3,562 research outputs found
Daphnias: from the individual based model to the large population equation
The class of deterministic 'Daphnia' models treated by Diekmann et al. (J
Math Biol 61: 277-318, 2010) has a long history going back to Nisbet and Gurney
(Theor Pop Biol 23: 114-135, 1983) and Diekmann et al. (Nieuw Archief voor
Wiskunde 4: 82-109, 1984). In this note, we formulate the individual based
models (IBM) supposedly underlying those deterministic models. The models treat
the interaction between a general size-structured consumer population
('Daphnia') and an unstructured resource ('algae'). The discrete, size and
age-structured Daphnia population changes through births and deaths of its
individuals and throught their aging and growth. The birth and death rates
depend on the sizes of the individuals and on the concentration of the algae.
The latter is supposed to be a continuous variable with a deterministic
dynamics that depends on the Daphnia population. In this model setting we prove
that when the Daphnia population is large, the stochastic differential equation
describing the IBM can be approximated by the delay equation featured in
(Diekmann et al., l.c.)
Numerical equilibrium analysis for structured consumer resource models
In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for âDaphnia consuming algaeâ models in C-code. The results obtained by way of this implementation are shown in the form of graphs
Second look at the spread of epidemics on networks
In an important paper, M.E.J. Newman claimed that a general network-based
stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to
a bond percolation model, where the bonds are the edges of the contact network
and the bond occupation probability is equal to the marginal probability of
transmission from an infected node to a susceptible neighbor. In this paper, we
show that this isomorphism is incorrect and define a semi-directed random
network we call the epidemic percolation network that is exactly isomorphic to
the SIR epidemic model in any finite population. In the limit of a large
population, (i) the distribution of (self-limited) outbreak sizes is identical
to the size distribution of (small) out-components, (ii) the epidemic threshold
corresponds to the phase transition where a giant strongly-connected component
appears, (iii) the probability of a large epidemic is equal to the probability
that an initial infection occurs in the giant in-component, and (iv) the
relative final size of an epidemic is equal to the proportion of the network
contained in the giant out-component. For the SIR model considered by Newman,
we show that the epidemic percolation network predicts the same mean outbreak
size below the epidemic threshold, the same epidemic threshold, and the same
final size of an epidemic as the bond percolation model. However, the bond
percolation model fails to predict the correct outbreak size distribution and
probability of an epidemic when there is a nondegenerate infectious period
distribution. We confirm our findings by comparing predictions from percolation
networks and bond percolation models to the results of simulations. In an
appendix, we show that an isomorphism to an epidemic percolation network can be
defined for any time-homogeneous stochastic SIR model.Comment: 29 pages, 5 figure
Connectivity, neutral theories and the assessment of species vulnerability to global change in temperate estuaries
One of the main adaptation strategies to global change scenarios, aiming to preserve ecosystem functioning and biodiversity, is to maximise ecosystem resilience. The resilience of a species metapopulation can be improved by facilitating connectivity between local populations, which will prevent demographic stochasticity and inbreeding. The objective of this investigation is to estimate the degree of connectivity among estuarine species along the north-eastern Iberian coast, in order to assess community vulnerability to global change scenarios. To address this objective, two connectivity proxy types have been used based upon genetic and ecological drift processes: 1) DNA markers for the bivalve cockle (Cerastoderma edule) and seagrass Zostera noltei, and 2) the decrease in the number of species shared between two sites with geographic distance; neutral biodiversity theory predicts that dispersal limitation modulates this decrease, and this has been explored in estuarine plants and macroinvertebrates. Results indicate dispersal limitation for both saltmarsh plants and seagrass beds community and Z. noltei populations; this suggests they are especially vulnerable to expected climate changes on their habitats. In contrast, unstructured spatial pattern found in macroinvertebrate communities and in C. edule genetic populations in the area suggests that estuarine soft-bottom macroinvertebrates with planktonic larval dispersal strategies may have a high resilience capacity to moderate changes within their habitats. Our findings can help environmental managers to prioritise the most vulnerable species and habitats to be restored
Stability of Localized Wave Fronts in Bistable Systems
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation, and spatially inhomogeneous activating agents. We determine the conditions under which wave-front localization is possible and analyze the stability thereof with respect to extrinsic perturbations and internal noise. It is found that stability is enhanced upon regulating a positional signal and, surprisingly, also for a low degree of binding cooperativity. We further show a contrasting impact of self-activation to the stability of these two sources of destabilization. DOI: 10.1103/PhysRevLett.110.03810
Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation
We investigate saturation effects in susceptible-infected-susceptible (SIS)
models of the spread of epidemics in heterogeneous populations. The structure
of interactions in the population is represented by networks with connectivity
distribution ,including scale-free(SF) networks with power law
distributions . Considering cases where the transmission
of infection between nodes depends on their connectivity, we introduce a
saturation function which reduces the infection transmission rate
across an edge going from a node with high connectivity . A mean
field approximation with the neglect of degree-degree correlation then leads to
a finite threshold for SF networks with . We
also find, in this approximation, the fraction of infected individuals among
those with degree for close to . We investigate via
computer simulation the contact process on a heterogeneous regular lattice and
compare the results with those obtained from mean field theory with and without
neglect of degree-degree correlations.Comment: 6 figure
The role of clustering and gridlike ordering in epidemic spreading
The spreading of an epidemic is determined by the connectiviy patterns which
underlie the population. While it has been noted that a virus spreads more
easily on a network in which global distances are small, it remains a great
challenge to find approaches that unravel the precise role of local
interconnectedness. Such topological properties enter very naturally in the
framework of our two-timestep description, also providing a novel approach to
tract a probabilistic system. The method is elaborated for SIS-type epidemic
processes, leading to a quantitative interpretation of the role of loops up to
length 4 in the onset of an epidemic.Comment: Submitted to Phys. Rev. E; 15 pages, 11 figures, 5 table
Epidemic threshold in structured scale-free networks
We analyze the spreading of viruses in scale-free networks with high
clustering and degree correlations, as found in the Internet graph. For the
Suscetible-Infected-Susceptible model of epidemics the prevalence undergoes a
phase transition at a finite threshold of the transmission probability.
Comparing with the absence of a finite threshold in networks with purely random
wiring, our result suggests that high clustering and degree correlations
protect scale-free networks against the spreading of viruses. We introduce and
verify a quantitative description of the epidemic threshold based on the
connectivity of the neighborhoods of the hubs.Comment: 4 pages, 4 figure
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