On the formulation and analysis of general deterministic structured population models

Numerical Bifurcation Analysis of Physiologically Structured Populations: Consumer–Resource, Cannibalistic and Trophic Models

“…Note that if the right hand side of (5-7) has I(t) dependence it can not be reproduced by defining such an operator and letting it act on (B t , I t , E t ) because pointwise evaluation in L 1 is not defined. A transformation to a system of the form (8) is possible under a reasonable assumption that includes that there exist components of γ that are independent of the I-variable, more precisely that γ has a hierarchical structure in this respect as formalized in Diekmann et al (2001). Such a transformation step is carried out in (3.56-3.59) in Diekmann et al (2007).…”

“…In Getto et al (2005) two resource populations, one for juveniles one for adults, are considered. In the formulation of the well-established fish cannibalism model in Claessen et al (2004) the natural density dependence of vital rates can be cut by introducing so-called environmental interaction variables describing ingestion and predation pressure, see Diekmann et al (2001) and Getto et al (2005), see also Alarcón et al (2014) for environmental interaction variables in a cell population model. We here define the environment via two components, the unstructured populations and the environmental interaction variables.…”

Function-valued adaptive dynamics and the calculus of variations

“…We consider the environmental interaction variable E that contains all essential information about the environment individuals experience on such an attractor. A necessary condition for the attractor having been reached is that the population's basic reproduction ratio, given by the expected number of offspring produced by an individual, is equal to one (Diekmann et al, 1998(Diekmann et al, , 2001),…”

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

“…We now consider the discrete version of the model, but we will later extend the model by taking the limit as M approaches infinity to obtain a continuum model, which is more tractable mathematically. For direct (but equivalent) approaches to the continuum model see Webb (1985); Metz and Diekmann (1986); Cushing (1998); Diekmann et al (1998Diekmann et al ( , 2001.…”

“…Therefore, population dynamic models of plant growth should be specifically addressed to certain habitat/forms type (e.g. trees in forest, shrubs in desert, annuals in early successional communities, herbaceous perennials in grasslands) and should account for both the spatial and size structures of the population (Leslie, 1945;Lefkovitch, 1965;Schaffer and Leigh, 1976;Antonovics and Levin, 1980;Pacala and Silander, 1985;Metz and Diekmann, 1986;Crawley, 1990;Czárán and Bartha, 1992;De Angelis and Gross, 1992;Bishir and Namkoong, 1992;Hara, 1992;Hara and Wyszomirski, 1994;Durrett and Levin., 1994;Takada and Hara, 1994;Diekmann et al, 1998;Cushing, 1998;Diekmann et al, 2001;Bolker et al, 2003).…”