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

中文 | Español | English | português | Turkish

library(ecoevoapps)
library(deSolve)
library(tidyverse)
library(patchwork)
library(RColorBrewer)
library(knitr)
library(kableExtra)
knitr::opts_chunk$set(echo=FALSE)
theme_set(ecoevoapps::theme_apps())

Lotka-Volterra eşitliği iki tür arası yiyecek, alan, ve diğer kaynaklar için rekabet dinamiğini özetler. Bu eşitliğin ana fikri basitçe şu şekilde özetlenebilir: bir popülasyon büyüdükçe hem kendi bireyleri (türler içi rekabet), hem de başka bir türün bireyleri ile arasında olan rekabetten (türler arasi rekabet) dolayı limitlenir. Bu modelin daha detaylı açıklamaları ekoloji kitaplarında ve internet sitelerinde yer almaktadır.

Klasik Lotka- Volterra rekabet eşitliğini yazmanın bir sürü yolu vardır. Öncü olarak, burada sunduğumuz iki adet diferansiyel denkleminde görüldüğü üzere, rekabet her iki türün taşıma kapasitesi ($K_1$ and $K_2$) ve türler arası rekabetin relatif kuvveti ($\alpha$ ve $\beta$) ile ifade edilir. "Tür çeşitliliğini sürdüren mekanizmalar" isimli 2000 yılında yayınlanan makalesinde Peter Chesson, Lotka-Volterra eşitliğinin absolut rekabet katsayılarıyla yazılmasını savunmuştur (ikinci sayfada bu aplikasyonu inceleyebilirsiniz).

{.tabset}

Taşıma kapasitesi ve relatif rekabet katsayılarıyla yazılan model

Taşıma kapasitesi Lotka-Volterra rekabeti denklemleri: $$\frac{dN_1}{dt} = r_1N_1\left(1 - \frac{N_1 + \alpha N_2}{K_1}\right)$$ $$\frac{dN_2}{dt} = r_2N_2\left(1 - \frac{N_2 + \beta N_1}{K_2}\right)$$

pars_vars <- c("$r_1$", 
               "$r_2$", 
               "$N_1$", 
               "$N_2$", 
               "$K_1$", 
               "$K_2$", 
               "$\\alpha$", 
               "$\\beta$")
descriptions <- c("Intrinsic growth rate of Species 1",
                 "Intrinsic growth rate of Species 2",
                 "Population size of Species 1",
                 "Population size of Species 2",
                 "Carrying capacity of Species 1",
                 "Carrying capacity of Species 2",
                 "Relative per capita effect of Species 2 on Species 1",
                 "Relative per capita effect of Species 1 on Species 2")
param_df <- data.frame(pars_vars, descriptions)
kable(x = param_df, format = "html", 
      col.names = c("Parametre/Değişkenler", "Tanımlar")) %>%
  kable_styling(full_width = FALSE, 
                bootstrap_options = c("striped", "hover", "condensed"),
                position = "center")

Sabit durum eşegim çizgileri ($N_2$ için çözülür):

$$N_2 = - \frac{N_1}{\alpha} + \frac{K_1}{\alpha}$$ $$N_2 = -\beta N_1 + K_2$$

---

sidebarLayout(
  sidebarPanel(
    # Allow user to select which plots to display
    checkboxGroupInput(inputId = "plots_to_show",
                       label = "Select plots",
                       choices = c("Zero net growth isoclines (ZNGIs)" = "ZNGI")),

    hr(),

    # User-defined parameter values
    sliderInput(inputId = "r1", 
                label = HTML("r<sub>1</sub>: Intrinsic growth rate of Species 1"),
                min = 0.01, max = 1, value = 0.2, step = 0.01),
    sliderInput(inputId = "r2", 
                label = HTML("r<sub>2</sub>: Intrinsic growth rate of Species 2"),
                min = 0.01, max = 1, value = 0.5, step = 0.01),
    numericInput(inputId = "K1", 
                 label = HTML("K<sub>1</sub>: Carrying capacity of Species 1"),
                 min = 1, value = 300),
    numericInput(inputId = "K2", 
                 label = HTML("K<sub>2</sub>: Carrying capacity of Species 2"),
                 min = 1, value = 200),
    sliderInput(inputId = "alpha", 
                label = HTML("&alpha;: Relative effect of Species 2 on Species 1"),
                min = 0.01, max = 2, value = 0.3, step = 0.01),
    sliderInput(inputId = "beta", 
                label = HTML("&beta;: Relative effect of Species 1 on Species 2"),
                min = 0.01, max = 2, value = 0.2, step = 0.01),
    # User-defined initial values
    numericInput(inputId = "N1", 
                 label = "Initial population size of Species 1",
                 min = 1, value = 50),
    numericInput(inputId = "N2", 
                 label = "Initial population size of Species 2",
                 min = 1, value = 70),

    numericInput(inputId = "max_time", 
                 label = "Length of simulation",
                 min = 1, value = 100)
  ),

  # Panel of plots
  mainPanel(
    renderPlot(N_vs_Time(), width = 600, height = 500),
      renderPlot(ZNGI(), width = 600, height = 500))
)

# Get user-defined parameters
init <- reactive({
  c(N1 = input$N1, N2 = input$N2)
})
time <- reactive({
  seq(from = 0, to = input$max_time, by = 0.1)
})
params <- reactive({
  c(r1 = input$r1, r2 = input$r2, K1 = input$K1, K2 = input$K2, 
    a = input$alpha, b = input$beta)
})



# Run lotka_volterra_competition function
lvcomp_out <- reactive({
  run_lvcomp_model(time = time(), init = init(), params = params()) %>% 
    data.frame()
})


N_vs_Time <- reactive({
  plot_lvcomp_time(lvcomp_out())
})

# Plot ZNGIs with population trajectories

ZNGI <- reactive({
  if ("ZNGI" %in% input$plots_to_show) {
    plot_lvcomp_portrait(lvcomp_out(), params = params())
  } 
})

# Make a list of plots to print based on user request
plot_list <- reactive({ 
  list(N_vs_Time(), ZNGI()) %>%
    discard(is.null)
  })

plots_to_print <- reactive({ 
  wrap_plots(plot_list(), ncol = 1)
  })

Absolut rekabet katsayılarıyla yazılan model

Taşıma kapasitesiz Lotka-Volterra rekabeti denklemleri: $$\frac{dN_1}{dt} = r_1N_1\left(1 - \alpha_{11}N_1 - \alpha_{12}N_2\right)$$ $$\frac{dN_2}{dt} = r_2N_2\left(1 - \alpha_{22}N_2 - \alpha_{21}N_1\right)$$

pars_vars_wo_K <- c("$r_1$",
                    "$r_2$",
                    "$N_1$",
                    "$N_2$",
                    "$\\alpha_{11}$",
                    "$\\alpha_{12}$",
                    "$\\alpha_{22}$",
                    "$\\alpha_{21}$")
descriptions_wo_K <- c("Intrinsic growth rate of Species 1",
                       "Intrinsic growth rate of Species 2",
                       "Population size of Species 1",
                       "Population size of Species 2",
                       "Per capita effect of Species 1 on itself",
                       "Per capita effect of Species 2 on Species 1",
                       "Per capita effect of Species 2 on itself",
                       "Per capita effect of Species 1 on Species 2")
param_df_wo_K <- data.frame(pars_vars_wo_K, descriptions_wo_K)
kable(x = param_df_wo_K, format = "html",
      col.names = c("Parametre/Değişkenler", "Tanımlar")) %>%
  kable_styling(full_width = FALSE,
                bootstrap_options = c("striped", "hover", "condensed"),
                position = "center")

Sabit durum eşegim çizgileri ($N_2$ için çözülür):

$$N_2 = -\frac{\alpha_{11}}{\alpha_{12}}N_1 + \frac{1}{\alpha_{12}}$$ $$N_2 = -\frac{\alpha_{21}}{\alpha_{22}}N_1 + \frac{1}{\alpha_{22}}$$

---

sidebarLayout(
  sidebarPanel(
    # Allow users to select which plots to display
    checkboxGroupInput(inputId = "plots_to_show_wo_K",
                       label = "Select plots to display",
                       choices = c("N vs. Time" = "N_vs_Time_wo_K",
                                   "Zero net growth isoclines (ZNGIs)" = "ZNGI_wo_K"),
                       selected = c("N_vs_Time_wo_K")),

    hr(),

    # User-defined parameter values
    sliderInput(inputId = "r1_wo_K",
                label = HTML("r<sub>1</sub>: Intrinsic growth rate of Species 1"),
                min = 0.01, max = 1, value = 0.2, step = 0.01),
    sliderInput(inputId = "r2_wo_K",
                label = HTML("r<sub>2</sub>: Intrinsic growth rate of Species 2"),
                min = 0.01, max = 1, value = 0.5, step = 0.01),

    # Allow user to choose input method for competition coefficients
    radioButtons(inputId = "alpha_input_wo_K",
                 label = "Input method for competition coefficients:",
                 choices = c("Slider" = "slider", "Manual" = "manual"),
                 selected = "slider"),

    # Conditional panel for slider input of competition coefficients
    conditionalPanel(
      condition = "input.alpha_input_wo_K == 'slider'",
      sliderInput(inputId = "alpha11_slider",
                  label = HTML("&alpha;<sub>11</sub>: Per capita effect of Species 1 on itself"),
                  min = 0.0001, max = 0.01, value = 0.0033, step = NULL),
      sliderInput(inputId = "alpha12_slider",
                  label = HTML("&alpha;<sub>12</sub>: Per capita effect of Species 2 on Species 1"),
                  min = 0.0001, max = 0.01, value = 0.001, step = NULL),
      sliderInput(inputId = "alpha22_slider",
                  label = HTML("&alpha;<sub>22</sub>: Per capita effect of Species 2 on itself"),
                  min = 0.0001, max = 0.01, value = 0.005, step = NULL),
      sliderInput(inputId = "alpha21_slider",
                  label = HTML("&alpha;<sub>21</sub>: Per capita effect of Species 1 on Species 2"),
                  min = 0.0001, max = 0.01, value = 0.001, step = NULL)
    ),

    # Conditional panel for manual input of competition coefficients
    conditionalPanel(
      condition = "input.alpha_input_wo_K == 'manual'",
      numericInput(inputId = "alpha11_manual",
                   label = HTML("&alpha;<sub>11</sub>: Per capita effect of Species 1 on itself"),
                   min = 0.0001, max = 1, value = 0.0033, step = 0.0001),
      numericInput(inputId = "alpha12_manual",
                   label = HTML("&alpha;<sub>12</sub>: Per capita effect of Species 2 on Species 1"),
                   min = 0.0001, max = 1, value = 0.001, step = 0.0001),
      numericInput(inputId = "alpha22_manual",
                   label = HTML("&alpha;<sub>22</sub>: Per capita effect of Species 2 on itself"),
                   min = 0.0001, max = 1, value = 0.005, step = 0.0001),
      numericInput(inputId = "alpha21_manual",
                   label = HTML("&alpha;<sub>21</sub>: Per capita effect of Species 1 on Species 2"),
                   min = 0.0001, max = 1, value = 0.001, step = 0.0001)
    ),

    # User-defined initial values
    numericInput(inputId = "N1_wo_K",
                 label = "Initial population size of Species 1",
                 min = 1, value = 50),
    numericInput(inputId = "N2_wo_K",
                 label = "Initial population size of Species 2",
                 min = 1, value = 70),

    numericInput(inputId = "max_time_wo_K",
                 label = "Length of simulation",
                 min = 1, value = 100)
  ),

  # Panel of plots 
  mainPanel(renderPlot(N_vs_Time_wo_K(), width = 600, height = 500),
            renderPlot(ZNGI_wo_K(), width = 600, height = 500))
)

# Store inputted competition coefficients as new reactive objects
alpha11_wo_K <- reactive({
  if (input$alpha_input_wo_K == "slider") {
    input$alpha11_slider
  } else if (input$alpha_input_wo_K == "manual") {
    input$alpha11_manual
  }
})
alpha12_wo_K <- reactive({
  if (input$alpha_input_wo_K == "slider") {
    input$alpha12_slider
  } else if (input$alpha_input_wo_K == "manual") {
    input$alpha12_manual
  }
})
alpha22_wo_K <- reactive({
  if (input$alpha_input_wo_K == "slider") {
    input$alpha22_slider
  } else if (input$alpha_input_wo_K == "manual") {
    input$alpha22_manual
  }
})
alpha21_wo_K <- reactive({
  if (input$alpha_input_wo_K == "slider") {
    input$alpha21_slider
  } else if (input$alpha_input_wo_K == "manual") {
    input$alpha21_manual
  }
})

# Get user-defined parameters
init_wo_K <- reactive({
  c(N1 = input$N1_wo_K, N2 = input$N2_wo_K)
})
time_wo_K <- reactive({
  seq(from = 0, to = input$max_time_wo_K, by = 0.1)
})
params_wo_K <- reactive({
  c(r1 = input$r1_wo_K, r2 = input$r2_wo_K,
    a11 = alpha11_wo_K(), a12 = alpha12_wo_K(),
    a22 = alpha22_wo_K(), a21 = alpha21_wo_K())
})


# Run lotka_volterra_competition_wo_K function
lvcomp_out_wo_K <- reactive({
    run_lvcomp_model(time = time_wo_K(), 
init = init_wo_K(), params = params_wo_K()) %>% 
      data.frame()
})

N_vs_Time_wo_K <- reactive({
  plot_lvcomp_time(lvcomp_out_wo_K())
})
# Convert data to long format

# Plot ZNGIs with population trajectories
ZNGI_wo_K <- reactive({
  if ("ZNGI_wo_K" %in% input$plots_to_show_wo_K) {
    plot_lvcomp_portrait(lvcomp_out_wo_K(), params = params_wo_K())
  } 
})

# Make a list of plots to print based on user request
plot_list_wo_K <- reactive({
  list(N_vs_Time_wo_K(), ZNGI_wo_K()) %>%
    discard(is.null)
})

plots_to_print_wo_K <- reactive({
  wrap_plots(plot_list_wo_K(), ncol = 1)
})

Referanslar

• Dr. Sarah Otto’nun Lotka-Volterra rekabeti üzerine ders notları.

• Vandermeer and Goldberg, 2013. Population Ecology., Bolum 8. (Bu kitabın dijital kopyasına kütüphaneniz üzerinden ulaşabilirsiniz).

• Rosenzweig and MacArthur, 1963. Graphical Representation and Stability Conditions of Predator-Prey Interactions. The American Naturalist. Not: bu makale türler arası rekabetten ziyade avcı ve av modellerine odaklanır fakat sabit durum eşegim çizgileri üzerine açıklamalar içerir.

---

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

gauravsk/ecoevoapps-mirror documentation built on April 5, 2025, 1:59 a.m.