Ecology Letters, (2003) 6: 1062–1067
doi: 10.1046/j.1461-0248.2003.00545.x
LETTER
Rates of spread of marine pathogens
Hamish McCallum1*, Drew
Harvell2 and Andy Dobson3
1
Department of Zoology and
Entomology, The University of
Queensland, Brisbane, Australia
2
Department of Ecology and
Evolutionary Biology, Cornell
University, Ithaca, NY, USA
3
Department of Biology,
Princeton University, Princeton,
NJ, USA
*Correspondence: E-mail:
hmccallum@zen.uq.edu.au
Abstract
Epidemics of marine pathogens can spread at extremely rapid rates. For example, herpes
virus spread through pilchard populations in Australia at a rate in excess of
10 000 km year)1, and morbillivirus infections in seals and dolphins have spread
at more than 3000 km year)1. In terrestrial environments, only the epidemics of
myxomatosis and calicivirus in Australian rabbits and West Nile Virus in birds in
North America have rates of spread in excess of 1000 km year)1. The rapid rates of
spread of these epidemics has been attributed to flying insect vectors, but flying vectors
have not been proposed for any marine pathogen. The most likely explanation for the
relatively rapid spread of marine pathogens is the lack of barriers to dispersal in some
parts of the ocean, and the potential for long-term survival of pathogens outside the
host. These findings caution that pathogens may pose a particularly severe problem in
the ocean. There is a need to develop epidemic models capable of generating these high
rates of spread and obtain more estimates of disease spread rate.
Keywords
Epidemic, epizootic, marine pathogens, rate of spread.
Ecology Letters (2003) 6: 1062–1067
INTRODUCTION
Over the last few years, it has become increasingly clear that
pathogen epidemics are as significant a component of the
ecology of marine systems as they are for terrestrial systems
(Harvell et al. 1999). The degree of connectivity and the
modes of dispersal are very different in terrestrial and
marine ecosystems. Obviously, a highly connected system
will allow wide and rapid spread of pathogenic organisms,
which will mean that emerging diseases may pose particularly serious problems. It is very likely that marine systems
are more open than their terrestrial counterparts, although it
is known that there is huge variation in degree of
connectivity between marine regions (Hellberg et al. 2002).
In this paper, we examine empirical data to see how the rate
of spread of pathogens in marine systems compares with the
rate of spread of similar pathogens in terrestrial systems.
Two previous studies have examined rates of spread in
ways that are pertinent to this study. Grosholz (1996)
reviewed rates of spread for introduced species in terrestrial
and marine systems. He did not specifically look at pathogens,
although his terrestrial data set included rabies in European
foxes and Yersina pestis (the black plague bacterium) in human
beings. His overall conclusion was that there were no
significant differences between the rates of spread of the
10 selected marine and terrestrial introduced species,
Ó2003 Blackwell Publishing Ltd/CNRS
although he did note that taxonomic differences between
them may have confounded the relationship (all Grosholz’s
marine introduced species were invertebrate animals, whereas
the terrestrial examples ranged from the pathogens mentioned above to a weed and several vertebrates). More
recently, Kinlan and Gaines (2003) have undertaken a detailed
comparison of propagule dispersal in marine and terrestrial
environments using both direct and genetic methods. Their
analysis suggests that rates of dispersal in marine systems
are two orders of magnitude faster than in terrestrial systems;
this result is strongly echoed in our analysis.
METHODS
We searched the literature, using ISI Web of ScienceÒ (ISI
Web of Science, Philadelphia, PA, USA) to locate cases of
measured rates of spread for marine pathogens causing
emergent disease. Our search focused on papers published
since 1980, although some of these reported earlier epidemics. Our examples are specific to cases in which a pathogen
has spread from an identifiable initial point to at least three
locations, or where spread along a ÔfrontÕ over at least three
time intervals was recorded. Although there may have been
anthropogenic involvement in the initial introduction of the
pathogen, or anthropogenic influence on environmental
conditions or host susceptibility that may have facilitated the
Rates of spread of marine pathogens 1063
spread of the pathogen, we have excluded cases where there
is clear human involvement in the transport of the pathogen
within the epidemic under consideration. We then searched
the literature for examples of measured rates of spread for
terrestrial pathogens that satisfied the same conditions, and
attempted to match the marine and terrestrial epidemics as
closely as was possible, by including as hosts vertebrates,
invertebrates and (to correspond with sessile corals) plants
(Table 1). We excluded cases where anthropogenic factors
were significantly involved in the continuing propagation of
Table 1 Rates of spread of epidemics in marine and terrestrial environments, sorted by decreasing order of rate of spread
Habitat
Pathogen
Host
Max. rate of spread
(km year)1)
Marine
Herpes virus
Pilchards
11 000
Marine
Marine
Herpes virus
Bacterium
Pilchards
Diadema (sea urchin)
5480
4990
Terrestrial
Terrestrial
Marine
RHV
Myxoma
Morbillivirus
Rabbits
Rabbits
Seals
4970
4740
3970
Marine
Morbillivirus
Striped dolphins
3230
Terrestrial
Marine
Marine
Terrestrial
Terrestrial
West Nile Virus
Amoeba
White pox bacterium
Myxoma
Mycoplasmal
conjunctivitis
Rinderpest
RHV
Rabies
Rabies
Nuclear polyhedrosis
virus
Baculovirus
Rickettsia
Dutch elm disease
Sarcoptic mange
Birds
Sea urchin
Coral
Rabbits
House finch
1150
936
600
600
512
Bovine tuberculosis
Black band disease
cyanobacterium
Nuclear polyhedrosis
virus
Phytophthera cinnamoni
fungus
Phytophthera cinnamoni
fungus
Armillaria ostoyae fungus
Inonotus tomentosus fungus
African Buffalo
Coral
Terrestrial
Terrestrial
Terrestrial
Terrestrial
Terrestrial
Terrestrial
Marine
Terrestrial
Terrestrial
Terrestrial
Marine
Terrestrial
Terrestrial
Terrestrial
Terrestrial
Terrestrial
Source
Date and location
Murray et al. (2001b),
Hyatt et al. (1997),
Jones et al. (1997),
Murray et al.
(2000, 2001a)
As above
Lessios et al. (1984),
Lessios (1988)
Kovaliski (1998)
Ratcliffe et al. (1952)
Heide-Jorgensen &
Härkönen (1992),
De Koeijer et al. (1998),
Swinton et al. (1998)
Aguilar & Raga (1993),
Cebrian (1995)
http://cindi/usgs/gov
Miller & Colodey (1983)
Richardson et al. (1998)
Fenner & Fantini (1999)
Dhondt et al. (1998)
1995: Australia
1999:
1980:
1995:
1952:
1994:
USA
Nova Scotia
Florida
France
Eastern USA
Dobson & May (1986)
Villafuerte et al. (1995)
Anderson et al. (1981)
Childs et al. (2000)
Entwistle et al. (1983)
1887:
1988:
1930:
1991:
1950:
Africa
Spain
Europe
North America
Canada
1970:
1985:
1944:
1993:
Tonga
California
Quebec
Spain
6
1.2
Entwistle et al. (1983)
Lafferty & Kuris (1993)
Gibbs (1978)
Fernandez-Moran et al.
(1997)
De Vos et al. (2001)
Bruckner et al. (1997)
Spruce sawfly
0.75
Entwistle et al. (1983)
1972: Scotland
Eucalyptus
0.4
Weste & Marks (1987)
c. 1960: Victoria
Banksia
0.0012
Hill et al. (1994)
Douglas fir
Spruce
0.0013
0.0002
Peet et al. (1996)
Hunt & Peet (1997)
c. 1960: Western
Australia
1986: Canada
c. 1890: Canada
Ungulates
Rabbits
Canids
Racoons
Forest tent caterpillar
Rhinoceros beetle
Abalone
American elm
Chamois
500
180
60
47
32
26.7
20.7
11.5
7.65
1997: Australia
1983: Caribbean
1995: Australia
1951: Australia
1988: Baltic
1990: Mediterranean
1990: Africa
1992: Jamaica
We have reported the upper limit, where the original source gives the rate of spread as a range. The dates given are the year that the epidemic
commenced. Multiple rates are given for the same host–pathogen interaction only where the epidemics are demonstrably separate events.
Ó2003 Blackwell Publishing Ltd/CNRS
1064 H. McCallum, D. Harvell and A. Dobson
the epidemic. For example, the most dramatic recent disease
outbreak in domestic animals has been the foot and mouth
disease epidemic in Britain in 2001, which spread very rapidly
over most of the UK. However, whilst there was certainly
continuing local spatial spread (Ferguson et al. 2001; Keeling
et al. 2001), the broad spatial extent of the epidemic was
determined by movements of animals between markets and
abattoirs before the epidemic was detected (Gibbens et al.
2001). Similarly, the fungus Phytophthora cinnamomi has spread
through forests in Australia, but much of the spread is
thought to have been on mud attached to vehicles (Weste &
Marks 1987). The figure for rate of spread of this pathogen
we include is for smaller scale ÔnaturalÕ transmission.
RESULTS
Figure 1 compares the rates of spread of epidemics in both
marine and terrestrial populations. Several patterns are
immediately apparent. Recorded rates of epidemic spread in
both types of environment vary by several orders of
magnitude. This means that any simple two sample test
used to compare rates of spread (along the lines used by
Grosholz 1996) will have very low power to detect
differences between terrestrial and marine environments.
As the data cannot be regarded as a truly random sample,
statistical analysis of the data has to be interpreted
cautiously, but can show whether the mean difference in
spread is consistent with a null hypothesis that our observed
rates of spread have been allocated randomly into ÔmarineÕ
and ÔterrestrialÕ categories. A two-way analysis of variance on
log rates of spread, when corrected for the effect of host
6
5
Terrestrial
4
3
Number of cases
2
1
0
5
4
Marine
3
2
1
0
1e – 4 1e – 3 1e – 2 1e – 1 1e + 0 1e + 1 1e + 2 1e + 3 1e + 4 1e + 5
Maxmimum rate of spread (km/year)
Figure 1 Maximum rates of spread of pathogens in terrestrial (top)
and marine (bottom) environments. Rates of spread for pathogens
with highly mobile vertebrate hosts are shown unshaded and rates
of spread for pathogens with sessile (or nearly sessile) nonvertebrate hosts are shown with diagonal hatching.
Ó2003 Blackwell Publishing Ltd/CNRS
mobility, suggests that marine pathogens spread significantly
faster than terrestrial pathogens (F ¼ 13.02, d.f. ¼ 1,25,
P ¼ 0.001). When corrected for the effect of habitat,
diseases with sessile (or nearly sessile) invertebrate or plant
hosts spread significantly more slowly than diseases with
mobile, vertebrate hosts (F ¼ 21.69, d.f. ¼ 1,25, P ¼
0.00001). The two order of magnitude difference in rate of
spread (estimated mean difference in log10 rate of spread ¼
2.1600, SE ¼ 0.5983) between marine and terrestrial systems
is very similar to that found by Kinlan and Gaines (2003) in
their survey of propagule dispersal in these systems.
It is also clear that some viral pathogens of marine
vertebrates have extraordinary rates of spread: more than
12 000 km year)1 for the pilchard epidemics on the
Australian coast, and 3000–6000 km year)1 for morbillivirus epidemics in seals and dolphins. These pathogens are
believed to be spread by contact, yet their rates of spread
may exceed (in the case of the pilchard virus) the mean
swimming speed of their hosts. Amongst terrestrial epidemics, viral pathogens of vertebrates also have the highest
rates of spread. The rates of spread of epidemics in Australia
of the introduced rabbit pathogens myxomatosis
(4700 km year)1) and rabbit calicivirus (5000 km year)1)
are of the same order of magnitude as the marine viral
epidemics. The rate of spread of these rabbit viruses is
usually attributed to long distance dispersal of insect vectors
by high altitude winds (Fenner & Fantini 1999; Cooke &
Fenner 2002). Similarly, the recent spread in North
America of West Nile Virus in birds at 1200 km year)1
and mycosal conjunctivitis amongst house finches at about
500 km year)1 are rapid, and also involve flying as a means
of pathogen dispersal. The fastest terrestrial epidemic in
which flight is not a clear mode of dispersal is the spread of
rinderpest through migratory African ungulates at the end
of the 19th century, at c. 500 km year)1. The rate of spread
of rabies, both in Europe and North America, has been
relatively modest, at 30–60 km year)1.
In both marine and terrestrial environments, infections of
relatively sessile hosts (corals, plants and invertebrates) tend
to have lower rates of spread than infections of mobile,
vertebrate hosts. Even amongst relatively sessile invertebrates, some marine epidemics have spread at extremely
high rates: for example, at least 2800 km year)1 in an
epidemic (suspected to be bacterial; Lessios 1988) amongst
sea urchins (Diadema) in the Caribbean, 900 km year)1 in an
amoebal epidemic amongst sea urchins in Nova Scotia, and
600 km year)1 in a bacterial white pox (Aurantimonas)
epidemic amongst corals in the Caribbean. In contrast,
rates of pathogen spread amongst terrestrial invertebrates
are typically slower. Plant epidemics are perhaps the closest
terrestrial analogues to epidemics amongst sessile corals. It is
clear from Table 1 that epidemics of soil borne fungal
pathogens may be very slow moving indeed.
Rates of spread of marine pathogens 1065
DISCUSSION
In the absence of flying vectors, to which the rapid spread
of some terrestrial pathogens has been attributed, how can
rates of epidemic spread in the oceans in excess of
2000 km year)1 be explained? There is good evidence that
pathogens may be transported on an intercontinental scale
by high-level winds (Brown & Hovmøller 2002), but these
are rare, one-off events that relate to colonization, rather
than spread through a continuum.
At least three hypotheses to account for the rapid spread
of marine epidemics can be proposed. First, the approximately one-dimensional (along coastlines) nature of some
marine epidemics (e.g. the two independent epidemics of
herpes virus amongst pilchards in Australia) may mean
that the linear rate of spread is greater than in comparable
terrestrial epidemics, which are more characteristically
two-dimensional. Second, marine environments may lack
barriers to dispersal of pathogens that characterize terrestrial
environments (see, e.g. Smith et al. 2002). Although there
has been significant new work emphasizing effective barriers
to gene flow in the ocean generated by small-scale currents
and eddies (Hellberg et al. 2002; Palumbi et al. 2003), many
locations are effectively open (Hellberg et al. 2002) and
nothing is known about barriers to pathogen flow. Third,
the strongly directional ocean currents that run along many
coastlines may be responsible for epidemic spread.
Although high altitude jet streams may act in a similar way
for some insect vectored terrestrial pathogens, only the
myxoma virus and rabbit calicivirus are likely to have been
influenced by this effect.
The simplest model of spatial spread of an invading
species is a diffusion model (Skellam 1951; van den Bosch
et al. 1992). These models often represent spread in twodimensions. Comparison of one- and two-dimensional
diffusion models shows that the rate of linear spread in a
one-dimensional model is the same as that in any direction
for a symmetric two-dimensional model, given the same
diffusion coefficient and intrinsic growth rate (Murray
1989). If the process can be described by a diffusion model,
there is nothing intrinsic to one-dimensional spread that
should increase the rate of linear spread.
As various authors have pointed out, diffusion may not
necessarily be a good model for the spread of organisms,
including pathogens. One problem is that diffusion models
assume that organisms have a finite (although infinitesimal)
probability of moving infinite distances. Telegraph models,
which assume that velocity is finite and direction is
maintained are alternatives, but in practice the difference
between their predictions of rate of spread from those of
diffusion models is small (Holmes 1993). At the other
extreme, despite the small probability of infinite dispersal,
diffusion models assume that the distribution of dispersers
through space follows a normal distribution, whereas it is
likely that dispersal distributions may have ÔfatterÕ tails. That
is, there may be a small number of very long distance
dispersers. Obviously, these might have a very major
influence on the rate of propagation of an epidemic. In
particular, fat tailed distributions increase the sensitivity of
the rate of propagation to R0 (Clark et al. 2001). Whether the
tails of dispersal kernels for marine organisms should be
fatter than those for terrestrial organisms is unclear. It is
likely that pathogens (whether viral, fungal or bacterial) may
survive better in the sea than in air (Colwell & Huq 2001),
which may increase the probability of occasional longdistance dispersal.
Not all marine disease outbreaks have been characterized
by a spatial spread of disease from one, or a few foci. For
example, the Ôwasting diseaseÕ of eelgrass (Zostera marina),
which caused a catastrophic decline in eelgrass beds on both
sides of the North Atlantic in the 1930s, did not appear to
spread in an epidemic manner (Rasmussen 1977). Indeed, it
is not entirely clear that a pathogen was the primary cause of
wasting disease. There have been mass mortalities of oysters
in most parts of the world, attributed to a variety of pathogens
(Sindermann 1990), but little information is available to
permit an estimate of the spatial spread of these epidemics.
There has been great recent interest in measuring degree
of connectivity in marine ecosystems. Many of these studies
have focused on the relatively few cases where apparently
open marine ecosystems are effectively closed by limited
gene flow (Hellberg et al. 2002). Even in cases where gene
flow is shown to be restricted, it is a very large assumption,
and completely untested, that marine pathogens will be
captured by the same barriers and processes that restrict fish
and invertebrate gene flow. Thus, it is very possible that
some pathogens, due to great longevity, rafting ocean
currents and diverse vectoring, will experience very few
barriers to dispersal. This renders estimates of pathogen
longevity and spread rates in the ocean as critical measurements to make, in testing the hypothesis that marine
epidemics spread faster than many terrestrial epidemics.
ACKNOWLEDGEMENTS
This letter arose from the NCEAS Working Group
ÔDiseases in the OceanÕ. We are also grateful to Professor
Frank Fenner, who provided information about the initial
spread of myxomatosis in Australia.
REFERENCES
Aguilar, A. & Raga, J.A. (1993). The striped dolphin epizootic in
the Mediterranean Sea. Ambio, 22, 524–528.
Anderson, R.M., Jackson, H.C., May, R.M. & Smith, A.M. (1981).
Population dynamics of fox rabies in Europe. Nature, 289, 765–771.
Ó2003 Blackwell Publishing Ltd/CNRS
1066 H. McCallum, D. Harvell and A. Dobson
van den Bosch, F., Hengeveld, F.R. & Metz, J.A.J. (1992).
Analysing the velocity of animal range expansion. J. Biogeogr., 19,
135–150.
Brown, J.K.M. & Hovmøller, M.S. (2002). Aerial dispersal of
pathogens on the global and continental scales and its impact on
plant disease. Science, 297, 537–541.
Bruckner, A.W., Bruckner, R.J. & Williams, E.H. (1997). Spread of
a black-band disease epizootic through the coral reef system in
St Ann’s Bay, Jamaica. Bull. Mar. Sci., 61, 919–928.
Cebrian, D. (1995). The striped dolphin Stenella-Coeruleoalba
epizootic in Greece, 1991–1992. Biol. Cons., 74, 143–145.
Childs, J.E., Curns, A.T., Dey, M.E., Real, L.A., Feinstein, L.,
Bjornstad, O.N. et al. (2000). Predicting the local dynamics of
epizootic rabies among raccoons in the United States. Proc. Natl.
Acad. Sci. USA, 97, 13666–13671.
Clark, J.S., Lewis, M. & Horvath, L. (2001). Invasion by extremes:
population spread with variation in dispersal and reproduction.
Am. Nat., 157, 537–554.
Colwell, R. & Huq, A. (2001). Marine ecosystems and cholera.
Hydrobiologia, 460, 141–145.
Cooke, B.D. & Fenner, F. (2002). Rabbit haemorragic disease and
the biological control of wild rabbits, Oryctolagus cuniculus, in
Australia and New Zealand. Wildl. Res., 29, 689–706.
De Koeijer, A., Diekmann, O. & Reijnders, P. (1998). Modelling
the spread of phocine distemper virus among harbour seals. Bull.
Math. Biol., 60, 585–596.
De Vos, V., Bengis, R.G., Kriek, N.P.J., Michel, A., Keet, D.F.,
Raath, J.P. et al. (2001). The epidemiology of tuberculosis in
free-ranging African buffalo (Syncerus caffer) in the Kruger
National Park, South Africa. Onderstepoort J. Vet. Res., 68, 119–
130.
Dhondt, A.A., Tessaglia, D.L. & Slothowa, R.L. (1998). Epidemic
mycoplasmal conjuntivitis in house finces from Eastern North
America. J. Wildl. Dis., 34, 265–280.
Dobson, A.P. & May, R.M. (1986). Disease and conservation. In:
Conservation Biology (ed. Soulé, M.E.). Sinauer, Sunderland, MA,
pp. 345–365.
Entwistle, P.F., Adams, P.H.W., Evans, H.F. & Rivers, C.F. (1983).
Epizootiology of a nuclear polyhedrosis virus (Baculoviridae) in
European spruce sawfly (Gilpinia hercyniae): spread of disease
from small epicentres in comparison with spread of baculovirus
diseases in other hosts. J. Appl. Ecol., 20, 473–487.
Fenner, F. & Fantini, B. (1999). Biological Control of Vertebrate Pests:
The History of Myxomatosis. An Experiment in Evolution. CABI
Publishing, Wallingford, Oxon, UK.
Ferguson, N.M., Donnelly, C.A. & Anderson, R.M. (2001). The
foot-and-mouth epidemic in Great Britain: pattern of spread and
impact of interventions. Science, 292, 1155–1160.
Fernandez-Moran, J., Gomez, S., Ballesteros, F., Quiros, P., Benito,
J.L., Feliu, C. et al. (1997). Epizootiology of sarcoptic mange in a
population of cantabrian chamois (Rupicapra pyrenaica parva) in
Northwestern Spain. Vet. Parasitol., 73, 163–171.
Gibbens, J.C., Sharpe, C.E., Wilesmith, J.W., Mansley, L.M.,
Michalopoulou, E., Ryan, J.B.M. et al. (2001). Descriptive epidemiology of the 2001 foot-and-mouth disease epidemic in
Great Britain: the first five months. Vet. Rec., 149, 729–743.
Gibbs, J.N. (1978). Intercontinental epidemiology of Dutch elm
disease. Ann. Rev. Phytopathol., 16, 287–307.
Grosholz, E.D. (1996). Contrasting rates of spread for introduced
species in terrestrial and marine systems. Ecology, 77, 1680–1686.
Ó2003 Blackwell Publishing Ltd/CNRS
Harvell, C., Kim, K., Burkholder, J., Colwell, R., Epstein, P.,
Grimes, J. et al. (1999). Emerging marine diseases – climate links
and anthropogenic factors. Science, 285, 1505–1510.
Heide-Jorgensen, M.P. & Härkönen, T. (1992). Epizootiology
of the seal disease in the eastern North Sea. J. Appl. Ecol., 29,
99–107.
Hellberg, M.E., Burton, R.S., Neigel, J.E. & Palumbi, S.R. (2002).
Genetic assessment of connectivity among marine populations.
Bull. Mar. Sci., 70, 273–290.
Hill, T.C.J., Tippett, J.T. & Shearer, B.L. (1994). Invasion of
Bassendean dune Banksia woodland by Phytophthora cinnamomi.
Aust. J. Bot., 42, 725–738.
Holmes, E.E. (1993). Are diffusion models too simple? A comparison with telegraph models of invasion. Am. Nat., 142, 779–795.
Hunt, R.S. & Peet, F.G. (1997). Annual spread rate of tomentosus
root disease. Plant Dis., 81, 1053–1056.
Hyatt, A.D., Hine, P.M., Jones, J.B., Whittington, R.J., Kearns, C.,
Wise, T.G. et al. (1997). Epizootic mortality in the pilchard
Sardinops sagax neopilchardus in Australia and New Zealand in
1995. II. Identification of a herpesvirus within the gill epithelium. Dis. Aquat. Org., 28, 17–29.
Jones, J.B., Hyatt, A.D., Hine, P.M., Whittington, R.J., Griffin,
D.A. & Bax, N.J. (1997). Special topic review: Australasian
pilchard mortalities. World J. Microbiol. Biotech., 13, 383–392.
Keeling, M.J., Woolhouse, M.E.J., Shaw, D.J., Matthews, L., ChaseTopping, M., Haydon, D.T. et al. (2001). Dynamics of the 2001
UK foot and mouth epidemic: stochastic dispersal in a heterogeneous landscape. Science, 294, 813–817.
Kinlan, B.P. & Gaines, S.D. (2003). Propagule dispersal in marine
and terrestrial environments: a community perspective. Ecology,
84, 2007–2020.
Kovaliski, J. (1998). Monitoring the spread of rabbit
hemorrhagic disease virus as a new biological agent for
control of wild European rabbits in Australia. J. Wildl. Dis.,
34, 421–428.
Lafferty, K.D. & Kuris, A.M. (1993). Mass mortality of Abalone
Haliotis cracherodii on the California Channel-Islands: tests of
epidemiologic hypotheses. Mar. Ecol. Prog. Ser., 96, 239–248.
Lessios, H.A. (1988). Mass mortality of Diadema antillarium in the
Caribbean: what have we learned? Ann. Rev. Ecol. Syst., 19, 371–
393.
Lessios, H.A., Robertson, D.R. & Cubit, J.D. (1984). Spread of
Diadema antillarum mass mortality through the Caribbean. Science,
226, 335–337.
Miller, R.J. & Colodey, A.G. (1983). Widespread mass mortalities
of the Green Sea-Urchin in Nova-Scotia, Canada. Mar. Biol., 73,
263–267.
Murray, J.D. (1989). Mathematical Biology. Springer-Verlag, Berlin.
Murray, A.G., O’Callaghan, M. & Jones, B. (2000). The development of
a model of the spread of the pilchard fish kill events in southern Australian
waters. CSIRO Marine Research, Hobart.
Murray, A.G., O’Callaghan, M. & Jones, B. (2001a). A model of
transmission of a viral epidemic among schools within a shoal of
pilchards. Ecol. Model., 144, 245–259.
Murray, A.G., O’Callaghan, M. & Jones, B. (2001b). Simple models
of massive epidemics of herpesvirus in Australian (and New
Zealand) pilchards. Env. Internat., 27, 243–248.
Palumbi, S.R. (2003). Population genetics, demographic connectivity, and the design of marine reserves. Ecol. Appl., 13, S146–
S158.
Rates of spread of marine pathogens 1067
Peet, F.G., Morrison, D.J. & Pellow, K.W. (1996). Rate of spread
of Armillaria ostoyae in two Douglas-fir plantations in the
southern interior of British Columbia. Can. J. Forest Res., 26,
148–151.
Rasmussen, E. (1977). The wasting disease of eelgrass (Zostera
marina) and its effects on environmental factors and fauna. In:
Seagrass Ecosystems: A Scientific Perspective (ed. McRoy, C.P. &
Helfferich, C.). Marcel Dekker, New York, pp. 1–51.
Ratcliffe, F.N., Myers, K., Fennessy, B.V. & Calaby, J.H. (1952).
Myxomatosis in Australia: a step towards biological control of
the rabbit. Nature, 170, 7–13.
Richardson, L., Goldberg, W., Kuta, K., Aronson, R., Smith, G.,
Ritchie, K. et al. (1998). Florida’s mystery coral-killer identified.
Nature, 392, 557–558.
Sindermann, C.J. (1990). Principal Diseases of Marine Fish and Shellfish.
Diseases of Marine Shellfish, Vol. 2, 2nd edn. Academic Press, San
Diego, pp. 364–388.
Skellam, J.G. (1951). Random dispersal in theoretical populations.
Biometrika, 38, 196–218.
Smith, D.L., Lucey, B., Waller, L.A., Childs, J.E. & Real, L.A.
(2002). Predicting the spatial dynamics of rabies epidemics on
heterogeneous landscapes. Proc. Natl. Acad. Sci. USA, 99, 3668–
3672.
Swinton, J., Harwood, J., Grenfell, B.T. & Gilligan, C.A. (1998).
Persistence thresholds for phocine distemper virus infection in
harbour seal Phoca vitulina metapopulations. J. Anim. Ecol., 67,
54–68.
Villafuerte, R., Calvete, C., Blanco, J.C. & Lucientes, J. (1995).
Incidence of viral hemorrhagic disease in wild rabbit populations
in Spain. Mammalia, 59, 651–659.
Weste, G. & Marks, G.C. 1987. The biology of Phytophthora cinnamomi in Australasian forests. Ann. Rev. Phytopathol., 25, 207–
229.
Editor, Peter Thrall
Manuscript received 29 August 2003
First decision made 25 September 2003
Manuscript accepted 13 October 2003
Ó2003 Blackwell Publishing Ltd/CNRS