2,150 research outputs found
The Role of Behavioral Dynamics in Determining the Patch Distributions of Interacting Species
The effect of the behavioral dynamics of movement on the population dynamics of interacting species in multipatch systems is studied. The behavioral dynamics of habitat choice used in a range of previous models are reviewed. There is very limited empirical evidence for distinguishing between these different models, but they differ in important ways, and many lack properties that would guarantee stability of an ideal free distribution in a single-species system. The importance of finding out more about movement dynamics in multispecies systems is shown by an analysis of the effect of movement rules on the dynamics of a particular two-species–two-patch model of competition, where the population dynamical equilibrium in the absence of movement is often not a behavioral equilibrium in the presence of adaptive movement. The population dynamics of this system are explored for several different movement rules and different parameter values, producing a variety of outcomes. Other systems of interacting species that may lack a dynamically stable distribution among patches are discussed, and it is argued that such systems are not rare. The sensitivity of community properties to individual movement behavior in this and earlier studies argues that there is a great need for empirical investigation to determine the applicability of different models of the behavioral dynamics of habitat selection
Inferential stability in systems biology
The modern biological sciences are fraught with statistical difficulties. Biomolecular
stochasticity, experimental noise, and the “large p, small n” problem all contribute to
the challenge of data analysis. Nevertheless, we routinely seek to draw robust, meaningful
conclusions from observations. In this thesis, we explore methods for assessing
the effects of data variability upon downstream inference, in an attempt to quantify and
promote the stability of the inferences we make.
We start with a review of existing methods for addressing this problem, focusing upon the
bootstrap and similar methods. The key requirement for all such approaches is a statistical
model that approximates the data generating process.
We move on to consider biomarker discovery problems. We present a novel algorithm for
proposing putative biomarkers on the strength of both their predictive ability and the stability
with which they are selected. In a simulation study, we find our approach to perform
favourably in comparison to strategies that select on the basis of predictive performance
alone.
We then consider the real problem of identifying protein peak biomarkers for HAM/TSP,
an inflammatory condition of the central nervous system caused by HTLV-1 infection.
We apply our algorithm to a set of SELDI mass spectral data, and identify a number of
putative biomarkers. Additional experimental work, together with known results from the
literature, provides corroborating evidence for the validity of these putative biomarkers.
Having focused on static observations, we then make the natural progression to time
course data sets. We propose a (Bayesian) bootstrap approach for such data, and then
apply our method in the context of gene network inference and the estimation of parameters
in ordinary differential equation models. We find that the inferred gene networks
are relatively unstable, and demonstrate the importance of finding distributions of ODE
parameter estimates, rather than single point estimates
Identifying Keystone Species in the Human Gut Microbiome from Metagenomic Timeseries using Sparse Linear Regression
Human associated microbial communities exert tremendous influence over human
health and disease. With modern metagenomic sequencing methods it is possible
to follow the relative abundance of microbes in a community over time. These
microbial communities exhibit rich ecological dynamics and an important goal of
microbial ecology is to infer the interactions between species from sequence
data. Any algorithm for inferring species interactions must overcome three
obstacles: 1) a correlation between the abundances of two species does not
imply that those species are interacting, 2) the sum constraint on the relative
abundances obtained from metagenomic studies makes it difficult to infer the
parameters in timeseries models, and 3) errors due to experimental uncertainty,
or mis-assignment of sequencing reads into operational taxonomic units, bias
inferences of species interactions. Here we introduce an approach, Learning
Interactions from MIcrobial Time Series (LIMITS), that overcomes these
obstacles. LIMITS uses sparse linear regression with boostrap aggregation to
infer a discrete-time Lotka-Volterra model for microbial dynamics. We tested
LIMITS on synthetic data and showed that it could reliably infer the topology
of the inter-species ecological interactions. We then used LIMITS to
characterize the species interactions in the gut microbiomes of two individuals
and found that the interaction networks varied significantly between
individuals. Furthermore, we found that the interaction networks of the two
individuals are dominated by distinct "keystone species", Bacteroides fragilis
and Bacteroided stercosis, that have a disproportionate influence on the
structure of the gut microbiome even though they are only found in moderate
abundance. Based on our results, we hypothesize that the abundances of certain
keystone species may be responsible for individuality in the human gut
microbiome
Chaotic provinces in the kingdom of the Red Queen
The interplay between parasites and their hosts is found in all kinds of
species and plays an important role in understanding the principles of
evolution and coevolution. Usually, the different genotypes of hosts and
parasites oscillate in their abundances. The well-established theory of
oscillatory Red Queen dynamics proposes an ongoing change in frequencies of the
different types within each species. So far, it is unclear in which way Red
Queen dynamics persists with more than two types of hosts and parasites. In our
analysis, an arbitrary number of types within two species are examined in a
deterministic framework with constant or changing population size. This general
framework allows for analytical solutions for internal fixed points and their
stability. For more than two species, apparently chaotic dynamics has been
reported. Here we show that even for two species, once more than two types are
considered per species, irregular dynamics in their frequencies can be observed
in the long run. The nature of the dynamics depends strongly on the initial
configuration of the system; the usual regular Red Queen oscillations are only
observed in some parts of the parameter region
Delayed acceptance ABC-SMC
Approximate Bayesian computation (ABC) is now an established technique for
statistical inference used in cases where the likelihood function is
computationally expensive or not available. It relies on the use of a~model
that is specified in the form of a~simulator, and approximates the likelihood
at a~parameter value by simulating auxiliary data sets and
evaluating the distance of from the true data . However, ABC is not
computationally feasible in cases where using the simulator for each
is very expensive. This paper investigates this situation in cases where
a~cheap, but approximate, simulator is available. The approach is to employ
delayed acceptance Markov chain Monte Carlo (MCMC) within an ABC sequential
Monte Carlo (SMC) sampler in order to, in a~first stage of the kernel, use the
cheap simulator to rule out parts of the parameter space that are not worth
exploring, so that the ``true'' simulator is only run (in the second stage of
the kernel) where there is a~reasonable chance of accepting proposed values of
. We show that this approach can be used quite automatically, with few
tuning parameters. Applications to stochastic differential equation models and
latent doubly intractable distributions are presented
Reconciling cooperation, biodiversity and stability in complex ecological communities
Empirical observations show that ecological communities can have a huge
number of coexisting species, also with few or limited number of resources.
These ecosystems are characterized by multiple type of interactions, in
particular displaying cooperative behaviors. However, standard modeling of
population dynamics based on Lotka-Volterra type of equations predicts that
ecosystem stability should decrease as the number of species in the community
increases and that cooperative systems are less stable than communities with
only competitive and/or exploitative interactions. Here we propose a stochastic
model of population dynamics, which includes exploitative interactions as well
as cooperative interactions induced by cross-feeding. The model is exactly
solved and we obtain results for relevant macro-ecological patterns, such as
species abundance distributions and correlation functions. In the large system
size limit, any number of species can coexist for a very general class of
interaction networks and stability increases as the number of species grows.
For pure mutualistic/commensalistic interactions we determine the topological
properties of the network that guarantee species coexistence. We also show that
the stationary state is globally stable and that inferring species interactions
through species abundance correlation analysis may be misleading. Our
theoretical approach thus show that appropriate models of cooperation naturally
leads to a solution of the long-standing question about complexity-stability
paradox and on how highly biodiverse communities can coexist.Comment: 25 pages, 10 figure
Bayesian Experimental Design For Bayesian Hierarchical Models With Differential Equations For Ecological Applications
Ecologists are interested in the composition of species in various ecosystems. Studying population dynamics can assist environmental managers in making better decisions for the environment. Traditionally, the sampling of species has been recorded on a regular time frequency. However, sampling can be an expensive process due to financial and physical constraints. In some cases the environments are threatening, and ecologists prefer to limit their time collecting data in the field. Rather than convenience sampling, a statistical approach is introduced to improve data collection methods for ecologists by studying the dynamics associated with populations of interest. Population models including the logistic equation and the Lotka-Volterra differential equations are employed to simulate species composition. This research focuses on sequentially learning about the behavior of dynamical systems to better inform ecologists of when to sample. The developed algorithm of sequential optimality designs sampling regimes to assist ecologists with resource allocation while providing maximum information from the data. This research in its entirety constructs a method for designing sampling schedules for ecologists based on the dynamics associated with temporal ecological models
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