27 research outputs found
Polymorphic evolution sequence and evolutionary branching
We are interested in the study of models describing the evolution of a
polymorphic population with mutation and selection in the specific scales of
the biological framework of adaptive dynamics. The population size is assumed
to be large and the mutation rate small. We prove that under a good combination
of these two scales, the population process is approximated in the long time
scale of mutations by a Markov pure jump process describing the successive
trait equilibria of the population. This process, which generalizes the
so-called trait substitution sequence, is called polymorphic evolution
sequence. Then we introduce a scaling of the size of mutations and we study the
polymorphic evolution sequence in the limit of small mutations. From this study
in the neighborhood of evolutionary singularities, we obtain a full
mathematical justification of a heuristic criterion for the phenomenon of
evolutionary branching. To this end we finely analyze the asymptotic behavior
of 3-dimensional competitive Lotka-Volterra systems
Assessing concurrent patterns of environmental niche and morphological evolution among species of horned lizards ( Phrynosoma
A developmental bottleneck in dispersing larvae: implications for spatial population dynamics
Omeprazole does not alter plasma methotrexate clearance.
We study the problem of designing group-strategyproof cost-sharing
mechanisms. The players report their bids for getting serviced and the
mechanism decides which players are going to be serviced and how much each one
of them is going to pay. We determine three conditions: \emph{Fence
Monotonicity}, \emph{Stability} of the allocation and \emph{Validity} of the
tie-breaking rule that are necessary and sufficient for
group-strategyproofness, regardless of the cost function. Fence Monotonicity
puts restrictions only on the payments of the mechanism and stability only on
the allocation. Consequently Fence Monotonicity characterizes
group-strategyproof cost-sharing schemes. Finally, we use our results to prove
that there exist families of cost functions, where any group-strategyproof
mechanism has unbounded approximation ratio.Comment: 29 page