[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-139028-105":59,"doc-detail-139028-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","termite-mounds-can-increase-the-robustness-of-dryland-ecosystems-to-climatic-change-supplementary-materials","Termite mounds can increase the robustness of dryland ecosystems to climatic change - Supplementary Materials","","Supplementary materials for a study examining how termite mounds interact with vegetation and water in semi-arid ecosystems under climate change. A theoretical reaction–diffusion framework is used on homogeneous backgrounds, then modified to represent mound-induced heterogeneity through nutrient availability and enhanced soil moisture on and near mounds. The document details the base model equations, parameter meanings, pattern regimes driven by precipitation, and the rationale for comparing original and modified model performance across environmental scenarios.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/termite-mounds-can-increase-the-robustness-of-dryland-ecosystems-to-climatic-change-supplementary-materials/139028/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/termite-mounds-can-increase-the-robustness-of-dryland-ecosystems-to-climatic-change-supplementary-materials/139028.png","ImageObject",300,407,{"name":92,"@type":93},"Bintang","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-19","2026-08-23",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the goal of the theoretical component in these supplementary materials?","Question",{"text":112,"@type":113},"To analyze how termite mounds change vegetation spatial patterns and ecosystem robustness under changing environmental conditions, including near a catastrophic shift toward desertification.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is the base reaction–diffusion model structured?",{"text":117,"@type":113},"It tracks plant biomass P, soil water W, and surface water O, with interaction terms for growth from water uptake, plant mortality, and diffusion, plus infiltration, evaporation, and surface circulation for water dynamics.",{"name":119,"@type":110,"acceptedAnswer":120},"How do termite mounds modify the model?",{"text":121,"@type":113},"They introduce heterogeneity by increasing nutrients and soil moisture on and near mounds, while areas away from mounds are treated as off-mounds; these effects are incorporated by changing how plant growth and water dynamics respond spatially.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},139028,1787494299,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},962085564381,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Supplementary Materials for  \n“Termite mounds can increase the robustness of dryland ecosystems to climatic change”Juan A. Bonachela, Robert M. Pringle, Efrat Sheffer, Tyler C. Coverdale, Jennifer A. Guyton, Kelly K. Caylor, Simon A. Levin & Corina E. Tarnita  \ncorrespondence to: [ctarnita@princeton.edu](ctarnita@princeton.edu)  \nThis PDF file includes:  \nSupplementary Text  \nFigs. S1 to S8  \nTable S1  \nCaptions for Movies S1 to S2  \nOther Suplementary Materials for this manuscript includes the following:  \nMovies S1 to S2  \nSupplementary Text  \n1 Theoretical component  \nHere we scrutinize different aspects of the interaction between termite mounds, vegetation, and water in semi-arid ecosystems. More specifically, we aim to understand how the presence of termite mounds (a) alters vegetation spatial distribution and shape, and (b) affects the robustness (or resilience, see text) of the ecosystem under changing environmental conditions, potentially modifying the susceptibility and behavior of the ecosystem close to the desertification point (that is, close to a so-called “catastrophic shift”) .  \nTo this end, we choose a theoretical reaction-diffusion model widely used to study vegetation patterns in semi-arid ecosystems on homogeneous backgrounds, and modify it to account for the heterogeneity introduced by the presence of termites in terms of nutrients and water dynamics on versus off mounds. Finally, we compare the performance of both the original and the modified models under various (static and dynamic) environmental scenarios.  \n1.1 The base model  \nIn this model taken from (10), three different interaction agents are present, namely plant biomass concentration, P (g m-2), soil water concentration, W (mm), and surface water concentration O (mm). The interaction between these densities is given by:  \n􀁷P􀁷(xt,~~ ~~t) 􀀠 cgmax WW􀀎k1~~ ~~ P 􀀐 dP 􀀎 DP􀂒 2P  \n􀁷W􀁷(xt,~~ ~~t) 􀀠 􀁄 ~~ ~~P􀀎Pk􀀎2Wk2~~ ~~0~~ ~~O 􀀐 gmax WW􀀎k1~~ ~~ P 􀀐 rW W 􀀎 DW􀂒 2W  \n􀁷O􀁷(xt,~~ ~~t) 􀀠 R 􀀐􀁄P􀀎Pk􀀎2Wk2~~ ~~0~~ ~~ O 􀀎 DO􀂒 2 O  \n(1)  \n(2)  \n(3)  \nIn Eq. ( 1), the first term represents plant vegetation growth by means of water uptake (Wis the only plant resource considered here); the second term, plant mortality; and the third term, diffusion as a result of, e.g. seed dispersal. Here, c is the conversion of water  \nuptake by plants to plant growth, gmax is the plant maximum uptake rate, k1 represents a half-saturation constant of specific plant growth and water uptake, d is the specific loss of plant density due to mortality, and DP the diffusivity constant giving plant dispersal (see units in table S1) . In Eq. (2), the first term models the infiltration of surface water (and, therefore, its conversion into soil water); the second and third terms encode water uptake by plants and evaporation; and the last term represents water circulation into the ground. Here, α is the maximum rate of infiltration, k2 represents the saturation constant of water infiltration, W0 is part of the infiltration capacity of the soil in the absence of plants, rW is the specific soil water loss due to evaporation and drainage, and DW is the underground water diffusivity. The first term in Eq. (3) represents the accumulation of surface water coming from precipitation, the second term represents water infiltration into the ground, and the last term represents circulation on the surface. Here, R is the precipitation rate, and DO is surface water diffusivity.  \nWith the model above, varying the precipitation rate R produces the three main patterns observed in semi-arid ecosystems (under the assumption of homogeneous soils) . For the parametrization in table 1, using the homogeneous plant-less solution as initial state, any initial perturbation will relax back to the homogeneous plant-less state if R≤0.55(5) (number in parenthesis indicates confidence interval; e.g., in this case 0.55 +/– 0.05); however, for R>0.55(5), a sufficiently high perturbation containing all possible spatial frequencie","cbCaimBlXnMVrAFA","https://ap.wps.com/l/cbCaimBlXnMVrAFA","pdf",1297914,25,"English","# Supplementary Materials\n## Supplementary Text\n### Theoretical component\n#### The base model\n#### Termite-mound-induced heterogeneity\n## Figures and Tables\n## Movies","[{\"question\":\"What is the goal of the theoretical component in these supplementary materials?\",\"answer\":\"To analyze how termite mounds change vegetation spatial patterns and ecosystem robustness under changing environmental conditions, including near a catastrophic shift toward desertification.\"},{\"question\":\"How is the base reaction–diffusion model structured?\",\"answer\":\"It tracks plant biomass P, soil water W, and surface water O, with interaction terms for growth from water uptake, plant mortality, and diffusion, plus infiltration, evaporation, and surface circulation for water dynamics.\"},{\"question\":\"How do termite mounds modify the model?\",\"answer\":\"They introduce heterogeneity by increasing nutrients and soil moisture on and near mounds, while areas away from mounds are treated as off-mounds; these effects are incorporated by changing how plant growth and water dynamics respond spatially.\"}]","Termite mounds can increase the robustness of dryland ecosystems to climatic change - Supplementary Materials | PDF",63]