DOI: 10.5061/dryad.ht76hdrrp
title: Computer code for a model describing the emergence of a long transient regular spatial pattern from interaction of competing aquatic macrophytes and a biocontrol agent

description: A spatially explicit simulation model was developed for competition
 between floating (FAV) and submersed (SAV) aquatic vegetation in which an
 insect biocontrol agent (weevil) consumes FAV biomass. In all simulations,
 a dynamic regular striped pattern of rock-scissors-paper (weevil-FAV-SAV)
 eventually forms and persists for thousands of days despite stochastic
 disturbances in the form of added adult weevils. At some point in the
 simulation, depending on the random number initiator, an apparently
 insignificant spatial deviation in small set of pixels triggers an
 instability that grows rapidly until the striped pattern has been replaced
 by a chaotic-appearing pattern. Investigation shows that the time lags
 involved in the weevil life cycle and assumptions on spatial movement lead
 to the instability and end of long transient.  This research
 reveals the detailed mechanisms by which a long transient striped pattern
 transitions to an irregular pattern, offering insights into how spatial
 pattern form and change.
description: No raw data were generated by this research.  All of the data
 used in the model simulations as parameter values are from published
 papers. McCann (2016) parameterized the model of competition between SAV
 and FAV based on the submersed plant Nuttall’s waterweed (<em>Elodea
 nuttallii</em>) and the floating duckweed <em>Lemna
 gibba</em>. We used the parameters of those species, and used the
 parameters of <em>N. eichhorniae</em>, as the biocontrol
 agent, from van Schalkwyk (2016) although that is only hypothetical for
 the present situation, as we do not know parameters for a relevant
 herbivore of <em>L. gibba</em>.  All these parameters are
 shown in Tables that have been uploaded. The parameter values are also in
 Xu and DeAngelis (2024). Hyperlinks for these papers have been
 uploaded.
description: # Computer Code for Xu and DeAngelis 30October2024
 [https://doi.org/10.5061/dryad.ht76hdrrp](https://doi.org/10.5061/dryad.ht76hdrrp) ## Description of the data and file structure There are two tables of parameter values that were used as input for the simulation model code “CAmodeltest_Switch_Biocontrol_15September2024”. ### Files and variables No data files or variables were uploaded. ## Code/software The Matlab code consists of the script “CAmodeltest_Switch_Biocontrol_15September2024”. The script CAmodeltest_diffuseN_07April2023_Biocontrol simulates the interaction of two competing aquatic macrophytes, on a 50 x 50 spatial lattice of patches. The variables are ‘WH(i,j)’ = floating aquatic vegetation (FAV) biomass, water hyacinth ‘S(i,j)’ =  submersed aquatic vegetation (FAV) biomass  An insect biocontrol agent feeds on the FAV. The variables for the adult are ‘Adult(i,j)’  =  adult biocontrol insect numbers. A fourth variable is the limiting nutrient concentration ‘nwh(i,j)’ = nutrient concentration. The interaction of WH and S is described by equations. All three biotic variables can move in space and the nutrient nwh diffuses.   The script code calls the function UpdateEachPatch_15September2024). The function describes the life cycle of sub-adults of the biocontrol insect.  It consists, for each of the 50 x 50 = 2500 patches, the variables “Eggs(k)”  =  eggs, in day-age classes k =1,12 “L1(k)” = first stage larvae in day-age classes  k = 1:29 “L2(k)” = second stage larvae in age classes k = 1:14 “Pupae(k)” = pupae in day-age classes k = 1:20 The function describes the feeding interaction of L2 larvae on the WH. The functional also describes density-dependence limitation of L1 larvae as a function of the ration of density of larvae to FAV biomass. The simulation can be run over X number of days and the spatial pattern of vegetation and insect life cycles are displayed for any selected days and the total numbers over space of each variable are plotted through time.