Ecological pyramids represent the distribution of abundance and biomass of living organisms across body-sizes. Our understanding of their expected shape relies on the assumption of invariant steady-state conditions. However, most of the world’s ecosystems experience disturbances that keep them far from such a steady state. Here, using the allometric scaling between population growth rate and body-size, we predict the response of size-abundance pyramids within a trophic guild to any combination of disturbance frequency and intensity affecting all species in a similar way. We show that disturbances narrow the base of size-abundance pyramids, lower their height and decrease total community biomass in a nonlinear way. An experimental test using microbial communities demonstrates that the model captures well the effect of disturbances on empirical pyramids. Overall, we demonstrate both theoretically and experimentally how disturbances that are not size-selective can nonetheless have disproportionate impacts on large species.

We conducted an experiment in aquatic microcosms inoculated with 13 protist species (Blepharisma sp., Cephalodella sp. Chilomonas sp., Chlorogonium euchlorum, Colpidium sp., Cyclidium sp., Euglena gracilis, Euplotes aediculatus, Loxocephalus sp., Paramecium aurelia, Paramecium caudatum, Spirostomum sp. and Tetrahymena sp.) and a set of common freshwater bacteria (Serratia fonticola, Bacillus subtilis and Brevibacillus brevis) as a food resource. These protist species cover a wide range of body-sizes (from 10–10³ microns) and densities (10–10⁵ individuals/ml, Giometto et al. 2013). All species are bacterivores whereas three of them can also photosynthesize and two species can feed on smaller protists (Table S7). General lab procedures follow the protocols described in (Altermatt et al. 2015). The microcosms consisted of a 250 ml Schott bottle filled to 100 ml. They were assembled by first filling each Schott bottle with 30 ml of pre-autoclaved standard protist medium (Carolina Biological Supply, Burlington NC, USA), and 5 ml of a bacteria solution. After 24 h, to allow time for bacteria growth, we added 65 ml of protist solution mixing 5 ml of each protist species at carrying capacity. All communities were allowed to grow for one week before disturbance treatments started.

Experimental design: We performed a factorial experiment in which we varied disturbance frequency and intensity, resulting in a total of twenty different disturbance regimes. Disturbance was achieved by boiling a fraction of the well-mixed community in a microwave. We let the medium cool down before putting it back into the microcosm. This procedure allowed to keep the composition of the microcosm constant and to avoid nutrient addition or loss. It mimics disturbances such as fire and flooding, that initially reduce population abundance but may also enhance the regeneration of nutrients (Haddad et al.2008). Disturbance intensities ranged from 10, 30, 50, 70 to 90%. We disturbed microcosms at four frequencies: f = 0.08, 0.11, 0.16 and 0.33, corresponding to a disturbance every 12, 9, 6 and 3 days respectively. The experiment lasted for 21 days, or 10–50 generations depending on species. Each disturbance regime was replicated six times. To control for the intrinsic variability of abundance pyramids, we cultured eight undisturbed microcosms under the same conditions.

Sampling: We sampled 0.2 ml of each microcosm daily to quantify individual body-sizes (i.e. mean cell area in μm²), protist abundances (individuals/μl) and total community biomass (i.e. total bioarea in μm²/μl) using a standardized video procedure (Altermatt et al. 2015; Pennekamp et al. 2017). A constant volume (14.9 μl) of each sample was placed under a dissecting microscope connected to a camera and a computer for the recording of videos (4 seconds per video). Then, using image processing software (IMAGEJ, National Institute of Health, USA) and the R-package bemovi (Pennekamp et al. 2015) we extracted the number of moving organisms per video frame and the size of each individual (mean cell area in μm²). We estimate total biomass as the sum area of all individuals averaged by video frames, assuming proportionality between area and mass. Other traits such as organisms’ speed and shape were used to filter out background movement noise (e.g. particles from the medium).

Statistical analyses: We binned the observed individuals into twelve size-classes ranging from 0 to 1.6 - 10⁵ μm² in order to get statistically comparable community size-structures. The mean abundance and its standard deviation in each size-class were calculated over 21 time points and 6 replicates (total of 126 observations) for each treatment and over 21 time points and 8 replicates (total of 168 observations) for the control communities. We performed Welch two sample t-tests of mean comparison (treatment versus control) to determine which disturbance regime had a significant effect on community size-structure and total community biomass. Results are presented in Table S2, Fig.4, Fig. S2 and Fig. S3 of the manuscript.

Experimental data and Rmarkdown code

Size_Abundance_Pyramid_Disturbances.Rmd : main file to produce the figures of the manuscript. Open it with statistical software R. To run it entirely, you will need the following R-packages: ‘Rcpp’, ‘RcppGSL’, ‘Rmisc’ and ‘sciplot’. You will also need the Rdata files provided along with this code in the same repository to produce the experimental figure. The C++ code is necessary to produce the simulations with variable disturbances (figure S6) and with the predator-prey dynamics (figures S9-S11). In addition, be aware that some parts of the code are extremly long to run (notably 1.5 hours for Figure 6c and 6.5 hours for Figure S6). We therefore provide some text files with pre-run simulation data which are necessary to keep in the same folder to run the whole code in a few minutes. All files were created using R version 3.5.1 (2018-07-02).

Size_Abundance_Pyramid_Disturbances.html : html file produced by the above Rmarkdown file.

microcosms.RData : experimental data file: information and average biomass (columns) for the 128 microcosms (rows).

N_temp_mean.Rdata : experimental data file: abundance temporal mean of the 128 microcosms (rows) in 12 size classes (columns).

size_classes.Rdata : experimental data file: size classes (length = 12). Body sizes are centers of classes.

treatments.RData : experimental data: factorial design of the experiment (treatments and controls).

dyn_disturbance_GSL.cpp : C++ code to produce the simulations with variable disturbances (section 5 of the Rmarkdown file and figure S6) and with the predator-prey dynamics (section 7 of the Rmarkdown file and figures S9-S11).

VariaDisturbance.txt : text file with pre-run simulation data.

bioI.txt : text file with pre-run simulation data.

bioF.txt : text file with pre-run simulation data.

FreqIntSize_Fig6c.txt : text file with pre-run simulation data.