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The aim of these notes is to illustrate, largely by way of examples, how standard ecological models can be put into an evolutionary perspective in order to gain insight in the role of natural selection in shaping life history characteristics. We limit ourselves to phenotypic evolution under clonal reproduction (that is, we simply ignore the importance of genes and sex). Another basic assumption is that mutation occurs on a time scale which is long relative to the time scale of convergence...
Eucalyptus globulus Labill is one of the most important economic forest species in Portugal, occupying an area of 875.10³ ha in a total forest area of 3346.10³ ha (Tomé et al., 2007). The main goal of this study is to develop a dominant height growth model for Eucalyptus, applicable throughout the country, representing an improve of the curves that are part of the whole stand model existing in Portugal, the GLOBULUS model (Tomé et al., 2001). The dominant height growth model will be built on a biological...
A simple model of biological evolution of community food webs is introduced. This model
is based on the niche model, which is known to generate model food webs that are very
similar to empirical food webs. The networks evolve by speciation and extinction.
Co-extinctions due to the loss of all prey species are found to play a major role in
determining the longterm shape of the food webs. The central aim is to design the model
such that the characteristic...
In investigating a certain optimization problem in biogeography, Simon [IEEE Trans. Evolutionary Comput. 12 (2008), 702-713] encountered a certain specially structured tridiagonal matrix and made a conjecture regarding its eigenvalues. A few years later, the validity of the conjecture was established by Igelnik and Simon [Appl. Math. Comput. 218 (2011), 195-201]. In this paper, we give another proof of this conjecture that is much shorter, almost computation-free, and does not resort to the eigenvectors...
In this paper, using Mawhin's continuation theorem of the coincidence degree theory, we obtain some sufficient conditions for the existence of positive almost periodic solutions for a class of delay discrete models with Allee-effect.
An optimal control problem is studied for a predator-prey system of PDE, with a logistic
growth rate of the prey and a general functional response of the predator. The control
function has two components. The purpose is to maximize a mean density of the two species
in their habitat. The existence of the optimal solution is analyzed and some necessary
optimality conditions are established. The form of the optimal control is found in some
particular...
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