ecological and evolutionary modeling of disease-induced extinction, with particular attention to fungal pathogens

1. Review of de Castro & Bolker (2005) New stuff References
Mechanisms of disease-induced extinction
Ben Bolker, McMaster University
Departments of Mathematics & Statistics and Biology
NCEAS
18 March 2013
Ben Bolker NCEAS
Disease-induced extinction

2. Review of de Castro & Bolker (2005) New stuff References
Outline
1 Review of de Castro & Bolker (2005)
2 New stuff
Ben Bolker NCEAS
Disease-induced extinction

3. Review of de Castro & Bolker (2005) New stuff References
Baseline: in a deterministic model . . .
. . . of a specialist parasite . . .
. . . with density-dependent transmission . . .
the parasite can never drive the host completely extinct
Exceptions:
Inhomogeneous mixing
(non-DD transmission, spatial structure)
Generalist pathogens
(biotic or abiotic reservoir)
Stochastic extinction
(small populations, or low troughs)
Ben Bolker NCEAS
Disease-induced extinction

4. Review of de Castro & Bolker (2005) New stuff References
Baseline: in a deterministic model . . .
. . . of a specialist parasite . . .
. . . with density-dependent transmission . . .
the parasite can never drive the host completely extinct
Exceptions:
Inhomogeneous mixing
(non-DD transmission, spatial structure)
Generalist pathogens
(biotic or abiotic reservoir)
Stochastic extinction
(small populations, or low troughs)
Ben Bolker NCEAS
Disease-induced extinction

5. Review of de Castro & Bolker (2005) New stuff References
What is virulence?
Plant biology: ability to infect
Animal biology: pathogenicity
Evolutionary biology: loss of host fitness
Theoretical evolutionary biology: rate of host mortality Day
(2002)
Popular media: generalized index of badness
G(host) × G(pathogen) × E (environment) interaction
Need to distinguish between individual impact and
population-level impact.
Ben Bolker NCEAS
Disease-induced extinction

6. Review of de Castro & Bolker (2005) New stuff References
What is virulence?
Plant biology: ability to infect
Animal biology: pathogenicity
Evolutionary biology: loss of host fitness
Theoretical evolutionary biology: rate of host mortality Day
(2002)
Popular media: generalized index of badness
G(host) × G(pathogen) × E (environment) interaction
Need to distinguish between individual impact and
population-level impact.
Ben Bolker NCEAS
Disease-induced extinction

7. Review of de Castro & Bolker (2005) New stuff References
Stochastic effects: predisposing conditions
small pre-epidemic population
(endangered/endemic species)
low disease-present endemic equilibrium
(intermediate virulence)
transient or periodic population troughs
(?? virulence)
Allee effects
inbreeding depression (extinction vortex?)
fecundity-reducing parasites
Ben Bolker NCEAS
Disease-induced extinction

8. Review of de Castro & Bolker (2005) New stuff References
Stochastic effects: empirical examples
Host Impact Reference
Tree snail (Partula turgida) Extinction Daszak & Cunningham (1999)
Thylacine (Thylacinus cynocephalus) Possible extinction Guiler (1961) (in McCallum &
Dobson 1995)
Golden toad (Bufo periglenes) Probable extinction Pounds et al. (1997)
Black-footed ferret (Mustela nigripes) Probable extinction Thorne & Williams (1988)
Mednyi arctic fox (Alopex lagopus semenovi) Probable extinction Goltsman et al. (1996)
African wild dog (Lycaon pictus) Population crash Burrows et al. (1994)
Boreal toad (Bufo boreas) Population crash Muths et al. (2003)
Noble crayfish (Astacus astacus) Population crash Taugbol et al. (1993)
Spanish Ibex (Capra pyrenaica hispanica) Population crash Fandos (1991),Leon-Vizcaino et
al. (1999)
Big-horn sheep (Ovis canadiensis) Population crash (model) Gross et al. (2000)
Florida torreya (Torreya taxifolia) Population crash and pre- Schwartz et al. (1995,2000)
dicted extinction (model)
Ben Bolker NCEAS
Disease-induced extinction

9. Review of de Castro & Bolker (2005) New stuff References
Inhomogeneous mixing: predisposing conditions
frequency-dependent transmission
sexually transmitted diseases
vector-borne disease
social behaviour
spatially localized populations
Ben Bolker NCEAS
Disease-induced extinction

10. Review of de Castro & Bolker (2005) New stuff References
Inhomogeneous mixing: empirical examples
Host Impact Reference
Koala/Chlamydia Possible population crash Augustine (1998)
(model)
Eupatorium makinoi Asteraceae Population crash Funayama et al. (2001)
Rabbit/Rabbit haemorrhagic disease Possible population crash White et al. (2003)
(model)
Common flax (Linum marginale) Possible population crash Thrall et al. (2003)
(model)
Ben Bolker NCEAS
Disease-induced extinction

11. Review of de Castro & Bolker (2005) New stuff References
Reservoirs: predisposing conditions
biotic: apparent competition (local congenerics??)
abiotic: amplification in environment (saprophytic stages)
Ben Bolker NCEAS
Disease-induced extinction

12. Review of de Castro & Bolker (2005) New stuff References
Reservoirs: empirical examples
Host Impact Reference
Iiwi (Vestiaria coccinea) Population crash Atkinson et al. (1995)
Amakihi (Hemignathus virens) Population crash Atkinson et al. (2000)
White-tailed deer (Odocoileus virginianus) / Population reduction Schmitz & Nudds (1994)
moose (Alces alces)
Red squirrel (Sciurus vulgaris) Population reduction Rushton et al. (2000)
Ethiopian wolf (Canis simensis) Population reduction Haydon et al. (2002)
(model)
Tussock moth (Orgya antiqua) Population crash Richards et al. (1999)
Ben Bolker NCEAS
Disease-induced extinction

13. Review of de Castro & Bolker (2005) New stuff References
Outline
1 Review of de Castro & Bolker (2005)
2 New stuff
Ben Bolker NCEAS
Disease-induced extinction

14. Review of de Castro & Bolker (2005) New stuff References
Interactions between mechanisms
Effect of reservoirs on R0 /equilibrium density/trough density
Detailed modeling of density/frequency-dependence?
Ben Bolker NCEAS
Disease-induced extinction

15. Review of de Castro & Bolker (2005) New stuff References
Final size curve (Ma & Earn, 2006)
1.0
Fraction never infected
0.8
0.6
0.4
0.2
0.0
1 2 3 4 5 6 7 8
R0
Effect of non-amplifying environmental reservoir (Rohani et al., 2009):
 

 β + ωρ  S0

 κη  γ
direct environmental
Ben Bolker NCEAS
Disease-induced extinction

16. Review of de Castro & Bolker (2005) New stuff References
Evolution of virulence
Tradeoff theory (Ebert & Bull, 2003a; Gandon & Day, 2003;
Ebert & Bull, 2003b; Alizon et al., 2009)
Connections between virulence and population outcome
Factors affecting selection on virulence? Many . . . including
presence of resting stages
(Bonhoeffer et al., 1996; Gandon, 1998; Kamo & Boots, 2004)
resistance vs. tolerance vs. virulence
(Carval & Ferriere, 2010)
capability of host to evolve resistance/tolerance:
genetic variation, length of trough
Ben Bolker NCEAS
Disease-induced extinction

17. Review of de Castro & Bolker (2005) New stuff References
Open questions
understand transient trough depth (King et al., 2009)
general host-switching/emergence issues:
virulence/population threat spectrum of novel pathogens
host vs. pathogen factors
ontogenetically structured models
effects of environmental variation (random, or seasonal)
Ben Bolker NCEAS
Disease-induced extinction

18. Review of de Castro & Bolker (2005) New stuff References
reports by pathogen type
fungus q q
virus q q
protozoan qq ref
q dCB2005
q Fisher+2012
helminth q
arthropod q
other q
0 4 8 12 16
count
Ben Bolker NCEAS
Disease-induced extinction

19. Review of de Castro & Bolker (2005) New stuff References
Ben Bolker NCEAS
Disease-induced extinction

20. Review of de Castro & Bolker (2005) New stuff References
Meta- stuff
Ask not what modellers can do for you . . . (actually, do!)
Lumpers vs. splitters
Strategic vs. tactical models: Levins (1966); Mollison (1991)
Why study detailed mechanism?
it’s really, really cool.
treatment
leverage limited information
extrapolation across levels (multi-scale models)
What are models for? Analytical, statistical, predictive,
synthetic, . . .
Ben Bolker NCEAS
Disease-induced extinction

21. Review of de Castro & Bolker (2005) New stuff References
Alizon, S, Hurford, A, Mideo, N, et al., 2009. Journal of Evolutionary Biology, 22(2):245–259. ISSN 1010061X.
doi:10.1111/j.1420-9101.2008.01658.x. URL
http://onlinelibrary.wiley.com/doi/10.1111/j.1420-9101.2008.01658.x/abstract.
Bonhoeffer, S, Lenski, RE, & Ebert, D, 1996. Proceedings: Biological Sciences, 263(1371):715–721. ISSN 0962-8452.
doi:10.2307/50702. URL http://www.jstor.org/stable/50702.
Carval, D & Ferriere, R, 2010. Evolution, 64(10):2988–3009. ISSN 0014-3820. doi:10.2307/40863389. URL
http://www.jstor.org/stable/40863389.
Day, T, 2002. Proceedings of the Royal Society B: Biological Sciences, 269(1498):1317–1323. ISSN 0962-8452.
doi:10.1098/rspb.2002.2021.
de Castro, F & Bolker, B, 2005. Ecology Letters, 8:117–126. doi:10.1111/j.1461-0248.2004.00693.x.
Ebert, D & Bull, JJ, 2003a. Trends in Microbiology, 11(1):15–20.
Ebert, D & Bull, JJ, 2003b. Trends in Microbiology, 11(5):208–209. ISSN 0966-842X.
doi:10.1016/S0966-842X(03)00072-6. URL http://www.sciencedirect.com.lp.hscl.ufl.edu/
science/article/B6TD0-487DKNM-1/2/a73a504c3c242a5c72c5288af0221ba1.
Gandon, S, 1998. Proceedings of the Royal Society of London Series B-Biological Sciences, 265(1405):1545–1552.
Gandon, S & Day, T, 2003. Trends in Microbiology, 11(5):206–207.
Kamo, M & Boots, M, 2004. Journal of Theoretical Biology, 231(3):435–441.
King, AA, Shrestha, S, Harvill, ET, et al., 2009. American Naturalist, 175(4):446–455. doi:10.1086/597217.
Levins, R, 1966. American Scientist, 54:421–431.
Ma, J & Earn, DJD, 2006. Bulletin of Mathematical Biology, 68(3):679–702. ISSN 0092-8240.
doi:10.1007/s11538-005-9047-7. URL http://www.ncbi.nlm.nih.gov/pubmed/16794950. PMID:
16794950.
Mollison, D, 1991. Mathematical Biosciences, 107, Issue 2:255–287.
Rohani, P, Breban, R, Stallknecht, DE, et al., 2009. Proceedings of the National Academy of Sciences,
106(25):10365–10369. ISSN 0027-8424, 1091-6490. doi:10.1073/pnas.0809026106. URL
http://www.pnas.org/content/106/25/10365.
Ben Bolker NCEAS
Disease-induced extinction