_caption_ricker <- reactive({
    latex2exp::TeX(paste0("Parameter values: $r = $", input$r_ricker, "; K = ", input$K_ricker))
})

# Make a list of plots  ----

plots_to_print_ricker <- reactive({{
  trajaectory_plot_ricker()/cobweb_ricker()} + 
    labs(caption = plot_caption_ricker())})

Beverton-Holt modeli

Üçüncü bir ayrık popülasyon büyüme model ise yine balıkçılık yönetimi icin yazılan Beverton-Holt modelidir:

$$N_{t+1} = \frac{RN_t}{1+\left(\frac{R-1}{K}\right)N_t}$$

sidebarLayout(
  sidebarPanel(
    # User defined lambda -------
    sliderInput("r_bh", label = "Population growth rate (R):",
                min = 0.01, max = 3, value = 1.25, step = .01),
    # User defined N0 -------
    numericInput("N0_bh", label = "Initial population size (N0)",
                min = 1, max = 100, value = 1),
    # User defined carrying capacity (K) ----------    
    numericInput("K_bh", label = "Carrying capacity (K)",
                 min = 1, max = 1000, value = 100),
    # User defined time ---------
    numericInput("time_bh", label = "Number of time steps to project",
                min = 1, max = 1000, value = 30, step = 5)

    ),

  # Panel of plots -----
  mainPanel(
    renderPlot({plots_to_print_bh()}, width = 450, height = 800)
  )
)
# Get user defined parameters for discrete logistic  ------
params_bh <- reactive({c(rd = input$r_bh, K = input$K_bh)})
bh_df <- reactive({
  run_beverton_holt_model(N0 = input$N0_bh, 
                          params = params_bh(),
                          time = input$time_bh)
})
# Generate trajectories for beverton-holt model --------
trajaectory_plot_bh <- reactive({
  plot_discrete_population_growth(bh_df()) +
    labs(title = "Population growth with the Beverton-Holt model")
})

# Generate cobweb for beverton-holt model --------
cobweb_bh <- reactive({
  plot_discrete_population_cobweb(bh_df(),
                                  params_vec = c(rd = input$r_bh, K = input$K_bh),
                                  model_type = "beverton_holt") 
})

# Make plot caption ----
plot_caption_bh <- reactive({
    latex2exp::TeX(paste0("Parameter values: $r = $", input$r_bh, "; K = ", input$K_bh))
})

# Make a list of plots  ----

plots_to_print_bh <- reactive({{trajaectory_plot_bh()/cobweb_bh()} + 
    labs(caption = plot_caption_bh())})

Referanslar

"Simple mathematical models with very complicated dynamics", Robert May, 1976.

"Stock and Recruitment", Bill Ricker, 1954.

UGA tarafından yayınlanan popülasyon ekolojisi dersi.

Dr. Sebastian Bonhoeffer'in Ekoloji ve Evrim Biyolojisi ders notları (bkz. Bölüm 1)

Dr. Jan Engelstädter'in biyolojik veri analizi üzerine e-kitabı.

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suppressWarnings(ecoevoapps::print_app_footer(language = "tr"))

gauravsk/ecoevoapps documentation built on July 9, 2024, 9:37 p.m.