DOI: 10.5061/dryad.gmsbcc2zj
title: Data from: Scaling of extinction time with habitat size across six orders of magnitude in experimental populations

description: Theoretical models suggest that the mean time to extinction scales with
 habitat size through either exponential or power-law relationships,
 depending on demographic and environmental stochasticity. Despite
 extensive theoretical work, empirical validation of these scaling
 relationships is limited. Here, we report a microcosm study of Daphnia
 magna populations in experimental chambers consisting of 1, 2, 4,
 8, 16, or 32 patches, with a total of 35 populations monitored daily until
 extinction. We tested the scaling of extinction time with patch count
 using nonlinear regression models for both exponential and power-law
 functions, comparing model fit with AIC. Although the study’s statistical
 power is constrained by sample size, this level of replication remains
 unmatched by previous work. Our experiment provides the first empirical
 test of long-standing theoretical predictions and lays a foundation for
 future studies to expand the understanding of extinction dynamics in
 ecological systems.
description: Stock monoclonal populations of <em>Daphnia
 magna</em> were cultured on green algae (<em>Ankistrodesmus
 falcatus</em>) in sufficient amounts for the experiment.
 Microcosms were constructed from cast acrylic sheet using a CNC
 (computer numerical control) router, which tests showed to be nontoxic to
 <em>Daphnia magna</em>. Each microcosm consisted of a linear
 network of cylindrical patches, each large enough to support multiple
 adult <em>Daphnia magna</em>, connected by uniform channels of
 sufficient width (3 mm) and depth to admit a single adult. Dead-end
 channels were added to the ends of each linear microcosm to hold the total
 volume of each patch (including connecting channels) constant.
 The primary experiment consisted of a single treatment (number of
 patches) with six levels (1, 2, 4, 8, 16, and 32 patches), replicated four
 times per level for a total of (N = 24) metapopulations. In addition,
 because smaller metapopulations were expected to go extinct quickly and
 because the labor involved in censusing the smaller metapopulations was
 minimal, we included an additional six 1-patch microcosms, three 2-patch
 microcosms, and two 4-patch microcosms. Positions of
 microcosms on the bench were randomized, stratifying by replicate, as
 described in Supplementary Table 1. On Day 0 of the
 experiment, microcosms were filled with hard water medium, and each
 microcosm was inoculated with an initial population of two individuals in
 each patch. To minimize contamination and evaporation,
 microcosms were kept covered throughout the experiment with a 4 mm sheet
 of clear acrylic, slightly elevated above the surface of the microcosms to
 allow gas exchange. The experiment was maintained under constant
 artificial light. Censusing was performed by visually
 counting free-swimming individuals and noting which patch each
 inhabited.<br>Occasionally, individuals were observed to be in
 channels connecting the patches, in which case they were assigned to the
 closest patch. A complete census was conducted twice
 each day in immediate succession. After censusing, the water level of each
 microcosm was checked and deionized water added as necessary to account
 for evaporation. A microcosm population was considered
 extinct if the total count for all patches in the microcosm was zero for
 three consecutive days. The experiment was conducted
 until all populations were extinct. The daily total
 abundance of each microcosm was obtained by summing population counts
 across all patches separately for each of the two censuses.
 The two estimates of abundance were then compared for
 discrepancies. The population counts agreed across
 censuses in 3,127 out of 4,164 (75.1%) of cases. Of the
 discrepant censuses, the two counts differed by six or fewer in 90% of
 cases. We reconciled discrepancies by taking the
 maximum of the population size across the two censuses as the measure of
 population size. The hypothesis that patch number had
 an effect on extinction time was tested using the Kruskal-Wallis
 test. Using <em>k</em> to represent the
 number of patches and unknown parameters <em>a</em> and
 <em>b</em>, the exponential (<em>T =
 ab<sup>k</sup></em>) and power models (<em>T =
 ak<sup>b</sup></em>) were fit to the observed extinction
 times using nonlinear least squares and compared with AIC.
description: # Scaling of extinction time with habitat size across six orders of
 magnitude in experimental populations
 [https://doi.org/10.5061/dryad.gmsbcc2zj](https://doi.org/10.5061/dryad.gmsbcc2zj) ## Description of the data and file structure ## Data Raw data are in the R data file 'DaphniaCounts.rds'. Column headings are defined as follows: * date: the date of observation * rep: replicate number, an identifier for randomization and experimental design * count: which census number the record is associated with (either "1" for first census or "2" for second census) * network.length: the number of chambers in the network * node: the specific chamber in the network associated with the observation (nodes are ordered, e.g. node 2 is connected both to node 1 and 3) * population: count of the number of individuals in the node * collector: the identity of the researcher making the observation ## Analysis R code for the analysis is in the pdf file 'analysis.pdf'. An executable script is in the R file 'analysis.R'. ### Files and variables #### File: DaphniaCounts.Rds **Description:** Raw data from the experiment. See README for column headings. #### File: analysis.pdf **Description:** Transcript of data analysis. ## Code/software R may be used to read the data file.