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