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

中文 | Español | English | português | Turkish

knitr::opts_chunk$set(echo = FALSE)
library(ecoevoapps)
library(tidyverse)
library(patchwork)
library(knitr)
library(kableExtra)

在互利关系(mutualism)中，两个互相影响的物种对彼此都有益。互利可以有多种形式，包括（但不限于）植物和传粉者之间的互动、动物帮助植物传播种子或防御天敌。比如，榕小蜂帮榕树传粉，同时也食用榕果并在其中产卵(Cook & Rasplus 2003)。另一个例子是蚂蚁和金合欢之间的互利关系：金合欢为蚂蚁提供食宿，而蚂蚁帮助金合欢抵御食草动物(Janzen 1966)。Bronstein (2015)一书详细概述了各种互利共生关系。

此app模拟了两个物种之间的直接互利关系(Holland 2012)。该模型的核心在于，每个物种的种群增长率($dN/dt$)同时受到同种个体和其互利物种个体的影响 -- 这有些类似于经典的Lotka-Volterra 竞争模型。当每个物种单独存在时，它们只受到种间竞争，并因此种群只能增长至其环境承载力。但当两个物种作用于彼此时，它们给彼此带来有利影响，因此可以使彼此的种群规模超过其环境承载力。这个模型假设了互利关系带来的边际收益是递减的，即互利收益会随种群增长而趋于饱和。

综上，模型可写为：

$$\frac{dN_1}{dt} = r_1N_1 + \frac{\alpha_{12}N_2}{b_2 + N_2}N_1 - d_1N_1^2$$ $$\frac{dN_2}{dt} = r_2N_2 + \frac{\alpha_{21}N_1}{b_1 + N_1}N_2 - d_2N_2^2$$

模型参数的描述可见下文表格。动态方程的第一项($r_iN_i$) 描述了种群在无任何种间竞争或互利关系下的增长。第二项($\frac{\alpha_{ij}N_j}{b_j + N_j}N_i$) 描述了各种群随其互利物种的增长而增长的饱和函数(呈Michaelis–Menten 曲线，其中半饱和常数为$b_i$)。最后一项表示种群增长率随其规模增长而减缓。

pars <- c("$r_1$",
          "$r_2$",
          "$N_1$",
          "$N_2$",
          "$\\alpha_{12}$",
          "$\\alpha_{21}$",
          "$d_1$",
          "$d_2$",
          "$b_i$")
descriptions <- c("物种1的人均增长率",
                  "物种2的人均增长率",
                  "物种1的种群规模",
                  "物种2的种群规模",
                  "物种2对于物种1的人均有利影响",
                  "物种1对于物种2的人均有利影响",
                  "物种1的自限性",
                  "物种2的自限性",
                  "Michelis-Menten方程的半饱和常数，即种群$i$对$j$的有利影响为最大值一半时，种群$i$的规模")
param_df <- data.frame(pars, descriptions)
kable(x = param_df, format = "html",
      col.names = c("参数/变量", "描述")) %>%
  kable_styling(full_width = FALSE,
                bootstrap_options = c("striped", "hover", "condensed"),
                position = "center")

这个模型可以模拟种群轨迹随时间的变化（选择“种群规模vs.时间”），该选项可帮助我们探索种群如何在互利影响下如何增长。我们也可以通过零增长等斜线 (zero net growth isocline)来研究互利关系对于种群的长期影响。零增长等斜线表述了在什么条件下各种群会零增长($dN_1/dt = dN_2/dt = 0$) ，以及两个种群会在什么规模下平衡（选择“相图”）。

##### UI #####

# Input panel
wellPanel(
  fluidRow(
    column(4, numericInput(inputId = "r1",
                           label = HTML("r<sub>1</sub>: 物种1的人均增长率"),
                           value = 0.5,
                           step = 0.1)),
    column(4, numericInput(inputId = "r2",
                           label = HTML("r<sub>2</sub>: 物种2的人均增长率"),
                           value = 0.5,
                           step = 0.1)),
    column(4, numericInput(inputId = "N1",
                           label = "物种1的起始种群规模",
                           value = 20,
                           min = 0,
                           step = 1))),
  fluidRow(
    column(4, numericInput(inputId = "a12",
                           label = HTML("&alpha;<sub>12</sub>: 物种2对1的影响"),
                           value = 0.8,
                           min = 0,
                           step = 0.1)),
    column(4, numericInput(inputId = "a21",
                           label = HTML("&alpha;<sub>21</sub>: 物种1对2的影响"),
                           value = 0.4,
                           min = 0,
                           step = 0.1)),
    column(4, numericInput(inputId = "N2",
                           label = "物种2的起始种群规模",
                           value = 40,
                           min = 0,
                           step = 1))),
  fluidRow(
    column(4, numericInput(inputId = "d1",
                           label = HTML("d<sub>1</sub>: 物种1的自限性"),
                           value = 0.02,
                           min = 0,
                           step = 0.01)),
    column(4, numericInput(inputId = "d2",
                           label = HTML("d<sub>2</sub>: 物种2的自限性"),
                           value = 0.01,
                           min = 0,
                           step = 0.01)),
    column(4, numericInput(inputId = "time",
                           label = "模拟时长",
                           value = 50,
                           min = 1,
                           step = 1))),
  fluidRow(
    column(4, numericInput(inputId = "b1",
                           label = HTML("b<sub>1</sub>: 物种1的半饱和常数"),
                           value = 10,
                           min = 0,
                           step = 1)),
    column(4, numericInput(inputId = "b2",
                           label = HTML("b<sub>2</sub>: 物种2的半饱和常数"),
                           value = 10,
                           min = 0,
                           step = 1)),
    column(2, radioButtons(inputId = "plot",
                           label = "图表",
                           choices = c("种群规模vs.时间" = "time",
                                       "相图（Phase portrait）" = "phase",
                                       "全选" = "both"),
                           selected = "both")),
    column(2, conditionalPanel(
      condition = "input.plot != 'time'",
      checkboxGroupInput(inputId = "phase_opt",
                         label = "包括",
                         choices = c("向量场" = "vec",
                                     "种群轨迹" = "traj"),
                         selected = c("vec", "traj")))))
)

# Output panel
fluidRow(
  column(12, renderPlot(plot(), height = 500))
)

##### Server #####

# Validate input
observeEvent(input$a12, {
  if (input$a12 <= 0) updateNumericInput(inputId = "a12", value = 0.1)
})
observeEvent(input$a21, {
  if (input$a21 <= 0) updateNumericInput(inputId = "a21", value = 0.1)
})
observeEvent(input$d1, {
  if (input$d1 <= 0) updateNumericInput(inputId = "d1", value = 0.01)
})
observeEvent(input$d2, {
  if (input$d2 <= 0) updateNumericInput(inputId = "d2", value = 0.01)
})
observeEvent(input$b1, {
  if (input$b1 <= 0) updateNumericInput(inputId = "b1", value = 1)
})
observeEvent(input$b2, {
  if (input$b2 <= 0) updateNumericInput(inputId = "b2", value = 1)
})
observeEvent(input$N1, {
  if (input$N1 <= 0) updateNumericInput(inputId = "N1", value = 1)
})
observeEvent(input$N2, {
  if (input$N2 <= 0) updateNumericInput(inputId = "N2", value = 1)
})
observeEvent(input$time, {
  if (input$time < 1) updateNumericInput(inputId = "time", value = 1)
})

# Retrieve user inputs
params <- reactive({c(r1 = input$r1,
                      r2 = input$r2,
                      a12 = input$a12,
                      a21 = input$a21,
                      d1 = input$d1,
                      d2 = input$d2,
                      b1 = input$b1,
                      b2 = input$b2)})
init <- reactive({c(N1 = input$N1, N2 = input$N2)})
time <- reactive({input$time})
vec <- reactive({"vec" %in% input$phase_opt})
traj <- reactive({"traj" %in% input$phase_opt})

# Run mutualism model
sim <- reactive({run_mutualism(time(), init(), params())})

# Plot population trajectories over time
plot <- reactive({
  if (input$plot == "time") {
    plot_mutualism_time(sim()) +
      ggplot2::theme(aspect.ratio = 1)
  } else if (input$plot == "phase") {
    plot_mutualism_portrait(sim(), vec(), traj()) +
      ggplot2::theme(aspect.ratio = 1)
  } else {
    wrap_plots(plot_mutualism_time(sim()),
                          plot_mutualism_portrait(sim(), vec(), traj()),
                          nrow = 1) +
      ggplot2::theme(aspect.ratio = 1)
  }
})

参考文献

• Bronstein, J.L. (2015). Mutualism. Oxford University Press, Oxford, UK.
• Cook, J.M. & Rasplus, J.-Y. (2003). Mutualists with attitude: coevolving fig wasps and figs. Trends in Ecology and Evolution, 18, 241-248.
• Holland, N.J. (2012). Population dynamics of mutualism. Nature Education Knowledge, 3, 2.
• Janzen, D.H. (1966). Coevolution between ants and acacias in Central America. Evolution, 20, 249-275.

---

# Print footer
suppressWarnings(print_app_footer())

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