Functional diversity buffers the effects of a pulse perturbation on the dynamics of tritrophic food webs

Biodiversity decline causes a loss of functional diversity, which threatens ecosystems through a dangerous feedback loop: this loss may hamper ecosystems' ability to buffer environmental changes, leading to further biodiversity losses. In this context, the increasing frequency of human-induced excessive loading of nutrients causes major problems in aquatic systems. Previous studies investigating how functional diversity influences the response of food webs to disturbances have mainly considered systems with at most two functionally diverse trophic levels. We investigated the effects of functional diversity on the robustness, i.e. resistance, resilience and elasticity, using a tritrophic ---and thus more realistic---plankton food web model. We compared a non-adaptive food chain with no diversity within the individual trophic levels to a more diverse food web with three adaptive trophic levels. The species fitness differences were balanced through trade-offs between defense/growth rate fo..., To study the response of tritrophic food webs with different levels of diversity to a pulse perturbation we used several scripts, libraries and programming languages. Ordinary differential equations were solved numerically in C using the SUNDIALS CVODE solver with relative and absolute tolerances set to 10-10. Output results were analyzed in Python using several packages among which NumPy, SciPy and Matplotlib.

We run simulations where we perturbed the system with an addition of nutrients and quantified different metrics (minimal and maximal biomasses, return time for each species and trophic level) to investigate the robustness (resistance, resilience and elasticity) of the food web. We used an extinction threshold of 10-9 microg C/L to prevent numerical problems when state variables are extremely close to 0.

When the attractor was a limit cycle or a chaotic attractor, we investigated how the effect of the perturbation on the dynamics depended on the moment of perturbation i.e. w..., In each file the aim is precised at the top of the script. There are two types of file: the ones for producing figures (files starting by figures) and the ones for producing simulations. For the first ones data are available in the folder datasets and if the variable savefig is set to 1 the figure is saved in the folder figures. For the files producing simulations some important steps should be checked before running the code. The corresponding c codes should be compiled and the executable file should be named as precised in the top of the .py and .c files (same name as the c file). We used the following command in the terminal:

gcc -Wall -I/usr/include/gsl -L/usr/local/lib script_name.c -lm -lgsl -lgslcblas -lsundials_cvode -lsundials_nvecserial -g -o script_name

Create also a folder c_ouput_files where all the files written by C will be saved