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Tyrant flycatchers (Aves: Tyrannidae) are endemic to the New World, and many species of this group are threatened or near-threatened at the global level. The aim of this study was to test the 18 microsatellite markers that have been published for other Tyrant flycatchers in the Strange-tailed Tyrant (Alectrurus risora) and the Sharp-tailed Tyrant (Culicivora caudacuta), two endemic species of southern South American grasslands that are classified as vulnerable. We also analyzed the usefulness of loci in relation to phylogenetic distance to the source species. Amplification success was high in both species (77 to 83%) and did not differ between the more closely and more distantly related species to the source species. Polymorphism success was also similar for both species, with 9 and 8 loci being polymorphic, respectively. An increased phylogenetic distance thus does not gradually lead to allelic or locus dropouts, implying that in Tyrant flycatchers, the published loci are useful independent of species relatedness.
In this chapter, equipped with our previously obtained knowledge of exit and transition times in the limit of small noise amplitude ??0 , we shall investigate the global asymptotic behavior of our jump diffusion process in the time scale in which transitions occur, i.e. in the scale given by ?0(?)=?(1?Bc?(0)),?,?>0 . It turns out that in this time scale, the switching of the diffusion between neighborhoods of the stable solutions ? ± can be well described by a Markov chain jumping back and forth between two states with a characteristic Q-matrix determined by the quantities ?((D±0)c)?(Bc?(0)) as jumping rates.
Asymptotic transition times
(2013)
Asymptotic exit times
(2013)
In this preparatory chapter, the tools of stochastic analysis needed for the investigation of the asymptotic behavior of the stochastic Chafee-Infante equation are provided. In the first place, this encompasses a recollection of basic facts about Lévy processes with values in Hilbert spaces. Playing the role of the additive noise processes perturbing the deterministic Chafee-Infante equation in the systems the stochastic dynamics of which will be our main interest, symmetric ?-stable Lévy processes are in the focus of our investigation (Sect. 3.1).
In this chapter, we introduce the deterministic Chafee-Infante equation. This equation has been the subject of intense research and is very well understood now. We recall some properties of its longtime dynamics and in particular the structure of its attractor. We then define reduced domains of attraction that will be fundamental in our study and give a result describing precisely the time that a solution starting form a reduced domain of attraction needs to reach a stable equilibrium. This result is then proved using the detailed knowledge of the attractor and classical tools such as the stable and unstable manifolds in a neighborhood of an equilibrium.