118 research outputs found
General relationships between consumer dispersal, resource dispersal and metacommunity diversity
One of the central questions of metacommunity theory is how dispersal of
organisms affects species diversity. Here we show that the diversity-dispersal
relationship should not be studied in isolation of other abiotic and biotic
flows in the metacommunity. We study a mechanistic metacommunity model in which
consumer species compete for an abiotic or biotic resource. We consider both
consumer species specialized to a habitat patch, and generalist species capable
of using the resource throughout the metacommunity. We present analytical
results for different limiting values of consumer dispersal and resource
dispersal, and complement these results with simulations for intermediate
dispersal values. Our analysis reveals generic patterns for the combined
effects of consumer and resource dispersal on the metacommunity diversity of
consumer species, and shows that hump-shaped relationships between local
diversity and dispersal are not universal. Diversity-dispersal relationships
can also be monotonically increasing or multimodal. Our work is a new step
towards a general theory of metacommunity diversity integrating dispersal at
multiple trophic levels.Comment: Main text: 15 pages, 4 figures. Supplement: 25 pages, 12 figure
Unifying Dynamical and Structural Stability of Equilibriums
We exhibit a fundamental relationship between measures of dynamical and
structural stability of equilibriums, arising from real dynamical systems. We
show that dynamical stability, quantified via systems local response to
external perturbations, coincides with the minimal internal perturbation able
to destabilize the equilibrium. First, by reformulating a result of control
theory, we explain that harmonic external perturbations reflect the spectral
sensitivity of the Jacobian matrix at the equilibrium, with respect to constant
changes of its coefficients. However, for this equivalence to hold, imaginary
changes of the Jacobian's coefficients have to be allowed. The connection with
dynamical stability is thus lost for real dynamical systems. We show that this
issue can be avoided, thus recovering the fundamental link between dynamical
and structural stability, by considering stochastic noise as external and
internal perturbations. More precisely, we demonstrate that a system's local
response to white-noise perturbations directly reflects the intensity of
internal white noise that it can accommodate before asymptotic mean-square
stability of the equilibrium is lost.Comment: 13 pages, 2 figure
Predicting coexistence of plants subject to a tolerance-competition trade-off
Ecological trade-offs between species are often invoked to explain species
coexistence in ecological communities. However, few mathematical models have
been proposed for which coexistence conditions can be characterized explicitly
in terms of a trade-off. Here we present a model of a plant community which
allows such a characterization. In the model plant species compete for sites
where each site has a fixed stress condition. Species differ both in stress
tolerance and competitive ability. Stress tolerance is quantified as the
fraction of sites with stress conditions low enough to allow establishment.
Competitive ability is quantified as the propensity to win the competition for
empty sites. We derive the deterministic, discrete-time dynamical system for
the species abundances. We prove the conditions under which plant species can
coexist in a stable equilibrium. We show that the coexistence conditions can be
characterized graphically, clearly illustrating the trade-off between stress
tolerance and competitive ability. We compare our model with a recently
proposed, continuous-time dynamical system for a tolerance-fecundity trade-off
in plant communities, and we show that this model is a special case of the
continuous-time version of our model.Comment: To be published in Journal of Mathematical Biology. 30 pages, 5
figures, 5 appendice
Resilience, reactivity and variability : A mathematical comparison of ecological stability measures
In theoretical studies, the most commonly used measure of ecological
stability is resilience: ecosystems asymptotic rate of return to equilibrium
after a pulse-perturbation or shock. A complementary notion of growing
popularity is reactivity: the strongest initial response to shocks. On the
other hand, empirical stability is often quantified as the inverse of temporal
variability, directly estimated on data, and reflecting ecosystems response to
persistent and erratic environmental disturbances. It is unclear whether and
how this empirical measure is related to resilience and reactivity. Here, we
establish a connection by introducing two variability-based stability measures
belonging to the theoretical realm of resilience and reactivity. We call them
intrinsic, stochastic and deterministic invariability; respectively defined as
the inverse of the strongest stationary response to white-noise and to
single-frequency perturbations. We prove that they predict ecosystems worst
response to broad classes of disturbances, including realistic models of
environmental fluctuations. We show that they are intermediate measures between
resilience and reactivity and that, although defined with respect to persistent
perturbations, they can be related to the whole transient regime following a
shock, making them more integrative notions than reactivity and resilience. We
argue that invariability measures constitute a stepping stone, and discuss the
challenges ahead to further unify theoretical and empirical approaches to
stability.Comment: 35 pages, 7 figures, 2 table
Unifying time evolution and optimization with matrix product states
We show that the time-dependent variational principle provides a unifying
framework for time-evolution methods and optimisation methods in the context of
matrix product states. In particular, we introduce a new integration scheme for
studying time-evolution, which can cope with arbitrary Hamiltonians, including
those with long-range interactions. Rather than a Suzuki-Trotter splitting of
the Hamiltonian, which is the idea behind the adaptive time-dependent density
matrix renormalization group method or time-evolving block decimation, our
method is based on splitting the projector onto the matrix product state
tangent space as it appears in the Dirac-Frenkel time-dependent variational
principle. We discuss how the resulting algorithm resembles the density matrix
renormalization group (DMRG) algorithm for finding ground states so closely
that it can be implemented by changing just a few lines of code and it inherits
the same stability and efficiency. In particular, our method is compatible with
any Hamiltonian for which DMRG can be implemented efficiently and DMRG is
obtained as a special case of imaginary time evolution with infinite time step.Comment: 5 pages + 5 pages supplementary material (6 figures) (updated
example, small corrections
A neutral theory of genome evolution and the frequency distribution of genes
<p>Abstract</p> <p>Background</p> <p>The gene composition of bacteria of the same species can differ significantly between isolates. Variability in gene composition can be summarized in terms of gene frequency distributions, in which individual genes are ranked according to the frequency of genomes in which they appear. Empirical gene frequency distributions possess a U-shape, such that there are many rare genes, some genes of intermediate occurrence, and many common genes. It would seem that U-shaped gene frequency distributions can be used to infer the essentiality and/or importance of a gene to a species. Here, we ask: can U-shaped gene frequency distributions, instead, arise generically via neutral processes of genome evolution?</p> <p>Results</p> <p>We introduce a neutral model of genome evolution which combines birth-death processes at the organismal level with gene uptake and loss at the genomic level. This model predicts that gene frequency distributions possess a characteristic U-shape even in the absence of selective forces driving genome and population structure. We compare the model predictions to empirical gene frequency distributions from 6 multiply sequenced species of bacterial pathogens. We fit the model with constant population size to data, matching U-shape distributions albeit without matching all quantitative features of the distribution. We find stronger model fits in the case where we consider exponentially growing populations. We also show that two alternative models which contain a "rigid" and "flexible" core component of genomes provide strong fits to gene frequency distributions.</p> <p>Conclusions</p> <p>The analysis of neutral models of genome evolution suggests that U-shaped gene frequency distributions provide less information than previously suggested regarding gene essentiality. We discuss the need for additional theory and genomic level information to disentangle the roles of evolutionary mechanisms operating within and amongst individuals in driving the dynamics of gene distributions.</p
The neutral theory of biodiversity with random fission speciation
International audienceThe neutral theory of biodiversity and biogeography emphasizes the importance of dispersal and speciation to macro-ecological diversity patterns. While the influence of dispersal has been studied quite extensively, the effect of speciation has not received much attention, even though it was already claimed at an early stage of neutral theory development that the mode of speciation would leave a signature on metacommunity structure. Here, we derive analytical expressions for the distribution of abundances according to the neutral model with recruitment (i.e., dispersal and establishment) limitation and random fission speciation which seems to be a more realistic description of (allopatric) speciation than the point mutation mode of speciation mostly used in neutral models. We find that the two modes of speciation behave qualitatively differently except when recruitment is strongly limited. Fitting the model to six large tropical tree data sets, we show that it performs worse than the original neutral model with point mutation speciation but yields more realistic predictions for speciation rates, species longevities, and rare species. Interestingly, we find that the metacommunity abundance distribution under random fission is identical to the broken-stick abundance distribution and thus provides a dynamical explanation for this grand old lady of abundance distributions
A mathematical synthesis of niche and neutral theories in community ecology
International audienceThe debate between niche-based and neutral community theories centers around the question of which forces shape predominantly ecological communities. Niche theory attributes a central role to niche differences between species, which generate a difference between the strength of intra- and interspecific interactions. Neutral theory attributes a central role to migration processes and demographic stochasticity. One possibility to bridge these two theories is to combine them in a common mathematical framework. Here we propose a mathematical model that integrates the two perspectives. From a niche-based perspective, our model can be interpreted as a Lotka-Volterra model with symmetric interactions in which we introduce immigration and demographic stochasticity. From a neutral perspective, it can be interpreted as Hubbell's local community model in which we introduce a difference between intra- and interspecific interactions. We investigate the stationary species abundance distribution and other community properties as functions of the interaction coefficient, the immigration rate and the strength of demographic stochasticity
Quantum dynamical entropies for classical stochastic systems
We compare two proposals for the dynamical entropy of quantum deterministic
systems (CNT and AFL) by studying their extensions to classical stochastic
systems. We show that the natural measurement procedure leads to a simple
explicit expression for the stochastic dynamical entropy with a clear
information-theoretical interpretation. Finally, we compare our construction
with other recent proposals.Comment: 15 page
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