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Multi-host, multi-parasite dynamics – Andy Dobson. Many thanks to Peter Hudson Mercedes Pascual and Stefano Allesina Anieke van Leeuwen & Claire Standley Kevin Lafferty, Jennifer Dunne, and Giulio de Leo Many, many NCEAS working groups. - PowerPoint PPT Presentation
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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
Tom 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.”
Outline
Parasite diversity and food webs
Parasites with multiple hosts
Parasites with sequential multiple hosts
Parasite communities : dynamics x immunity.
“The unpredictable and the predetermined unfold together to make everything the way it is.” ― Tom Stoppard, Arcadia
Food webs and parasites.Carpinteria salt marsh, California
Traditional resource-consumerweb. Trophic levels = 3.77
Food web that incudes basic parasite linksTrophic levels = 5.68
Dunne et al, PLoS Biology, (2013)
Parasites are central to healthy ecosystems!! (Hudson et al, 2005)
Number of trophic levels = 7.16 Includes parasite trophic linksFree-living species – red : Macroparasites – blue Not yet added microparasites or “microbiome”
Dunne et al, 2013, PLoS Biology.
Parasites and food websFood webs are even more complex when we
include parasites: ◦Many more species -> more links◦Simple cascade model is instantly falsified
How 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.
S Allesina & S Tang Nature 000, 1-4 (2012) doi:10.1038/nature10832
.
We use the criteria to prove that, counterintuitively, the probability of stability for predator–prey networks decreases when a realistic food web structure is imposed7, 8 or if there is a large preponderance of weak interactions9, 10.
Stable predator–prey networks can be arbitrarily large and complex, provided that predator–prey pairs are tightly coupled. The stability criteria are widely applicable, because they hold for any system of differential equations.
Sta
bilit
y
Diversity - Number of Species
Stability criteria for different types of interaction
Multiple 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
Walter PlowrightWalter 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
Multiple 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
A cartoon of the talk…..
Three Species of Hosts
Spatially distributedWithin Species Transmission
Between Species Transmission
Rinderpest – Serengeti
Basic model structure..
1,
( ( )) ( ) / ( )ii i i i i i ii i ij i n
j n
dS b d S I S I I S Ndt
1,
/ ( ) / ( ) (1 )i ii i ij i n i i ij n
dI dt I I S N d I
Susceptibles
InfectedsWithin Between
Scale virulenceas a proportion
of life expectancyBetween species transmission
ij ii jjc
Allometric scaling of all birth and death rates
De Leo and Dobson (1996)
Time
Susc
eptib
le d
ensit
y
Between sps. transmission
Buffering: dynamics in DD case
Buffering: dynamics in DD case
Between/within species transmission
Max
./Min
. sus
cept
ible
de
nsity
Multiple hosts species IIObligatory and sequential use of multiple
hosts to complete complex life cycle
Can next-generation methods be useful here?
Food-web perspective Long loops ‘may’ be stabilizing Often multiple alternative hosts on same trophic
level Types of pathogen where most likely to see dilution
effects
Cestodes of the Serengeti (host)
Multiple definitive hosts
Multiple intermediate hosts
Beetles….
Cestodes of the Serengeti….
Insight: There are multiple ways to go around the life cycle…
Insight 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
..then a pattern began to emerge…
0 0 0 00 0 0 0
0 0 00 0 0 00 0 0 0
DMJM
WD WJBW
MB
0 0 00 0 0 00 0 0 0
0 0 00 0 0
WJWDMWVW
JM JVDM DV
14
0 . . . . . .R BW DM MBWD BW JM MBWJ 13
0 . . . . . . . .R DM MWWD JM MWWJ DV VWWD JV VWWJ
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.
ScienceArt.comRibeiroia ondatrae Flatworm Life Cycle Contact Elizabeth Morales
Convert to a more theory friendly format….
Multiple Parasite speciesCommunities of parasites that share
the same hosts species Initial work by Robert’s and Dobson at Newton
Much current interest in role that immunity plays
BUT, current work tends to ignore earlier work on aggregation and persistence.
So need to find a framework to bring the two together!
Anderson and May macroparasite models – with multiple parasitesOriginal 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 species
Multi-parasite version has underlying structural similarities to Hubbell’s Neutral theory.
Phase plane for simple competition
Mean burden of species A
Mea
n bu
rden
of s
pecie
s B
B
AA
B
1
1
2
2
Coexistence requires
2 1
0 10 1 1( 1)'
A AB B
B A A
A AR MR M
k
And vice versa for B2 and B1
Thus coexistence requires k’>>1Both species have to be aggregated
Interference competitioneg (nearly) all immunological interactions!!
Mean burden of species A
Mea
n bu
rden
of s
pecie
s B
B
AA
B
1
1
2
2 Here we assume competitionis asymmetrical: B can exclude A, but not vice versa.
Coexistence still requiresA2>A1 and B2>B1
Synergistic interactionsmost of the other immunological interactions
Mean burden of species A
Mea
n bu
rden
of s
pecie
s B
B
AA
B
1
1
2
2
Coexistence still requiresA2>A1 and B2>B1
So we need to know how immunity impacts virulence and aggregation
N-species of parasite
Note – curiously related to “Neutral theory of Ecology - Hubbell……
Intrinsic growth rate of parasite species 1.
Intri
nsic
grow
th ra
te o
f par
asite
spec
ies 2
Both parasite species co-exist
Stomach
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 Dynamics2. Interference competition
What is the nature of competition?Competition for spaceCompetition for foodCompetition via excreted material
Food-veappears
+ve
Isabella Cattadori’s work on helminth Communities in rabbits with and w/oMyxomatosis – P. Hudson on Thursday
Mixed macro and micro parasite modelsSome initial work by Andy
Fenton.
Within Host dynamics of parasite communities will be driven by Immunological dynamics regulated by Th1-Th2 cytokine interactions
• Joint work with my Post-Docs : • Anieke van Leeuwen • and earlier explorations with Claire Standley
Background
• 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
Th1
Th2
Th1
Th2
ThAPC
IL-4IL-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
Tempting to think of this as a food-web
Th1
Th2
Th1
Th2
ThAPC
+ -
+
- -
+
+
+
+AICD
AICD
Simplified representation
After Yates et al. 2000 - JTB
Activation
Th1
Th2
Th1
Th2
ThAPC
+ -
+
- -
+
+
+
+
AICD
AICD
Yates et al. 2000 - JTB
Th1
Th2
Proliferation
Th1
Th2
Th1
Th2
ThAPC
+ -
+
- -
+
+
+
+
AICD
AICD
Yates et al. 2000 - JTB
Mortality
Th1
Th2
Th1
Th2
ThAPC
+ -
+
- -
+
+
+
+
AICD
AICD
Yates et al. 2000 - JTB
Model equations
Th1
Th2
Th1
Th2
ThAPC
+ -
+
- -
+
+
+
+
AICD
AICD
Yates et al. 2000 - JTB
Model dynamicsbifurcation over Th2 activation parameter, σ2
Th1 Th2
Parameterization
σ1 = 1.5π1 = 2.0δ1 = 0.1σ2 = variedπ2 = 2.0ρ = 0.1δ2 = 0.0
σ2 = 0.4
Model dynamicsScenario 1: low Th2 activation level
a b
initial levels: Th1: low Th2: low initial levels: Th1: high Th2: low
a bParameterization
σ1 = 1.5π1 = 2.0δ1 = 0.1σ2 = variedπ2 = 2.0ρ = 0.1δ2 = 0.0
σ2 = 0.6
Model dynamicsScenario 2: intermediate Th2 activation level
initial levels: Th1: low Th2: low initial levels: Th1: high Th2: low
a bParameterization
σ1 = 1.5π1 = 2.0δ1 = 0.1σ2 = variedπ2 = 2.0ρ = 0.1δ2 = 0.0
σ2 = 1.2
Model dynamicsScenario 3: high Th2 activation level
initial levels: Th1: low Th2: low initial levels: Th1: high Th2: low
LP1 BPx2
BPx1
H LP2
bistability:Th1-Th2: damped oscillationsTh1 dominance
Th1 dominance
bistability:Th1-Th2: cyclesTh1 dominance
Th1-Th2cycles
Th1-Th2damped oscillations
Th2 dominance
bistability:Th1-Th2: cyclesTh2 dominance
δ1 = 0.1
δ2 = 0.0
θ1,2 = 0.0
χ0 = 0.0
ρ = 0.1
Ultimately we need to know how activation energies of Th1, Th2 impact virulence and
aggregation!
Conclusions• Parasite diversity and food webs
– Parasites look increasingly viable as the ‘missing links’ in food webs, the ‘dark matter’ that helps stabilize otherwise unstable structures.
• Parasites with multiple hosts– Strong form of frequency dependent selection for stability if within
species transmission < between.• Parasites with sequential multiple hosts
– Possible powerful use of next generation matrices• Parasite communities : dynamics x immunity.
– Rapidly developing area, but needs to resolve how diversity in immune response impacts aggregation as well as abundance.
Penultimate 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
Deconstructing this..• What did I take away from Newton meeting 20 years ago?
• Collaborations in small mixed groups is the best way to do new science
• Mathematics will constantly find new, innovative and exciting ways to solve old problems in disease and ecology
• But…. 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 Ecology
• Hard to interpret the bit about the corkscrew, but they have been known to come in useful as social facilitators!
Thank you!
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