We study the evolution of a gynodioecious species under
mixed-mating through a nucleocytoplasmic male sterility model. We consider two
cytoplasmic types and a nuclear locus with two alleles. Here, the interaction
between one cytoplasmic type and a recessive nuclear male-sterility factor gives
rise to only one female genotype, while the remaining types correspond to
hermaphroditic plants. We include two fitness paramaters: the advantageous
female fitness t of females
relative to that of hermaphrodites; and a silent and dominant cost of
restoration, that is, a diminished fitness for plants carrying a dominant
restorer gene relative to that of hermaphrodites. The parameter related to the
cost of restoration is assumed to be present on outcrossing male fertility only.We find
that every population converges to a stable population. We also determine the
nature of the attracting stable population, which could be a nucleocytoplasmic
polymorphism, a nuclear polymorphism or another population with some
genotypes absent. This depends on the position of t with respect to critical values expressed in terms of the other
parameters and also on the initial population.

Abstract:
in this essay the principal concepts and methods applied on projects aimed at ecological restoration are reviewed, with emphasis on the relationship between conservation, biodiversity and restoration. the most common definitions are provided and the steps to take into account to develop projects on ecological restoration, which will be determined by the level of degradation of the ecosystem to be intervened.

Abstract:
For a power series which converges in some neighborhood of the origin in the complex plane, it turns out that the zeros of its partial sums---its sections---often behave in a controlled manner, producing intricate patterns as they converge and disperse. We open this thesis with an overview of some of the major results in the study of this phenomenon in the past century, focusing on recent developments which build on the theme of asymptotic analysis. Inspired by this work, we derive results concerning the asymptotic behavior of the zeros of partial sums of power series for entire functions defined by exponential integrals of a certain type. Most of the zeros of the n'th partial sum travel outwards from the origin at a rate comparable to n, so we rescale the variable by n and explicitly calculate the limit curves of these normalized zeros. We discover that the zeros' asymptotic behavior depends on the order of the critical points of the integrand in the aforementioned exponential integral. Special cases of the exponential integral functions we study include classes of confluent hypergeometric functions and Bessel functions. Prior to this thesis, the latter have not been specifically studied in this context.

Abstract:
We are interested in studying the asymptotic behavior of the zeros of partial sums of power series for a family of entire functions defined by exponential integrals. The zeros grow on the order of O(n), and after rescaling we explicitly calculate their limit curve. We find that the rate that the zeros approach the curve depends on the order of the singularities/zeros of the integrand in the exponential integrals. As an application of our findings we derive results concerning the zeros of partial sums of power series for Bessel functions of the first kind.

Abstract:
We investigate Dilcher and Stolarsky's polynomial analogue of the Stern diatomic sequence. Basic information is obtained concerning the distribution of their zeros in the plane. Also, uncountably many subsequences are found which each converge to a unique analytic function on the open unit disk. We thus generalize a result of Dilcher and Stolarsky from their second paper on the subject.

Abstract:
We discuss analogues of Newman and Rivlin's formula concerning the ratio of a partial sum of a power series to its limit function and present a new general result of this type for entire functions with a certain asymptotic character. The main tool used in the proof is a Riemann-Hilbert formulation for the partial sums introduced by Kriecherbauer et al. This new result makes some progress on verifying a part of the Saff-Varga Width Conjecture concerning the zero-free regions of these partial sums.