momeq2s.bib
@INCOLLECTION{vanb00,
AUTHOR = {Minus van Baalen},
TITLE = {Pair Approximations for Different Spatial Geometries},
CROSSREF = {DLM00},
PAGES = {359-387},
CHAPTER = {19}
}
@INCOLLECTION{Law+01,
AUTHOR = {R. Law and D. W. Purves. and D. J. Murrell and U. Dieckmann},
TITLE = {Causes and
effects of small-scale spatial structure in plant populations},
BOOKTITLE = {Integrating Ecology and Evolution in a Spatial
Context},
PAGES = {21-44},
PUBLISHER = {Blackwell Science},
YEAR = {2001},
EDITOR = {J. Silvertown and J. Antonovics},
ADDRESS = {Oxford, UK},
ABSTRACT = {This chapter is a slightly more gentle introduction to moment dynamics and
the importance of considering local interactions for plant populations and
communities}
}
@ARTICLE{vanbrand98,
AUTHOR = {van Baalen, M. and D. A. Rand},
TITLE = {The unit of selection in viscous populations and the
evolution of altruism},
JOURNAL = {Journal of Theoretical Biology},
VOLUME = {193},
NUMBER = {4},
PAGES = {631-648},
YEAR = {1998}
}
@ARTICLE{bol99,
AUTHOR = {Benjamin M. Bolker},
TITLE = {Analytic Models for the Patchy Spread of Plant Disease},
JOURNAL = {Bulletin of Mathematical Biology},
VOLUME = 61,
PAGES = {849-874},
YEAR = 1999,
ABSTRACT = {Basic application of spatial moment closure (power-1) to
dynamics of a simple epidemic. Considers the covariance dynamics in
a Poisson-distributed and aggregated host populations, and looks
briefly at epidemics with removal/recovery.}
}
@ARTICLE{bolkpaca97,
AUTHOR = {B. M. Bolker and S. W. Pacala},
TITLE = {Using moment equations to understand stochastically driven
spatial pattern formation in ecological systems},
JOURNAL = {Theoretical Population Biology},
VOLUME = {52},
PAGES = {179-197},
YEAR = 1997,
ABSTRACT = {Spatial moment equations (power-1 closure) for the spatial
logistic model, one-species competition. Analytical methods for
solving for equilibrium are presented (but these methods are somewhat
clumsy, and are superseded
by those in Bolker and Pacala 1999). Predicts when equilibrium
population patterns will be even vs. aggregated.}
}
@ARTICLE{bp98,
AUTHOR = {B. M. Bolker and S. W. Pacala},
TITLE = {Spatial moment equations for plant competition:
understanding spatial strategies and the advantages of
short dispersal},
JOURNAL = {American Naturalist},
VOLUME = {153},
PAGES = {575-602},
YEAR = 1999,
ABSTRACT = {Analyzes the "spatial Lotka-Volterra model": two-species
competition in a point process model. Decomposes spatial covariances
into a series of terms that affect competitive invasion, attributing
different terms to competition-colonization tradeoffs, successional
niches, or phalanx growth. Uses power-1 closure and Bessel-function
competition and dispersal kernels to get analytically tractable
invasion criteria. (However, power-1 closure means that
invasion criteria only act sensibly when the invader would lose
in the non-spatial case.)}
}
@INPROCEEDINGS{bpl97,
AUTHOR = {Benjamin M. Bolker and Stephen W. Pacala and Simon A.
Levin},
TITLE = {Moment methods for stochastic processes in continuous
space and time},
BOOKTITLE = {The Geometry of Ecological Interactions: Simplifying
Spatial Complexity},
EDITOR = {U. Dieckmann and R. Law and J. A. J. Metz},
PAGES = {388-411},
PUBLISHER = {Cambridge University Press},
YEAR = 2000
}
@ARTICLE{cdg+01,
AUTHOR = {T. Caraco and M. C. Duryea and S. Glavanakov and W.
Maniatty and B. K. Szymanski},
TITLE = {Host spatial heterogeneity and the spread of vector-borne
infection},
JOURNAL = {Theoretical Population Biology},
VOLUME = {59},
NUMBER = {3},
PAGES = {185-206},
YEAR = {2001}
}
@INCOLLECTION{diecklaw00b,
AUTHOR = {Ulf Dieckmann and Richard Law},
TITLE = {Relaxation Projections and the Method of Moments},
CROSSREF = {DLM00},
PAGES = {412-455},
CHAPTER = {21}
}
@BOOK{dlm00,
EDITOR = {Ulf Dieckmann and Richard Law and Johan A. J. Metz},
TITLE = {The Geometry of Ecological Interactions: Simplifying
Spatial Complexity},
PUBLISHER = {Cambridge University Press},
YEAR = {2000},
SERIES = {Cambridge Studies in Adaptive Dynamics},
ADDRESS = {Cambridge, UK}
}
@ARTICLE{dow99,
AUTHOR = {U. Dieckmann and B. O'Hara and W. Weisser},
TITLE = {The evolutionary ecology of dispersal},
JOURNAL = {Trends in Ecology \& Evolution},
VOLUME = {14},
NUMBER = {3},
PAGES = {88-90},
YEAR = {1999}
}
@ARTICLE{dush98,
AUTHOR = {Jonathan Dushoff},
TITLE = {Host Heterogeneity and Disease Endemicity: A Moment-Based
Approach},
JOURNAL = {Theoretical Population Biology},
VOLUME = 56,
PAGES = {325-335},
YEAR = {1999},
ABSTRACT = {non-spatial moment closure for the dynamics of the
distribution of host susceptibility. Incorporates a
particularly clever "scaled closure" that interpolates
between invasion-phase and equilibrium-phase statistics}
}
@ARTICLE{elln01,
AUTHOR = {S. P. Ellner},
TITLE = {Pair approximation for lattice models with multiple
interaction scales},
JOURNAL = {Journal of Theoretical Biology},
VOLUME = {210},
NUMBER = {4},
PAGES = {435-447},
MONTH = {jun 21},
YEAR = {2001}
}
@ARTICLE{ellner98,
AUTHOR = {Stephen P. Ellner and Akira Sasaki and Yoshihiro Haraguchi
and Hirotsugu Matsuda},
TITLE = {Speed of invasion in lattice population models: pair-edge
approximation},
JOURNAL = {Journal of Mathematical Biology},
VOLUME = {36},
NUMBER = {5},
PAGES = {469-484},
YEAR = 1998
}
@ARTICLE{fili99,
AUTHOR = {J. A. N. Filipe},
TITLE = {Hybrid closure-approximation to epidemic models},
JOURNAL = {Physica A},
VOLUME = {266},
NUMBER = {1-4},
PAGES = {238-241},
YEAR = {1999},
ABSTRACT = {A hybrid approximation method that elaborates on the
common pair approximation is proposed and shown to give
very accurate predictions for the order parameter (epidemic
size) over the whole parameter-space, including the
critical region.}
}
@ARTICLE{filigibs01,
AUTHOR = {J. A. N. Filipe and G. J. Gibson},
TITLE = {Comparing approximations to spatio-temporal models for
epidemics with local spread},
JOURNAL = {Bulletin of Mathematical Biology},
VOLUME = {63},
NUMBER = {4},
PAGES = {603-624},
MONTH = JUL,
YEAR = {2001},
ABSTRACT = {Here we review and report recent progress on closure
approximations applicable to lattice models with
nearest-neighbour interactions, including cluster
approximations and elaborations on the pair (or pairwise)
approximation. (SIS model) A hybrid pairwise approximation
is shown to provide the best predictions of transient and
long-term, stationary behaviour over the whole parameter
range of the model.}
}
@ARTICLE{filigibs98,
AUTHOR = {J. A. N. Filipe and G. J. Gibson},
TITLE = {Studying and approximating spatio-temporal models for
epidemic spread and control},
JOURNAL = {Philosophical Transactions of the Royal Society of London
Series B-biological Sciences},
VOLUME = {353},
NUMBER = {1378},
PAGES = {2153-2162},
MONTH = {dec 29},
YEAR = {1998},
ABSTRACT = {A class of simple spatio-temporal stochastic models for
the spread and control of plant disease is investigated. We
consider a lattice-based susceptible-infected model in
which the infection of a host occurs through two distinct
processes: a background infective challenge representing
primary infection from external sources, and a short-range
:interaction representing the secondary infection of
susceptibles by infectives within the population. Recent
data-modelling studies have suggested that the above model
may describe the spread of aphid-borne virus diseases in
orchards. In addition, we extend the model to represent the
effects of different control strategies involving
replantation (or recovery). The Contact Process is a
particular case of this model. The behaviour of the model
has been studied using cellular-automata simulations. An
alternative approach is to formulate a set of deterministic
differential equations that captures the essential dynamics
of the stochastic system. Approximate solutions to this set
of equations, describing the time evolution over the whole
parameter range, have been obtained using the pairwise
approximation (PA) as well as the most commonly used
mean-field approximation (MF). Comparison with simulation
results shows that PA is significantly superior to MF,
predicting accurately both transient and long-run,
stationary behaviour over relevant parts of the parameter
space. The conditions for the validity of the
approximations to the present model and extensions thereof
are discussed.}
}
@ARTICLE{glo00,
AUTHOR = {A. Gandhi and S. Levin and S. Orszag},
TITLE = {Moment expansions in spatial ecological models and moment
closure through gaussian approximation},
JOURNAL = {Bulletin of Mathematical Biology},
VOLUME = {62},
NUMBER = {4},
PAGES = {595-632},
MONTH = JUL,
YEAR = {2000}
}
@ARTICLE{hei+95,
AUTHOR = {Y. Harada and H. Ezoe and Y. Iwasa and H. Matsuda and K.
Sato},
TITLE = {Population persistence and spatially limited
social-interaction},
JOURNAL = {Theoretical Population Biology},
VOLUME = {48},
NUMBER = {1},
PAGES = {65-91},
MONTH = AUG,
YEAR = {1995}
}
@ARTICLE{haraiwas94,
AUTHOR = {Yuko Harada and Yoh Iwasa},
TITLE = {Lattice Population Dynamics for Plants with Dispersing
Seeds and Vegetative Propagation},
JOURNAL = {Researches on Population Ecology},
YEAR = {1994},
VOLUME = {36},
NUMBER = {2},
PAGES = {237-249}
}
@ARTICLE{haraiwas96,
AUTHOR = {Y. Harada and Y. Iwasa},
TITLE = {Analyses of spatial patterns and population processes of
clonal plants},
JOURNAL = {Researches On Population Ecology},
VOLUME = {38},
NUMBER = {2},
PAGES = {153-164},
MONTH = DEC,
YEAR = {1996}
}
@ARTICLE{harasasa00,
AUTHOR = {Y. Haraguchi and A. Sasaki},
TITLE = {The evolution of parasite virulence and transmission rate
in a spatially structured population},
JOURNAL = {Journal of Theoretical Biology},
VOLUME = {203},
NUMBER = {2},
PAGES = {85-96},
MONTH = {mar 21},
YEAR = {2000}
}
@ARTICLE{hieb00,
AUTHOR = {D. Hiebeler},
TITLE = {Populations on fragmented landscapes with spatially
structured heterogeneities: landscape generation and local
dispersal},
JOURNAL = {Ecology},
VOLUME = {81},
NUMBER = {6},
PAGES = {1629-1641},
MONTH = JUN,
YEAR = {2000}
}
@ARTICLE{hieb97,
AUTHOR = {D. Hiebeler},
TITLE = {Stochastic spatial models: from simulations to mean field
and local structure approximations},
JOURNAL = {Journal of Theoretical Biology},
VOLUME = {187},
NUMBER = {3},
PAGES = {307-319},
MONTH = {aug 7},
YEAR = {1997}
}
@INCOLLECTION{iwas00,
AUTHOR = {Yoh Iwasa},
TITLE = {Lattice Models and Pair Approximation in Ecology},
CROSSREF = {DLM00},
PAGES = {227-251},
CHAPTER = {13}
}
@ARTICLE{inl98,
AUTHOR = {Y. Iwasa and M. Nakamaru and S. A. Levin},
TITLE = {Allelopathy of bacteria in a lattice population:
competition between colicin-sensitive and colicin-producing
strains},
JOURNAL = {Evolutionary Ecology},
VOLUME = {12},
NUMBER = {7},
PAGES = {785-802},
MONTH = OCT,
YEAR = {1998}
}
@INCOLLECTION{keel00c,
AUTHOR = {Matthew J. Keeling},
TITLE = {Evolutionary Dynamics in Spatial Host-Parasite Systems},
CROSSREF = {DLM00},
PAGES = {271-291},
CHAPTER = {15}
}
@ARTICLE{keel00,
AUTHOR = {M. J. Keeling},
TITLE = {Metapopulation moments: coupling, stochasticity and
persistence},
JOURNAL = {Journal of Animal Ecology},
VOLUME = {69},
NUMBER = {5},
PAGES = {725-736},
MONTH = SEP,
YEAR = {2000}
}
@ARTICLE{keel00b,
AUTHOR = {M. J. Keeling},
TITLE = {Multiplicative moments and measures of persistence in
ecology},
JOURNAL = {Journal of Theoretical Biology},
VOLUME = {205},
NUMBER = {2},
PAGES = {269-281},
MONTH = {jul 21},
YEAR = {2000}
}
@ARTICLE{keel99,
AUTHOR = {M. J. Keeling},
TITLE = {Correlation equations for endemic diseases: externally
imposed and internally generated heterogeneity},
JOURNAL = {Proceedings of the Royal Society of London Series B},
VOLUME = {266},
NUMBER = {1422},
PAGES = {953-960},
YEAR = 1999
}
@ARTICLE{krm97,
AUTHOR = {M. J. Keeling and D. A. Rand and A. J. Morris},
TITLE = {Correlation models for childhood epidemics},
JOURNAL = {Proceedings of the Royal Society of London B},
YEAR = {1997},
VOLUME = {264},
PAGES = {1149-1156}
}
@ARTICLE{kif96,
AUTHOR = {T. Kubo and Y. Iwasa and N. Furumoto},
TITLE = {Forest spatial dynamics with gap expansion: total gap area
and gap size distribution},
JOURNAL = {Journal of Theoretical Biology},
VOLUME = {180},
NUMBER = {3},
PAGES = {18},
YEAR = {1996}
}
@INCOLLECTION{lawdiec00,
AUTHOR = {Richard Law and Ulf Dieckmann},
TITLE = {Moment Approximations of Individual-Based Models},
CROSSREF = {DLM00},
PAGES = {252-270},
CHAPTER = {14}
}
@ARTICLE{lawdiec00b,
AUTHOR = {R. Law and U. Dieckmann},
TITLE = {A dynamical system for neighborhoods in plant communities},
JOURNAL = {Ecology},
VOLUME = {81},
NUMBER = {8},
PAGES = {2137-2148},
MONTH = AUG,
YEAR = {2000}
}
@INCOLLECTION{levipaca96,
AUTHOR = {S.A. Levin and S.W. Pacala},
TITLE = {Theories of simplification and scaling in ecological
systems},
BOOKTITLE = {Spatial Ecology: The Role of Space in Population Dynamics
and Interspecific Interactions},
PUBLISHER = {Princeton University Press},
YEAR = {1998},
EDITOR = {D. Tilman and P. Kareiva},
ADDRESS = {Princeton, NJ}
}
@ARTICLE{lewi00,
AUTHOR = {M. A. Lewis},
TITLE = {Spread rate for a nonlinear stochastic invasion},
JOURNAL = {Journal of Mathematical Biology},
VOLUME = {41},
NUMBER = {5},
PAGES = {430-454},
MONTH = NOV,
YEAR = {2000}
}
@ARTICLE{lewipaca00,
AUTHOR = {M. A. Lewis and S. Pacala},
TITLE = {Modeling and analysis of stochastic invasion processes},
JOURNAL = {Journal of Mathematical Biology},
VOLUME = {41},
NUMBER = {5},
PAGES = {387-429},
MONTH = NOV,
YEAR = {2000}
}
@ARTICLE{mats+92,
AUTHOR = {Hirotsuga Matsuda and Naofumi Ogita and Akira Sasaki and
Kazunori Sat\=o},
TITLE = {Statistical Mechanics of Population: The Lattice
{Lotka-Volterra} Model},
JOURNAL = {Progress of Theoretical Physics},
YEAR = {1992},
VOLUME = {88},
NUMBER = {6},
PAGES = {1035-1049}
}
@INPROCEEDINGS{lin97,
AUTHOR = {Ryan McAllister and Juan Lin and Benjamin Bolker and
Stephen W. Pacala},
TITLE = {Spatial correlations in population models with competition
and dispersal},
BOOKTITLE = {Proceedings of the Symposium on Biological Complexity},
YEAR = {to appear},
ADDRESS = {Montevideo, Uruguay},
MONTH = {Dec. 12-14, 1995}
}
@ARTICLE{murrlaw00,
AUTHOR = {D. J. Murrell and R. Law},
TITLE = {Beetles in fragmented woodlands: a formal framework for
dynamics of movement in ecological landscapes},
JOURNAL = {Journal of Animal Ecology},
VOLUME = {69},
NUMBER = {3},
PAGES = {471-483},
MONTH = MAY,
YEAR = {2000},
ABSTRACT = {This paper uses a moment approximation
to an individual-based model of animals moving through a heterogeneous
landscape taken from a satellite image of the UK. Note that the moment
closure used here works only when the first moments (population densities)
have no dynamics; i.e. when only the spatial structure of the population
changes. }
}
@ARTICLE{BootSasa99,
AUTHOR = {M. Boots and A. Sasaki},
TITLE = {'Small worlds' and the evolution of virulence:
infection occurs locally and at a distance},
JOURNAL = { Proceedings of the Royal Society
of London, Series B},
YEAR = {1999},
VOLUME = { 266},
PAGES = { 1933-1938},
ABSTRACT = {Uses the pairwise approach
to look at the effects of long range (global) dispersal and short range
dispersal on the evolutionary dynamics of infectious diseases}
}
@ARTICLE{nmi97,
AUTHOR = {M. Nakamaru and H. Matsuda and Y. Iwasa},
TITLE = {The evolution of cooperation in a lattice-structured
population},
JOURNAL = {Journal of Theoretical Biology},
VOLUME = {184},
NUMBER = {1},
PAGES = {65-81},
MONTH = {jan 7},
YEAR = {1997}
}
@INCOLLECTION{pacalevi96,
AUTHOR = {S.W. Pacala and S.A. Levin},
TITLE = {Biologically generated spatial pattern and the coexistence
of competing species},
BOOKTITLE = {Spatial Ecology: The Role of Space in Population Dynamics
and Interspecific Interactions},
PUBLISHER = {Princeton University Press},
CHAPTER = {9},
PAGES = {204-232},
YEAR = {1998},
EDITOR = {D. Tilman and P. Kareiva},
ADDRESS = {Princeton, NJ}
}
@INCOLLECTION{rand98,
AUTHOR = {D. A. Rand},
EDITOR = {J. McGlade},
TITLE = {Correlation equations and pair approximations for spatial
ecologies},
BOOKTITLE = {Theoretical Ecology 2},
PUBLISHER = {Blackwell},
YEAR = {1999}
}
@INCOLLECTION{satoiwas00,
AUTHOR = {Kazunori Sat{\=o} and Yoh Iwasa},
TITLE = {Pair Approximations for Lattice-based Ecological Models},
CROSSREF = {DLM00},
PAGES = {341-358},
CHAPTER = {18}
}
@ARTICLE{sms94,
AUTHOR = {K. Sato and H. Matsuda and A. Sasaki},
TITLE = {Pathogen invasion and host extinction in lattice
structured populations},
JOURNAL = {Journal of Mathematical Biology},
VOLUME = {32},
NUMBER = {3},
PAGES = {251-268},
MONTH = FEB,
YEAR = {1994}
}
@ARTICLE{sato+94,
AUTHOR = {Kazunori Sat\=o and Hirotsugu Matsuda and Akira Sasaki},
TITLE = {Pathogen invasion and host extinction in lattice
structured populations},
JOURNAL = {Journal of Mathematical Biology},
YEAR = {1994},
VOLUME = {32},
PAGES = {251-268}
}
@ARTICLE{snydnisb00,
AUTHOR = {Robin E. Snyder and Roger M. Nisbet},
TITLE = {Spatial structure and fluctuations in the contact process and related
models},
JOURNAL = {Bulletin of Mathematical Biology},
YEAR = {2000},
VOLUME = 62,
NUMBER = 5,
PAGES = {959-975},
ABSTRACT = {The contact process is used as a simple spatial model in many
disciplines, yet because of the buildup of spatial correlations, its
dynamics remain difficult to capture analytically. We introduce an
empirically based, approximate method of characterizing the spatial
correlations with only a single adjustable parameter. This approximation
allows us to recast the contact process in terms of a stochastic
birth-death process, converting a spatiotemporal problem into a simpler
temporal one. We obtain considerably more accurate predictions of
equilibrium population than those given by pair approximations, as well
as good predictions of population variance and first passage time
distributions to a given (low) threshold. A similar approach is
applicable to any model with a combination of global and nearest-neighbor
interactions.}
}
@ARTICLE{tain88,
AUTHOR = {Kei{-}ichi Tainaka},
TITLE = {Lattice Model for the {Lotka-Volterra} System},
JOURNAL = {Journal of the Physical Society of Japan},
YEAR = {1988},
VOLUME = {57},
NUMBER = {88},
PAGES = {2588-2590}
}
@ARTICLE{tain94,
AUTHOR = {Kei-ichi Tainaka},
TITLE = {Vortices and strings in a model ecosystem},
JOURNAL = {Physical Review E},
YEAR = {1994},
VOLUME = {50},
NUMBER = {5},
PAGES = {3401-3409}
}
@ARTICLE{tmi97,
AUTHOR = {Y. Takenaka and H. Matsuda and Y. Iwasa},
TITLE = {Competition and evolutionary stability of plants in a
spatially structured habitat},
JOURNAL = {Researches On Population Ecology},
VOLUME = {39},
NUMBER = {1},
PAGES = {67-75},
MONTH = JUN,
YEAR = {1997}
}
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