Self-thinning and community persistence in a simple size-structured dynamical model of plant growth

Insights into plant size-density relationships from models and agricultural crops

“…Two approaches traditionally have been used to study these interactions. One focuses on theoretical models and empirical measurements of abundance, spacing, survival, mortality, and recruitment as functions of plant size in relatively undisturbed natural populations and communities, especially forests (4)(5)(6)(7)(8)(9)(10)(11), where the thinning process is complicated by effects of shading and other factors on asymmetries in resource supply and resulting growth and mortality rates (11)(12)(13)(14)(15)(16). The second approach focuses on the structure and dynamics of plants in agricultural settings (17)(18)(19)(20)(21)(22), where plants of nearly identical age grow under controlled conditions.…”

An analytical model of stand dynamics as a function of tree growth, mortality and recruitment: The shade tolerance-stand structure hypothesis revisited

“…These kind of models has been used by many authors in plant ecology (Nagano, 1978;Hara, 1984aHara, , b, 1985Hara, , 1992Takada and Iwasa, 1986;Kohyama, 1991aKohyama, , b, 1992Hara and Yokozawa, 1994;Kraev, 2001;Dercole et al, 2005) as well as in various other fields of biology (Von Foerster, 1959), demography (Keyfitz, 1968) and epidemiology (Kermack and McKendrick, 1933) to cite just the pioneers. Likewise, the Sharpe-Lotka-McKendrick equation is a particular version of the more general Fokker-Plank equation (also known as diffusion or Kolmogorov forward equation) to incorporate the spatial and stochastic fluctuations of the size density distribution, see Hara (1984aHara ( , b, 1985Hara ( , 1992.…”

Modeling the Dynamics of Age-Structured Polycyclic Population of Biological Cells on the Parameterized Set of Algebraic Functions

“…If the functions appearing in~( , ) ( ) q k u q and F 1 ( ) ( ) k u are continuous in their arguments for each fixed k K = 1, , then the infinite functional series in (13) and (16) are uniformly converging and the solution of Eq. (10) written in the form of (13) or (15) exists and is unique [28].…”

“…In 1974, the Gurtin and Maccamy model [1] was actually a starting point for many publications related to mathematical methods of the analysis and solution of systems of linear and quasilinear transport equations with nonlocal boundary conditions for age-structured models of population dynamics [2][3][4][5]. Theoretical and applied studies based on reproduction of biological cells and organisms are now the central aspect of the majority of biological processes, among which is the dynamics of a population of bacteria (M. Gyllenberg et al [6,7]), modeling of the growth of cancer cells and treatment of cancer (M. Gyllenberg and G. Webb [8], R. Axelrod et al [9], G. Webb et al [8,10]), evolution of infectious diseases (E. Massad et al [11]), growth of epidermis (A. Gandolfi et al [12]), self-thinning and persistence of plants (F. Dercole et al [13]), monoclonal transitions in human innards (P. K. Maini et al [14]), synchronization of cell growth dynamics in biological cycles (J. Clairambault et al [15]), modeling of the dynamics of various label-structured populations (J. Hasenauer et al [16], H. T. Banks et al [17], S. I. Lyashko et al [18], Yu. M. Onopchuk et al [19], V. P. Martseniuk [20]), etc.…”