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SUMMARY:The coexistence and its sustainability in Batesian mimicry
DTSTART;VALUE=DATE-TIME:20180711T064000Z
DTEND;VALUE=DATE-TIME:20180711T070000Z
DTSTAMP;VALUE=DATE-TIME:20200813T145547Z
UID:indico-contribution-421@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Hayato Kato (Hokkaido University)\nBatesian mimicry
is a common phenomenon in nature\, and it has been reported in various tax
a. In Batesian mimicry\, there are two species that have a similar coloura
tion. One species is toxic or unpalatable\, we call it “model-species”
. The other is nontoxic or palatable\, we call it “mimic”.\n\nWhile ma
ny mathematical models focused on the evolution of mimicry\, only a few ma
thematical models focused on community dynamics. Furthermore\, the sustain
ability of the coexistence has not been studied. Here\, we addressed the c
ommunity dynamics and its sustainability in this study.\n\nA part of the p
revious mathematical models has a common framework based on simple and pla
usible assumptions such as density-dependent effect and frequency-dependen
t predation. However\, even a simple mathematical model based on the frame
work has not been analyzed completely. The simple mathematical model is al
so important mathematically because it is one of the basic models that hav
e both density- and frequency-dependent effects and actually it includes a
ratio-dependent predator-prey model.\n\nThe objective of our study is as
follows\; first\, to solve a mathematical model based on the common framew
ork completely and understand its properties. Secondly\, to examine the im
pact of mimicry on community dynamics. Thirdly\, to discuss the sustainabl
e coexistence of model-species and mimic.\n\nWe focused on the case that t
he intrinsic growth rate of model-species is less than mimic because model
-species pay some cost for acquiring toxicity and defined “predation imp
act (PI)” as the predation rate divided by the intrinsic growth rate. Th
e result is divided into two types using PIs of model-species and mimic sp
ecies\; type I is when the predation impact of model-species is small\, ty
pe II is when the predation impact of model-species is large. In type I\,
model-species and mimic always coexist. In type II\, they can coexist\, bu
t not always. In particular\, in type II\, when the ratio of the carrying
capacity change and become less than a threshold\, model-species become ex
tinct. Thus\, the coexistence of model-species and mimic is unlikely to be
maintained in type II under a varying environment. Therefore\, Batesian m
imicry in nature is supposed to be maintained in type I.\n\nIn our mathema
tical model\, there are only three stable states\; coexistence\, mimic alo
ne and both extinction. This result can explain the geographic distributio
n of model-species and mimic in more than 10 mimicry systems. For example\
, eastern coral snake is a toxic model and scarlet kingsnake is a nontoxic
mimic in North America. In their geographic distribution\, the areas of c
oexistence\, mimic alone and both-absence were observed with latitude grad
ient. This pattern of the geographic distribution is consistent with the r
esult of our mathematical model.\n\nIn addition to the above study\, we co
nstruct some models\, taking predator’s learning process into account. W
e present the results derived from these models and compare them.\n\nhttps
://conferences.maths.unsw.edu.au/event/2/contributions/421/
LOCATION:University of Sydney New Law School/--022
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/421/
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