Robust permanence for ecological equations with internal and external feedbacks.

Species experience both internal feedbacks with endogenous factors such as trait evolution and external feedbacks with exogenous factors such as weather. These feedbacks can play an important role in determining whether populations persist or communities of species coexist. To provide a general mathematical framework for studying these effects, we develop a theorem for coexistence for ecological models accounting for internal and external feedbacks. Specifically, we use average Lyapunov functions and Morse decompositions to develop sufficient and necessary conditions for robust permanence, a form of coexistence robust to large perturbations of the population densities and small structural perturbations of the models. We illustrate how our results can be applied to verify permanence in non-autonomous models, structured population models, including those with frequency-dependent feedbacks, and models of eco-evolutionary dynamics. In these applications, we discuss how our results relate to previous results for models with particular types of feedbacks

Effects of processes at the population and community level on carbon dynamics of an ecosystem model

Ecological processes at the population and community level are often ignored in biogeochemical models, however, the effects of excluding these processes at the ecosystem level is uncertain. In this study we analyzed the set of behaviors that emerge after introducing population and community processes into an ecosystem carbon model. We used STANDCARB, a hybrid model that incorporates population, community, and ecosystem processes to predict carbon dynamics over time. Our simulations showed that at the population level, colonization and mortality rates can limit the maximum biomass achieved during a successional sequence. Specifically, colonization rates control temporal lags in the initiation of carbon accumulation, and mortality rates can have important effects on annual variation in live biomass. At the community level, differences in species traits and changes in species composition over time introduced significant changes in carbon dynamics. Species with different set of parameters, such as growth and mortality rates, introduce patterns of carbon accumulation that could not be reproduced using a single species with the average of parameters of multiple species or by simulating the most abundant species (strategies commonly employed in terrestrial biogeochemical models). We conclude that omitting population and community processes from biogeochemical models introduces an important source of uncertainty that can impose important limitations for predictions of future carbon balances

Searching for interacting QTL in related populations of an outbreeding species

Many important crop species are outbreeding. In outbreeding species the search for genes affecting traits is complicated by the fact that in a single cross up to four alleles may be present at each locus. This paper is concerned with the search for interacting quantitative trait loci (QTL) in populations which have been obtained by crossing a number of parents. It will be assumed that the parents are unrelated, but the methods can be extended easily to allow a pedigree structure. The approach has two goals: (1) finding QTL that are interacting with other loci and also loci which behave additively; (2) finding parents which segregate at two or more interacting QTL. Large populations obtained by crossing these parents can be used to study interactions in detail. QTL analysis is carried out by means of regression on predictions of QTL genotypes

Deriving mesoscopic models of collective behaviour for finite populations

Animal groups exhibit emergent properties that are a consequence of local interactions. Linking individual-level behaviour to coarse-grained descriptions of animal groups has been a question of fundamental interest. Here, we present two complementary approaches to deriving coarse-grained descriptions of collective behaviour at so-called mesoscopic scales, which account for the stochasticity arising from the finite sizes of animal groups. We construct stochastic differential equations (SDEs) for a coarse-grained variable that describes the order/consensus within a group. The first method of construction is based on van Kampen's system-size expansion of transition rates. The second method employs Gillespie's chemical Langevin equations. We apply these two methods to two microscopic models from the literature, in which organisms stochastically interact and choose between two directions/choices of foraging. These `binary-choice' models differ only in the types of interactions between individuals, with one assuming simple pair-wise interactions, and the other incorporating higher-order effects. In both cases, the derived mesoscopic SDEs have multiplicative, or state-dependent, noise. However, the different models demonstrate the contrasting effects of noise: increasing order in the pair-wise interaction model, whilst reducing order in the higher-order interaction model. Although both methods yield identical SDEs for such binary-choice, or one-dimensional, systems, the relative tractability of the chemical Langevin approach is beneficial in generalizations to higher-dimensions. In summary, this book chapter provides a pedagogical review of two complementary methods to construct mesoscopic descriptions from microscopic rules and demonstrates how resultant multiplicative noise can have counter-intuitive effects on shaping collective behaviour.Comment: Second version, 4 figures, 2 appendice

Dynamics and evaporation of defects in Mott-insulating clusters of boson pairs

Repulsively bound pairs of particles in a lattice governed by the Bose-Hubbard model can form stable incompressible clusters of dimers corresponding to finite-size n=2 Mott insulators. Here we study the dynamics of hole defects in such clusters corresponding to unpaired particles which can resonantly tunnel out of the cluster into the lattice vacuum. Due to bosonic statistics, the unpaired particles have different effective mass inside and outside the cluster, and "evaporation" of hole defects from the cluster boundaries is possible only when their quasi-momenta are within a certain transmission range. We show that quasi-thermalization of hole defects occurs in the presence of catalyzing particle defects which thereby purify the Mott insulating clusters. We study the dynamics of one-dimensional system using analytical techniques and numerically exact t-DMRG simulations. We derive an effective strong-interaction model that enables simulations of the system dynamics for much longer times. We also discuss a more general case of two bosonic species which reduces to the fermionic Hubbard model in the strong interaction limit.Comment: 12 pages, 10 figures, minor update

Recent developments in Quantum Monte-Carlo simulations with applications for cold gases

This is a review of recent developments in Monte Carlo methods in the field of ultra cold gases. For bosonic atoms in an optical lattice we discuss path integral Monte Carlo simulations with worm updates and show the excellent agreement with cold atom experiments. We also review recent progress in simulating bosonic systems with long-range interactions, disordered bosons, mixtures of bosons, and spinful bosonic systems. For repulsive fermionic systems determinantal methods at half filling are sign free, but in general no sign-free method exists. We review the developments in diagrammatic Monte Carlo for the Fermi polaron problem and the Hubbard model, and show the connection with dynamical mean-field theory. We end the review with diffusion Monte Carlo for the Stoner problem in cold gases.Comment: 68 pages, 22 figures, review article; replaced with published versio

Thermodynamic Analysis of Interacting Nucleic Acid Strands

Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality

Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems - the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression