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

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knitr::opts_chunk$set(echo = TRUE)

library(ggplot2)
library(tidyr)
library(purrr)
library(dplyr)
library(deSolve)
library(ecoevoapps)
library(patchwork)
library(RColorBrewer)
library(kableExtra)

biotic_competition <- function(time, init, params) {
  with (as.list(c(time, init, params)), {
    # description of parameters:
    # r = per capita growth rate (prey)
    # q = 1/prey carrying capacity
    # a = attack rate
    # T_h = handling time
    # e = conversion efficiency
    # d = predator death rate

    dH_dt = r*H*(1 - q*H) - (a1*H*P1)/(1 + a1*T_h1*H) - (a2*H*P2)/(1 + a2*T_h2*H)
    dP1_dt = e1*(a1*H*P1)/(1 + a1*T_h1*H) - d1*P1
    dP2_dt = e2*(a2*H*P2)/(1 + a2*T_h2*H) - d2*P2
    return(list(c(dH = dH_dt, dP1 = dP1_dt, dP2 = dP2_dt)))

  })
}

run_biotic_competition_model <- function(time, init, params) {
  deSolve::ode(func = biotic_competition,
                y = init, times = time, parms = params)
}

Bu aplikasyon büyümek için aynı biyotik kaynağa, ya da tüketilen türe (ava, $H$) ihtiyaç duyan iki tüketici türün ($P_1$ and $P_2$) dinamiğini gösterir. Dolayısıyla, iki tüketici türün rekabeti halinde, $P_1$'in artışı, $P_2$'nin büyüme oranını, $P_1$'in kaynakları tüketmesiyle azaltır.

Bu basit varsayımlarla bile bahsedilen dinamik çok farklı şekilde modellenebilir (mesela, her iki tüketicinin yokluğunda tüketilen türün, H’nin, S veya J tipi popülasyon büyümesini değerlendirebiliriz).

The models can also consider different relationships between the density of resources and rate at which they are attacked by consumers. This relationship is called the functional response, and we consider two types of relationships. First, we consider a "Type 1 functional response", in which the rate at which consumers consume resources is a linear function of the resource density. The second relationship is the "Type II functional response", in which the amount of resources consumed is a saturating function of resource density. The idea of the Type II functional response was developed by C.S. Holling in the 1959 paper "Some characteristics of simple types of predation and parasitism".

Aşağıdaki denklem sistemi bu modelin karmaşık versiyonudur:

[ \begin{align} \frac{dH}{dt} &= rH \bigl(1-qH\bigr) - \frac{a_1HP_1}{1+a_1T_{h1}H} - \frac{a_2HP_2}{1+a_2T_{h2}H} \ \ \frac{dP_1}{dt} &= e_{1} \frac{a_1HP_1}{1+a_1T_{h1}H} - d_1P_1 \ \ \frac{dP2}{dt} &= e_2 \frac{a_2HP_2}{1+a_2T_{h2}H} - d_2P_2 \end{align} ]

pars_vars <- c("$H$", 
               "$P_i$", 
               "$r$", 
               "$q$", 
               "$a_i$", 
               "$T_{h_i}$", 
               "$e_i$", 
               "$d_i$")
descriptions <- c("Population size of the prey",
                 "Population size of predator $i$",
                 "Per capita growth rate of prey",
                 "Per capita prey self-limitation",
                 "Attack rate of predator $i$",
                 "Handling time of predator $i$",
                 "Conversion efficiency of predator $i$",
                 "Death rate of predator $i$")
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")

• $q =0$ olduğu takdirde, gıda üstel büyüme gösterir. Eger $q>0$, gıda $K = \frac{1}{q}$ taşıma kapasitesiyle lojistik büyüme gösterir.
• Eğer $T_{h_{i}} = 0$ ise, tüketici $i$ tip 1 fonksiyonel büyüme gösterir.

wellPanel(
  fluidRow(
    column(4, 
           ### Ask users for parameter values ----
           ## start with Prey params
           numericInput("H", label = "Initial population size of Prey", min = 1, value = 30),
           sliderInput("r", label = "Per capita growth rate of Prey (r)", min = .0001, max = 1.0, value = .2),
           sliderInput("q", label = "Prey self-limitation rate (q)", min = 0, max = 0.10, step = 0.0001, value = .0066),
           br(),
           hr(),
           numericInput("t", label = "Timesteps", min = 1, value = 1000),
           checkboxGroupInput("fxnrep", 
                              label = "Display plot of functional responses?",
                              choices = c("Yes" = "Yes"),
                              selected = NULL)

    ),

    column(4,
           ## now pred1 params + initial conditions
           numericInput("P1", label = "Initial population size of Predator 1", min = 1, value = 25),
           sliderInput("a1", label = "Predator 1 attack rate (a1)", min = .001, max = 1.0, value = .02),
           sliderInput("T_h1", label = "Predator 1 handling time (Th_1)", min = 0, max = 1.0, value = 0.1),
           sliderInput("e1", label = "Predator 1 conversion efficiency (e1)", min = .001, max = 1.0, value = 0.4),
           sliderInput("d1", label = "Per capita death rate of Predator 1 (d1)", min = .0001, max = 1.0, value = .1)
    ),

    column(4,
           ## now pred2 params + initial conditions
           numericInput("P2", label = "Initial population size of Predator 2", min = 1, value = 25),
           sliderInput("a2", label = "Predator 2 attack rate (a2)", min = .001, max = 1.0, value = .02),
           sliderInput("T_h2", label = "Predator 2 handling time (Th_2)", min = 0, max = 1.0, value = 0.1),
           sliderInput("e2", label = "Predator 2 conversion efficiency (e2)", min = .001, max = 1.0, value = 0.39),
           sliderInput("d2", label = "Per capita death rate of Predator 2 (d2)", min = .0001, max = 1.0, value = .1)
    )
  ))


fluidRow(
  column(12,
         renderPlot(plots_to_print())
  ))


# Set the initial population sizes

init <- reactive({c(H = input$H , P1 = input$P1, P2 = input$P2)})

# Set the parameter values

# description of parameters:
# r = per capita growth rate (prey)
# a = attack rate 
# T_h = handling time
# e = conversion efficiency
# d = predator death rate 

params <- reactive({c(r = input$r, q = input$q,
                      a1 = input$a1, T_h1 = input$T_h1, 
                      e1 = input$e1, d1 = input$d1, 
                      a2 = input$a2, T_h2 = input$T_h2, 
                      e2 = input$e2, d2 = input$d2)})

# Time over which to simulate model dynamics
time <- reactive({seq(0,input$t, by = .1)})

# Simulate the dynamics
out <- reactive({ run_biotic_comp_model(time = time(), 
                                        init = init(), 
                                        params = params())
})

# Make a plot of abundance over time
abund_plot <- reactive({
  plot_biotic_comp_time(out())
})

## functional responses of the two consumers
plot_fxnreps <- reactive({
    wrap_plots(plot_functional_responses(params()), ncol = 1)
})

# Make a list of plots and print out plots based on which ones were requested ----
plots_to_print <- reactive({
  if("Yes" %in% input$fxnrep){
    wrap_plots(abund_plot(), plot_fxnreps(), design = "AAB")
  } else {
    wrap_plots(abund_plot(), ncol = 1)
  }

})

Referanslar

• Armstrong and McGeehee, 1976. Coexistence of species competing for shared resources. Theoretical Population Biology.
• Armstrong and McGeehee, 1980. Competitive Exclusion. The American Naturalist.
• Chesson, 1990. MacArthur’s consumer–resource model Theoretical Population Biology.
• Chesson and Kuang, 2008. The interaction between predation and competition. Nature.

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

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