550 research outputs found
A short proof of a symmetry identity for the -deformed Binomial distribution
We give a short and elementary proof of a -deformed Binomial
distribution identity arising in the study of the -Boson process
and the -TASEP. This identity found by Corwin in [4] was a key
technical step to prove an intertwining relation between the Markov transition
matrices of these two classes of discrete-time Markov chains. This was used in
turn to derive exact formulas for a large class of observables of both these
processes.Comment: 3 page
The -Hahn asymmetric exclusion process
We introduce new integrable exclusion and zero-range processes on the
one-dimensional lattice that generalize the -Hahn TASEP and the -Hahn
Boson (zero-range) process introduced in [Pov13] and further studied in
[Cor14], by allowing jumps in both directions. Owing to a Markov duality, we
prove moment formulas for the locations of particles in the exclusion process.
This leads to a Fredholm determinant formula that characterizes the
distribution of the location of any particle. We show that the model-dependent
constants that arise in the limit theorems predicted by the KPZ scaling theory
are recovered by a steepest descent analysis of the Fredholm determinant. For
some choice of the parameters, our model specializes to the
multi-particle-asymmetric diffusion model introduced in [SW98]. In that case,
we make a precise asymptotic analysis that confirms KPZ universality
predictions. Surprisingly, we also prove that in the partially asymmetric case,
the location of the first particle also enjoys cube-root fluctuations which
follow Tracy-Widom GUE statistics.Comment: 40 pages,11 figures. v3: Presentation improved in Introduction and
Section 4. to appear in Ann. Appl. Proba
How self-regulation, the storage effect and their interaction contribute to coexistence in stochastic and seasonal environments
Explaining coexistence in species-rich communities of primary producers
remains a challenge for ecologists because of their likely competition for
shared resources. Following Hutchinson's seminal suggestion, many theoreticians
have tried to create diversity through a fluctuating environment, which impairs
or slows down competitive exclusion. However, fluctuating-environment models
often only produce a dozen of coexisting species at best. Here, we investigate
how to create richer communities in fluctuating environments, using an
empirically parameterized model. Building on the forced Lotka-Volterra model of
Scranton and Vasseur (Theor Ecol 9(3):353-363, 2016), inspired by phytoplankton
communities, we have investigated the effect of two coexistence mechanisms,
namely the storage effect and higher intra- than interspecific competition
strengths (i.e., strong self-regulation). We tuned the intra/inter competition
ratio based on empirical analyses, in which self-regulation dominates
interspecific interactions. Although a strong self-regulation maintained more
species (50%) than the storage effect (25%), we show that none of the two
coexistence mechanisms considered could ensure the coexistence of all species
alone. Realistic seasonal environments only aggravated that picture, as they
decreased persistence relative to a random environment. However, strong
self-regulation and the storage effect combined superadditively so that all
species could persist with both mechanisms at work. Our results suggest that
combining different coexistence mechanisms into community models might be more
fruitful than trying to find which mechanism best explains diversity. We
additionally highlight that while biomass-trait distributions provide some
clues regarding coexistence mechanisms, they cannot indicate unequivocally
which mechanisms are at play.Comment: 27 pages, 9 figures, Theor Ecol (2019
Fitting stochastic predator-prey models using both population density and kill rate data
Most mechanistic predator-prey modelling has involved either parameterization
from process rate data or inverse modelling. Here, we take a median road: we
aim at identifying the potential benefits of combining datasets, when both
population growth and predation processes are viewed as stochastic. We fit a
discrete-time, stochastic predator-prey model of the Leslie type to simulated
time series of densities and kill rate data. Our model has both environmental
stochasticity in the growth rates and interaction stochasticity, i.e., a
stochastic functional response. We examine what the kill rate data brings to
the quality of the estimates, and whether estimation is possible (for various
time series lengths) solely with time series of population counts or biomass
data. Both Bayesian and frequentist estimation are performed, providing
multiple ways to check model identifiability. The Fisher Information Matrix
suggests that models with and without kill rate data are all identifiable,
although correlations remain between parameters that belong to the same
functional form. However, our results show that if the attractor is a fixed
point in the absence of stochasticity, identifying parameters in practice
requires kill rate data as a complement to the time series of population
densities, due to the relatively flat likelihood. Only noisy limit cycle
attractors can be identified directly from population count data (as in inverse
modelling), although even in this case, adding kill rate data - including in
small amounts - can make the estimates much more precise. Overall, we show that
under process stochasticity in interaction rates, interaction data might be
essential to obtain identifiable dynamical models for multiple species. These
results may extend to other biotic interactions than predation, for which
similar models combining interaction rates and population counts could be
developed
Agricultural land-use and biological conservation
Land use change is a main driver of biodiversity erosion, especially in agricultural landscapes. Incentive-based land-use policies aim at influence land-use pattern, and are usually evaluated with habitat suitability scores, without accounting explicitly for the ecology of the studied population. In this paper, we propose a methodology to define and evaluate agricultural land-use policies with respect to their ecological outcomes directly. We use an ecological-economic model to link the regional abundance of a bird species to the economic context. Policies based on such ecological economics approaches appear to be more efficient than that based on landscape evaluation, from both economic and ecological viewpoints.Ecological-economic model, agriculture, land-use, landscape, conservation
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