12,314 research outputs found
Fitting stochastic predator-prey models using both population density and kill rate data
Most mechanistic predator-prey modelling has involved either parameterization
from process rate data or inverse modelling. Here, we take a median road: we
aim at identifying the potential benefits of combining datasets, when both
population growth and predation processes are viewed as stochastic. We fit a
discrete-time, stochastic predator-prey model of the Leslie type to simulated
time series of densities and kill rate data. Our model has both environmental
stochasticity in the growth rates and interaction stochasticity, i.e., a
stochastic functional response. We examine what the kill rate data brings to
the quality of the estimates, and whether estimation is possible (for various
time series lengths) solely with time series of population counts or biomass
data. Both Bayesian and frequentist estimation are performed, providing
multiple ways to check model identifiability. The Fisher Information Matrix
suggests that models with and without kill rate data are all identifiable,
although correlations remain between parameters that belong to the same
functional form. However, our results show that if the attractor is a fixed
point in the absence of stochasticity, identifying parameters in practice
requires kill rate data as a complement to the time series of population
densities, due to the relatively flat likelihood. Only noisy limit cycle
attractors can be identified directly from population count data (as in inverse
modelling), although even in this case, adding kill rate data - including in
small amounts - can make the estimates much more precise. Overall, we show that
under process stochasticity in interaction rates, interaction data might be
essential to obtain identifiable dynamical models for multiple species. These
results may extend to other biotic interactions than predation, for which
similar models combining interaction rates and population counts could be
developed
Evolution of predator dispersal in relation to spatio-temporal prey dynamics : how not to get stuck in the wrong place!
Peer reviewedPublisher PD
Diffusion-driven instabilities and emerging spatial patterns in patchy landscapes
Spatial variation in population densities across a landscape is a feature of many ecological systems, from
self-organised patterns on mussel beds to spatially restricted insect outbreaks. It occurs as a result of
environmental variation in abiotic factors and/or biotic factors structuring the spatial distribution of
populations. However the ways in which abiotic and biotic factors interact to determine the existence
and nature of spatial patterns in population density remain poorly understood. Here we present a new
approach to studying this question by analysing a predator–prey patch-model in a heterogenous
landscape. We use analytical and numerical methods originally developed for studying nearest-
neighbour (juxtacrine) signalling in epithelia to explore whether and under which conditions patterns
emerge. We find that abiotic and biotic factors interact to promote pattern formation. In fact, we find a
rich and highly complex array of coexisting stable patterns, located within an enormous number of
unstable patterns. Our simulation results indicate that many of the stable patterns have appreciable
basins of attraction, making them significant in applications. We are able to identify mechanisms for
these patterns based on the classical ideas of long-range inhibition and short-range activation, whereby
landscape heterogeneity can modulate the spatial scales at which these processes operate to structure
the populations
Memory and mutualism in species sustainability: a time-fractional Lotka-Volterra model with harvesting
We first present a predator-prey model for two species and then extend the
model to three species where the two predator species engage in mutualistic
predation. Constant effort harvesting and the impact of by-catch issue are also
incorporated. Necessary sufficient conditions for the existence and stability
of positive equilibrium points are examined. It is shown that harvesting is
sustainable, and the memory concept of the fractional derivative damps out
oscillations in the population numbers so that the system as a whole settles on
an equilibrium quicker than it would with integer time derivatives. Finally,
some possible physical explanations are given for the obtained results. It is
shown that the stability requires the memory concept in the model
Predator-prey cycles from resonant amplification of demographic stochasticity
In this paper we present the simplest individual level model of predator-prey
dynamics and show, via direct calculation, that it exhibits cycling behavior.
The deterministic analogue of our model, recovered when the number of
individuals is infinitely large, is the Volterra system (with density-dependent
prey reproduction) which is well-known to fail to predict cycles. This
difference in behavior can be traced to a resonant amplification of demographic
fluctuations which disappears only when the number of individuals is strictly
infinite. Our results indicate that additional biological mechanisms, such as
predator satiation, may not be necessary to explain observed predator-prey
cycles in real (finite) populations.Comment: 4 pages, 2 figure
Evolutionary ecology in-silico:evolving foodwebs, migrating population and speciation
We have generalized our ``unified'' model of evolutionary ecology by taking
into account the possible movements of the organisms from one ``patch'' to
another within the same eco-system. We model the spatial extension of the
eco-system (i.e., the geography) by a square lattice where each site
corresponds to a distinct ``patch''. A self-organizing hierarchical food web
describes the prey-predator relations in the eco-system. The same species at
different patches have identical food habits but differ from each other in
their reproductive characteristic features. By carrying out computer
simulations up to time steps, we found that, depending on the values of
the set of parameters, the distribution of the lifetimes of the species can be
either exponential or a combination of power laws. Some of the other features
of our ``unified'' model turn out to be robust against migration of the
organisms.Comment: 12 pages of PS file, including LATEX text and 9 EPS figure
Spontaneous emergence of spatial patterns ina a predator-prey model
We present studies for an individual based model of three interacting
populations whose individuals are mobile in a 2D-lattice. We focus on the
pattern formation in the spatial distributions of the populations. Also
relevant is the relationship between pattern formation and features of the
populations' time series. Our model displays travelling waves solutions,
clustering and uniform distributions, all related to the parameters values. We
also observed that the regeneration rate, the parameter associated to the
primary level of trophic chain, the plants, regulated the presence of
predators, as well as the type of spatial configuration.Comment: 17 pages and 15 figure
Evolutionary ecology in-silico: Does mathematical modelling help in understanding the "generic" trends?
Motivated by the results of recent laboratory experiments (Yoshida et al.
Nature, 424, 303-306 (2003)) as well as many earlier field observations that
evolutionary changes can take place in ecosystems over relatively short
ecological time scales, several ``unified'' mathematical models of evolutionary
ecology have been developed over the last few years with the aim of describing
the statistical properties of data related to the evolution of ecosystems.
Moreover, because of the availability of sufficiently fast computers, it has
become possible to carry out detailed computer simulations of these models. For
the sake of completeness and to put these recent developments in the proper
perspective, we begin with a brief summary of some older models of ecological
phenomena and evolutionary processes. However, the main aim of this article is
to review critically these ``unified'' models, particularly those published in
the physics literature, in simple language that makes the new theories
accessible to wider audience.Comment: 28 pages, LATEX, 4 eps figure
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