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

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# Set default parameters for R chunks in Rmd
knitr::opts_chunk$set(echo = FALSE, warning = FALSE)

# Load the ecoevoapps package
library(ecoevoapps)
library(ggplot2)

一些种群适合表示为一系列处于不同年龄级、或不同大小等级的个体(Tenhumberg, 2010)。这类结构式种群的增长率取决于一个等级向另一个等级过渡的速率。例如，幼体期至成体期的存活率可能不同于成体期至更大龄级的存活率。我们可以用一个年龄（或阶段）等级至下一个等级的存活率，以及各年龄（或阶段）通过繁殖对于种群增长的贡献，来模拟此类种群的动态。

通过调整这些存活率的数值，我们可以得知哪些年龄（或阶段）间的过渡对于整个种群的增长最为重要（灵敏度分析）。

Leslie（莱斯利）矩阵

Leslie矩阵 是系统整理龄组过渡率（生存和繁殖）的一个有效方法。Leslie 矩阵是一个NxN的矩阵，其中N是种群周期中年龄等级的数量。我们可以从矩阵的元素得知各列龄级中的个体如何过渡至各行代表的龄级。例如，矩阵第一行第二列的元素表示了龄级2向龄级1的过渡。

除了可以方便地整理存活率和繁殖率信息，此矩阵还有三个重要属性：

1. 如要模拟种群在下一个时间点（时间$t+1$）的状态，只要将Leslie矩阵乘以一个代表初始种群规模（在时间$t$）的矩阵。

2. Leslie矩阵的最大特征值$\lambda$是整个种群的渐近增长率。当$\lambda < 1$，种群衰退直至灭绝；当$\lambda > 1$，种群呈指数型增长；当$\lambda = 1$, 种群大小不随时间变化。

3. 矩阵最大特征值所对应的特征向量代表了种群的稳定结构，即种群达到平衡后各年龄级的比例。

使用下文的app来探索结构式种群的属性：

### APP
fluidPage(
  ## INPUT
  sidebarPanel(

    # Initial sizes
    numericInput(inputId = "N1",
                  label = "龄级1的初始个体数量",
                  min = 0,
                  max = NA,
                  value = 100),
    numericInput(inputId = "N2",
                   label = "龄级2的初始个体数量",
                   min = 0,
                   max = NA,
                   value = 100),
    numericInput(inputId = "N3",
                   label = "龄级3的初始个体数量",
                   min = 0,
                   max = NA,
                   value = 100),

    # Leslie matrix
    numericInput(inputId = "F1",
                  label = "龄级1的繁殖率",
                  min = 0,
                  max = NA,
                  value = 0),
    numericInput(inputId = "F2",
                  label = "龄级2的繁殖率",
                  min = 0,
                  max = NA,
                  value = 8),          
    numericInput(inputId = "F3",
                  label = "龄级3的繁殖率",
                  min = 0,
                  max = NA,
                  value = 1),
    sliderInput(inputId = "S12",
                  label = "龄级1至龄级2的存活率(%)",
                  min = 1,
                  max = 100,
                  value = 40),
    sliderInput(inputId = "S23",
                  label = "龄级2至龄级3的存活率 (%)",
                  min = 0,
                  max = 100,
                  value = 80),
    width=4),

  ## OUTPUT
  mainPanel(
  tabsetPanel(type = "pills",
              tabPanel("种群示意图和Leslie矩阵",
                       renderPlot({ diagr() }, width = 500),
                       br(),
                       column(width = 5,
                              style='border-right: 0.02px solid grey',
                              br(),
                              h4("Leslie矩阵"),
                              renderTable({ Leslie_to_print() })),
                       column(width = 7,
                              h4("特征值分析"),
                              em(strong("种群渐近增长率(lambda)")),
                              renderText({ eigenval() }),
                              br(), # br(), br(),
                              em(strong("种群稳定结构")),
                              renderTable({ eigenvec() })
                       )),
              tabPanel("种群轨迹",
                       h4("种群各龄级的轨迹"),
                       renderPlot({ plot_pop_trajectory() }),
                       h4("龄级分布的轨迹"),
                       renderPlot({ plot_pop_agedist() }),
                       h4("种群整体增长率的轨迹"),
                       renderPlot({ plot_pop_lambda() }))
  )
  )
)


## Leslie matrix
Leslie_matrix <- reactive({
  matrix(
      c(input$F1,input$F2, input$F3,
        input$S12/100,0,0,
        0, input$S23/100,0),
      ncol = 3, byrow = T
      )
  })

Leslie_to_print <- reactive({
  ll <- Leslie_matrix()
  colnames(ll) <- paste("龄级",1:3)
  ll
})

init <- reactive({
  c(input$N1,input$N2,input$N3)
})

## Largest eigenvalue
eigenval <- reactive({
  paste0("Leslie矩阵的最大特征值 = ",round(eigen(Leslie_matrix())$values,2)[1])
  })

## Eigenvector corresponding to largest eigenvalue
tmp <- reactive({
  round(eigen(Leslie_matrix())$vectors[,1]*100/
          sum(eigen(Leslie_matrix())$vectors[,1]))
})

eigenvec <- reactive({
  matrix(
    c("特征向量", round(eigen(Leslie_matrix())$vectors[,1],2),
      "%", tmp()[1], tmp()[2], tmp()[3]),
    ncol=4, byrow=T,
    dimnames = list(NULL, c(" ","龄级1","龄级2", "龄级3"))
  )
})


diagr <- reactive({ 
  plot_leslie_diagram(Leslie_matrix())
  })

# Simulation plots

pop_trajectory <- reactive({
  ecoevoapps::run_structured_population_simulation(leslie_mat = Leslie_matrix(), init = init(), time = 1000)
})

plot_pop_trajectory <- reactive({
  ecoevoapps::plot_structured_population_size(pop_trajectory()) +
    labs(title = "") +
    theme(legend.text = element_text(size = 13),
          legend.title = element_text(size = 13))
})

plot_pop_agedist <- reactive({
  ecoevoapps::plot_structured_population_agedist(pop_trajectory(), 
                                                 leslie_mat = Leslie_matrix())+
    labs(title = "") +
    theme(legend.text = element_text(size = 13),
          legend.title = element_text(size = 13),
          plot.caption = element_text(size = 13))
})

plot_pop_lambda <- reactive({
  plot_structured_population_lambda(pop_trajectory(), 
                                    leslie_mat = Leslie_matrix()) +
    labs(title = "") +
    theme(legend.text = element_text(size = 13),
          legend.title = element_text(size = 13),
          plot.caption = element_text(size = 13))
})

# plots <- reactive({
#   plot_pop_trajectory() + plot_pop_agedist() + plot_pop_lambda() + guide_area() +
#     plot_layout(guides = "collect")
# })

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

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