34 research outputs found

### Stochastic spatial models of host-pathogen and host-mutualist interactions I

Mutualists and pathogens, collectively called symbionts, are ubiquitous in
plant communities. While some symbionts are highly host-specific, others
associate with multiple hosts. The outcomes of multispecies host-symbiont
interactions with different degrees of specificity are difficult to predict at
this point due to a lack of a general conceptual framework. Complicating our
predictive power is the fact that plant populations are spatially explicit, and
we know from past research that explicit space can profoundly alter plant-plant
interactions. We introduce a spatially explicit, stochastic model to
investigate the role of explicit space and host-specificity in multispecies
host-symbiont interactions. We find that in our model, pathogens can
significantly alter the spatial structure of plant communities, promoting
coexistence, whereas mutualists appear to have only a limited effect. Effects
are more pronounced the more host-specific symbionts are.Comment: Published at http://dx.doi.org/10.1214/105051605000000782 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org

### Individual versus cluster recoveries within a spatially structured population

Stochastic modeling of disease dynamics has had a long tradition. Among the
first epidemic models including a spatial structure in the form of local
interactions is the contact process. In this article we investigate two
extensions of the contact process describing the course of a single disease
within a spatially structured human population distributed in social clusters.
That is, each site of the $d$-dimensional integer lattice is occupied by a
cluster of individuals; each individual can be healthy or infected. The
evolution of the disease depends on three parameters, namely the outside
infection rate which models the interactions between the clusters, the within
infection rate which takes into account the repeated contacts between
individuals in the same cluster, and the size of each social cluster. For the
first model, we assume cluster recoveries, while individual recoveries are
assumed for the second one. The aim is to investigate the existence of
nontrivial stationary distributions for both processes depending on the value
of each of the three parameters. Our results show that the probability of an
epidemic strongly depends on the recovery mechanism.Comment: Published at http://dx.doi.org/10.1214/105051605000000764 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org

### A spatially explicit model for competition among specialists and generalists in a heterogeneous environment

Competition is a major force in structuring ecological communities. The
strength of competition can be measured using the concept of a niche. A niche
comprises the set of requirements of an organism in terms of habitat,
environment and functional role. The more niches overlap, the stronger
competition is. The niche breadth is a measure of specialization: the smaller
the niche space of an organism, the more specialized the organism is. It
follows that, everything else being equal, generalists tend to be more
competitive than specialists. In this paper, we compare the outcome of
competition among generalists and specialists in a spatial versus a nonspatial
habitat in a heterogeneous environment. Generalists can utilize the entire
habitat, whereas specialists are restricted to their preferred habitat type. We
find that although competitiveness decreases with specialization, specialists
are more competitive in a spatial than in a nonspatial habitat as patchiness
increases.Comment: Published at http://dx.doi.org/10.1214/105051606000000394 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org

### Spatially explicit non-Mendelian diploid model

We introduce a spatially explicit model for the competition between type $a$
and type $b$ alleles. Each vertex of the $d$-dimensional integer lattice is
occupied by a diploid individual, which is in one of three possible states or
genotypes: $aa$, $ab$ or $bb$. We are interested in the long-term behavior of
the gene frequencies when Mendel's law of segregation does not hold. This
results in a voter type model depending on four parameters; each of these
parameters measures the strength of competition between genes during meiosis.
We prove that with or without a spatial structure, type $a$ and type $b$
alleles coexist at equilibrium when homozygotes are poor competitors. The
inclusion of a spatial structure, however, reduces the parameter region where
coexistence occurs.Comment: Published in at http://dx.doi.org/10.1214/09-AAP598 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org

### Coexistence for a multitype contact process with seasons

We introduce a multitype contact process with temporal heterogeneity
involving two species competing for space on the $d$-dimensional integer
lattice. Time is divided into seasons called alternately season 1 and season 2.
We prove that there is an open set of the parameters for which both species can
coexist when their dispersal range is large enough. Numerical simulations also
suggest that three species can coexist in the presence of two seasons. This
contrasts with the long-term behavior of the time-homogeneous multitype contact
process for which the species with the higher birth rate outcompetes the other
species when the death rates are equal.Comment: Published in at http://dx.doi.org/10.1214/09-AAP599 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org

### Contact and voter processes on the infinite percolation cluster as models of host-symbiont interactions

We introduce spatially explicit stochastic processes to model multispecies
host-symbiont interactions. The host environment is static, modeled by the
infinite percolation cluster of site percolation. Symbionts evolve on the
infinite cluster through contact or voter type interactions, where each host
may be infected by a colony of symbionts. In the presence of a single symbiont
species, the condition for invasion as a function of the density of the habitat
of hosts and the maximal size of the colonies is investigated in details. In
the presence of multiple symbiont species, it is proved that the community of
symbionts clusters in two dimensions whereas symbiont species may coexist in
higher dimensions.Comment: Published in at http://dx.doi.org/10.1214/10-AAP734 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org

### Opinion dynamics: models, extensions and external effects

Recently, social phenomena have received a lot of attention not only from
social scientists, but also from physicists, mathematicians and computer
scientists, in the emerging interdisciplinary field of complex system science.
Opinion dynamics is one of the processes studied, since opinions are the
drivers of human behaviour, and play a crucial role in many global challenges
that our complex world and societies are facing: global financial crises,
global pandemics, growth of cities, urbanisation and migration patterns, and
last but not least important, climate change and environmental sustainability
and protection. Opinion formation is a complex process affected by the
interplay of different elements, including the individual predisposition, the
influence of positive and negative peer interaction (social networks playing a
crucial role in this respect), the information each individual is exposed to,
and many others. Several models inspired from those in use in physics have been
developed to encompass many of these elements, and to allow for the
identification of the mechanisms involved in the opinion formation process and
the understanding of their role, with the practical aim of simulating opinion
formation and spreading under various conditions. These modelling schemes range
from binary simple models such as the voter model, to multi-dimensional
continuous approaches. Here, we provide a review of recent methods, focusing on
models employing both peer interaction and external information, and
emphasising the role that less studied mechanisms, such as disagreement, has in
driving the opinion dynamics. [...]Comment: 42 pages, 6 figure

### Behavioral Modernity and the Cultural Transmission of Structured Information: The Semantic Axelrod Model

Cultural transmission models are coming to the fore in explaining increases
in the Paleolithic toolkit richness and diversity. During the later
Paleolithic, technologies increase not only in terms of diversity but also in
their complexity and interdependence. As Mesoudi and O'Brien (2008) have shown,
selection broadly favors social learning of information that is hierarchical
and structured, and multiple studies have demonstrated that teaching within a
social learning environment can increase fitness. We believe that teaching also
provides the scaffolding for transmission of more complex cultural traits.
Here, we introduce an extension of the Axelrod (1997} model of cultural
differentiation in which traits have prerequisite relationships, and where
social learning is dependent upon the ordering of those prerequisites. We
examine the resulting structure of cultural repertoires as learning
environments range from largely unstructured imitation, to structured teaching
of necessary prerequisites, and we find that in combination with individual
learning and innovation, high probabilities of teaching prerequisites leads to
richer cultural repertoires. Our results point to ways in which we can build
more comprehensive explanations of the archaeological record of the Paleolithic
as well as other cases of technological change.Comment: 24 pages, 7 figures. Submitted to "Learning Strategies and Cultural
Evolution during the Paleolithic", edited by Kenichi Aoki and Alex Mesoudi,
and presented at the 79th Annual Meeting of the Society for American
Archaeology, Austin TX. Revised 5/14/1

### Opinion formation in multiplex networks with general initial distributions

We study opinion dynamics over multiplex networks where agents interact with bounded confidence. Namely, two neighbouring individuals exchange opinions and compromise if their opinions do not differ by more than a given threshold. In literature, agents are generally assumed to have a homogeneous confidence bound. Here, we study analytically and numerically opinion evolution over structured networks characterised by multiple layers with respective confidence thresholds and general initial opinion distributions. Through rigorous probability analysis, we show analytically the critical thresholds at which a phase transition takes place in the long-term consensus behaviour, over multiplex networks with some regularity conditions. Our results reveal the quantitative relation between the critical threshold and initial distribution. Further, our numerical simulations illustrate the consensus behaviour of the agents in network topologies including lattices and, small-world and scale-free networks, as well as for structure-dependent convergence parameters accommodating node heterogeneity. We find that the critical thresholds for consensus tend to agree with the predicted upper bounds in Theorems 4 and 5 in this paper. Finally, our results indicate that multiplexity hinders consensus formation when the initial opinion configuration is within a bounded range and, provide insight into information diffusion and social dynamics in multiplex systems modeled by networks