Code and data from: Demographic signals of population decline and time to extinction in a seasonal, density-dependent model

<b>Summary</b>We modified a bi-seasonal Ricker model previously developed by Betini et al. (2013) to examine the effects of season-specific habitat loss in either the breeding or non-breeding period and different strengths of density dependence on the production of experimentally-derived signals of population decline. The bi-seasonal habitat loss model is parameterized using the r-K formulation of the Ricker model, with separate values of growth rate (r) and carrying capacity (K) for each season (i.e., <i>r</i>_<em>b</em><i> </i>= reproductive output, <i>r</i>_<em>nb</em><i> </i>= non-breeding mortality, <i>K</i>_<em>b</em><i> </i>= carrying capacity in the breeding period, <i>K</i>_<em>nb</em><i> </i>= carrying capacity in the non-breeding period). Exponential habitat decay is simulated in either season using two additional terms: <i>H</i>_<em>b</em> (the proportion of initial food remaining in the breeding period) and <i>H</i>_<em>nb</em> (the proportion of initial food remaining in the non-breeding period). The code here is used to simulate five different rates of habitat loss in either the breeding or non-breeding period over breeding or non-breeding of 50 generations, with habitat loss commencing after 20 generations. We ran 1,000 replicates simulations for each scenario/parameterization (see below). Initial starting parameters for a particular simulation are sampled from a distribution to allow for some degree of variability (but not strictly stochasticity) in population dynamics. We randomly sampled 25 replicates from each parameterization for subsequent plotting and analysis, data from which are provided in the CSV file.<br>A complete description of the simulation methods and analysis is available in the pre-print on <i>EcoEvoRxiv</i>.<br><b>Contents</b><i>biseasonal_Ricker_code.R</i> — R code to produce a bi-seasonal Ricker model in which habitat loss is simulated in either the breeding or non-breeding period.<i>biseasonal_Ricker_simdata.csv</i> — a sample of 25 simulated time series of bi-seasonal population abundance under different seasons and rates of habitat loss and strengths of density dependence.<br><b>Variable definitions</b><i>nitt_t_DD </i>= unique replicate identifier (factor) combining the replicate number (nitt), treatment type (t), and strength of density dependence (DD) simulated (e.g., "14_control_flies" references simulation 14 for the control treatment with the strength of density dependence based on values derived from an experimental population of fruit flies) — see variables below.<i>nitt </i>= replicate identification number (not strictly unique to different treatments)<i>strength_DD </i>= four-level factor (flies, weak, moderate, strong) indicating the initial strength of density dependence used to parameterize the model. In all cases, the strength was the same in both the breeding and non-breeding period (i.e., weak and weak, moderate and moderate, etc.). See values in the methods section of the paper or in the specific code for each model parameterization.<i>treat </i>= 11-level factor (control, b02, b5, b10, b20, b25, n02, n05, n10, n20, n25) indicating the season and rate of habitat loss being simulated where "control" indicates no habitat loss and "bXX" and "nXX" indicate breeding habitat and non-breeding habitat loss, respectively, at 2, 5, 10, 20, or 25% per generation.<i>seasonT </i>= three-level factor (c, b, n) indicating the season of treatment (c = control = no habitat loss, b = breeding, n = non-breeding).<i>lossT </i>= 6-level factor (0, 2, 5, 10, 20, 25) indicating the rate of habitat loss as a percent decrease per generation. A value of zero (0) indicates no habitat loss applied (i.e., for controls).<i>time </i>= integer (range = 1 to 100) indicating the time step in the model. Each generation (see below) consists of two timesteps (one each for the non-breeding and breeding seasons).<i>gen </i>= integer (range = 1 to 50) indicating the generation in each simulation. Each generation is repeated twice (with one row for each season). Each replicate was simulated for 20 generations under control conditions before the commencement of habitat loss in generation 21.<i>season </i>= two-level factor (n = non-breeding, b = breeding) indicating the season within each generation.<i>count </i>= integer value indicating the population size simulated in each season of each generation.<i>rate</i> = continuous value expressing the change in population size from the previous timestep to the current (e.g., if the previous (non-breeding) population size was 189 and the current (breeding) value is 249, then rate = 249/189 = 1.32). For rows where season = b = breeding, this value represents the breeding growth rate; when season = n = non-breeding, this value indicates non-breeding survival.<i>first_match </i>= integer indicates the first timestep in which population size reached zero (0) indicating the season and generation in which a simulation became extinct.<br><b>References</b>Betini, G.S., Griswold, C.K., and Norris, D.R. (2013), Carry-over effects, sequential density dependence and the dynamics of populations in a seasonal environment. <i>Proceedings of the Royal Society B</i> 280: 20130110. https://doi.org/10.1098/rspb.2013.0110

<b>摘要</b>我们修改了Betini等人（2013）此前开发的双季节Ricker模型（bi-seasonal Ricker model），以探究繁殖期或非繁殖期的季节特异性生境丧失，以及不同强度的密度依赖（density dependence）对实验衍生的种群下降信号生成的影响。该双季节生境丧失模型采用Ricker模型的r-K参数化形式进行参数设定，为每个季节分别设置增长率（growth rate, r）与环境容纳量（carrying capacity, K）的取值（即：<i>r</i>_<em>b</em> 代表繁殖输出，<i>r</i>_<em>nb</em> 代表非繁殖期死亡率，<i>K</i>_<em>b</em> 代表繁殖期环境容纳量，<i>K</i>_<em>nb</em> 代表非繁殖期环境容纳量）。通过两个额外参数在任意季节中模拟指数型生境衰减：<i>H</i>_<em>b</em>（繁殖期剩余初始食物占比）与<i>H</i>_<em>nb</em>（非繁殖期剩余初始食物占比）。<br>本代码用于在50代的繁殖或非繁殖周期中，模拟繁殖期或非繁殖期的5种不同生境丧失速率，并设置生境丧失在第20代后启动。我们为每种情景/参数组合运行了1000次重复模拟（详见下文）。特定模拟的初始起始参数从分布中采样，以允许种群动态存在一定程度的变异（但并非严格的随机性）。我们从每种参数组合中随机抽取25次重复模拟结果，用于后续绘图与分析，相关数据已提供于CSV文件中。<br>关于模拟方法与分析的完整说明可在<i>EcoEvoRxiv</i>平台的预印本中获取。<br><b>数据集内容</b><i>biseasonal_Ricker_code.R</i> — 用于构建双季节Ricker模型的R代码，该模型可模拟繁殖期或非繁殖期的生境丧失。<i>biseasonal_Ricker_simdata.csv</i> — 包含25条模拟时间序列的样本数据，对应不同季节、生境丧失速率与密度依赖强度下的双季节种群丰度。<br><b>变量定义</b><i>nitt_t_DD</i> — 唯一的重复模拟标识符（因子型变量），由重复编号（nitt）、处理类型（t）与模拟的密度依赖强度（DD）组合而成（例如，"14_control_flies" 代表第14次对照处理模拟，其密度依赖强度基于果蝇实验种群的参数取值）——详见下文变量说明。<i>nitt</i> — 重复模拟标识编号（不同处理下的编号并非严格唯一）。<i>strength_DD</i> — 四分类因子型变量（取值为flies、weak、moderate、strong），代表用于模型参数设定的初始密度依赖强度。所有情景中，繁殖期与非繁殖期的密度依赖强度均保持一致（例如均为弱强度、均为中强度等）。具体取值可参见论文的方法部分或各模型参数设定的对应代码。<i>treat</i> — 十一分类因子型变量（取值为control、b02、b5、b10、b20、b25、n02、n05、n10、n20、n25），代表当前模拟的生境丧失季节与速率：其中“control”代表无生境丧失，“bXX”与“nXX”分别代表繁殖期生境丧失与非繁殖期生境丧失，对应每代丧失2%、5%、10%、20%或25%的生境。<i>seasonT</i> — 三分类因子型变量（取值为c、b、n），代表处理实施的季节：c=对照（无生境丧失），b=繁殖期，n=非繁殖期。<i>lossT</i> — 六分类因子型变量（取值为0、2、5、10、20、25），代表每代生境丧失的百分比速率。取值为0代表未施加生境丧失（即对照情景）。<i>time</i> — 整数型变量（取值范围1~100），代表模型中的时间步长。每一代（详见下文）包含两个时间步（分别对应非繁殖期与繁殖期）。<i>gen</i> — 整数型变量（取值范围1~50），代表单次模拟中的世代数。每个世代会被重复记录两次（每个季节对应一行数据）。每次模拟在生境丧失启动前，均会在对照条件下运行20代，生境丧失从第21代开始实施。<i>season</i> — 二分类因子型变量（n=非繁殖期，b=繁殖期），代表每个世代内的季节。<i>count</i> — 整数型数值，代表每个世代每个季节下模拟得到的种群规模。<i>rate</i> — 连续型数值，代表种群规模从前一个时间步到当前时间步的变化倍率（例如：若前一个时间步（非繁殖期）的种群规模为189，当前时间步（繁殖期）的种群规模为249，则rate=249/189=1.32）。当season=b（繁殖期）时，该值代表繁殖增长率；当season=n（非繁殖期）时，该值代表非繁殖期存活率。<i>first_match</i> — 整数型数值，代表种群规模首次降至0的时间步，用于指示模拟种群灭绝的季节与世代。<br><b>参考文献</b>Betini, G.S., Griswold, C.K. 与 Norris, D.R. (2013)，携带效应、序列密度依赖与季节性环境中的种群动态。<i>Proceedings of the Royal Society B</i> 280: 20130110. https://doi.org/10.1098/rspb.2013.0110