Microparasitic disease dynamics in benthic suspension feeders: Infective dose, non-focal hosts, and particle diffusion

Mic opa asi ic disease dynamics in ben hic suspension eede s:1
in ec i e dose, non- ocal hos s, and pa icle di↵usion2
G. Bidegain a,⇤, E.N. Powell a, J.M. Klinck b, T. Ben-Ho in c,d, E.E. Ho mann b
3
aGul Coas Resea ch Labo a o y, Uni e si y o Sou he n Mississippi, 703 Eas Beach D i e, Ocean Sp ings, Mississippi 3954 USA4
bCen e o Coas al Physical Oceanog aphy, Old Dominon Uni e si y, 4111 Mona ch Way, No olk, Vi ginia 23529 USA5
cHaskin Shell ish Resea ch Labo a o y, Ru ge s Uni e si y, 6959 Mille A enue, Po No is, New Je sey 08349 USA6
dDepa men o Fishe ies, Animal and Ve e ina y Science, Uni e si y o Rhode Island, 20A Woodwa d Hall, 9 Eas Alumni A enue, Kings on,7
Rhode Island 02881, USA8
Abs ac 9
Ben hic suspension- eede s can accumula e subs an ial numbe s o mic opa asi ic pa hogens by con ac ing o il e ing pa icles10
while eeding, hus making hem highly ulne able o in ec ious diseases. The s udy o disease dynamics in hese ma ine o ganisms11
equi es an inno a i e app oach o modeling. To do so, we de eloped a single-popula ion de e minis ic compa men al model12
adap ed om he ma hema ical heo y o epidemics. The model is a con inuous- ime model, uns uc u ed in spa ial o age e ms,13
and con igu ed o simula e he dynamics o di e se dose (body bu den)–dependen in ec ious disease ansmission p ocesses in14
suspension eede s caused by suscep ible indi iduals con ac ing o abso bing ( il e ing) in ec ious wa e bo ne pa hogens. Di↵e en 15
scena ios we e simula ed o explo e he e↵ec o ec ui men , il a ion a e, pa icle loss, di↵usion-like p ocesses in he wa e 16
column and non- ocal hos s (i.e. non-suscep ible in e ms o disease) on disease incidence. An inc ease in ec ui men (i.e. new17
disease ee suscep ibles) can educe he p e alence o in ec ion due o he dilu ion e↵ec o adding mo e suscep ibles, bu he18
disease can sp ead as e o he same eason. Lowe in ec i e pa icle accumula ion a es o inc easing pa icle loss a es in he19
en i onmen educe he p e alence o in ec ion. This e↵ec is i ial when he wa e is sa u a ed wi h in ec i e pa icles eleased20
by in ec ed and/o dead animals. Di↵usion o pa icles om he local pool a ailable o suspension eede s o he adjacen emo e21
pool, p omp ed by a la ge emo e olume and high pa icle exchange, limi s epizoo ic de elopmen . Simila ly, he likelihood o an22
epizoo ic can be cons ained in a la ge suscep ible popula ion when compe i ion o pa hogens, mo e ’ac i e’ in ac i e il e eede s23
han in passi e suspension eede s, educes he pe capi a in ec i e pa icle accumula ion a e. In passi e suspension eede s,24
dec easing he a ea o he eeding su ace has he same e↵ec in cons aining disease de elopmen . The e↵ec o compe i ion o 25
in ec i e pa icles in essence dilu ing he in ec i e pa icle concen a ion in he wa e column is magni ied when he suscep ible26
popula ion is pa o a communi y wi h non- ocal il e eede s, and is pa icula ly e↵ec i e in limi ing disease de elopmen in27
high in ec i e dose sys ems. A he same ime, his ac i e o aging s a egy makes il e eede s mo e ulne able o epizoo ics.28
The model is a sui able amewo k o s udying he disease dynamics and de e minan s o disease ou b eaks in ben hic suspension29
eede s.30
c
2015 Published by Else ie L d.
Keywo ds:
31
disease model, epizoo ic, ansmission, suspension eede s, il e eede s, in ec i e-dose, o e il a ion, non– ocal hos 32
© Re ised 2016. Manusc ip This manusc ip e sion is made a ailable unde he CC-BY-NC-ND 4.0
license Click he e o iew linked Re e ences h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0/
Bidegain, G., Powell, E. N., Klinck, J. M., Ben-Ho in, T., & Ho mann, E. E.
(2016). Mic opa asi ic disease dynamics in ben hic suspension eede s: in ec i e
dose, non- ocal hos s, and pa icle di usion. Ecological Modelling, 328, 44-61
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 2
1. In oduc ion33
34
Ben hic suspension- eede s a e among he op imal o age s in he ma ine con ex because he ene ge ic cos o 35
cap u ing p ey is almos nil in passi e sessile animals and e y low in ac i e il e eede s (Riisgå d e al.,1993;36
Riisgå d and La sen,1995). Suspension eede s play a majo ole in he s uc u e and unc ion o ma ine ecosys-37
ems (Dame,1993;Newell,2004) by ans e ing ene gy om he pelagic zone o he ben hos (Newell,2004;Po e 38
e al.,2004). This eeding mode as a o aging s a egy has a downside in e ms o he ansmission and sp ead o 39
wa e bo ne diseases. In addi ion o ood pa icles, suspension- eede s can also accumula e a subs an ial numbe o 40
in ec ious pa hogens such as bac e ia, ungi, p o ozoans, and i uses om he wa e . Fo ins ance, he scle ac inian41
co al Mad acis mi abilis can accumula e 1 x 107bac e ial cells cm2h1and clea ance a es in bi al es can be much42
highe (e.g., 8 L h1in oys e s, Powell e al. (1992)). This po en ial o accumula e pa icles, in u n can ca alyze majo 43
epizoo ics and massi e mo ali ies causing subs an ial changes o ecosys em s uc u e and se ious losses in shell ish-44
e ies and aquacul u e (La↵e y e al.,2015). Among he bes cha ac e ized, geog aphically wide-sp ead, and i ulen 45
in ec ious diseases in suspension eede s a e MSX and De mo in oys e s (Villalba e al.,2004), whi e plague disease46
and black band disease (BBD) in co als (Sokolow e al.,2009;Z uloni e al.,2009), and b own ing disease BRD,47
and Pe kinsosis in clams (Pailla d,2004;Dang e al.,2010).48
P oli e a ion–based disease models ha e been conside ed su icien o desc ibe disease impac in ben hic suspen-49
sion eede popula ions cha ac e ized by apid non–poin –sou ce ansmission, such as bi al es (Cal o e al.,2001;50
Powell e al.,2011,2012b;Powell and Ho mann,2015). Hos p oli e a ion models alone o oge he wi h hyd o-51
dynamic models can explo e he e↵ec o en i onmen al ac o s, such as empe a u e and salini y, on he p ocess52
o pa hogen p oli e a ion and, consequen ly, on he in ec ion in ensi y. These models assume high p e alence and53
simula e epizoo ic de elopmen and hos mo bidi y and mo ali y based upon popula ion in ec ion in ensi y as he54
pa hogen p oli e a es wi hin he hos . Fo hese diseases he dynamics o ansmission a e ypically poo ly desc ibed55
(Fo d,1992;Fo d and Smolowi z,2007;G ay e al.,2009) and cu so ily in eg a ed in o disease models (Powell e al.,56
1996,1999). Only a ew s udies ha e adap ed he epidemic SIRmodels (Ke mack and McKend ick,1927;Ande son57
and May,1981) o ben hic ma ine o ganisms, despi e he ac ha he s uc u e o hese models as commonly used o 58
e es ial diseases is equally applicable and adap able o desc ibe he epizoo iology in ben hic animals (McCallum59
e al.,2004). Fo his pu pose, howe e , some ma ine sys em-speci ic ea u es such as he buoyancy and he high60
po en ial o dispe sion and dilu ion o wa e bo ne pa hogens (S a hmann,1990;McCallum e al.,2003) and ce ain61
unique eeding modes such as suspension eeding may need o be inco po a ed. Ku is and La↵e y (1992) de eloped a62
model inco po a ing bo h ec ui men o he pa asi e and he hos o compa e he e↵ec o a ious managemen s a e-63
gies on a hypo he ical c us acean pa asi ized by a pa asi ic cas a o . In his non-poin -sou ce hos -pa hogen sys em,64
he numbe o nea by in ec ed animals is ela i ely unimpo an in compa ison wi h he numbe o in ec i e pa hogens65
in he wa e . McCallum e al. (2005) modeled he dynamics o wi he ing synd ome in abalones by inco po a ing he66
ee-li ing pa hogen s age and disease ansmission h ough con ac be ween his s age and he hos . Mo e ecen ly,67
Sokolow e al. (2009) and Yakob and Mumby (2011) o mula ed he dynamics o disease in co als desc ibing he68
ansmission o disease by con ac be ween he hos and ee-li ing pa hogens. (Bidegain e al.,2016) o mula ed sim-69
ple compa men al models o yield he basic ep oduc ion numbe R0 o a a ie y o ma ine hos -pa hogen sys ems70
o explo e he ela i e impo ance o he hos and pa hogen ai s ha de e mine ansmission.71
Mos compa men al disease models (e.g., SI, SIR, SEIR, e c.) ollow he classic mass ac ion app oach whe e72
disease ansmission is a unc ion o he numbe o con ac s be ween suscep ible indi iduals and in ec i e pa icles73
in he wa e (Regoes e al.,2002;Sokolow e al.,2009;Yakob and Mumby,2011). Howe e , i may be impo an o74
include he well-known dose-e↵ec in disease ansmission o some suspension eede s such as oys e s (Bushek e al.,75
1997;Fo d e al.,1999;Powell e al.,1999); e↵ec i e dose is a cha ac e is ic wi h po en ially in e es ing e↵ec s on76
disease ansmission ha seems c ucial o ake in o accoun . Ac i e il e eede s can be su icien ly dense o compe e77
o ood (e.g., F ´
eche e e al.,1992;Wilson–O mond e al.,1997;Widdows e al.,2002) pa icula ly unde condi ions78
o slow low and limi ed e ical ad ec ion. Simila ly, hey may ‘compe e’ o pa hogens, p esumably educing he79
concen a ion o in ec i e pa icles su icien ly o limi body bu den below he in ec i e dose and, in u n, limi ing80
epizoo ic de elopmen (i.e. he o e il a ion scena io – Bidegain e al. in p ess). Passi e il e eede s may show his81
mechanism less ob iously since hey mo e impo an ly depend on he ambien low and he body su ace exposed o82
ha low, a he han on an ac i e pumping o wa e om he en i onmen h ough a il e (Sebens e al.,1996,1998).83
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 3
When hos di e si y inc eases, he disease isk can dec ease in wha is known as he dilu ion e↵ec . This well-84
s udied e↵ec in Lyme disease (Os eld and Keesing,2000) appea s o be a mo e gene al phenomenon ha elies on he85
idea ha a ce ain communi y wi h high species di e si y will con ain a p opo ion o incompe en hos s, in e ms o 86
disease, ha compe e o pa icles and de lec in ec ious pa hogens away om he suscep ible hos s, he eby educing87
in ec ion p e alence and disease isk. This ma ine suspension eede communi y could be composed, o ins ance,88
by he scle ac inian co al Mad acis mi abilis and he colonial ascidian T ididemnum solidun, since da a show ha 89
bo h o ganisms a e e↵ec i e bac e ial suspension eede s (Bak e al.,1998). O he examples may by a ee composed90
by oys e s and mussels, since mussels ha a ach o oys e ee s and shells can double he ee ’s il a ion capaci y91
(Gedan e al.,2014), o by oys e s and ascidian unica es (T. Ben-Ho in, unpublished da a).92
Ano he in e es ing cha ac e is ic o some diseases o suspension eede s is he impo ance o dead in ec ed ani-93
mals as a sou ce o in ec i e pa icles and, hence, he ole o mo ali y and subsequen sca enging and issue decay in94
disease ansmission. Fo ins ance, he pa hogen body bu den in dead oys e s in ec ed by De mo disease is commonly95
highe and he po en ial elease a e upon dea h is ela i ely much as e han ha o in ec ed li e animals (Bushek96
e al.,2002). Dead co als in ec ed by he black band disease may also elease pa hogens h ough b eakdown o decay-97
ing issue (Richa dson,2004). Once eleased, di↵usion p ocesses in he wa e column may ha e an e↵ec in pa hogen98
dynamics and consequen ly, in disease ansmission. The popula ion u no e a e (i.e. high mo ali y and ec ui men 99
a es) hus is ano he mechanism o con olling epizoo ics in suspension eede s. Yakob and Mumby (2011) ound ha 100
allowing o a mo e dynamic popula ion u no e in an epizoological model o co al disease no only gi es a supe io 101
i o empi ical da a, bu also sugges s ha eme ging co al assemblages could be a less p one o epizoo ics. The ole102
o p eda ion in he con ex o SIR models has been conside ed (Su and Hui,2011;Wang e al.,2011), bu has a ely103
been applied in he ma ine con ex (Liao e al.,2008). In il e eede s such as oys e s he impo an con ibu ion o 104
dead animals eleasing in ec i e pa icles may coun e weigh he e↵ec o he popula ion u no e a e as a es aining105
in luence on epizoo ics (Bidegain e al., unpublished).106
A heo e ical ansmission-based model o a hos -popula ion model ha inco po a es all o hese ea u es and de-107
sc ibes he dynamics o he hos in all possible s ages (i.e. suscep ible, li e in ec ed, dead in ec ed) and he wa e bo ne108
pa hogens does no exis o ac i e o passi e suspension eede s. In his pape , we de elop an SI model capable o 109
ep oducing hese p ocesses. Fo his pu pose, we adap he Ke mack and McKend ick (1927) epidemiological he-110
o y and he mic opa asi ic epidemic model o Ande son and May (1981). The model ep oduces he dynamics o 111
bo h suscep ible and in ec i e s ages o he hos , whe he ali e o dead, and he wa e bo ne in ec i e pa hogens. Ou 112
s udy sys em includes dose-dependen (i.e. body bu den dependen ) disease ansmission whe ein suspension eede s113
con ac o abso b ( il e ing) wa e bo ne in ec i e pa hogens eleased by li e o dead in ec ed animals. The model con-114
empla es he e↵ec on disease ansmission o non-poin sou ces o pa hogens and di↵usion p ocesses in he wa e 115
column. Mo eo e , he model pe mi s he s udy o po en ial mechanisms by which suspension eede s migh dilu e116
he disease isk, such as compe i i e in e ac ions among and be ween species, and he e↵ec o ec ui men o new117
suscep ible indi iduals. Finally, he model yields he o mula ion o he basic ep oduc ion numbe R0 o bo h ac i e118
and passi e il e eede s, o comp ehensi ely desc ibe he ela i e impo ance o some o hese p ocesses d i ing119
epizoo ics.120
2. The model121
2.1. Ma hema ical heo y and model s uc u e122
123
The model is a one-popula ion de e minis ic compa men al model con inuous in ime, uns uc u ed in spa ial o 124
age e ms (Cudding on and Beisne ,2005), and con igu ed o simula e he dynamics o a di e si y o in ec ious disease125
ansmission p ocesses in suspension eede s caused by suscep ible indi iduals con ac ing o abso bing ( il e ing)126
in ec ious wa e bo ne pa hogens such as bac e ia, ungi, p o ozoans, and i uses om he wa e column.127
As a compa men al model, which is he mos equen ly used class o model in epidemiology (Diekmann e al.,128
2013), indi iduals and pa hogens can ake on a ini e numbe o disc e e s a es. Each s a e is ep esen a i e o a129
subpopula ion o indi iduals o pa hogens a a gi en ime (Table 1) which, in u n, oge he wi h he co esponding130
pa ame e s (Table 2) sa is y a sys em o nonlinea o dina y di↵e en ial equa ions (ODEs) desc ibing he dynamics131
o he hos -pa hogen associa ion. The inco po a ion o a dead in ec ed subpopula ion s ems o m he ac ha some132
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 4
suspension eede s such as oys e s o co als may also ansmi he disease by eleasing pa hogens upon dea h (Bushek133
e al.,2002;Richa dson,2004). A a ian o he model inco po a es ano he a iable ep esen ing an al e na e suspen-134
sion eede hos popula ion which is incompe en in e ms o disease (H), ha is, he al e na e hos does no de elop135
he disease and pa hogens a e inac i a ed inside he animals ac ing as an impo an mechanism o con olling he136
concen a ion o in ec i e pa icles in he wa e column and as a sink o pa hogens.137
The popula ion o wa e bo ne pa hogens is di ided in o h ee classes depending upon hei loca ion in he sys em138
based on he di ision o he en i onmen in o wo olumes o wa e : The i s is de ined as he ‘local pool’ o pa hogens139
P. This pool is he pa hogen concen a ion in he ‘local olume’ de ined as Vl, adjacen o he bo om, wi hin which140
pa hogens a e eleased by in ec ed and dead in ec ed indi iduals and emain ee loa ing. Pa hogens in his olume141
a e suscep ible o con ac wi h o being il e ed by hos s, and can lose hei in ec i e p ope ies a e some ime o 142
o he wise be los (i.e ad ec ion, di↵usion, p eda ion). Fo example, o oys e s, he heigh o he local olume o he143
olume a ailable o il a ion is conside ed o be a ound 10 cm (Wilson–O mond e al.,1997). This is a ypical heigh 144
o an oys e clump (Powell e al.,1987,2012a), bu his heigh would exagge a e he e↵ec o an in aunal il e eede 145
(E man and Juma s,1988;Monismi h e al.,1990;Widdows e al.,1998). The second s a e a iable o pa hogens146
is he emo e pool U. This second pool is he concen a ion o pa hogens in a second olume con iguous o he local147
olume, de ined as he emo e olume V , whe e a emo e pool o pa icles can accumula e wi hou di ec in e ac ion148
wi h hos s. The size o he emo e olume would depend on how deep he wa e column is abo e he nea -bo om laye 149
di ec ly a↵ec ed by he il e ing ben hic popula ion. Di↵usional exchange o pa icles be ween hese wo olumes is150
assumed. The hi d subpopula ion o pa hogens is ha accumula ed in he suscep ible popula ion h ough con ac o 151
il a ion (F).152
The in ec ion s a e in he model is p esence/absence, ha is, he animals a e in ec ed o a e no , and i hey a e153
in ec ed, hey ha e he ’a e age’ pa asi e load. We assume his because mic opa asi es a e usually (bu no always)154
unicellula mic oo ganisms, such as i uses, bac e ia and p o ozoans ha can mul iply apidly wi hin a hos (McCal-155
lum e al.,2004) ela i e o a one yea ime s ep. The ans e o indi iduals om absence o p esence o disease is by156
a dose-dependen o body bu den dependen ansmission p ocess de ailed in sec ion 2.4.1.157
2.2. Miscellany158
159
Va iables ela ed o he hos popula ion a e de ined wi h espec o he concen a ion o indi iduals in a gi en160
su ace a ea o he bo om, whe eas a iables ela ed o he pa hogens a e de ined in numbe o pa icles in a gi en161
wa e olume o he numbe o pa icles in i o. No e ha o simplici y in ende ing equa ions, he ecip ocals o he162
local and emo e olumes Vland V ,sl and s espec i ely, a e o en used.163
Va iable De ini ion Uni
SSuscep ible hos s in he popula ion Numbe o indi iduals
IIn ec ed indi iduals in he popula ion Numbe o indi iduals
DI Dead in ec ed indi iduals in he popula ion Numbe o indi iduals
DS Dead suscep ible indi iduals in he popula ion Numbe o indi iduals
PF ee-li ing pa hogens in he en i onmen , local pool Numbe o pa icles
FTo al numbe o pa hogens abso bed o il e ed by he popula ion Numbe o pa icles
UPa hogens om a emo e olume, emo e pool Numbe o pa icles
HAl e na e non–compe en ese oi hos Numbe o indi iduals
Table 1: Va iables o he model. No e ha he model has an implici su ace a ea o olume o he hos subpopula ions and pa hogens, espec i ely.
Fis he excep ion and he co esponding uni is in e nal pa icles in he suscep ible popula ion.
The ma hema ical heo y o his model con empla es ha disease ansmission equi es he pa hogen o exis 164
ou side he hos and emain in ec ious o some ime ini e pe iod. Thus, he suscep ible and in ec ed indi iduals a e165
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 5
no necessa ily in con ac o e en componen s o he same local popula ion, since he ee-li ing pa hogen s age can166
d i in he luid and con ac o be il e ed by suscep ible animals loca ed nea o a away om he pa icle sou ce.167
Na u al mo ali y o he hos and mo ali y due o disease a e also in eg a ed in o he o mula ion o he model. Thus,168
he in ec ed indi iduals can die due o bo h na u al causes and disease. The model also assumes an open popula ion169
since i con empla es demog aphic u no e ; ha is, he ec ui men p ocess is in eg a ed in he dynamics o he170
hos . The model does no inco po a e he p ocess o eco e y om disease because only a ew examples o ma ine171
wild popula ions eco e ing om disease a e known in ma ine sys ems (Gilmou e al.,2013;Pailla d e al.,2014;172
Vega Thu be e al.,2014). Consequen ly, indi iduals ne e eco e om he disease and in ec ed indi iduals emain173
in ec ed un il hey die.174
2.3. Model scheme175
176
The low diag am o he model (Fig. 1) shows he mos impo an p ocesses in he disease ansmission p ocess in177
suspension eede s. Disease is ansmi ed o he suscep ible popula ion S ho ough il a ion (ac i e suspension eed-178
e s) o con ac (passi e suspension eede s) a a a e by a dose-dependen ansmission. In ec ed animals Idie due179
o bo h na u al mo ali y mSand disease mo ali y mI, while suscep ible indi iduals Sonly die due o na u al causes.180
The al e na e incompe en (i.e. no suscep ible o he disease) suspension eede hos Hcompe ing o wa e bo ne181
pa hogens wi h he suscep ible hos is also loca ed in he bo om. This al e na e hos only dies by na u al mo ali y182
assuming ha i is esis an o he disease and does no elease pa icles o he wa e ; ha is, hey a e assumed o be183
inac i a ed by he immune sys em o by diapedesis. An exchange be ween he local nea –bo om pa hogen pool P184
and he emo e pool Uoccu s a a ce ain exchange a e by a di↵usion-like p ocess p opo ional o he di↵e ence in185
concen a ion be ween he wo pools.186
mS S!
d bDI DI!
a F!
c bI I!
I P!
!
F!
S P!
!
D"
SI!DI!
P
β S !mI I!
P!
U"
σ
U
!
Remo e&Volume&
V #
Local&Volume&
Vl#
γ (s
U
– sl P)!
H!
H P!
DS!
Figu e 1: Model low diag am. The model a iables a e ep esen ed by capi al le e s: suscep ible animals (S), in ec ed animals (I), dead
suscep ible (DS ) and dead in ec ed animals (DI), wa e bo ne pa hogens (P), in e nal pool o pa hogens (F), emo e pool o pa hogens (U) and
al e na e hos popula ion (H). Dashed a ows ep esen he main p ocesses in he model. The pa ame e s in ol ed in hese ansmission a e
desc ibed in Table 2.
2.4. Model equa ions187
188
The equa ions ha ollow ep esen he disease ansmission p ocess and he model a iables. The hos and189
pa hogen s a es o subpopula ions sa is y a sys em o ODEs desc ibing he dynamic o he hos -pa hogen associa ion.190
The nume ical model o his ODE sys em is p og ammed in Ma lab 8.1. The se o coupled di↵e en ial equa ions191

G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 6
is sol ed wi h a 4 h–o de p edic o co ec o scheme using he Adams-Bash o h p edic o and he Adams-Moul on192
co ec o .193
2.4.1. In ec i e dose and disease ansmission194
195
Disease ansmission in suspension eede s, a leas in il e eede s, mos likely occu s ia an in ec i e dose196
(Bushek e al.,1997;Fo d e al.,1999;Powell e al.,1999) a he han by unique con ac be ween a single pa hogen197
o omi e and hos . Consequen ly, he ansmission p ocess in he model is based on he ac ha suscep ible animals198
equi e some minimum le el o body bu den o in ec ious pa icles, he in ec i e dose, o become in ec ious. Fu he -199
mo e, he model assumes ha as hos s abso b o il e pa icles, some suscep ible indi iduals will ha e a ela i ely200
la ge body bu den whe eas mos will ha e a smalle body bu den. The dis ibu ion o he numbe o suscep ible201
animals (S) wi h each le el o body bu den (b) (Fig. 2) is assumed o ha e he o m202
S(b)=S0e⇢b,(1)
which has a simple exp ession bu simila beha io o he nega i e binomial dis ibu ion, e y common in ben hic203
in ec ed hos s (Ande son and Go don,1982;Fo d e al.,1999)), in ha ing a long ail desc ibing he declining equency204
o indi iduals o inc easing in ec ion in he popula ion dis ibu ion. S0is he o al numbe o suscep ible indi iduals.205
Fo body bu dens up o se e al hund ed, ⇢is a well app oxima ed by ˆ
S/F, whe e ˆ
Sis he numbe o suscep ible206
animals and Fis he numbe o in ec ious pa icles housed in he suscep ible subpopula ion (Eq. (2)). Thus F/S207
ep esen s he a e age concen a ion o in ec ious pa icles in suscep ible indi iduals.208
dF
d =(F+mS+a+cS)F+ SASSP.(2)
In ec ious pa icles a e il e ed ou (ac i e il e eede s) by o come in o con ac (passi e il e eede s) wi h209
suscep ible indi iduals a he il a ion o con ac a e S, being he con ac a e p opo ional o he eeding su ace AS
210
o passi e il e eede s (see sec ion 2.4.2 o a mo e de ailed desc ip ion o pa icle up ake). In ec ious pa icles can211
be emo ed om he suscep ible popula ion by ou p ocesses: (i) he educ ion o he in e nal pool o pa icles in he212
suscep ible popula ion due o emo al o suscep ible indi iduals ha become in ec ed F(see de ails in Eq. (6)), (ii)213
he backg ound mo ali y mSas i emo es indi iduals wi h inco po a ed in ec ed pa icles, (iii) he inac i a ion inside214
suscep ible animals (a), con olled by some componen o he immune esponse such as phagocy osis, inac i a ion by215
oxygen adicles, binding by lec ins, e c. (Renw an z,1986;Villalba e al.,2004), and (i ) he elease o pa icles om216
suscep ibles h ough, o ins ance, aeces. Whe he a suscep ible becomes in ec ed is a balance be ween a, he elease217
a e o pa icles cS, he il a ion o pa icles by suscep ibles sSP, and he concen a ion o in ec i e pa icles ha 218
needs o be eached o gene a e he in ec i e dose (bmin, see Fig. 2).219
The dis ibu ion o in ec i e pa icle body bu den in suscep ible hos s in Fig. 2has a e y long ail so ha a ew220
unin ec ed animals ha e a high body bu den. The po ion o he suscep ible pool eligible o ansi ion o he in ec ed221
pool is ci cumsc ibed by bmax, he maximum body bu den o any animal conside ed o be unin ec ed and bmin, he222
minimum body bu den o animals eligible o ansi ion o he in ec ed pool. A any ime, he e will be some numbe 223
o suscep ible animals (S) wi h a o al abso bed pool o in ec ious pa icles (F). These alues a e used o de e mine224
how many suscep ible animals wi h a body bu den be ween bmin and bmax should become in ec ed.225
The o al numbe o suscep ible animals a any ime is226
S=Zbmax
0
ˆ
S0e⇢bdb =ˆ
S0
⇢(1 ebmax ) (3)
whe e ˆ
S0is he numbe o suscep ibles pe body bu den. The o al body bu den o he popula ion is
F=Zbmax
0
ˆ
S0be
⇢bdb =ˆ
S0
⇢2(1 (1 +⇢bmax)e⇢bmax .(4)
Fand ˆ
Sa e bo h known a any s ep in he model. Consequen ly, he alues o S0and ⇢can be calcula ed easily.227
The o al numbe o suscep ible indi iduals mo ed o he in ec ed popula ion is228
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 7
0!
50!
100!
150!
200!
250!
300!
0!50!100!150!200!250!300!350!400!
Suscep ible popula ion !
(indi iduals/a ea)!
Body bu den (pa hogens/indi idual)!
bmin
bmax
Figu e 2: A heo e ical dis ibu ion o he popula ion wi h each le el o in ec i e pa icle body bu den (b). The minimum body bu den a which
suscep ible animals a e conside ed o be in ec ed and hus ans e ed o he in ec ed popula ion is bmin. The maximum body bu den o any
suscep ible animal conside ed o be unin ec ed is bmax.
S=Zbmax
bmin
ˆ
S0e⇢bdb =ˆ
S0
⇢(e⇢bmin e⇢bmax ).(5)
The o al numbe o in ec ious pa icles ha should be emo ed om he suscep ible in e nal pool as a consequence is229
F=Zbmax
bmin
bˆ
S0e⇢bdb =ˆ
S0
⇢2((1 +⇢bmin)e⇢bmin )(1 +⇢bmax)e⇢bmax ).(6)
No e ha since he hea ily in ec ed suscep ibles a e he ones ha a e mo ed o he in ec ed pool, a la ge numbe 230
o in e nal in ec ious pa icles will be emo ed om he in e nal pool o he suscep ibles. Based on hese calcula ions,231
a ac ion S/So he suscep ibles need o be mo ed o he in ec ed pool and F/Fo he in e nal in ec ious pa icles232
need o be emo ed om he suscep ible in e nal pool. These changes a e assumed o occu a a ce ain a e ↵[1/day]233
depending on he hos -pa hogen sys em. Fo ins ance, o a change ha occu s a a a e o 10% pe day, ↵is 2.3. The234
e ms in he go e ning equa ions ep esen ing disease ansmission hus ha e he o m235
S=↵ S
S(7)
whe e ↵is a speci ic a e o mo e a ac ion o he indi iduals om he suscep ible popula ion S o he in ec ed236
popula ion I. Simila ly, he a e a which he in e nal pa icles a e emo ed om he in e nal pool Fis237
F=↵ F
F.(8)
No e ha he s anda d mass ac ion model wi h in ec i e pa icles wi h an ins an aneous dose esponse, ypically238
ep esen ed as PS (Bidegain e al., in p ess), is a speci ic case o he dose- esponse model p esen ed he e. Fo ⇢=0,239
Eq. (5) becomes240
S=ˆ
S0(bmax bmin),(9)
and consequen ly, S=ˆ
S0bmax and S=↵(1 bmin
bmax ). The s anda d mass ac ion model does no explici ly speci y241
pa icle accumula ion o body bu den, so ha bmin =0; hus, Eq. 7simpli ies o he case o an ins an aneous dose242
esponse ansmission S=↵.243
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 8
2.4.2. Up ake o pa icles by il a ion o con ac : ac i e and passi e suspension eede s244
245
The model is o mula ed o pe mi he s udy o bo h ac i e (e.g., bi al es) and passi e (e.g. co als) suspension246
eede s. The main eeding di↵e ence be ween hese o ganisms is ha ac i e il e eede s pump wa e ac i ely h ough247
a sie e while passi e suspension eede s a e in ec ed by passi ely con ac ing pa icles anspo ed by wa e cu en s.248
Thus, disease ansmission in il e eede s depends on he speci ic il a ion a e (Powell e al.,1999) whe eas, o 249
passi e suspension eede s, he ansmission o disease is a unc ion o he exposed su ace a ea o he indi idual o 250
colony de o ed o ood collec ion and he wa e low speed [Sebens e al. (1996) and Sebens e al. (1998) demons a ed251
ha ood cap u e is highe in co als wi h high polyp and colony exposed su ace a ea in ela ion o hei biomass, and252
is limi ed a low low condi ions]. The model inco po a es he e m o ep esen hese wo o aging s a egies. In253
bo h cases, we conside ha he cap u e a e o ood and in ec i e pa icles is simila . Consequen ly, o ac i e il e 254
eede s ep esen s he a e a which pa icles a e il e ed by one indi idual pe uni o ime, whe eas o passi e255
suspension eede s ep esen s he a e a which he pa icles con ac he exposed su ace a ea o an indi idual pe 256
uni o ime (see Table 2).257
258
Ac i e il e eede s259
260
Pa icle emo al om he wa e due o ac i e il a ion by suscep ible indi iduals (see Eq. (14)) has he o m261
SSP, whe e Sis he il a ion a e ( olume il e ed) pe suscep ible indi idual, Sis he numbe o ben hic sus-262
cep ible indi iduals, and Pis he concen a ion. Simila ly, he e m o ep esen he pa icle emo al due o ac i e263
il a ion o in ec ed indi iduals (I) and non- ocal o al e na e incompe en hos s in e ms o disease (H) would be264
IIPand HHP, espec i ely. The inco po a ion o speci ic il a ion a es o suscep ible and in ec ed indi iduals265
pe mi s simula ion o disease dynamics o cases whe e in ec ed o se e ely diseased indi iduals show a educ ion in266
clea ance a e. Simila ly, he non- ocal hos has a speci ic il a ion a e.267
268
Passi e suspension eede s269
270
Fo passi e suspension eede s, he pa icle emo al om he wa e by passi e con ac (see Eq. (15)) has he o m271
SA
SP, whe e S is he ad i pa icle con ac a e pe suscep ible indi idual and ASis he exposed su ace a ea272
pe indi idual. Simila ly, he e m o ep esen he pa icle emo al due o passi e con ac o in ec ed indi iduals (I)273
and non- ocal o al e na e incompe en hos s (H) wi h pa icles would be IIA
IPand HHA
sP, espec i ely. The274
model also speci ies speci ic con ac a es o suscep ible and in ec ed indi iduals, and o non- ocal hos s. Howe e ,275
conside ing ha (i) he wa e mo emen is he p ima y mechanism b inging zooplank on in o con ac wi h passi e276
suspension eede s and ha exposed su ace is c ucial (Sebens e al.,1998), and (ii) he model al eady inco po a es a277
e m o indi idual exposed su ace a ea, he e m may be a unc ion o he wa e low speed a he han a disease-278
a↵ec ed cha ac e is ic and, hus, may likely be conside ed he same o di↵e en subpopula ions o he same hos .279
2.4.3. Suscep ible Indi iduals280
281
Sis he numbe o suscep ible animals in a gi en su ace a ea o he bo om. Suscep ible indi iduals a e los by282
wo p ocesses: in ec ion and na u al mo ali y. The disease ansmission a e is con olled by Swhich is a unc ion283
o body bu den, allowing o a dose- esponse o in ec ion, and i is an es ima e o he a e a which indi iduals become284
in ec ed (see de ails in sec ion 2.4.1), whe eas he na u al mo ali y a e is mS(Eq. (10)).285
The model allows ec ui men o new suscep ible indi iduals when he popula ion densi y (S+I) alls below he286
ca ying capaci y K. Suscep ible and in ec ed animals can p oduce ec ui s a di↵e en a es nSand nI, espec i ely287
allowing o educed ec ui men associa ed wi h in ec ed indi iduals (Yakob and Mumby,2011). Finally, he model288
pe mi s an ex e nal sou ce o ec ui s (SRCS).289
dS
d =(S+mS)S+⇣1S+I
K⌘(nSS+nII+SRCS) (10)
whe e, i 1 S+I
K>0, hen he ca ying capaci y is no eached and new indi iduals can be ec ui ed o he suscep ible290
popula ion as a unc ion o he ec ui men a es nS,nI, and he po en ial ex e nal sou ce o ec ui s S c
S.291
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 9
2.4.4. In ec ed Indi iduals292
293
In ec ed indi iduals a e ans e ed om he suscep ible subpopula ion o he in ec ed subpopula ion a he a e S
(Eq. (11)). In ec ed indi iduals die a a a e con olled by na u al mo ali y mSand disease mo ali y mI.
dI
d =SS(mS+mI)I(11)
2.4.5. Dead Suscep ible Indi iduals294
295
Suscep ible indi iduals die a a a e mSwhich is a backg ound mo ali y no ela ed o disease p ocesses (Eqs.296
(10) and (12)). The subpopula ion o dead indi iduals is educed a a a e d, which ep esen s bac e ial decomposi ion297
o sca enging p ocesses. Al hough ue sca enge s do no exis in he ma ine wo ld, many p eda o s sca enge ad en-298
i iously (Hoese,1962;Veale e al.,2000;Mo ello e al.,2005). These dead suscep ible indi iduals a e a diagnos ic299
and do no a↵ec he beha io o he model.300
d DS
d =mSSd DS (12)
2.4.6. Dead In ec ed Indi iduals301
302
In ec ed indi iduals die om disease a a mo ali y a e mIand su↵e backg ound mo ali y a a e mS(Eqs. (11)303
and (13)). Simila ly o dead suscep ible animals, hese dead in ec ed indi iduals decay o a e sca enged a a a e d.304
dDI
d =(mS+mI)IdDI (13)
2.4.7. In ec ious Pa icles in he local olume305
306
The ben hic communi y comp ises suscep ible hos s, in ec ed hos s, and al e na e hos s, il e ing ou o con ac ing307
pa icles. The model analyses wo si ua ions in e ms o he ype o ben hic sys em con ibu ing o he emo al o 308
pa icles om he sys em.309
2.4.7.1. Suscep ible and in ec ed animals emo ing and eleasing pa icles.310
311
Pis he numbe o in ec ious pa icles in he olume o wa e immedia ely accesible o he suspension eede 312
popula ion (Eqs. (14) and (15) ). In ec ious pa icles a e mainly added o he wa e by elease om in ec ed indi iduals313
a a a e cI(e.g. by aeces) and om dead in ec ed indi iduals a a a e cDI. Suscep ibles and dead suscep ibles can314
elease a small amoun o pa icles h ough aeces a a a e cSand upon dea h h ough decomposi ion and sca enging315
p ocesses a a a e cDS . I dead in ec ed animals elease hei en i e body bu den o pa icles, hen cDI =d, o hey316
may elease a much smalle numbe depending on he cha ac e is ics o he decay o sca enging p ocess emo ing317
dead animals, which may inac i a e a subs an ial p opo ion o o all o he in ec i e pa icles be o e hey can be318
eleased in o he wa e column. In ec ious pa icles a e emo ed om he local olume by one o wo p ocesses: (i)319
inac i a ion a a a e , by dilu ion, anspo downs eam, o by educ ion o in ec iousness by inac i a ion o dea h,320
and (ii) il a ion by o con ac wi h suscep ible and in ec ed indi iduals.321
The local wa e olume can exchange pa icles wi h he e ically adjacen olume i he concen a ions a e di -322
e en , h ough a di↵usion-like p ocess con olled by pa ame e (see sec ion 2.2) (Eqs. (14) and (15)). Finally, an323
unspeci ied sou ce o in ec ious pa icles om ano he ben hic communi y (SRCP) is also pe mi ed.324
325
Ac i e il e eede s326
327
A his poin , he model di↵e en ia es be ween ac i e il e eede s (e.g., bi al es) (Eq. (14)) and passi e suspen-328
sion eede s (e.g., co als) (Equa ion 15) (see also sec ion 2.4.2) o ep esen he dis inc emo al o pa icles om he329
wa e . Thus, he change in he numbe o in ec i e pa icles in a gi en wa e olume o ac i e il e eede s is330
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 16
We examined he po en ial impo ance o in ec i e pa icle loss in luencing in ec ion p e alence. Fo his pu pose,473
we a ied he a e o pa icle loss in he local pool, ha is he a e o inac i a ion o pa hogens due o dilu ion, ad ec-474
ion, and mo ali y. Inc easing pa icle loss limi s he p e alence o in ec ion (Fig. 7c) due o he educed a ailabili y475
o pa icles o be il e ed o con ac ed. The p og essi e sa u a ion o pa icles in he wa e olume accessible o he476
ben hic popula ion (Fig. 6c) cancels he pa icle loss e↵ec educing he in ec ion p e alence. La e in he simula ion,477
he elease a e om in ec ed animals clea ly o e whelms he inac i a ion a e o pa hogens in he wa e due o dilu-478
ion, ad ec ion, and na u al mo ali y o he wo lowe pa icle loss scena ios es ed (see solid and dashed black lines479
in Fig. 7c). In con as , a he highes pa icle loss a e es ed (see g ay solid line in Fig. 7c), he inac i a ion a e480
o pa hogens exceeds he elease a e, esul ing in he absence o in ec ion o he i s 800 days and a ela i ely low481
p e alence (30%) in he las days o he simula ion.482
3.3.4. Di↵usion o pa icles483
484
Th ee a es o pa icle di↵usion we e simula ed, by means o h ee emo e olume V /local olume Vl a ios (Fig.485
7d). Fo mos suspension eede s, he olume di ec ly in luenced by il e o suspension eeding Vlwill be small (e.g.,486
a olume wi h a heigh o 0-15 cm o oys e popula ions (Wilson–O mond e al.,1997)). Consequen ly, he size o 487
he emo e olume V may be a p ima y de e minan o he p e alence o in ec ion. While he local olume (0.1m3)488
was main ained cons an , inc easing he size o he emo e olume om 0.1m3 o 1 m3 esul ed in a dec ease in he489
p e alence o in ec ion o 40% a he beginning o he simula ion. Ini ially, he wo lowe emo e olumes es ed490
showed no in ec ions (see black dashed and g ay solid lines in Fig. 7d), bu as he simula ion p og essed only he491
la ge emo e olume limi ed disease ansmission (see g ay solid line in Fig. 7d). Simila ly o he p e ious case,492
whe e pa icle loss om he local pool was a ied, he p og essi e sa u a ion o pa icle concen a ion (Fig. 6a,b)493
esul ed, a he end o simula ion, in a supp ession o he di↵usion e↵ec ini ially obse ed o inc easing emo e494
olumes.495
3.4. Epizoo iology and R0
496
497
The gene a ion o an epizoo ic is egula ed by a es in ol ed in he dynamics o bo h he hos and he pa hogen,498
and ac o s associa ed wi h he pa icle di↵usion p ocesses. R0inc eases linea ly wi h inc easing ansmission a e S,499
and nonlinea ly wi h inc easing ini ial popula ion N(Fig. 9a, black solid line), pa hogen body bu den and elease a e500
om in ec ed animals cIbIand dead in ec ed animals cDIbDI, and wi h inc easing il a ion o con ac a e o pa icles501
Sand local olume sizes Vl(Eq. (17)). The likelihood o an epizoo ic dec eases linea ly wi h inc easing inac i a ion502
a e o pa icles inside he body o he animal a, and nonlinea ly wi h inc easing disease mo ali y mI, he emo al o 503
dead indi iduals om he sys em d, he emo e olume size V , he exchange a e o pa icles be ween local olume504
and he emo e olume , and he loss o pa icles in he local olume and he emo e olume (Eq. (16)). Fo 505
passi e suspension eede s, in addi ion o il a ion o con ac a e o pa icles S, ansmission o disease inc eases506
nonlinea ly wi h he su ace a ea o he suscep ible indi idual exposed o con ac wi h wa e bo ne pa hogens AS.507
508
Hos and non- ocal hos densi y509
510
In a scena io whe e an in ec ed animal is in oduced in o a o ally suscep ible popula ion, once he popula ion den-511
si y ises su icien ly o compe e o pa hogens and lowe he pe capi a body bu den in he suscep ible subpopula ion,512
he p obabili y o an epizoo ic de eloping emains ela i ely cons an wi h inc easing N (Fig. 9a, black solid line).513
In a scena io wi h ela i ely low pa hogen body bu den, his compe i ion, mo e likely o occu in ac i e il e eede s514
han in suspension eede s, esul s in a educ ion o disease isk (R0<1) (Fig. 9a, black dashed line).515
In a sys em wi h non- ocal suspension- eeding hos s H(Equa ion 20), wi h a ela i ely high il a ion/con ac a e516
o pa icles H, he compe i ion e↵ec be ween hos ypes is in ensi ied and, consequen ly, he likelihood o an epi-517
zoo ic dec eases wi h inc easing ini ial abundance o he non- ocal hos (Fig. 9a, g ay solid line). Thus, he h eshold518
o he ini ial hos popula ion N o an epizoo ic o occu may be subs an ially inc eased wi h inc easing abundance o 519
he non- ocal hos popula ion. Fo ins ance, in he Fig. 9a scena io, he epizoo ic h eshold o he ini ial hos popula-520
ion in a sys em wi hou non- ocal il e eede s (N=30) is inc eased o N=80 a e adding he same non- ocal hos 521

G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 17
0 500 1000
0
100
200
300
Time (days)
Suscep ible indi iduals
0 500 1000
0
500
1000
1500
Time (days)
Pa icles in local pool
(numbe m−3)
0 500 1000
0
100
200
300
Time (days)
In ec ed indi iduals
0 500 1000
0
5
10
15
Time (days)
Pa icle up ake a e
(pa icles ind−1 day−1)
a) !b) !
c) !d) !
Rec ui men a e !
( ime -1) !
1 x 10-2 !
1 x 10-3 !
1 x 10-4!
Rec ui men a e !
( ime -1) !
1 x 10-2 !
1 x 10-3 !
1 x 10-4!
Rec ui men a e !
( ime -1) !
1 x 10-2 !
1 x 10-3 !
1 x 10-4!
Rec ui men a e !
( ime -1) !
1 x 10-2 !
1 x 10-3 !
1 x 10-4!
Figu e 8: Compa ison o he e↵ec o a ying ec ui men a e on (a) he suscep ible popula ion, (b) he in ec ed popula ion, (c) he pa icle
concen a ion in he local olume, and (d) pa icle up ake a e.
popula ion (H=30) .522
523
Remo e olume size and pa icle loss524
525
In a scena io wi h a ela i ely high exchange a e o pa icles be ween he local and emo e pools (=1), an in-526
c easing emo e olume size, esul ing in a di↵usion-like ans e o pa icles o he emo e pool, educes he pa icle527
concen a ion in he local olume a ailable o suspension- eede s and, hus, he likelihood o an epizoo ic (Fig. 9b,528
dashed line). The e↵ec o inc easing pa icle loss a e in he emo e pool on disease de elopmen has a simila 529
end and in ensi y (Fig. 9b, dash-do line). No e o compa ison ha he cu e is o a emo e olume size V =1.530
The e↵ec o inc easing in e nal in i o inac i a ion a e aalso has a simila end making R0es ima e much mo e531
sensi i e o small changes in his pa ame e (Fig. 9b).532
533
In ec i e dose534
535
Finally, we explo e he simila i y o inc easing emo e olumes and non- ocal hos densi ies, speci ically ocusing536
on he in luence o he in ec i e dose on disease de elopmen . When compa ing he e↵ec o inc easing he emo e537
olume size and non- ocal hos densi y on disease de elopmen o a high in ec i e dose (200 pa icles), he R0es i-538
ma e shows ha an inc ease in non- ocal hos popula ion densi y o 100 indi iduals m2has he same limi ing e↵ec 539
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 18
0!0.002!0.004!0.006!0.008!0.01!
0.0!
0.5!
1.0!
1.5!
0.0!1.0!2.0!3.0!
R0!
Remo e ese oi !
Pa icle loss in emo e ese oi !
In e nal inac i a ion o pa icles!
Pa icle in e nal inac i a ion a e a ( ime-1)!
VΓ
σ
a
σ!
Remo e ese oi VΓ (m3) Pa icle loss a e ( ime-1) "
b) "
0.0!
0.5!
1.0!
1.5!
2.0!
0!100!200!300!400!500!600!
R0!
Ini ial popula ion, hos N and non- ocal hos H !
Hos N!
Non-Focal Hos , H (N=80)!
Hos N - O e il a ion!
a) "
(VΓ =1)
Figu e 9: R0 o inc easing (a) ini ial suscep ible Nand non- ocal hos popula ion densi y (indi iduals m2) wi h he o e il a ion scena io o N
(wi h hal o he pa icles), and (b) emo e olume size V , pa icle loss a e in he emo e pool , and pa icle in e nal inac i a ion a e a. The black
do ed line ep esen s he ou b eak h eshold le el R0=1; abo e his le el he likelihood o an epizoo ic is high; below his le el, an ou b eak is
no expec ed.
on epizoo ics as a emo e olume o 0.1 m3(Fig. 10). This ela ionship is nonlinea ; hus, a non- ocal hos popula ion540
o 500 indi iduals m2may ha e he same limi ing e↵ec on epizoo ics as a emo e olume o 2.5 m3. Fo lowe 541
in ec i e doses (50 pa icles), he change in non- ocal hos popula ion abundance o emo e olume is much smalle 542
o ob ain he same e↵ec on educing R0. Fo ins ance, an inc ease in non- ocal hos popula ion om 0 o 200 indi id-543
uals m2o in emo e olume om 0 o 0.3 m3p oduces a d op in R0 om 6 o 3, whe eas o a high in ec i e dose544
(200 pa icles), he same inc ease in non- ocal hos popula ion abundance o emo e olume p oduces a much smalle 545
dec ease (R0 om 1.5 o 0.8). Howe e , i he lowe dose disease sys em has a highe R0 han he high dose sys em, a546
smalle d op in R0in he high dose sys em may con ibu e mo e impo an ly limi ing an epizoo ic han he subs an ial547
d op p oduced by he same change in non- ocal hos popula ion abundance o emo e olume in he low dose sys em548
(Fig. 10).549
550
Passi e suspension eede s and he exposed su ace a ea551
552
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 19
The ansmission o disease in passi e suspension- eede s no only depends on he con ac a e wi h pa icles, bu 553
also he su ace a ea o he suscep ible indi idual exposed o con ac wi h wa e bo ne pa hogens (As) (Eq. (17)). Fi s ,554
we conduc ed a simula ion o e alua e he e↵ec o a ying Ason he accumula ion o pa icles. The simula ion was555
un wi h he condi ions o pa ame e s gi en in Table 2 o Case 2, wi h a ca ying capaci y Ko 300 indi iduals.556
Suscep ible indi iduals accumula e pa icles (Fig. 11a) wi h ime as disease p og esses and he wa e becomes sa u-557
a ed wi h pa icles. The simula ion shows an inc ease in he a e age hos body bu den o in ec i e pa icles as he558
exposed su ace a ea inc eases. A he highe exposed su ace a ea es ed, he a e age in e nal numbe o pa icles pe 559
suscep ible inc eases o he in ec i e dose (200 pa icles) by day 150.560
Second, we in oduced an in ec ed animal in a suscep ible popula ion o 300 indi iduals and calcula ed R0 o 561
a ange o alues o o As, including possible ealis ic eeding su aces in suspension eede s such as co als (Fig.562
11b). These simula ions we e conduc ed o low and high in ec i e doses (50 and 200 pa icles). The likelihood o an563
epizoo ic inc eases nonlinea ly wi h he su ace a ea exposed by he indi idual o wa e bo ne pa hogens AS, esul ing564
in he equi emen o 3 imes la ge exposed su ace a ea o an epiozoo ic o occu in he highe in ec i e dose case565
(Fig. 11b).566
0!0.5!1!1.5!2!2.5!3!
0.0!
1.0!
2.0!
3.0!
4.0!
5.0!
6.0!
0!100!200!300!400!500!600!
R0!
Ini ial non- ocal hos popula ion, H!
Non ocal hos H - High dose!
Non ocal hos H - Low dose!
Remo e ese oi - High dose!
Remo e ese oi - Low dose!
Remo e ese oi VΓ (m3)"
Figu e 10: R0 o inc easing non- ocal hos popula ion densi y (indi iduals m2) and emo e olume size (m3) o a high in ec i e dose (200
in ec i e pa icles) and o a low in ec i e dose (50 pa icles). The g ay do ed line ep esen s he ou b eak h eshold le el (R0=1).
4. Discussion567
568
The de e minis ic compa men al model accoun s o he dynamics and epizoo iology o wa e bo ne mic opa asi c569
in ec ious diseases in suspension- eede s, ocusing on bo h he hos and he pa hogen dynamics. In his model,570
ansmission occu s ia pa icle up ake by con ac o passi e il e eede s o by il a ion o ac i e il e eede s,571
o wa e bo ne in ec i e pa hogens unde a body-bu den based dose- esponse mechanism. The model yields a se he572
basic ep oduc ion numbe s R0which gi e insigh abou he ela i e impo ance o he pa ame e s de e mining he573
ou b eaks o epizoo ics. The gene a ion o an epizoo ic is egula ed by a es in ol ed in he dynamics o bo h he hos 574
and he pa hogen, and ac o s associa ed wi h he pa icle di↵usion p ocesses.575
4.1. Hos dynamics576
577
Simula ion esul s indica e ha a ela i ely high ini ial concen a ion o in ec i e pa icles a ailable o suspension578
eede s, whe e pa icle inac i a ion is slow, he p e alence o disease inc eases apidly in he i s six mon hs o a high579
and s eady le el (Fig. 4). Mo ali y is also ela i ely high, inc easing o a 60% o he popula ion a he end o he580
simula ion. Disease mo ali y a es in bi al e il e eede s can be 50% o mo e pe yea . Ra es his high a e epo ed581
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 20
b) !
a) !
0 200 400 600 800 1000
0
50
100
150
200
250
300
350
400
Time (days)
A e age Pa icle accumula ion pe S
As=1 cm2
As=0.1cm2
As=0.01 cm2
0.0!
1.0!
2.0!
3.0!
4.0!
5.0!
0.0!0.1!0.2!0.3!0.4!0.5!
R0!
Exposed su ace pe indi idual As (cm-2) !
High dose!
Low dose!
Figu e 11: E↵ec o inc easing su ace a ea o suscep ible indi iduals exposed o con ac wi h wa e bo ne pa hogens Ason (a) pa icle accumula ion
wi h ime, and (b) disease isk (R0) o high (200 in ec i e pa icles) and low (50 in ec i e pa icles) in ec i e doses. The g ay do ed line ep esen s
he ou b eak h eshold le el (R0=1).
in oys e s in he Gul o Mexico (Sonia and B ody,1988). In Delawa e Bay, he mo ali y a e is lowe ; howe e ,582
de mo disease a leas doubles he na u al mo ali y a e o he ma ke -size animals in epizoo ic yea s (Fo d e al.,583
2006;Powell e al.,2008). The ungal disease Aspe gillosis can impac sea an co als wi h mo ali ies esul ing in he584
loss o >50% o he sea an colony a ea in six yea s (Kim and Ha ell,2004). Wo ldwide dis ibu ed clam species585
such as Rudi pes philippina um show simila mo ali y a es associa ed o b own ing disease (Pailla d e al.,2014).586
The ec ui men o new suscep ible indi iduals o he sys em (Case 1, Fig. 4) pe mi s le els o p e alence lowe 587
han 100% (e.g., 90%, Fig. 4). This simula ion wi h a low pa icle loss a e in he local olume o wa e sa u a ed wi h588
in ec i e pa icles, likely ep oduces a ”wa e - ank” sys em whe e e en ually all he pa icles in he wa e a e coming589
in o con ac wi h o il e ed ou by suscep ible indi iduals and so p e alence in he popula ion eaches high le els and590
emains high, e en wi h ec ui men . The de elopmen and main enance o high pa icle concen a ions in he wa e 591
column (Fig. 6d) esul ing in pandemic in ec ion mus be one o he easons o he apid ansmission o De mo592
disease and he high mo ali ies in Eas e n oys e popula ions obse ed in he ea ly 1990s in Delawa e Bay (Fo d593
e al.,2006;Bushek e al.,2012) and in o he bays whe e mos newly se led ju eniles become in ec ed well wi hin594
he i s yea o li e (Powell e al.,1996;Ragone Cal o e al.,2003;McCollough e al.,2007;Sonia e al.,2012).595
Geog aphically expansi e egions wi h high concen a ions o in ec i e pa icles leading o pandemic in ec ion mus 596
occu commonly o diseases like De mo and o he Pe kinsus-caused diseases in o de o explain he con inuously597
high p e alence o in ec ion (e.g., Pa k and Choi,2001;Powell and Ho mann,2015).598
The numbe o dead animals is small (<1m
2) in bo h simula ions (Case 1 and 2) due o he high emo al a e o 599
hese animals om he sys em. In gene al, in ma ine sys ems, he bac e ial decomposi ion o o ganic ma e (Allison,600
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 21
1990;Lo z and So o,2002;Smi h,1953) o he ac ion o sca enge s emo ing dead animals (Veale e al.,2000;601
Mo ello e al.,2005) is a ela i ely as p ocess and hus, dead animal issue is emo ed quickly om he en i onmen .602
The ini ial inc ease o dead in ec ed indi iduals o a maximum is ela ed o he inc ease o in ec ed indi iduals as he603
disease ansmission p og esses in he popula ion. The in ec ed animals and hei decay o sca enging can con ibu e604
pi o ally o ansmission by he eleasing o pa icles o he local olume and ul ima ely supplying he emo e pool605
(Fig. 6c) o hey can be inconsequen ial i he ac o decay o sca enging esul s in he loss o in ec i i y. Few s udies606
ha e examined he impo ance o pos -mo em p ocesses in disease ansmission.607
Simula ions show he e↵ec o a ying ansmission a e and ca ying capaci y on he hos popula ion (Case 1,608
Fig. 3 s Case 2, Fig. 4). When he popula ion is below ca ying capaci y, he suscep ible popula ion ini ially609
inc eases (Fig. 4) as he ec ui men o new suscep ible indi iduals is as e han he a e o in ec ion. As he disease610
ansmission p og esses in he popula ion wi h a subs an ial inc ease o pa icles in he en i onmen , he educ ion611
o suscep ible indi iduals due o in ec ion exceeds he inco po a ion o new indi iduals. The slowe ansmission612
a e in Case 2 (Fig. 4) impo an ly educes he sp ead o he disease in he popula ion, lowe ing he p e alence o 613
in ec ion. O e all, inc easing ansmission a e leads o highe p e alence o in ec ion in il e eede s, especially614
a low ca ying capaci ies o a low popula ion densi ies whe e he ca ying capaci y is high. Inc easing popula ion615
densi y, and pa icula ly in cases whe e ca ying capaci y is high, can educe educe p e alence o in ec ion e en o 616
ela i ely high disease ansmission a es (Fig. 5). In a con ac –based densi y–dependen disease, a popula ion a i s617
ca ying capaci y has a highe likelihood o disease ansmission han when he popula ion is below ca ying capaci y618
(Gao and He hco e,1992). Howe e , dense il e eede popula ions a ca ying capaci y may be less ulne able o619
disease; indi idual hos s may ‘compe e’ o pa hogens educing he concen a ion o in ec i e pa icles su icien ly o620
limi body bu den below he in ec i e dose and, in u n, limi ing he p obabili y o epizoo ic de elopmen (i.e. he621
o e il a ion scena io, Bidegain e al., in p ess).622
4.2. Pa icle dynamics623
624
Many disease models o ma ine il e - eede s ha e add essed he p oli e a ion o in ec ion and subsequen disease625
impac , accep ing widesp ead and apid ansmission o be he no m (Fo d e al.,1999;Powell e al.,1999,1996).626
O he s ha e examined he e↵ec s o diseases on hos popula ion dynamics (Ku is and La↵e y,1992;Yakob and627
Mumby,2011). Howe e , models o ma ine diseases ha inco po a e pa icles as a a iable, pe mi ing he wa e 628
column o ac as a ‘ ese oi ’, condui , o sink o in ec i e pa icles, a e ew and none also include an in ec i e629
dose e↵ec based on an in i o compa men o in ec i e pa icles seques e ed in he suscep ible pool o hos s. The630
model ha we p opose he e acks pa hogen dynamics in (i) he local olume wi h a pa icle pool in e ac ing wi h he631
hos popula ion, (ii) a emo e olume ha can ac as a sou ce o sink o in ec i e pa icles depending on he ela i e632
concen a ion be ween he wo olumes, and (iii) a ansien pool o in ec i e pa icles in he suscep ible indi iduals633
ha may ul ima ely be inac i a ed o ansi ion he indi idual o he in ec ed pool.634
Simula ions show ha ini ial in ec ions o a ew suscep ible indi iduals ini ia es he p ocess (Fig. 3a,b) by which635
subs an ial numbe s o in ec i e pa icles a e eleased in o he wa e he eby becoming a ailable o suscep ibles and636
sa u a ing he wa e wi h pa icles (Fig. 6c). This esul s in an ini ial di↵usion-like ans e o pa icles o he adjacen 637
emo e olume and, e en ually, in a ’balance’ in pa icle concen a ion be ween he wo wa e compa men s (Fig. 6d).638
A sys em wi h a high elease a e o pa hogens om in ec ed animals o a high a e o elease o in ec i e pa icles upon639
dea h, and a limi ed inac i a ion a e o in ec i e pa icles ei he in he wa e column o in he suscep ible hos , migh 640
easily lead o be a highly ansmissible sys em cha ac e ized by a ela i ely high incidence o disease ou b eaks. This641
is he case, o ins ance, o oys e s and he pa hogen Pe kinsus ma inus (Bushek e al.,2002), bu migh also occu in642
co als, whe e he decay o issue o in ec ed colonies in ec ed by black-band disease o aspe gillosis eleases in ec ious643
omi es o indi idual pa icles in o he wa e which hen d i o nea by co als (Jolles e al.,2002;Richa dson,2004;644
Z uloni e al.,2009) o in he case o wi he ing synd ome in abalone whe e in ec i e elemen s o omi es eleased645
by in ec ed indi iduals be o e o a e dea h sp ead in ec ion o e wide expanses (La↵e y e al.,2015). We suspec 646
a simila scena io o he disease o long-spined sea u chins ha a aged he Ca ibbean popula ions la e in he las 647
cen u y (Lessios e al.,1984). Consequen ly, in hese sys ems, pa ame e s inco po a ed in o he model, such as he648
body bu den o pa hogens in in ec ed (bI) o dead animals (bDI) and he ela i e impo ance o he elease a e (c)649
and he emo al a e o pa hogens in he issue (a) o wa e column ( and sigma) migh ha e p o ound in luence in650
de e mining he equency and geog aphic ex ensi eness o epizoo ics.651

G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 22
The model p esen he e also acks pa icle dynamics inside he suscep ible popula ion. The dynamics o he652
in ec i e dose e↵ec in il e and suspension eede s is poo ly unde s ood (e.g., Chu and Vole y,1997;Wang e al.,653
2010). Ou model sugges ha he accumula ion o pa icles inc eases o a maximum in he ini ial phase o he disease654
p ocess as suscep ible animals ake up pa icles wi hou eaching an in ec i e dose and ha a numbe o in i o and655
ex e nal p ocesses de e mine he deg ee o his accumula ion and he p obabili y ha su icien in ec i e pa icles656
will be accumula ed o p oduce an in ec ion. Among hese is he immune esponse, bu equally impo an a e he657
p ocesses con olling up ake, namely he pa icle acquisi ion a e ( il e ing o su ace a ea impingemen ) and pa icle658
concen a ion which i sel is con olled by he a e o addi ion and loss o pa icles om he local wa e olume. This659
dynamic is likely eno mously impo an , ye o da e has been li le s udied. Assuming ha he disease ansmission in660
il e eede s (Bushek e al.,1997;Fo d e al.,1999;Powell e al.,1999), and p obably in o he suspension eede s,661
occu s ia an in ec i e dose so ha suscep ible animals need o ha e some minimum le el o body bu den o in ec ious662
pa icles be o e hey become in ec ed, some suscep ible indi iduals will hen ha e a ela i ely high body bu den while663
mos will ha e a small body bu den (see sec ion 2.4.1). P esumably, hese animals will ha e some unique a ibu es664
ei he gene ically o en i onmen ally ha has esul ed in hei highe body bu dens. Unde s anding he con ibu ing665
ac o s ha esul in a ew animals ini ia ing in ec ions han hen can p opaga e by suppo ing inc eased pa icle666
concen a ion in he wa e column is a c i ical need. In his ega d, simula ions show ha he a e age pe capi a667
dose in suscep ible popula ion is 150 pa icles (Fig. 6b). This demons a e he adequa e pe o mance o dose-based668
ansmission e m, conside ing ha he a e age pe capi a dose is lowe han he minimum dose o suscep ibles o669
become in ec ed bmin (200 pa icles).670
4.3. Rec ui men 671
672
Rec ui men in oduces new, heal hy indi iduals in o he popula ion which ha e he ne e↵ec o educing disease673
p e alence. Howe e , in his case, his e↵ec o ec ui men on educing p e alence does no di ec ly limi disease; a674
dec ease in p e alence o in ec ion is no a consequence, o ins ance, o new indi iduals inc easing popula ion pa icle675
il a ion a e and hen educing he local pool o in ec i e pa icles su icien ly o dec ease pe capi a accumula ion676
below he in ec i e dose. The p e alence is lowe only due o he addi ion o mo e suscep ibles o he sys em. The677
in luence o hese new suscep ible indi iduals will depend upon hei ole as new p oduces o in ec i e pa icles o as678
new ‘inac i a o s’ o in ec i e pa icles. O en hese new ec ui s will p omo e he disease as he numbe o indi iduals679
becoming in ec ed inc eases (Fig. 8b) despi e he educ ion o (i) pa icles in he wa e column due o inc easing680
popula ion pa icle il a ion (Fig 8c) and (ii) he pa icle up ake a e pe animal (Fig. 8d). Ra he , hese indi iduals681
p o ide inc eased p oduc ion o in ec i e pa icles, aising hei concen a ion in he local pool and ul ima ely he682
emo e pool. This explains he occu ence o pandemic in ec ions in ma ine il e eede s such as oys e s ega dless683
o inc easing ec ui men in ensi ies (Fo d,1996;Bushek e al.,2012).684
Howe e , he e↵ec o ec ui men in limi ing he occu ence o he du a ion o disease epizoo ics can be subs an ial685
in bo h ac i e and passi e suspension eede s when enough ec ui s en e he popula ion o educe he in ec i e pa icle686
concen a ion in he wa e column such ha he pa icle up ake a e pe animal d ops o a poin whe e an inc easing687
numbe o animals e ain a ansien body bu den below he in ec i e dose. This e↵ec has been sugges ed o occu in688
oys e popula ions ollowing high in ensi y ec ui men e en s. E en a high salini y, sui able o disease ansmission,689
an oys e popula ion migh be able o esis epizoo ic de elopmen as long as ec ui men sus ains he inc ease in690
popula ion densi y (Ho mann e al.,1995;Powell e al.,1996).691
4.4. Fil a ion/con ac a e692
693
Fil a ion a e in il e eede s, such as bi al es, can be a↵ec ed by di e se cha ac e is ics o he pa icles il e ed,694
such as he concen a ion o phy oplank on and suspended solids and he quali y and size o ood pa icles (Ho mann695
e al.,1994;Khalil,1996). The physical pa ame e s o he na u al habi a such as empe a u e, salini y, and wa e 696
low (MacDonald and Thompson,1986) and he size o he animal can also a↵ec he il a ion a e (Dame,2011).697
In passi e suspension eede s, such as co als, he con ac a e depends on he polyp o colony exposed su ace a ea698
and he low condi ions (Sebens e al.,1996,1998). Such ac o s a↵ec he inco po a ion o pa hogens by suscep ible699
animals and, hus, he disease incidence.700
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 23
We a ied il a ion/con ac a es o explo e his e↵ec (Fig. 7b). A ela i ely low il a ion o pa icle con ac 701
a e limi s disease ansmission, due o lowe pe capi a exposu e o pa hogens. Inc easing il a ion a e has an e↵ec 702
on disease ansmission when he concen a ion o pa icles in he wa e is ela i ely low. In his case, as il a ion703
o con ac a e inc eases, he a e o disease ansmission inc eases co espondingly. Howe e , a change in il a ion704
o con ac a e ceases o exe a signi icance in luence on ansmission when he local olume becomes sa u a ed705
wi h in ec i e pa icles. A his poin , highe il a ion a es (Fig. 7b) esul in he same high p e alence; ha is, he706
pe capi a dose ecei ed by indi iduals is abo e he in ec ious dose o e a wide ange o popula ion il a ion a es.707
Howe e , ac i e il e eede s in pa icula , and suspension eede s possibly ha e wo mechanisms, explo ed he e,708
o educe he incidence o in ec ion despi e ha ing high il a ion a es and con ac a es wi h subs an i e numbe s709
o in ec i e pa icles in he wa e column. The i s ob iously is a highe in ec i e dose which migh esul om710
selec ion o mo e disease esis an geno ypes, o example (Mun oe e al.,2015) (Fig. 10) and he second is a dense711
assemblage o hos s compe ing o pa hogens and educing he pe capi a dose (i.e. he o e il a ion scena io –712
Bidegain e al. in p ess) (Fig. 9a, black dashed line). Because i is well es ablished ha dense concen a ions o 713
bi al es can become ood limi ed (Heasman e al.,1998;Jiang and Gibbs,2005;Powell e al.,1995), i s ands o714
eason ha he same p ocess would limi pe -capi a inco po a ion a es o in ec i e pa icles. In passi e suspension715
eede hos s in en i onmen s wi h high pa icle concen a ions and con ac a es, educed exposed eeding a eas may716
esul in lowe ing he accumula ion o pa icles (Fig. 11a), and hus he p e alence o in ec ion. Whe he passi e717
suspension eede s can become su icien ly dense o limi pe capi a pa icle up ake a e is unclea .718
4.5. Pa icles loss and di↵usion719
720
The model inco po a es wo pa ame e s o pa icle loss in he wa e column. The pa ame e accoun s o he721
pa icle loss wi hin he local olume Vldue o na u al mo ali y o o he p ocesses o inac i a ion such as sedimen a-722
ion, and ad ec ion and di↵usion o he emo e olume V . The pa ame e accoun s o he subsequen inac i a ion723
h ough na u al mo ali y o o he sou ces o inac i a ion such as sedimen a ion in his emo e pool o pe haps loss724
om his compa men h ough, o example, ou welling. These wo olumes in he model a e o mula ed in o de o725
accoun o pa icle di↵usion by means o concen a ion g adien s be ween hem. Ini ially, in he simula ion when he726
local olume is no sa u a ed wi h pa icles, inc easing pa icle loss h ough di↵usion o pa icles o he emo e pool727
can limi epizoo ic de elopmen . When, he en i onmen is sa u a ed wi h pa icles, his e↵ec becomes inconsequen-728
ial (Fig. 7c,d) unless he inac i a ion a e in he emo e pool is high (Fig. 9b). A la ge emo e olume oge he wi h a729
high exchange a e o pa icles be ween pools and a ela i ely high inac i a ion a e o pa hogens in he emo e pool730
ais an e↵ec i e mechanism o educe pa icle concen a ion locally and p e en ansmission (Bidegain e al., in p ess)731
(Fig. 9b). Thus, a scena io simila o wha is shown in Fig. 7d (g ay line), in which he emo e olume is subs an ially732
la ge han he local olume, he eby leading o a apid ans e o pa hogens om he local pool o he emo e pool,733
is pa icula ly e↵ec i e a limi ing he incidence o in ec ion. This scena io could easily occu in es ua ies wi h sho 734
wa e esidence imes (A ms ong,1982;Ma shall and Alden,1997)du ing pe iods o inc eased eshwa e in low o 735
du ing sp ing ides whe e he la ge idal olume esul s in inc eased ou welling o pa icles, he eby educing pa icle736
concen a ion in he wa e column (Ellien e al.,2004;Banas e al.,2007;G ay e al.,2009;Na ´
aez e al.,2012).737
On he o he hand, a high concen a ion o in ec i e pa icles in he emo e olume could o e come any local loss738
mechanisms such as o e il a ion o he emo al by non- ocal hos s, and hus main ain high p e alence. The dynamic739
in e change be ween local and emo e pools i no unique o he ma ine ealm is a leas pa icula ly cha ac e is ic o 740
he disease ansmission p ocesses aking place he e. This model is a heo e ical model ha explo es he p ocesses741
ha ini ia e and e mina e an epizoo ic. The simpli ica ion o hyd odynamics o wo olumes, he olume di ec ly742
impac ed by he il e eede and he olume o e lying i , wi h pa icle di↵usion occu ing ac oss he in e ace is743
su icien o explain hese p ocesses heo e ically. The s udy o a speci ic case such as he disease ansmission on744
a ee o in an es ua y would equi e he use o simila disease models coupled o a hyd odynamic model. While745
complex models o la al dispe sal using loca ion-speci ic hyd odynamics ha e been employed o en (No h e al.,746
2008;Aya a e al.,2009;Bidegain e al.,2013), he ansmission o disease pa icles in such applica ions has been747
li le in es iga ed (Mu ay and Jackson,1992).748
4.6. Epizoo iology and R0
749
750
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 24
Simula ion esul s o hos and pa icle dynamics showed ha dead in ec ed animals, likely wi h highe body751
bu den and elease a es o in ec i e pa icles han mos li e in ec ed animals (Bushek e al.,2002;Richa dson,2004),752
a e de e minan in he gene a ion o epizoo ics in ben hic il e and suspension eede s. A ela i ely small ex e nal753
sou ce o in ec i e pa icles ini ially a ailable o a ben hic suspension– eede popula ion may in ec ew indi iduals.754
Al hough his ex e nal sou ce is consumed apidly o los and inac i a ed in he wa e column, hese ini ially in ec ed755
indi iduals can igge he gene a ion o he epizoo ic by means o pa icle elease in he li e-in ec ed s age and,756
pa icula ly, upon dea h.757
Howe e , mechanisms po en ially exis ha migh lead o a lowe ing o he epizoo ic likelihood in a ben hic758
popula ion o suspension eede s e en i a ela i ely la ge numbe o pa icles is a ailable. High densi ies o sus-759
pension eede s, pa icula ly il e - eede s, may compe e o ood, bu also o wa e bo ne pa hogens. Mo eo e , a760
non- ocal hos popula ion inges ing o o he wise collec ing in ec i e pa icles (e.g., bi al es, sponges o unica es),761
may enhance he compe i ion e↵ec , which could lead o a lowe pe capi a exposu e o pa hogens (Pe e son and762
And e,1980;Beukema and Cad´
ee,1996;Powell e al.,2012c). Thus, he h eshold o he ini ial hos popula ion763
o an epizoo ic o occu may be subs an ially inc eased wi h inc easing numbe s o non- ocal hos s (Fig. 9). This764
in a- o in e -speci ic compe i ion (Fig. 9a and 8) by i sel o oge he wi h pa icle di↵usion (Fig. 9b) may educe765
subs an ially he likelihood o an epizoo ic.766
The e↵ec o inc easing pa icle loss on limi ing he epizoo ic de elopmen is simila o ha p oduced by an767
inc ease in emo e olume size (Fig. 9b). This means ha he emo e olume is an e↵ec i e mechanism o limi ing768
an epizoo ic as i can emo e pa icles om he local pool by di↵usion. Thus, an inc ease in he emo e olume size769
may exe a limi ing e↵ec on epizoo ic de elopmen compa able o ha p oduced by in e -speci ic compe i ion wi h770
a non- ocal hos popula ion. Mo eo e , an inc ease in hese wo disease limi ing ac o s will ha e a highe impac on771
disease con ol in hos s wi h a ela i ely high in ec i e dose (Fig. 10). Howe e , an inc ease in he emo e olume772
needs o be accompanied by pa icle inac i a ion o loss (i.e. ) in o de o ha e an e↵ec on epizoo ic de elopmen .773
In absence o his pa icle emo al, he emo e olume may become sa u a ed wi h pa icles and di↵use hem back o774
he local pool he eby making hem a ailable o suscep ible hos s. In con as , in i o inac i a ion a e o pa icles,775
by limi ing pa icle body bu den below he in ec i e dose, has a mo e in ense e↵ec on disease de elopmen han he776
emo e olume size o he pa icle loss in his olume (Fig. 9b).777
O e all, hese disease limi ing mechanisms apply simila ly, bu no in equi alen measu e, o ac i e and passi e778
suspension eede s. In he case o passi e suspension eede s, he compe i ion o pa icles may be less e↵ec i e han779
in ac i e il e - eede s. The exposed su ace a ea o he indi iduals Asin a colony o passi e suspension eede s (e.g.780
co als) is as impo an as he densi y o indi iduals; hus, high densi y popula ions wi h a small exposed su ace a ea781
pe indi idual, esul ing in a educed pa icle accumula ion, may limi he disease ou b eak (Fig. 11) jus as well as782
ewe indi iduals wi h a la ge su ace a ea o pa icle cap u e. Thus, i seems ha he ac i e o aging s a egy o il e 783
eede s pe mi s hese o ganisms o e↵ec i ely limi disease ou b eaks in compa ison o passi e eede s, bu he same784
a ibu e makes hem mo e ulne able o epizoo ics when popula ion densi ies a e inadequa e o con ol local pa icle785
concen a ions benea h he h eshold yielding an e↵ec i e dose (Fig. 9a and Fig. 11).786
5. Conclusions787
788
A la ge numbe o ma ine diseases a e ansmi ed h ough he wa e column om one hos o ano he . This789
wa e column p o ides a ‘ ese oi ’ o in ec i e pa icles and he mechanisms by which pa icles a e added o i o 790
los om i exe an impo an in luence on he p e alence o disease and mo e impo an ly he di↵e ence be ween a791
disease exe ing a local impac on a hos popula ion and pandemic disease a↵ec ing he hos o e la ge geog aphic792
egions. The local popula ion modula es his e↵ec h ough gene ic cha ac e is ics ha a↵ec he in ec i e dose and793
h ough a ying local a ailabili y by modula ing pa icle inco po a ion and elease a es. The dynamic imposed by794
his complex in e ac ion be ween popula ion and wa e column, po en ially o e me apopula ion scales, is ela i ely795
unique o he ma ine wo ld. Unde s anding he de ails o his dynamic is c i ical o unde s anding he disease p ocess796
in hos popula ions and o imp o ing managemen esponses o ma ine disease challenges. Models ha inco po a e797
hese p ocesses, such as he one desc ibed he e, a e impo an ools, li le used he e o o e in he ma ine con ex , o798
explain he epizoo iology o ma ine diseases. Only when a disease can be unde s ood a he in i o scale o he799
G. Bidegain e al. /Ecological Modelling XXX (2022) 1–28 25
indi idual, he local scale o he popula ion, and he geog aphic scale o he me apopula ion will e↵ec i e app oaches800
o managemen become ou inely achie able.801
Acknowledgemen s802
This in es iga ion was unded by he NSF Ecology and o In ec ious Diseases P og am G an # OCE-1216220.803
We app ecia e his suppo .804
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