37 research outputs found
Join forces or cheat: evolutionary analysis of a consumer-resource system
International audienceIn this contribution we consider a seasonal consumer-resource system and focus on the evolution of consumer behavior. It is assumed that consumer and resource individuals live and interact during seasons of fixed lengths separated by winter periods. All individuals die at the end of the season and the size of the next generation is determined by the the consumer-resource interaction which took place during the season. Resource individuals are assumed to reproduce at a constant rate, while consumers have to trade-off between foraging for resources, which increases their reproductive abilities, or reproducing. Firstly, we assume that consumers cooperate in such a way that they maximize each consumer's individual fitness. Secondly, we consider the case where such a population is challenged by selfish mutants who do not cooperate. Finally we study the system dynamics over many seasons and show that mutants eventually replace the original cooperating population, but are finally as vulnerable as the initial cooperating consumers
A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models
In recent years, advances in computational power and spatial data analysis
(GIS, remote sensing, etc) have led to an increase in attempts to model the
spread and behvaiour of wildland fires across the landscape. This series of
review papers endeavours to critically and comprehensively review all types of
surface fire spread models developed since 1990. This paper reviews models of a
simulation or mathematical analogue nature. Most simulation models are
implementations of existing empirical or quasi-empirical models and their
primary function is to convert these generally one dimensional models to two
dimensions and then propagate a fire perimeter across a modelled landscape.
Mathematical analogue models are those that are based on some mathematical
conceit (rather than a physical representation of fire spread) that
coincidentally simulates the spread of fire. Other papers in the series review
models of an physical or quasi-physical nature and empirical or quasi-empirical
nature. Many models are extensions or refinements of models developed before
1990. Where this is the case, these models are also discussed but much less
comprehensively.Comment: 20 pages + 9 pages references + 1 page figures. Submitted to the
International Journal of Wildland Fir
Evolutionary Substitution and Replacement in N-Species Lotka-Volterra Systems
The successful invasion of a multi-species resident system by mutants has received a great deal of attention in theoretical
ecology but less is known about what happens after the successful invasion. Here, in the framework of Lotka-Volterra (LV) systems, we
consider the general question where there is one resident phenotype in
each species and the evolutionary outcome after invasion remains one
phenotype in each species but these include all the mutant phenotypes. In the first case, called evolutionary substitution, a mutant appears
in only one species, the resident phenotype in this species dies out and
the mutant coexists with the original phenotypes of the other species.
In the second case, called evolutionary replacement, a mutant appears
in each species, all resident phenotypes die out and the evolutionary
outcome is coexistence among all the mutant phenotypes. For general
LV systems, we show that dominance of the resident phenotype by
the mutant (i.e. the mutant is always more fit) in each species where
the mutant appears leads to evolutionary substitution/replacement.
However, it is shown by example that, when dominance is weakened
to only assuming the average fitness of the mutants is greater than
the average for the resident phenotype, the residents may not die out.
We also show evolutionary substitution occurs in two-species competitive LV systems when the initial invasion of the resident system
(respectively, of the new coexistence system) is successful (respectively, unsuccessful). Moreover, if sequential evolutionary substitution
occurs for either order that the two mutant phenotypes appear (called
historically independent replacement), then it is shown evolutionar