dynamics Andy Dobson Many thanks to Peter Hudson Mercedes Pascual and Stefano Allesina Anieke van Leeuwen amp Claire Standley Kevin Lafferty Jennifer Dunne and Giulio ID: 927794
Download Presentation The PPT/PDF document "Multi-host, multi-parasite" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Multi-host, multi-parasite dynamics – Andy Dobson
Many thanks to Peter HudsonMercedes Pascual and Stefano AllesinaAnieke van Leeuwen & Claire StandleyKevin Lafferty, Jennifer Dunne, and Giulio de Leo Many, many NCEAS working groups
Ancient cures for diseases will reveal themselves once more. Mathematical discoveries glimpsed and lost to view will have their time again.”
―
Tom Stoppard
,
Arcadia
Slide2Tom Stoppard, Arcadia
“It's the best possible time to be alive, when almost everything you thought you knew is wrong.” “It's the wanting to know that makes us matter.” “We're better at predicting events at the edge of the galaxy or inside the nucleus of an atom than whether it'll rain on auntie's garden party three Sundays from now.”
Slide3Outline
Parasite diversity and food websParasites with multiple hostsParasites with sequential multiple hostsParasite communities : dynamics x immunity.“The unpredictable and the predetermined unfold together to make everything the way it is.” ― Tom Stoppard, Arcadia
Slide4Food webs and parasites.Carpinteria salt marsh, California
Traditional resource-consumerweb. Trophic levels = 3.77
Food web that incudes
b
asic parasite links
Trophic levels = 5.68
Dunne et al,
PLoS
Biology, (2013)
Slide5Parasites are central to healthy ecosystems!! (Hudson et al, 2005)
Number of trophic levels = 7.16 Includes parasite trophic
links
Free-living species – red :
Macroparasites
– blue
Not yet added
microparasites
or “
microbiome
”
Dunne et al, 2013,
PLoS
Biology.
Slide6Parasites and food webs
Food webs are even more complex when we include parasites: Many more species -> more linksSimple cascade model is instantly falsifiedHow does this effect May’s (1973) stability-complexity paradigm?Main focus of this talk is to consider how work since “Ro or Not Newton” has developed insights into this central problem in Ecology.
Slide7S
Allesina
& S Tang
Nature
000
,
1
-
4
(2012) doi:10.1038/nature10832
.
Stability
Diversity - Number of Species
Stability criteria for different types of interaction
Slide8Multiple host species I.
What happens when multiple host species share the same pathogen ?Rinderpest would be classic example here – eradicated since last Newton…Also rabies and other species that jump between hosts.Can be modeled with coupled sets of SI and SIR equations
Slide9Walter Plowright
Walter Plowright, CMG, FRS[1], FRCVS (born 20 July 1923, Holbeach, Lincolnshire – 19 February 2010 London[2]) was an English veterinary scientist who devoted his career to the
eradication
of the cattle plague
rinderpest
. Dr
Plowright
received the 1999
World Food Prize
for his development of tissue culture
rinderpest
vaccine (TCRV), the key element in the quest to eliminate
rinderpest
.
[3]
Rinderpest
became the first animal disease to be eliminated worldwide
Slide10Multiple host species I.
What happens when multiple host species share the same pathogen ?Rinderpest would be classic example here – eradicated since last Newton…Also rabies and other species that jump between hosts.Can be modeled with coupled sets of SI and SIR equations
Slide11A cartoon of the talk…..
Slide12Rinderpest – Serengeti
Slide13Basic model structure..
Susceptibles
Infecteds
Within
Between
Scale virulence
as a proportion
of life expectancy
Between species transmission
Allometric scaling of all birth and death rates
Slide14De Leo and Dobson (1996)
Slide15Time
Susceptible density
Between sps. transmission
Buffering: dynamics in DD case
Slide16Buffering: dynamics in DD case
Between/within species transmissionMax./Min. susceptible density
Slide17Multiple hosts species II
Obligatory and sequential use of multiple hosts to complete complex life cycleCan next-generation methods be useful here?Food-web perspective Long loops ‘may’ be stabilizingOften multiple alternative hosts on same trophic levelTypes of pathogen where most likely to see dilution effects
Slide18Cestodes of the Serengeti (host)
Slide19Multiple definitive hosts
Slide20Multiple intermediate hosts
Slide21Slide22Beetles….
Cestodes
of the Serengeti….
Slide23Insight:
There are multiple ways to go around the life cycle…
Slide24Insight 2: Ro is a root of the sum of all possible routes
around the life cycle…..
hmmmm
!
But why does the magnitude of the root keep changing
Slide25..then a pattern began to emerge…
Although these expressions look at first sight slightly incongruous, they both have the same properties in that they define R0 as the ‘n-th’ root of the sum of all the possible transmission routes around the life cycle; notice that ‘n’ is the number of trophic levels that the parasite passes through in the course of its life cycle. This creates a beautiful link to the need to study complex life cycles parasites within a food-web context.
Slide26ScienceArt.com
Ribeiroia ondatrae
Flatworm Life Cycle Contact Elizabeth Morales
Slide27Convert to a more theory friendly format….
Slide28Slide29Multiple Parasite species
Communities of parasites that share the same hosts speciesInitial work by Robert’s and Dobson at NewtonMuch current interest in role that immunity playsBUT, current work tends to ignore earlier work on aggregation and persistence.So need to find a framework to bring the two together!
Slide30Anderson and May macroparasite models – with multiple parasites
Original two parasite version developed by Dobson (1985), extended to n-species by Roberts and Dobson (1995)Simple graphical ways for initially considering this with two speciesMulti-parasite version has underlying structural similarities to Hubbell’s Neutral theory.
Slide31Phase plane for simple competition
Coexistence requires
And vice versa for B
2
and B
1
Thus coexistence requires k’>>1
Both species have to be aggregated
Slide32Interference competition
eg (nearly) all immunological interactions!!
Here we assume competition
is asymmetrical:
B can exclude A,
but not vice versa.
Coexistence still requires
A
2
>A
1
and B
2
>B
1
Slide33Synergistic interactions
most of the other immunological interactions
Coexistence still requires
A2>A1 and B2>B1
So we need to know how immunity impacts virulence and aggregation
Slide34N-species of parasite
Note – curiously related to “Neutral theory of Ecology - Hubbell……
Slide35Intrinsic growth rate of parasite species 1.
Intrinsic growth rate of parasite species 2
Both parasite species co-exist
Slide36Slide37Slide38Stomach
Small Intestine
Large Intestine
Worm 1
Worm 3
Worm 2
Worm 4
Food -ve
Space
-ve
Direct competition
Excreta -ve
When should we expect competition?
Applying the findings from community ecology…this should be greater when parasites are related
Interestingly this contrasts with exploitation competition
Parasite Community Dynamics
2. Interference competition
What is the nature of competition?
Competition for space
Competition for food
Competition via excreted material
Food
-ve
appears
+ve
Isabella
Cattadori’s
work on
helminth
Communities in rabbits with and w/o
Myxomatosis
– P. Hudson on Thursday
Slide39Mixed macro and micro parasite models
Some initial work by Andy Fenton.
Slide40Slide41Slide42Within Host dynamics of
parasite communities will be driven by Immunological dynamics regulated by Th1-Th2 cytokine interactionsJoint work with my Post-Docs : Anieke van Leeuwen and earlier explorations with Claire Standley
Slide43Background
Th1 cytokines -> microparasite infection control [viruses, bacteria, fungi, protozoa]Th2 cytokines -> macroparsite infection control [helminths, nematodes]Th1 and Th2 responses are supposed to have mutual inhibitory effects (competition)Hosts are often co-infected with multiple parasite species (e.g. Fenton & Pedersen 2007)How does the interaction of the th1 and th2 immune responses work out?=> Mathematical modeling
Slide44Th1
Th2Th1
Th2
Th
APC
IL-4
IL-10
+
-
IFN-
γ
+
IL-12
+
-
-
IFN-
γ
IFN-
γ
+
IL-2
+
TGF-
β
IL-10
IL-4
-
-
IFN-
γ
+
IL-2
+
IL-2
+
IL-2
+
IL-4
+
-
TGF-
β
AICD
AICD
After Yates et al. 2000 - JTB
Processes in detail
Slide45Tempting to think of this as a food-web
Slide46Th1
Th2Th1
Th2
Th
APC
+ -
+
-
-
+
+
+
+
AICD
AICD
Simplified representation
After Yates et al. 2000 - JTB
Slide47Activation
Th1
Th2
Th1
Th2
Th
APC
+ -
+
-
-
+
+
+
+
AICD
AICD
Yates et al. 2000 - JTB
Th1
Th2
Slide48Proliferation
Th1
Th2
Th1
Th2
Th
APC
+ -
+
-
-
+
+
+
+
AICD
AICD
Yates et al. 2000 - JTB
Slide49Mortality
Th1
Th2
Th1
Th2
Th
APC
+ -
+
-
-
+
+
+
+
AICD
AICD
Yates et al. 2000 - JTB
Slide50Model equations
Th1
Th2
Th1
Th2
Th
APC
+ -
+
-
-
+
+
+
+
AICD
AICD
Yates et al. 2000 - JTB
Slide51Model dynamicsbifurcation over Th2 activation parameter,
σ2Th1Th2
Slide52Parameterization
σ1 = 1.5π1 = 2.0δ1 = 0.1
σ
2
= varied
π
2
= 2.0
ρ
= 0.1
δ
2
= 0.0
σ
2
= 0.4
Model dynamics
Scenario 1: low Th2 activation level
a
b
initial levels: Th1
: low
Th2: low
initial levels: Th1: high Th2: low
Slide53a
b
Parameterization
σ
1
= 1.5
π
1
= 2.0
δ
1
= 0.1
σ
2
= varied
π
2
= 2.0
ρ
= 0.1
δ2 = 0.0σ2 = 0.6
Model dynamicsScenario 2: intermediate Th2 activation level
initial levels: Th1: low Th2: low
initial levels: Th1: high Th2: low
Slide54a
b
Parameterization
σ
1
= 1.5
π
1
= 2.0
δ
1
= 0.1
σ
2
= varied
π
2
= 2.0
ρ
= 0.1
δ2 = 0.0σ2 = 1.2
Model dynamicsScenario 3: high Th2 activation level
initial levels: Th1: low Th2: low
initial levels: Th1
: high Th2: low
Slide55LP1
BPx2
BPx1
H
LP2
bistability:
Th1-Th2
: damped oscillations
Th1
dominance
Th1
dominance
bistability:
Th1-Th2
: cycles
Th1
dominance
Th1-Th2
cycles
Th1-Th2
damped oscillationsTh2 dominance
bistability:Th1-Th2: cyclesTh2
dominance
δ1 = 0.1δ
2 = 0.0θ1,2 = 0.0χ0 = 0.0
ρ = 0.1
Slide56Ultimately we need to know how activation energies of Th1, Th2 impact virulence and aggregation!
Slide57Conclusions
Parasite diversity and food websParasites look increasingly viable as the ‘missing links’ in food webs, the ‘dark matter’ that helps stabilize otherwise unstable structures.Parasites with multiple hostsStrong form of frequency dependent selection for stability if within species transmission < between.Parasites with sequential multiple hostsPossible powerful use of next generation matricesParasite communities : dynamics x immunity.Rapidly developing area, but needs to resolve how diversity in immune response impacts aggregation as well as abundance.
Slide58Penultimate word from Tom Stoppard
“We shed as we pick up, like travellers who must carry everything in their arms, and what we let fall will be picked up by those behind. The procession is very long and life is very short. We die on the march. But there is nothing outside the march so nothing can be lost to it. The missing plays of Sophocles will turn up piece by piece, or be written again in another language. Ancient cures for diseases will reveal themselves once more. Mathematical discoveries glimpsed and lost to view will have their time again. You do not suppose, my lady, that if all of Archimedes had been hiding in the great library of Alexandria, we would be at a loss for a corkscrew?” ― Tom Stoppard, Arcadia
Slide59Deconstructing this..
What did I take away from Newton meeting 20 years ago?Collaborations in small mixed groups is the best way to do new scienceMathematics will constantly find new, innovative and exciting ways to solve old problems in disease and ecologyBut…. there are still a whole bunch of unexamined questions out there in Nature and mathematics is the best way to focus those questions. So go into the field, talk to people and find ways to turn problems of disease, ecology and evolution into new problems.Ecologists now see parasites as central to EcologyHard to interpret the bit about the corkscrew, but they have been known to come in useful as social facilitators!
Slide60Thank you!