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SUMMARY:A prey-predator model with gestation period
DTSTART;VALUE=DATE-TIME:20180709T011000Z
DTEND;VALUE=DATE-TIME:20180709T013000Z
DTSTAMP;VALUE=DATE-TIME:20220819T202127Z
UID:indico-contribution-65-219@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Yoichi Enatsu (Tokyo University of Science)\nIn this
talk\, we consider the dynamics of a Lotka-Volterra prey-predator model b
y a class of delay differential equations. The number of prey varies due t
o a general nonlinear predators' consumption rate with delays. Under the a
ssumption that the consumption rate is monotonically increasing with respe
ct to the number of prey\, we investigate the effect of the nonlinearity a
nd delays on the asymptotic behaviour of the model. For the case where the
consumption rate is described not only as Holling type I\,II but also as
Holling type III\, some ongoing studies are also introduced. Comparison fo
r the assumptions on the incidence rates appearing in prey-predator models
with those in epidemiological models\, will be also discussed.\n\nhttps:/
/conferences.maths.unsw.edu.au/event/2/contributions/219/
LOCATION:University of Sydney New Law School/--028
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/219/
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SUMMARY:Bayesian modelling on the expected extinction time of species.
DTSTART;VALUE=DATE-TIME:20180709T021000Z
DTEND;VALUE=DATE-TIME:20180709T023000Z
DTSTAMP;VALUE=DATE-TIME:20220819T202127Z
UID:indico-contribution-65-342@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Saritha Kodikara (Discipline of Mathematical Science
s\, School of Science\, RMIT University\, Melbourne\, Australia)\nIn this
study\, we propose a new Bayesian approach to calculate the expected extin
ction time of a species based on historical sighting record data. Unlike o
ther work\, our model allows comprehensively for uncertainties\, provides
the expected extinction time and the probability of extinction. It is ex
tremely difficult to determine whether a species is extinct based on histo
rical sighting records because knowing whether the last surviving individu
al of a species has finally died\, or is just unobserved\, remains proble
matical. Moreover\, an incorrect classification of a species as extinct c
an lead to failure in conserving a threatened species. On the other hand\,
it is also undesirable to classify a species as extant when it is actuall
y extinct as it can lead to misallocation of funds. Sightings with uncerta
in validity (uncertain sightings) play an important role in the inferences
made and need to be taken into account better than they have been. Recen
t studies have considered uncertain sightings while making inferences abou
t extinction\; however\, the difficulty of the problem requires making a n
umber of limiting assumptions that significantly reduce realism. We have a
ttempted to derive a more general model by incorporating sighting validity
into a new Bayesian model development. We employ the underlying idea of t
he beta-geometric/beta-binomial (BG/BB) model to build our Bayesian approa
ch for the analysis of extinction. Using the likelihood for the sighting d
ata\, along with the prior distributions of sighting probability and extin
ction probability\, we calculate the expected extinction time using a Mark
ov Chain Monte Carlo (MCMC) method which we simulate with JAGS. We apply t
his new approach to the sighting records of Caribbean monk seal (CMS)\, Do
do and Ivory-Billed Woodpecker species. Unlike other approaches that consi
der uncertainties in the sightings\, our model gives Bayesian confidence i
ntervals for the expected extinction time of a species.\n\nhttps://confere
nces.maths.unsw.edu.au/event/2/contributions/342/
LOCATION:University of Sydney New Law School/--028
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/342/
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SUMMARY:Optimal monitoring and decision support for the end of an eradicat
ion campaign
DTSTART;VALUE=DATE-TIME:20180709T015000Z
DTEND;VALUE=DATE-TIME:20180709T021000Z
DTSTAMP;VALUE=DATE-TIME:20220819T202127Z
UID:indico-contribution-65-305@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Christopher Baker (The University of Queensland)\nIn
troduced species are a critical threat to Australian ecosystems and specie
s. Particularly noxious examples include the European carp\, feral cats\,
and a variety of weeds. A central aspect of introduced species management
is eradication â€“ if they can be completely removed from a region\, the i
mpact can be nullified. A central problem population eradications is knowi
ng whether the species has been successfully removed or not. We develop a
framework to model populations through time\, explicitly accounting for im
perfect detection and unknown detection probability. We use changing detec
tion rates throughout a removal project to calibrate the model\, which pro
vides a quantitative method to trigger the end of a project. While invasiv
e species are often the focus of removal efforts\, they can also occur to
prevent disease spread in an endangered species. I will describe how we ap
plied this method to a Tasmanian devil depopulation\, which enabled the es
tablishment of a Tasmanian devil facial tumour disease population on Fores
tier Peninsular\, Tasmania.\n\nhttps://conferences.maths.unsw.edu.au/event
/2/contributions/305/
LOCATION:University of Sydney New Law School/--028
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/305/
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SUMMARY:Individual based modelling of the effects of cannibalism on geneti
c resistance to Bt in the fall armyworm
DTSTART;VALUE=DATE-TIME:20180709T005000Z
DTEND;VALUE=DATE-TIME:20180709T011000Z
DTSTAMP;VALUE=DATE-TIME:20220819T202127Z
UID:indico-contribution-65-340@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: William Jamieson (University of Nebraska-Lincoln)\nT
he fall armyworm (*Spodoptera frugiperda*) is a pest insect which has the
propensity to destroy a wide variety of common crops. It ranges over Easte
rn and Central North America and\, since 2016\, has been invasive in Afric
a resulting in significant economic damage. The fall armyworm is susceptib
le to Bt derived insecticides\, making Bt modified crops a viable method f
or controlling this species. However\, there is evidence to suggest that t
here is a small subpopulation of the fall armyworm which is resistant to B
t. This population remains relatively small in the wild due to the cost of
resistance\, which is partially mediated by the aggressive cannibalism ex
hibited by the larvae\, since resistant larvae grow at a slower rate. Thus
it may be possible to control the rise of resistance to Bt in a fall army
worm population via the creation of refuges for the nonresistant larvae wh
o will in turn cannibalize the resistant larvae.\n\nHere we use an individ
ual base modelling (IBM) approach to model an infestation of fall armyworm
s\, which models every individualâ€™s entire life cycle including cannibal
istic encounters and the effects of its Bt resistance genotype. First\, we
explore the best underlying mathematical models to describe the individua
l insects in the IBM. Then we examine the problem of controlling the accum
ulation of resistance to Bt via adjustments to the size and spacial layout
of the refuge while limiting the damage to the effected crops.\n\nhttps:/
/conferences.maths.unsw.edu.au/event/2/contributions/340/
LOCATION:University of Sydney New Law School/--028
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/340/
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SUMMARY:Inequality in resource allocation among individuals and population
dynamics models
DTSTART;VALUE=DATE-TIME:20180709T013000Z
DTEND;VALUE=DATE-TIME:20180709T015000Z
DTSTAMP;VALUE=DATE-TIME:20220819T202127Z
UID:indico-contribution-65-427@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Masahiro Anazawa (Tohoku Institute of Technology)\nT
he Hassell equation is a classic discrete-time population model which has
been widely used to model population dynamics of species with seasonal rep
roduction. This equation is a generalization of the Beverton-Holt equatio
n with an additional exponent\, and can describe various types of reproduc
tion curves exhibiting from exact-compensation (contest competition) to ov
er-compensation (scramble competition) depending on the value of the expon
ent. The value of the exponent and the resulting density dependence is th
ought to be related to the degree of inequality in resource allocation amo
ng individuals\; contest curves result from unequal resource allocation\,
and scramble curves\, from equal allocation. However\, as the model is a
phenomenological one at the population level\, this relation between the e
xponent and the inequality in resource allocation has mostly been discusse
d only phenomenologically. Although some authors have actually derived th
e Hassell equation from first-principles by considering specific competiti
on models among individuals\, the exponent of the derived models does not
match the naive expectation above. This study explores whether it is poss
ible to derive from first-principles such a Hassell model that its exponen
t is related to the inequality in resource allocation by considering resou
rce competition among individuals. I demonstrate that such a Hassell mode
l can indeed be derived by assuming that each individual obtains a constan
t amount of resources (a resource unit) at a time\, and that the competiti
on for such a discrete resource unit among individuals is repeated many ti
mes. Different sizes of the resource unit generate different degrees of i
nequality\, and the exponent of the derived model turns out to depend on t
hat size\, thus being related to the degree of the inequality. The derive
d model reduces to the Beverton-Holt model when the inequality is highest\
, and to the Ricker model when the inequality is lowest. Finally\, I disc
uss how replacing an assumption on fecundity with more realistic one chang
es the functional form of the derived model\, and the extension to two-spe
cies competition models as well.\n\nhttps://conferences.maths.unsw.edu.au/
event/2/contributions/427/
LOCATION:University of Sydney New Law School/--028
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/427/
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SUMMARY:Predation or frequency dependence\, which of them controls dimorph
ism oscillations in prey predator system?
DTSTART;VALUE=DATE-TIME:20180709T003000Z
DTEND;VALUE=DATE-TIME:20180709T005000Z
DTSTAMP;VALUE=DATE-TIME:20220819T202127Z
UID:indico-contribution-65-468@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Satoshi Takahashi (Nara Women's University)\nOscilla
tion of lateral asymmetry diorphism is first found in scale eating cichlid
\, Perrisodus microlepis. Fraction of their lefty morph oscillates around
0.5 in about 5 year period. Other fish or aquatic invertebrates also rev
eal lateral asymmetry dimorphism and oscillation of morph fractions. One
of key factors of oscillation is cross predation dominance: lefty predator
eats more righty prey than lefty prey\, and vice versa. When lefty is ma
jor in predator\, righty prey decrease\, then larger fraction of lefty pre
y increases righty predator\, and so on. This cycle appears to lead to th
e laterality oscillation. However the story is not such simple. A simple
ODE model of prey predator system with cross predation dominance has no l
imit cycles\, its coexisting equilibrium is stable\, though almost neutral
. Introduction of time delays due to growth periods destabilizes the coex
isting equilibrium and leads to a limit cycle of oscillating dimorphism fr
action. However\, this laterality dimorphism oscillation due to time dela
ys of growth periods and predation cycle can not explains that observed in
fields. Amplitude and period of fraction oscillation are almost 1.0 and
50 ~ 250 years in the model\, while they are 0.1 ~ 0.3 and 3 ~ 6 years in
fields. Another factor of oscillation in morph fraction is frequency dep
endence. When lefty scale eaters are more common\, righties eat more scal
es and have higher reproductive success. We introduce frequency dependent
predation success into the model: rarer predator eats more prey. This fr
equency dependence\, however\, ends up with the vanish of oscillation by e
ither stabilization of coexisting equilibrium\, or fixation one laterality
morph. Another frequency dependence\, that of prey selection\, i.e. pred
ator eats more common prey morph\, stabilizes coexisting equilibrium. The
model with both of frequency dependence finally shows oscillations with r
ealistic amplitudes and periods. We conclude that oscillation of lateral
asymmetry morphs is caused not by predation cycle\, but by frequency depen
dence in both of prey and predator\, i.e. rarer predator or prey morph is
advantageous and become common after a few years.\n\nhttps://conferences.m
aths.unsw.edu.au/event/2/contributions/468/
LOCATION:University of Sydney New Law School/--028
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/468/
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