Transcript Multi-host, multi-parasite dynamics

Multi-host, multi-parasite
dynamics – Andy Dobson
Ancient cures for diseases will reveal
themselves once more. Mathematical
discoveries glimpsed and lost to view will have
their time again.”
― Tom Stoppard, Arcadia
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
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
“The unpredictable and the predetermined
unfold together to make everything the way it
is.”
― Tom Stoppard, Arcadia

Parasite diversity and food webs

Parasites with multiple hosts

Parasites with sequential multiple hosts

Parasite communities : dynamics x immunity.
Food webs and parasites.
Carpinteria salt marsh, California
Traditional resource-consumer
web. Trophic levels = 3.77
Food web that incudes
basic parasite links
Trophic 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 links
Free-living species – red : Macroparasites – blue
Not yet added microparasites or “microbiome”
Dunne et al, 2013, PLoS Biology.
Parasites and food webs

Food 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) stabilitycomplexity 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.
. types of interaction
Stability criteria for different
Stability
S Allesina & S Tang Nature 000, 1-4 (2012) doi:10.1038/nature10832
Diversity - Number of Species
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.
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 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
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 distributed
Within Species Transmission
Between Species Transmission
Rinderpest – Serengeti
Basic model structure..
Susceptibles
dSi
Allometric scaling of all birth and death rates
 (bi  di   i ( Si  I i )) Si  ( ii I i   ij I i ) S / (  N n )

dt
j 1, n
Within
Between
Infecteds
dI i / dt  ( ii I i   ij I i ) S / (  N n )  di (1   i ) I i

j 1, n
Between species transmission
ij  c ii  jj
Scale virulence
as a proportion
of life expectancy
De Leo and Dobson (1996)
Susceptible density
Buffering: dynamics in DD case
Between sps.
transmission
Time
Max./Min. susceptible density
Buffering: dynamics in DD case
Between/within species transmission
Multiple hosts species II

Obligatory 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
Cestodes of the Serengeti….
Beetles….
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
0

WD WJ

0
 0
 0
0
R0 
1
4
0
0
0
BW
0
 0
 MW

 VW

 0
 0
0 DM 
0 JM 
0 0 

0 0 
MB 0 
.
 BW .JM .MBWJ
. 
 BW .DM .MBWD
R0 
1
3
0
0
0
JM
DM
WJ WD 
0
0 0 
0
0 0 

JV
0 0 
DV 0 0 
0
 DM .MW .WD  JM .MW .WJ  DV .VW .WD  JV .VW .WJ 
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.
Ribeiroia ondatrae Flatworm Life
Cycle Contact Elizabeth Morales
ScienceArt.com
Convert to a more theory friendly format….
Multiple Parasite species

Communities 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 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 species

Multi-parasite version has underlying
structural similarities to Hubbell’s Neutral
theory.
Phase plane for simple competition
Mean burden of species B
Coexistence requires
B2
A2  A1
( R0 B  1) M 1B
B
B1

 R0 A  1 M1A
 Ak 'A
And vice versa for B2 and B1
Thus coexistence requires k’>>1
Both species have to be aggregated
A1
Mean burden of species A
A2
Interference competition
Mean burden of species B
eg (nearly) all immunological interactions!!
B2
Here we assume competition
is asymmetrical:
B can exclude A,
but not vice versa.
B1
Coexistence still requires
A2>A1 and B2>B1
A1
Mean burden of species A
A2
Synergistic interactions
Mean burden of species B
most of the other immunological interactions
B2
B1
Coexistence still requires
A2>A1 and B2>B1
A1
Mean burden of species A
So we need to know how immunity impacts virulence and aggregation
A2
N-species of parasite
Note – curiously related to “Neutral theory of Ecology - Hubbell……
Intrinsic growth rate of parasite species 2
Both parasite species co-exist
Intrinsic growth rate of parasite species 1.
Parasite Community Dynamics
2. Interference competition
What is the nature of competition?
Competition for space
Competition for food
Competition via excreted material
When should we expect competition?
Applying the findings from
community ecology…this should be
greater when parasites are related
Direct competition
Worm 1
Food -ve
Excreta -ve
Worm 3
Space
-ve
Worm 2
Food
appears
-ve
+ve
Small Intestine
Interestingly this contrasts with
exploitation competition
Isabella Cattadori’s work on helminth
Communities in rabbits with and w/o
Myxomatosis – P. Hudson on Thursday
Stomach
Worm 4
Large Intestine
Mixed macro and micro parasite
models

Some 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
Processes in detail
After Yates et al. 2000 - JTB
+IL-2
+IL-2
Th1
+IFN-γ +IL-12
APC
IL-4
+
Th
1
IFN-γ
Th
+IFN-γ
IL-10
- - TGF-β
IL-2
IL-10 IL-4
TGF-β
Th
2
IL-2
IL-4
AICD
+
+
+
IFN-γ
+
Th2
AICD
Tempting to think of this as a food-web
Simplified representation
+
+
Th1
+
AICD
Th1
APC
Th
-
-
+
Th2
+
After Yates et al. 2000 - JTB
Th2
+
AICD
Activation
+
+
Th1
+
AICD
Th1
APC
Th
-
-
+
Th2
+ Th2
AICD
+
Th1
Th2
Yates et al. 2000 - JTB
Proliferation
+
+
Th1
+
AICD
Th1
APC
Th
-
-
+
Th2
+ Th2
AICD
+
Yates et al. 2000 - JTB
Mortality
+
+
Th1
+
AICD
Th1
APC
Th
-
-
+
Th2
+ Th2
AICD
+
Yates et al. 2000 - JTB
Model equations
+
+
Th1
+
AICD
Th1
APC
Th
-
-
+
Th2
+ Th2
AICD
+
Yates et al. 2000 - JTB
Model dynamics
bifurcation over Th2 activation parameter, σ2
Th1
Th2
Model dynamics
Scenario 1: low Th2 activation level
Parameterization
a
b
σ1 = 1.5
π1 = 2.0
δ1 = 0.1
σ2 = varied
π2 = 2.0
ρ = 0.1
δ2 = 0.0
σ2 = 0.4
initial levels:
Th1: low
Th2: low
initial levels:
Th1: high
Th2: low
Model dynamics
Scenario 2: intermediate Th2 activation level
Parameterization
a
b
σ1 = 1.5
π1 = 2.0
δ1 = 0.1
σ2 = varied
π2 = 2.0
ρ = 0.1
δ2 = 0.0
σ2 = 0.6
initial levels:
Th1: low
Th2: low
initial levels:
Th1: high
Th2: low
Model dynamics
Scenario 3: high Th2 activation level
Parameterization
a
b
σ1 = 1.5
π1 = 2.0
δ1 = 0.1
σ2 = varied
π2 = 2.0
ρ = 0.1
δ2 = 0.0
σ2 = 1.2
initial levels:
Th1: low
Th2: low
initial levels:
Th1: high
Th2: low
δ1 = 0.1
δ2 = 0.0
θ1,2 = 0.0
χ0
= 0.0
ρ
= 0.1
LP1
BPx2
bistability:
Th1-Th2: damped oscillations
Th1 dominance
bistability:
Th1-Th2: cycles
Th1 dominance
Th1-Th2
damped oscillations
BPx1
Th1-Th2
cycles
Th2 dominance
Th1 dominance
H
LP2
bistability:
Th1-Th2: cycles
Th2 dominance
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!