for a Population under Climate Change Joy Ying Zhou Mark Kot Department of Applied Mathematics University of Washington 1 Cartoon of a Range Shift 2 3 Global mean 042kmyr Cartoon of a Range Shift ID: 240213
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Slide1
Non-local Dispersal Models for a Population under Climate Change
(Joy) Ying Zhou, Mark KotDepartment of Applied MathematicsUniversity of Washington
1Slide2
Cartoon of a Range Shift
2Slide3
3Global mean: 0.42km/yrSlide4
Cartoon of a Range Shift
4
Population Dynamics MatterSlide5
Talk Outline5Population Models on Range Shifts under:
Constant-speed climate changeAccelerated climate changeSlide6
Organisms of Interest
Well-defined life stages (growth, dispersal)Growth and dispersal occur in separate time periodsNon-overlapping generations
Larvae
Adult
Egg mass
Flower
Seed
Seedling
Cocoon
Growth
Dispersal
Growth
DispersalSlide7
Integrodifference
equation
7
Integrodifference
eqn
(IDE)
kernel
Assuming no
Allee
effectsSlide8
How To Mathematize Climate Warming?
8Slide9
Climatically Suitable Habitat
Habitat shifts
9
Combination of two classical problems
Zhou and
Kot
2011 Th
eoretical EcologySlide10
Two Classic IDE Models
10Slide11
Two Classic IDE Models
11Slide12
What Population Dynamics Will We Observe?
A Steady Range Shift For Small
c
12
Zhou and
Kot
2011 Th
eoretical EcologySlide13
Extinction When c Large
13Zhou and
Kot 2011 Theoretical EcologySlide14
Critical Speed “c*”
14Slide15
Eigenvalue Problem
Net reproductive rate
Analytic method for “separable” kernels
Numerical method “
Nystrom’s
method”
Delves and Wash 1974Slide16
Larger Net R
eproductive Rate Helps16Zhou and Kot 2011 Th
eoretical EcologySlide17
More Dispersal, But Not Over-dispersal17
Dispersal radiusradiusZhou and Kot 2011 Theoretical EcologySlide18
18Lockwood et al. 2002Slide19
Clark 1998
Mean deviation19Schultz 1998Slide20
Result for a typical leptokurtic kernel
The “Tail” of The Dispersal KernelResult for a typical leptokurtic kernel
Result for a typical
platykurtic
kernel
20
Zhou and
Kot
2011 Th
eoretical EcologySlide21
Population projection matrix
Matrix of dispersal kernelsVector of population density in each stageSlide22
Climatically Suitable Habitat
Climatically Suitable Habitat
Habitat shifts
Heterogeneous Habitat Suitability
22
Habitat quality function
Latore
et al. 1999Slide23
Consider linearized equation
For normally distributed habitat qualitya Gaussian dispersal kernelSlide24
and a special initial condition (Gaussian initial profile), then we have an ansatz
: peak of the pulse
: amplitude of the pulse
Latore
et al. 1999Slide25
25Slide26
26
“climate deficit”Slide27
27
Declining population if Slide28
Accelerated Climate Change
Same ansatzSlide29
The mean of the Gaussian ansatzSlide30
30The “climate deficit”Slide31
Time
SpeedTSlide32
32
vs.
For large
t
Comparison of climate deficitSlide33
33Slide34
34Slide35
SummaryAn integrodifference equation model with shifting boundariesCritical speedAcceleration may hurt a lot (more than average)
35Slide36
Thank you!Questions?36