Validating the model of Thompson et al. (2020)

comdynamite was implemented from the published equations of Thompson et al. (2020), so we checked it in three ways: against analytical results, against mcomsimr, the R implementation by the same authors, and against the patterns in the article. The last check showed that the article and the code archived with it differ in several points. They are listed here because they change results, and anyone reimplementing the model from the text alone will not reproduce the figures.

All scripts are in data-raw/.

Analytical results

tests/testthat/test-analytic.R compares simulations with results derived by hand: single-species and multispecies equilibria, competitive exclusion, source-sink dynamics, flow through the dispersal kernel and the survival of isolated populations under extirpation.

Comparison with mcomsimr

validation_mcomsimr.R gives both implementations the same environment, traits, competition and dispersal, with 25 sites, 12 species and 200 replicates in each of 32 scenarios, and compares the distributions of five statistics. None of the 160 comparisons was significant (Kolmogorov-Smirnov tests, false discovery rate of 5%).

Without extirpation, mean differences in alpha, gamma and total abundance stayed below 1%. With extirpation, the largest difference was 8%, in alpha on a grid with dispersal of 0.001. The cause is the immigration step. comdynamite draws immigrants from a Poisson distribution, as does the authors’ Julia code, so that a few emigrants may produce no immigrant. mcomsimr conserves dispersers. In that scenario, alpha was 1.75 with Poisson immigrants, 1.85 with multinomial immigrants and 1.85 in mcomsimr (600 runs each, standard error 0.015).

Article and archived code

We compared the article with the code archived for it, Meta_com_framework v1.0. We cannot tell whether this is exactly the code that produced every figure, but the values in Figure 3 agree with the code in the first row of the table: for example, in panel c, gamma is about 40, alpha about 4 and spatial beta about 10, which is gamma / alpha and not gamma - alpha.

Item	Article	Archived code
Spatial and temporal beta	gamma - alpha, Table 1	gamma / alpha
Empty patches and time points	Not mentioned	Left out of alpha and gamma
Environment	Between 0 and 1, mean and variance of 0.5	Field rescaled, then converted to ranks over all patches and steps, so it is uniform on [0, 1]
Lowest dispersal	0.0001 in the text, 0.00001 on the axes of Figures 3 and 4	0.00001
Seeding	Every 10 steps up to step 100	Every 20 steps up to step 100
Emigrants	Binomial	Poisson
Sampling	Every 20 steps after step 1000	Every 22 steps, from about step 1040
Replicate landscapes	30 in the text, 15 in the captions of Figures S1 and S2	The scripts loop over 15
Competition-colonisation: immigrants	Not mentioned	Halved in this scenario only
Competition-colonisation: dominants	Dominant effects from U(1, 1.5)	The same, but only on species later in the order, so dominants form a hierarchy

The conversion to ranks matters most. Our first version rescaled a Gaussian field to [0, 1] without it. The standard deviation among sites was then 0.11, against 0.29 with ranks, which made niches effectively broader. Without ranks, the peak of spatial beta at intermediate niche breadths under stabilising competition does not appear.

As of November 2026 we found no report of these differences in the issue trackers of either repository, no correction registered for the article in Crossref, and nothing in a web search. This does not show that nobody has noticed them.

Patterns in the article

validation_thompson.R follows the archived code, with 100 patches, 50 species, 15 dispersal rates, 30 landscapes, three types of competition and 6 of the 13 niche breadths. Two differences remain. RandomFields is no longer on CRAN, so the field before conversion to ranks is an AR(1) process with spatial covariance, not a single covariance over space and time, and emigrants are binomial, as in the article.

Values at dispersal of 0.00001 are close to Figure 3, read from the plot because the article has no table of values:

Competition	Niche breadth	alpha	gamma	Spatial beta
Equal	0.5	1.0	39	38.8
Equal	10	1.0	44	43.1
Mixed	0.5	1.9	40	21.5
Mixed	10	2.3	43	18.6
Stabilising	0.5	4.6	42	9.1
Stabilising	10	6.6	46	7.0

Median spatial and temporal beta across dispersal, niche breadth and competition. Blank cells are combinations in which species persisted in fewer than 10 of 30 landscapes.

Their hypotheses H1, H2, H3, H5 and H6 appear. H4 states that spatial and temporal beta are promoted by narrow niches or strong competition. The part on competition holds: at the lowest dispersal and a niche breadth of 0.5, spatial beta is 38.8 with equal competition, 21.5 with mixed competition and 9.1 with stabilising competition.

The part on niches depends on the scenario. Under stabilising competition, spatial beta peaks at a niche breadth of 0.215 (14.4, against 7.0 at 10). Under mixed competition the peak is weak. Under equal competition and low dispersal, beta increases with niche breadth (16.5, 38.8 and 43.1 at 0.215, 0.5 and 10), because drift fixes a different species in each patch. Narrow niches raise beta under equal competition only from a dispersal of about 0.02. Figure 4 of the article shows the same pattern, so the difference lies between that figure and the wording of H4.

The competition-colonisation scenario, in validation_thompson_cc.R, uses extirpation = 0.002 and reproduces the code in the two last rows of the table. At a niche breadth of 0.5, gamma rises from 3.6 to about 6 near a dispersal of 0.0005 and then falls. At 10, the metacommunity collapses to one species from a dispersal of about 0.02. Both agree with Figure 3g and h by eye.

References

Thompson, P. L., Guzman, L. M., De Meester, L., Horváth, Z., Ptacnik, R., Vanschoenwinkel, B., Viana, D. S., & Chase, J. M. (2020). A process-based metacommunity framework linking local and regional scale community ecology. Ecology Letters, 23, 1314–1329. https://doi.org/10.1111/ele.13568