DOI: 10.5061/dryad.b8gtht7kf
title: Time dependent interaction modification generated from plant-soil feedback

description: Pairwise interactions between species can be modified by other community
 members, leading to emergent dynamics contingent on community composition.
 Despite the prevalence of such higher-order interactions, little is known
 about how they are linked to the timing and order of species’ arrival. We
 generate population dynamics from a mechanistic plant-soil feedback model,
 then apply a general theoretical framework to show that the modification
 of a pairwise interaction by a third plant depends on its germination
 phenology. These time-dependent interaction modifications emerge from
 concurrent changes in plant and microbe populations and are strengthened
 by higher overlap between plants’ associated microbiomes. The interaction
 between this overlap and the specificity of microbiomes further determines
 plant coexistence. Our framework is widely applicable to mechanisms in
 other systems from which similar time-dependent interaction modifications
 can emerge, highlighting the need to integrate temporal shifts of species
 interactions to predict the emergent dynamics of natural communities.
description: # Time dependent interaction modification generated from plant-soil
 feedback ## Code Files All simulations were run in R version 4.2.1. *
 `Functions_PSF.R` contains all functions used for contructing the
 plant-soil feedback model. * `GenerateData.R` contains code for generating
 data using the mechanistic plant-soil feedback model. *
 `GenerateData_MultipleParams.R` contains code for generating data using
 randomly selected parameters; this is required for the sensitivity
 analysis (see Appendix I). * `ExamineModels.R` contains code for comparing
 the performance of several dynamic models and generate Figure S1. *
 `FeedbackRatios.R` contains code for calculating the ratio of intra- vs.
 interspecific effect from microbiomes using empirical data (Yan et al.
 2022 *[PNAS](https://www.pnas.org/doi/abs/10.1073/pnas.2122088119)*). *
 `ModelFitting.R` contains all code for fitting the simulated data to
 phenomenological models of higher-order interactions. *
 `Analysis_Tidy.Rmd` contains code for creating all figures in the main
 text and Appendix. ## Data The `Data` directory contains six
 subdirectories that are categorized below. The name of raw data (i.e.,
 data simulated from the plant-soil feedback model) has three components: *
 `ij` or `ijk`: data generated from two- or three-plant models; * `al`,
 `nc`, or `co`: representing different degrees of overlap between
 microbiomes; `al` represents low overlap, `nc` represents no overlap, and
 `co` represents high overlap (see also Figure 1); * `ts` or `rs`: `ts`
 represents data generated from a time series, `rs` represents data
 generated by a response surface design for one year (see Methods). All
 data are `.csv` files. ## Population Dynamics * `Standard` is the default
 directory that contains population dynamics used to produce all results in
 the main text. * `m_ii_small` contains population dynamics with a set of
 parameters that specifies a smaller intraspecific microbial effect. *
 `m_ij_small` contains population dynamics with a set of parameters that
 specifies a larger intraspecific microbial effect. `Group` denotes the
 type of population (plants, seeds, or microbiomes), and `init1`, `init2`,
 and `init3` denotes the initial population of plants, seeds, or
 microbiomes $i$, $j$, and $k$. `pi`, `pj`, and `pk` denotes germination
 phenology of plants $i$, $j$, and $k$; `pij` is the phenological
 difference calculated by $p_j-p_i$ (see Methods and Figure 1). For
 datasets ending in `rs` (response surface), `Time` ranges from 1 to 12
 because we only data of one year to estimate the interaction coefficients
 (see Methods). ## Interaction Coefficients * `Repetition` contains *fitted
 interaction coefficients* and their standard error reported by the model
 from simulations with random parameters. This set of simulations is only
 performed with three-plant models. * `RealisticProp` contains *fitted
 interaction coefficients* and their standard error reported by the model
 from simulations with random parameters drawn from distribution of ratios
 of intra- vs. interspecific effect from microbiomes using empirical data
 (see below). This set of simulations is only performed with three-plant
 models. Coefficients starting with `alpha` are pairwise, coefficients
 starting with `beta` are higher-order (see Methods). `pi`, `pj`, and `pk`
 denotes germination phenology of plants $i$, $j$, and $k$; `pij` is the
 phenological difference calculated by $p_j-p_i$ (see Methods and Figure
 1). `rep` denotes the repetition (from 1 to 100). ## Empirical Data *
 `Metaanalysis_Yan` contains data used to calculate the ratio of intra- vs.
 interspecific effect from microbiomes using empirical data. See [Yan et
 al. 2022](https://doi.org/10.5281/zenodo.6513066) for the original data
 and formatting.Time dependent interaction modification generated from
 plant-soil feedback