Evidence for the plant apparency and Janzen Connell hypotheses in a subtropical forest

Evidence for the plant apparency and Janzen Connell hypotheses in a subtropical forest | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 3 September 2025 V1 Latest version Share on Evidence for the plant apparency and Janzen Connell hypotheses in a subtropical forest Authors : Gang Zhou 0000-0002-7184-5049 , Daniel Petticord , Yuanzhi Qin 0000-0002-1240-274X , Biao Dong 0009-0008-4005-4683 , Xiujuan Qiao 0000-0003-4647-399X [email protected] , and Mingxi Jiang 0000-0002-9719-3093 Authors Info & Affiliations https://doi.org/10.22541/au.175692133.34505834/v1 101 views 98 downloads Contents Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract documentclassarticle We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions documentclassarticle Abstract We prove results on unique continuation at the boundary for the solutions of real analytic elliptic partial differential equations of the form \begin{equation} \sum_{i,j=1}^{n}a_{ij}(x)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}+\sum_{k=1}^{n}b_{k}(x)\frac{\partial u}{\partial x_{k}}+c(x)u=0\nonumber \\ \end{equation} This work is motivated by and generalized the main results of, \cite{berhanu2021boundary} , \cite{berhanu2021local} , X.Huang et al in, \cite{huang1993unique} , \cite{huang1995hopf} and M.S Baouendi and L.P. Rothschild in \cite{baouendi1993local} Key words: Elliptic partial differential equation ; Hopf Lemma ; Unique continuation principle ; Real analytic hypersurface ; Real analytic functions Figure 2 FIGURE 3 Information & Authors Information Version history V1 Version 1 03 September 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Authors Affiliations Gang Zhou 0000-0002-7184-5049 Chinese Academy of Sciences Wuhan Branch View all articles by this author Daniel Petticord Cornell University View all articles by this author Yuanzhi Qin 0000-0002-1240-274X Chinese Academy of Sciences Wuhan Botanical Garden View all articles by this author Biao Dong 0009-0008-4005-4683 Yangtze University View all articles by this author Xiujuan Qiao 0000-0003-4647-399X [email protected] Wuhan Botanical Garden View all articles by this author Mingxi Jiang 0000-0002-9719-3093 View all articles by this author Metrics & Citations Metrics Article Usage 101 views 98 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Gang Zhou, Daniel Petticord, Yuanzhi Qin, et al. Evidence for the plant apparency and Janzen Connell hypotheses in a subtropical forest. Authorea . 03 September 2025. 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