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!