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.

Stock monoclonal populations of Daphnia magna were cultured on green algae (Ankistrodesmus falcatus) 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 Daphnia magna. Each microcosm consisted of a linear network of cylindrical patches, each large enough to support multiple adult Daphnia magna, 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.
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 k to represent the number of patches and unknown parameters a and b, the exponential (T = ab^k) and power models (T = ak^b) were fit to the observed extinction times using nonlinear least squares and compared with AIC.