De elopmen and Valida ion o a Wea he -Based Model
o P edic ing In ec ion o Loqua F ui by
Fusicladium
e iobo yae
Elisa Gonza
´lez-Domı
´nguez
1
*, Josep A mengol
1
, Vi o io Rossi
2
1Ins i u o Ag o o es al Medi e a
´neo, Uni e sidad Poli e
´cnica de Valencia, Valencia, Spain, 2Is i u o di En omologia e Pa ologia ege ale, Uni e si a
`Ca olica del Sac o
Cuo e, Piacenza, I aly
Abs ac
A mechanis ic, dynamic model was de eloped o p edic in ec ion o loqua ui by conidia o Fusicladium e iobo yae, he
causal agen o loqua scab. The model simula es scab in ec ion pe iods and hei se e i y h ough he sub-p ocesses o
spo e dispe sal, in ec ion, and la ency (i.e., he s a e a iables); change om one s a e o he ollowing one depends on
en i onmen al condi ions and on p ocesses desc ibed by ma hema ical equa ions. Equa ions we e de eloped using
published da a on F. e iobo yae mycelium g ow h, conidial ge mina ion, in ec ion, and conidial dispe sion pa e n. The
model was hen alida ed by compa ing model ou pu wi h h ee independen da a se s. The model accu a ely p edic s he
occu ence and se e i y o in ec ion pe iods as well as he p og ess o loqua scab incidence on ui (wi h conco dance
co ela ion coe icien s .0.95). Model ou pu ag eed wi h expe assessmen o he disease se e i y in se en loqua -
g owing seasons. Use o he model o scheduling ungicide applica ions in loqua o cha ds may help op imise scab
managemen and educe ungicide applica ions.
Ci a ion: Gonza
´lez-Domı
´nguez E, A mengol J, Rossi V (2014) De elopmen and Valida ion o a Wea he -Based Model o P edic ing In ec ion o Loqua F ui by
Fusicladium e iobo yae. PLoS ONE 9(9): e107547. doi:10.1371/jou nal.pone.0107547
Edi o : E jun Ling, Ins i u e o Plan Physiology and Ecology, China
Recei ed Ap il 25, 2014; Accep ed Augus 3, 2014; Published Sep embe 18, 2014
Copy igh : ß2014 Gonza
´lez-Domı
´nguez e al. This is an open-access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License, which
pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal au ho and sou ce a e c edi ed.
Da a A ailabili y: The au ho s con i m ha all da a unde lying he indings a e ully a ailable wi hou es ic ion. All ele an da a a e included wi hin he pape .
Funding: This wo k was unded by Coope a i a Ag ı
´cola de Callosa d’En Sa ia
`(Alican e, Spain). Th ee mon hs’ s ay o E. Gonza
´lez-Domı
´nguez a he Uni e si a
`
Ca olica del Sac o Cuo e (Piacenza, I aly) was suppo ed by he P og ama de Apoyo a la In es igacio
´n y Desa ollo (PAID-00-12) de la Uni e sidad Poli e
´cnica de
Valencia. The unde s had no ole in s udy design, da a collec ion and analysis, decision o publish, o p epa a ion o he manusc ip .
Compe ing In e es s: The au ho s ha e decla ed ha no compe ing in e es s exis .
* Email: [email p o ec ed]
In oduc ion
Scab, caused by he plan -pa hogenic ungus Fusicladium
e iobo yae (Ca a a) Sacc., is he main disease a ec ing loqua in
Spain and in he whole Medi e anean basin [1,2]. The ungus
a ec s young wigs, lea es and ui s, causing ci cula oli e-colo ed
spo s ha , on ui s, educe hei comme cial alue [1].
Fusicladium spp. a e he anamo phic s ages o he ascomyce e
genus Ven u ia bu he sexual s age o F. e iobo yae has ne e
been ound in na u e [2].
Al hough loqua scab is a well-known p oblem in he a eas
whe e loqua ees a e cul i a ed, he biology o F. e iobo yae and
he epidemiology o he disease ha e been seldom s udied [1,3–8].
These s udies ha e depic ed F. e iobo yae as a highly ain-
dependen pa hogen ha equi es mild empe a u es and long we
pe iods o in ec loqua ees.
En i onmen al equi emen s o in ec ion and he dispe sion
pa e ns ha e been s udied in de ail o o he Ven u ia spp., such
as Ven u ia inaequalis [9–16], V. nashicola [17–19], V. py ina
[20–24], F. ca pophilum [25,26], F. e usum [27–29], and F.
oleagineum [30–35]. These s udies ha e been used o elabo a e
epidemiological models o some o hese pa hogens including V.
py ina [36], V. nashicola[37], V. inaequalis [38,39], F. oleagineum
[40], and F. e usum [41]. Fo V. inaequalis, he use o
epidemiological models o schedule ungicide applica ions has
educed he numbe o ea men s [42–45]. To da e, no
epidemiological model has been de eloped o F. e iobo yae.
Disease modelling is an impo an s ep owa ds he implemen-
a ion o sus ainable ag icul u e [46,47]. Since he 1990 s, mode n
c op p oduc ion has ocused on he implemen a ion o less
in ensi e sys ems wi h educed inpu s o e ilize s and pes icides,
and educed use o na u al esou ces [46]. Sus ainable ag icul u e
has i s oo s in In eg a ed Pes Managemen (IPM) [48]. IPM
concep s o igina ed as a eac ion o he dis up ion o ag o-
ecosys ems caused by massi e applica ions o b oad-spec um
pes icides in he middle o he las cen u y [46] and also because o
conce n abou he e ec s o excessi e pes icide use on human
heal h [49].
In Eu ope, he implemen a ion o IPM has been legisla i ely
manda ed in ecen yea s because o Di ec i e 2009/128/CE
ega ding sus ainable use o pes icides. Among o he ac ions, he
Di ec i e encou ages EU Membe S a es o p omo e low
pes icide-inpu pes con ol and he implemen a ion o ools o
pes moni o ing and decision making, as well as ad iso y se ices
(A . 14 o he Di ec i e). De ac o, he ‘‘sus ainable use’’ di ec i e
has made IPM manda o y in Eu opean ag icul u e as o 2014. As
a consequence, he e is an inc eased in e es in he de elopmen
and use o plan disease models o imp o e he iming o pes icide
applica ions and o hus limi unnecessa y ea men s [46,50,51].
PLOS ONE | www.plosone.o g 1 Sep embe 2014 | Volume 9 | Issue 9 | e107547
Ou aims in his pape we e (i) o de elop a mechanis ic,
dynamic model o p edic in ec ion o loqua ui by he scab
ungus F. e iobo yae, and (ii) o e alua e he model agains h ee
independen da a se s. The model was elabo a ed based on he
p inciples o ‘‘sys ems analysis’’ [52,53] and by using ecen da a
on he biology and epidemiology o F. e iobo yae ob ained unde
en i onmen ally con olled and ield condi ions [1,6,7].
Model De elopmen
Based on he a ailable in o ma ion [1,3–8], he li e cycle o F.
e iobo yae unde he Medi e anean clima e is desc ibed in
Figu e 1. The ungus o e summe s in lesions on b anches and
lea es and on mummi ied ui s ha emain in he ee a e
ha es ; du ing summe , high empe a u es and low humidi y may
p e en spo ula ion on hese lesions. Unde a o able condi ions in
he all, he conidia p oduced by he o e summe ing lesions se e
as he p ima y inoculum and in ec young lea es o loqua ui s.
Conidia a e dispe sed by splashing ain o nea by ui s and lea es;
wi h sui able empe a u e and we ness, conidia ge mina e and
pene a e he issue, p obably di ec ly h ough he cu icle o
h ough s oma a. Once in ec ion has occu ed and i he
empe a u e is a o able, he ungus g ows unde he cu icle;
conidiopho es hen e up h ough he cu icle and p oduce new
conidia. These conidia cause seconda y in ec ions du ing he
en i e ui ing season as long as ains dispe se hem and as long as
empe a u e and we ness du a ion pe mi conidial ge mina ion,
in ec ion, and lesion g ow h.
Model desc ip ion
The ela ional diag am o he model o loqua ui in ec ion by
F. e iobo yae is shown in Figu e 2, and he ac onyms a e
explained in Table 1. The ime s ep o he model is 1 hou .
The model s a s a ui se and ends a ha es because ui s
a e assumed o be always suscep ible o in ec ion. The model
conside s he lesions om he p e ious season on b anches, old
lea es, and mummi ied ui s as he sou ces o p ima y inoculum.
Because he abundance o hese lesions in an o cha d may a y
depending on se e al condi ions–on, o ins ance, he le el o
disease o he ungicide ea men s in he p e ious season–and
because i is di icul o quan i y hese lesions, he model assumes
ha o e summe ed o ms a e p esen in he o cha d and ha hey
hold conidia a ui se and onwa ds.
The model conside s ha any measu able ain (i.e., R$0.2 mm
in 1 hou ) causes dispe sal and deposi ion o conidia on loqua ui
[7] and igge s an in ec ion p ocess ha po en ially ends wi h he
appea ance o scab symp oms. Each si e on he ui ha is
occupied by a conidium o conidia is conside ed a po en ial
in ec ion si e and is e e ed o as a lesion uni (LU). Du ing he
in ec ion p ocess, in ec ion on any LU can ail because conidia
may ail o ge mina e o may ge mina e bu hen die because o
un a o able condi ions. The e o e, he p opo ion o LUs ha
become scabbed a he end o he in ec ion p ocess may be less
han ha occupied by splashing conidia a he beginning o he
p ocess.
The model p edic s he p og ess o in ec ion on single LUs,
which a e he su ace uni o he ui which can become occupied
by a scab lesion. This app oach is ela ed o he concep o
‘‘ca ying capaci y’’. In ecology, he ca ying capaci y is
in e p e ed b oadly as he maximum popula ion size ha any
a ea o land o wa e can sus ain [54,55]. In plan pa hology, he
hos ’s ca ying capaci y o disease is he maximum possible
numbe o lesions ha a plan (o an o gan) can hold [56]. The
ca ying capaci y is a common concep in plan disease modeling
[57–60]. In he model desc ibed he e, a LU is ini ially heal hy
(LUH) bu hen becomes occupied by: unge mina ed conidia
Figu e 1. Disease cycle o loqua scab caused by
Fusicladium e iobo yae
.
doi:10.1371/jou nal.pone.0107547.g001
Epidemiological Model o Loqua Scab
PLOS ONE | www.plosone.o g 2 Sep embe 2014 | Volume 9 | Issue 9 | e107547
Table 1. Lis o a iables used in he model.
Ac onym Desc ip ion Uni
TAi empe a u e uC
RH Rela i e humidi y %
RRain all mm
VPD Vapou p essu e de ici hPa
WD We ness du a ion hou s
Teq Tempe a u e equi alen uC
LUH Uni o loqua ui su ace wi hou conidia o F. e iobo yae Numbe (0–1)
LUUC Uni o loqua ui su ace wi h unge mina ed conidia o F. e iobo yae Numbe (0–1)
LUGC Uni o loqua ui su ace wi h ge mina ed conidia o F. e iobo yae Numbe (0–1)
LULI Uni o loqua ui su ace wi h la en in ec ion by F. e iobo yae Numbe (0–1)
LUVI Uni o loqua ui su ace wi h isible scab lesions Numbe (0–1)
GER Cumula ed conidial ge mina ion Numbe (0–1)
INF Cumula ed in ec ion Numbe (0–1)
SUR Cumula ed conidial su i al Numbe (0–1)
GER9Ge mina ion a e ( i s de i a i e o GERM) Numbe (0–1)
INF9In ec ion a e ( i s de i a i e o INF) Numbe (0–1)
SUR9Su i al a e ( i s de i a i e o SUR) Numbe (0–1)
CCo ec ion ac o Numbe (0–1)
DD Deg ee days Numbe
doi:10.1371/jou nal.pone.0107547. 001
Figu e 2. Rela ional diag am showing how he model simula es in ec ion by
Fusicladium e iobo yae
.Legend: boxes a e s a e a iables;
line a ows show luxes and di ec ion o changes om a s a e a iable o he nex one; al es de ine a es egula ing hese luxes; diamonds show
swi ches (i.e., condi ions ha open o close a lux); ci cles c ossed by a line show pa ame e s and ex e nal a iables; do ed a ows show luxes and
di ec ion o in o ma ion om ex e nal a iables o pa ame e s o a es o in e media e a iables; ci cles a e in e media e a iables. See Table 1 o
ac onym explana ion.
doi:10.1371/jou nal.pone.0107547.g002
Epidemiological Model o Loqua Scab
PLOS ONE | www.plosone.o g 3 Sep embe 2014 | Volume 9 | Issue 9 | e107547
(LUUC) a he ime o conidial dispe sal; ge mina ed conidia
(LUGC) a he ime o conidial ge mina ion; la en in ec ion a e
pene a ion (i.e., hyphae a e in ading he ui cu icle; LULI); and
isible and spo ula ing scab lesions a he end o la ency (LUVI).
Bo h LUUC and LUGC can ail o p og ess i unge mina ed o
ge mina ed conidia die; hese LUs hen e u n o being LUHs
because hey can s a a new in ec ion p ocess whene e new
conidia a e splashed on hem.
A any dispe sal e en on hou h, he model conside s ha
LUUC
h
= 1. The a e a which LUUC
h
ad ances o LUGC
h
depends on a ge mina ion a e (GER9), and he a e a which
LUGC
h
ad ances o LULI
h
depends on an in ec ion a e (INF9)
(Figu e 2). Bo h GER9and INF9a e in luenced by empe a u e (T
in uC) and we ness du a ion (WD, in hou s) (i.e., ee wa e on he
su ace o he loqua ui ) caused by ei he ain o dew. F ui
su aces a e assumed o be we on any hou when R
h
.0 mm, o
RH
h
.89%, o VPD
h
,1, whe e VPD is he apou p essu e
de ici (in hPa) calcula ed using T
h
and RH
h
, ollowing Buck [61].
The a e a which LUUC
h
and LUGC
h
e u ns o LUH
h
depends
on a su i al a e (SUR9), which depends in u n on he leng h o
he d y pe iod (DP), i.e., he numbe o hou s wi h no we ness on
he ui su ace (Figu e 2).
GER9, INF9, and SUR9a e calcula ed a hou ly in e als by
using he i s de i a i e o he equa ions desc ibed in Gonza´lez-
Domı
´nguez e al. [6] in he o m:
GER0~
116:249|Teq4:347|1{Teq2:882

|
3:215|e({0:376|WD)|e{8:551|e{0:376|WDðÞ

ð1Þ
INF0~
4:961|Teq1:700|1{TeqðÞ
0:771|
0:409|e{0:087|WD|e4:704|e{0:087|WDðÞ

ð2Þ
SUR0~0:165
DP ð3Þ
whe e: Teq is he empe a u e equi alen in he o m
Teq~T{Tmin
ðÞ=Tmax{Tmin
ðÞwhe e: Tis he empe a u e
egime, T
min
=0uC and T
max
=35uC in equa ion (1), and
T
min
=0uC and T
max
=25uC in equa ion (2); WD = numbe o
consecu i e hou s wi h we ness; DP = numbe o consecu i e
hou s wi h no we ness. When DP =0, SUR9=1
A any ime o he in ec ion p og ess (i):
LUGCh~X
i~
i~1
GER0
i|(1{X
i~
i~1
SUR0i)|Ci
LUUCh~X
i~
i~1
(1{LUGCh)i|(1{X
i~
i~1
SUR0
i)|Ci
LULIh~X
i~
i~1
INF’
i
ðÞ
LUGChzLUUChzLULIhzLUHh~1
whe e Cis a co ec ion ac o C~1{LULIh
ðÞ
.
Any in ec ion pe iod igge ed by a conidial dispe sal e en ends
when no iable conidia a e p esen on any LUs, exac ly when
LUUC#0.01. An example o model ou pu o a single in ec ion
pe iod is shown in Figu e 3.
The model conside s ha any u he ain e en causes u he
dispe sal and deposi ion o conidia i .5 hou s ha e passed a e
he p e ious dispe sal e en . This is he ime equi ed by a lesion
o p oduce new conidia.
Model ou pu
The model ou pu consis s o : (i) he a ailable inoculum on ui s
(i.e., he equency o LUs wi h unge mina ed conidia on each day)
as a measu e o he po en ial o in ec ion o occu ; (ii) he
dynamics o LULI o each in ec ion p ocess; and (iii) he seasonal
dynamics o he accumula ed alues o LULI (SLULI) as an
es ima e o he disease in he o cha d.
Examples o model ou pu o he 2011 and 2012 loqua
g owing seasons a e shown in Figu es 4 and 5, espec i ely. The
ou pu is based on he wea he da a egis e ed by a wea he s a ion
o he Regional Ag ome e ological Se ice (h p:// iegos.i ia.es/)
loca ed in Callosa d’En Sa ia`, Alican e P o ince, sou heas e n
Spain.
Model Valida ion
Th ee da a se s we e used o alida e he model: (i) incidence o
a ec ed ui s in a loqua o cha d du ing g owing seasons 2011
and 2012; (ii) disease occu ence on loqua ui s in single-exposu e
expe imen s in 2013; and (iii) expe assessmen o he disease
se e i y in se en loqua g owing seasons.
To ope a e he model, hou ly alues o ai empe a u e (T, uC),
ela i e humidi y (RH, %), and o al ain all (R, mm) we e
egis e ed by he wea he s a ion o Callosa d’En Sa ia`, which is
#3.5 km om he o cha ds conside ed o alida ion.
P edic ed s. obse ed disease incidence in o cha ds
In da a se (i), obse a ions we e ca ied ou in a loqua o cha d
in Callosa d’En Sa ia`, Alican e P o ince, sou heas e n Spain.
De ails on hese da a ha e been p e iously published [7]. B ie ly,
ui s om ou shoo s o each o 46 loqua ees we e assessed
weekly, and disease incidence was exp essed as he pe cen age o
ui s wi h scab symp oms. The disease incidence was lowe in
2011 han 2012, wi h 27.3% and 97.6% o ui s a ec ed by loqua
scab a ha es , espec i ely [7]. This di e ence in disease
incidence may be ela ed o he ac ha he o cha d was ea ed
wi h ungicides o scab con ol in 2010 bu no in 2011 o 2012.
Gi en ha he inoculum sou ces o ui in ec ion in 2011 was
e y low because o e ec i e disease con ol in 2010, a co ec ion
ac o o LUUC was applied o he in ec ion p ocesses ini ia ed
in Janua y 2011, i.e., LUUC = 0.1 ins ead o = 1 in Janua y 2011.
Model alida ion was pe o med by compa ing SLULI wi h
obse ed da a o disease incidence. Because he e is a ime lag (i.e.,
a la ency pe iod) be ween he p edic ed disease (as SLULI) and
he disease incidence es ima ed in he o cha d (DI), DI was shi ed
back by one la ency pe iod o compa ison be ween p edic ed and
obse ed disease. Sanchez-To es e al. [1] obse ed a la ency
pe iod o 21 days a a cons an empe a u e o 20uC, which is a
deg ee-day accumula ion (DD base 0uC) o 420. The e o e, DI
was shi ed back by ei he 21 days o 420 DD. To calcula e he
Epidemiological Model o Loqua Scab
PLOS ONE | www.plosone.o g 4 Sep embe 2014 | Volume 9 | Issue 9 | e107547
DD, he a e age empe a u e o each day was conside ed wi h
base empe a u e o 0uC.
P edic ed s. obse ed disease incidence in single-
exposu e expe imen s
In da a se (ii), da a we e collec ed in an abandoned loqua
o cha d in Callosa d’En Sa ia` om 4 Feb ua y o 15 Ap il 2013.
On 25 Janua y, 200 andom shoo s bea ing ui s we e co e ed
wi h wa e - esis an pape bags (one shoo pe bag) o p e en
deposi ion o ain-splashed conidia. On 4 Feb ua y, 10 andom
bags we e opened o ecei e splashed inoculum; a e se en
addi ional days, he bags we e closed again. Ten o he andomly
selec ed bags we e opened on 11 Feb ua y and closed again 7 days
la e . This ope a ion was epea ed un il nine g oups o shoo s had
been sequen ially exposed o ain. A he end o he expe imen (15
Ap il 2013), disease incidence (pe cen age o ui s a ec ed by
loqua scab) and se e i y we e assessed in each g oup o shoo s.
Disease se e i y e e s o he pe cen age o ui a ea co e ed by
scab lesions and was measu ed as desc ibed by Gonza´lez-
Domı
´nguez e al. [8].
Model alida ion was pe o med by compa ing he model
ou pu in he week when a g oup o shoo s was exposed o
splashing ain wi h inal disease se e i y in ha g oup.
Expe assessmen
Fo da a se (iii), Es e e Sole ( echnical ad iso o he
‘Coope a i a Ag icola de Callosa d’En Sa ia`’) was asked o
p o ide a subjec i e es ima e o he se e i y (low, medium, o high)
o loqua scab in he a ea o eigh g owing seasons ( om 2005/
2006 o 2012/2013). M . Sole ’s es ima es we e based on his
ex ensi e expe ience in managing loqua o cha ds, on his scou ing
ac i i ies in he o cha ds o he coope a i e, and on he numbe o
ungicide ea men s ha we e equi ed o con ol he disease in
he a ea.
Fo each season, he model was ope a ed om 1 No embe o
31 Ma ch, and he numbe s o disease ou b eaks p edic ed by he
model we e coun ed. A disease ou b eak was de ined as SLULI.
0.1 in 1 day, when no ou b eaks we e p edic ed in he p e ious 5
days. A e age and s anda d e o o he numbe o p edic ed
ou b eaks we e calcula ed o each ca ego y (low, medium, o
high) o scab se e i y de i ed om he expe assessmen .
Da a analysis
Linea eg ession was used o compa e he p edic ed and
obse ed da a o da a se s (i) and (ii). To make da a homogeneous,
SLULI alues a he ime o each disease assessmen in he
o cha ds we e escaled o he SLULI a he end o he season;
disease incidence was also escaled o he inal disease incidence. A
- es was used o es he null hypo heses ha ‘‘a’’ (in e cep o
eg ession line) was equal o 0 and ha ‘‘b’’ (slope o eg ession
line) was equal o 1 [62]. The dis ibu ion o esiduals o p edic ed
e sus obse ed alues was examined o e alua e he goodness-o -
i . The conco dance co ela ion coe icien (CCC) was calcula ed
as a measu e o model accu acy [63]; CCC is he p oduc o wo
e ms: he Pea son p oduc -momen co ela ion coe icien
be ween obse ed and p edic ed alues and he coe icien Cb
(bias es ima ion ac o ), which is an indica ion o he di e ence
be ween he bes i ing line and he pe ec ag eemen line
(CCC = 1 indica es pe ec ag eemen ). The ollowing indexes o
goodness-o - i we e also calcula ed [64]: NS model-e icacy
Figu e 3. Dynamics o lesion uni s (LUs) du ing an in ec ion pe iod o
Fusicladium e iobo yae
.The g aph shows he ela i e equency o
LUs occupied by unge mina ed conidia (LUUC, in g een), ge mina ed conidia (LUGC, in ed), and la en in ec ions (LULI in blue). Blue ba s a he op
indica e hou s wi h ee wa e on he ui su ace. An in ec ion pe iod s a s when a ain e en splashes conidia on LUs and ends when no iable
conidia a e p esen on any LUs, i.e., when LUUC#0.01.
doi:10.1371/jou nal.pone.0107547.g003
Epidemiological Model o Loqua Scab
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coe icien , which is he a io o he mean squa e e o o he
a iance in he obse ed da a, sub ac ed om uni y (when he
e o is ze o, NS = 1, and he p o ides a pe ec i ); he W index o
ag eemen which is he a io be ween mean squa e e o and o al
po en ial e o (W = 1 ep esen s a pe ec i ); model e iciency
(EF) which is a dimensionless coe icien ha akes in o accoun
bo h he index o disag eemen and he a iance o he obse ed
alues (when EF inc eases owa d 1, he i inc eases); and he
coe icien o esidual mass (CRM) which is a measu e o he
endency o he o o e es ima e o unde es ima e he obse ed
alues (a nega i e CRM indica es a endency o he model owa d
o e es ima ion).
Fo da a se (iii), a one-way analysis o a iance (ANOVA) was
pe o med o de e mine whe he he numbe s o ou b eaks
p edic ed by he model in each ca ego y o loqua scab se e i y
de ined by he expe (i.e., low, medium, o high) we e signi ican ly
di e en om one ano he .
Resul s o Model Valida ion
P edic ed s. obse ed disease incidence in o cha ds
In 2011 be ween 1 Janua y ( ui se ) and 23 May (ha es ),
257.6 mm o ain ell, dis ibu ed in h ee main pe iods: he las
week o Janua y, he second week o Ma ch (wi h 64.8 mm o ain
in 1 day), and he las 2 weeks o Ap il (wi h daily empe a u e .
15uC) (Fig. 4A). Acco ding o he model, a o al o 33 in ec ion
pe iods we e igge ed by hese ain e en s, and he i s was on 17
Janua y (Fig. 4B and 4C). In he analysis o his model ou pu ,
in ec ion pe iods we e clus e ed in ‘‘in ec ion clus e s’’ based on an
in e al o a minimum o 5 days elapsed be ween he beginning o
wo consecu i e in ec ion clus e s (i.e., he p o ec ion p o ided by
a coppe -based ungicide applica ion as desc ibed in [65]);
he e o e, he e we e 10 in ec ion clus e s in he conside ed
pe iod. SLULI began o inc ease om mid-Janua y o mid-
Feb ua y (wi h h ee in ec ion clus e s), bu h ee in ec ion clus e s
in Ma ch esul ed in a subs an ial inc ease in SLULI o 0.5;
Figu e 4. Wea he da a and model ou pu in 2011. A: daily wea he da a; B: p edic ed equency (%) o lesion uni s (LUs) wi h unge mina ed
conidia; C: p edic ed inc ease o LUs wi h la en in ec ions (LULIs) o each in ec ion pe iod (a ows ep esen clus e s o in ec ion pe iods, clus e ing is
based on an in e al o a leas 5 days be ween he beginning o wo consecu i e clus e s); D: p edic ed seasonal dynamics o he cumula i e alues
o LULI (SLULI).
doi:10.1371/jou nal.pone.0107547.g004
Epidemiological Model o Loqua Scab
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Ma ch had 12 in ec ions pe iods, and he epea ed and abundan
ain e en s p o ided .18 h o we ness on mos days (Fig. 4). F om
mid-Ap il o he end o he conside ed pe iod, a cons an inc ease
in SLULI was associa ed wi h abundan ain e en s and
inc easing empe a u e, which igge ed ou in ec ion clus e s
(Fig. 4).
In 2012, al hough he o al olume o ain ha ell om 15
Decembe o 10 May was simila (255.8 mm) o ha in 2011,
he e we e ewe ain e en s. The model p edic ed 20 in ec ion
pe iods ha we e g ouped in o 12 in ec ion clus e s (Fig. 5B and
5C). In 2012, ainy pe iods we e sepa a ed by d y pe iods; om
he end o Janua y o mid-Ma ch, d y pe iods caused no
subs an ial in ec ion o de elop (Fig. 5C). The e o e, he e we e
wo main pe iods o SLULI inc ease: he las hal o Janua y and
om he end o Ma ch o May (Fig. 5D).
Goodness-o - i o p edic ed (SLULI) e sus obse ed da a
(loqua scab incidence) was g ea e when a ixed pe iod o 21 days
was conside ed o he la ency. In his case, alues o R
2
, CCC, ,
Cb, NS, W, and EF we e .0.95 (Table 2). Howe e , when a
la ency pe iod o 420 DD was conside ed he alues o R
2
and
CCC we e ,0.88, and alues o model e icacy (NS) and model
e iciency (EF) we e 0.75 (Table 2) as a consequence o he high
dispe sion o esidues in 2012 (Figu e 6). The model sligh ly
o e es ima ed scab incidence when a la ency o 21 days was used
(CRM = 20.009) and unde es ima ed scab incidence when DD
we e used (CRM = 0.182) (Table 2; Figu e 6). Fo bo h la ency
op ions, he eg ession equa ions o p edic ed e sus obse ed da a
had slopes and in e cep s ha we e no signi ican ly di e en om
1 and 0, espec i ely.
P edic ed s. obse ed disease incidence in single-
exposu e expe imen s
F om 4 Feb ua y o 15 Ap il 2013, he model p edic ed 15
loqua scab in ec ion pe iods bu disease ou b eaks we e subs an-
ial (i.e., hey esul ed in a .10% inc ease in se e i y) in only wo
exposu e pe iods. In hese wo cases, LULI alues we e .0.1;
Figu e 5. Wea he da a and model ou pu in 2012. A: daily wea he da a; B: p edic ed equency (%) o lesion uni s (LUs) wi h unge mina ed
conidia; C: p edic ed inc ease o LUs wi h la en in ec ions (LULIs) o each in ec ion pe iod (a ows ep esen clus e s o in ec ion pe iods, clus e ing is
based on an in e al o a leas 5 days be ween he beginning o wo consecu i e clus e s); D: p edic ed seasonal dynamics o he cumula i e alues
o LULI (SLULI).
doi:10.1371/jou nal.pone.0107547.g005
Epidemiological Model o Loqua Scab
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when he e we e no o ligh ou b eaks, LULI alues we e ,0.06
(Figu e 7). The goodness-o - i o p edic ed e sus obse ed o
da a se (ii) (Table 2) p o ided alues .0.97 o R
2
, CCC, , Cb,
NS, W, and EF. Al hough he slope was no signi ican ly di e en
om 1, he in e cep was di e en om 0 a P= 0.02 (Table 2).
The nega i e alue o CRM indica ed ha he model somewha
o e es ima ed disease, mainly when obse ed disease se e i y was
low (Figu e 7).
Expe assessmen
The loqua scab epidemics ha occu ed in he eigh seasons o
da a se (iii) we e conside ed by he expe o be o low, medium,
o high se e i y in wo, h ee, and h ee seasons, espec i ely. The
numbe o ou b eaks p edic ed by he model anged om 4 o 17
among he eigh seasons; in a e age, 8.560.5 ou b eaks we e
p edic ed o yea s wi h low alue o loqua scab se e i y, 1063 o
yea wi h medium alue and 1262.9 o yea s wi h high alue.
Al hough he a e age numbe o ou b eaks p edic ed by he model
inc eased as he expe assessmen o disease se e i y inc eased, he
numbe o p edic ed epidemics did no signi ican ly di e among
he se e i y ca ego ies (P= 0.71).
Discussion
In his wo k, a dynamic model was de eloped o p edic
in ec ion o loqua ui s by conidia o F. e iobo yae. The model
uses a mechanis ic app oach o desc ibe he in ec ion p ocess
[53,66,67]: he model spli s he disease cycle o F. e iobo yae in o
di e en s a e a iables, which change om one s a e o he
ollowing s a e based on a e a iables o swi ches ha depend on
en i onmen al condi ions by means o ma hema ical equa ions.
The ma hema ical equa ions we e de eloped using published da a
on F. e iobo yae conidial dispe sion pa e ns [7] and on F.
e iobo yae g ow h, conidial ge mina ion, and in ec ion unde
di e en en i onmen al condi ions [1,6]. In he absence o p ecise
in o ma ion, assump ions we e made based on a ailable knowl-
edge.
Model alida ion showed ha he model co ec ly p edic ed he
occu ence o in ec ion pe iods and he se e i y o any in ec ion
pe iod, as demons a ed by he goodness-o - i o he da a
collec ed on ui s exposed o single ainy pe iods. Because he
pu pose o he model is o be pa o a wa ning sys em o loqua
scab managemen , he abili y o co ec ly p edic in ec ion pe iods
is c ucial. Accu acy o he model was also con i med by he
compa ison o model ou pu wi h expe assessmen . E en hough
he numbe s o p edic ed ou b eaks did no di e among seasons
ha he expe had ca ego ized as ha ing low, medium, o high
disease se e i y, he numbe o p edic ed ou b eaks inc eased wi h
inc eases in assessed disease se e i y.
Fo model alida ion, he la ency pe iod equi ed o he
appea ance o scab was exp essed as a ixed numbe o days o o
deg ee-days (DD) based on esul s om Sa´nchez-To es e al. [1].
Goodness-o - i o model p edic ion was o e all be e using a ixed
pe iod o 21 days ins ead o 420 DD. In pa icula , he model
unde es ima ed he disease in he ea ly season o 2012 when DD
we e used. The unde es ima ion was p obably caused by low
empe a u es in ha pe iod, which delayed DD accumula ion.
This esul is ques ionable, because he physiological de elopmen
o ungi is usually mo e closely ela ed o DD han o calenda days
[68,69]. In his wo k, DD was ixed based on he la ency pe iod
obse ed in loqua plan s kep a he op imal empe a u e o F.
e iobo yae de elopmen , i.e., 21 days a 20uC [1]. The e o e, he
DD alue used in his s udy did no accoun o he non-linea
esponse o F. e iobo yae g ow h o empe a u es be ween 5 and
Table 2. S a is ics and indices used o e alua ing he goodness-o - i o loqua scab in ec ion p edic ed by he model e sus disease obse ed in ield.
Da a se
a
A
b
b
P
(a = 0)
P
(b = 1)
R
2
CCC Cb NS W EF CRM
Da a se 1
(la ency = 21 days)
0.038 0.939 0.190 0.070 0.952 0.974(0.946–0.988) 0.975 0.999 0.951 0.987 0.951 20.009
Da a se 1
(la ency = 420 DD)
20.066 0.928 0.274 0.110 0.841 0.882(0.758–0.944) 0.921 0.960 0.753 0.939 0.752 0.182
Da a se 2 0.043 0.965 0.02 0.1 0.984 0.986(0.942–0.996) 0.993 0.993 0.971 0.992 0.971 20.247
a
Da a se 1 co esponds o compa ison o daily accumula ed LUVI p edic ed by he model e sus obse ed da a o loqua scab incidence in an o cha d in sou heas e n Spain du ing 2 yea s (2011 and 2012). The model used a
la ency pe iod o 21 days ( i s ow) o 420 DD (second ow). Da a se 2 compa es he inc ease o model ou pu in weeks in which loqua shoo s we e exposed o splashing ain ( igge ing in ec ion) wi h inal disease se e i y in
hose shoo s.
b
a and b, pa ame e s o he eg ession line o he p edic ed agains obse ed alues; P, p obabili y le el o he null hypo heses ha a = 0 and b = 1; R
2
,coe icien o de e mina ion o he eg ession line; CCC, conco dance
co ela ion coe icien ; , Pea son p oduc -momen co ela ion coe icien ; Cb, bias es ima ion ac o ; NS, model e icacy; W, index o ag eemen ; EF, model e iciency; CRM, coe icien o esidual mass.
doi:10.1371/jou nal.pone.0107547. 002
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30uC [6]. I a unc ion o p edic ing he appea ance o scab
symp oms is needed in he model, such a unc ion should be
empe a u e dependen , as i is in models o V. nashicola [37] and
F. oleagineum [40]. Sale no e al. [4] epea edly exposed po ed
loqua plan s unde he canopies o a ec ed ees o 3 days and
hen incuba ed hese plan s unde a oo un il he appea ance o
symp oms. Scab appea ed in 11 o 26 days a empe a u es
anging om 11.4 o 17uC (wi h a DD ange o 157 o 340) and
a e .220 days a empe a u es .20uC. P skialadze [5] ound
scab symp oms on bo h lea es and ui s 34 and 16 days a e
in ec ion a 1–4uC and 21–25uC, espec i ely. E en hough he
calcula ion o la ency can be imp o ed, he model e o in
p edic ing disease onse due o a ix la ency pe iod may no educe
he abili y o he model o co ec ly p edic in ec ion pe iods o
educe he alue o he model o iming ungicides applica ions.
The model capi alized on ecen esea ch conce ning loqua
scab [1,6,7]. These s udies ha e conside ed mos o he
componen s o he disease cycle, including dispe sion o conidia,
in ec ion, incuba ion, and la ency. Ne e heless, o he componen s
should be elucida ed o imp o e ou knowledge and hus o
imp o e he model [66]. Cu en ly, he model assumes ha
inoculum sou ces a e always p esen in scab-a ec ed loqua
o cha ds and ha iable F. e iobo yae inoculum is always p esen
a ui se (i.e., when he model begins ope a ing) and beyond.
Sale no e al. [4] ound ha lesions appea in au umn on lea es
ha we e in ec ed he p e ious sp ing, and P o a [3] ound ha
he lesions appea ing in au umn p oduce conidia o 5 o 6 mon hs
and ha hose iable conidia a e p esen all yea long. These
obse a ions we e ca ied ou in Sicily and Sa dinia, espec i ely
(i.e., unde a Medi e anean clima e); he e o e, he model
assump ions seem plausible. The assump ions ha inoculum
sou ces and iable conidia a e always p esen in scab-a ec ed
loqua o cha ds a e bo h p ecau iona y because hey can lead o
o e p edic ion o in ec ion (which would occu i wea he
condi ions we e sui able o in ec ion bu no iable conidia we e
a ailable) and hus o unnecessa y applica ions o ungicides o
o he disease managemen measu es. Because unnecessa y ungi-
cide applica ions en ail cos s o g owe s, consume s, and he
en i onmen [51], he model should be expanded o include he
o e summe ing and a ailabili y o conidia.
Wi h espec o o e summe ing, modeling he do man s age o
ungal pa hogens is challenging [66], and he do man s age has
he e o e been included in only a ew models [70–74]. Fo his
pu pose, wo key aspec s mus be add essed: (i) he inoculum dose
(i.e., he quan i y o inoculum ha o e summe s), which depends
on he se e i y o he disease in each o cha d a he end o he
Figu e 6. Compa ison be ween model ou pu and scab obse ed on loqua ui in sou heas e n Spain. (A) da a om 2011 and (B) da a
om 2012. Blue lines ep esen he escaled in ec ion p edic ed by he model as he seasonal summa ion o he lesion uni s wi h la en in ec ions
(SLULI). Poin s ep esen escaled incidence o loqua ui wi h scab obse ed in he o cha ds; escaled incidence is shi ed back by 21 days ( ed
poin s) o 420 DD (base 0uC, g een poin s) o accoun o he la ency pe iod, i.e., he ime elapsed be ween in ec ion and isible symp oms in he
o m o spo ula ing scab lesions.
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