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Oppo unis ic andom sea che
e sus in en ional sea ch image
use
Józse Ga ay1,2, Zol án Va ga3, Tamás F. Mó i4, Inmaculada López5, Manuel Gámez6, Juan R.
Gallego6 & Tomás Cabello
6
We conside wo ypes o op imal o age s: a andom sea che and a sea ch image use . A sea ch
image use can ind i s desi ed p ey wi h highe and undesi ed p ey wi h lowe p obabili y han a
andom sea che . Ou model conside s he densi y-dependen a elling ime and he ime du a ion
o ep oduc ion (o iposi ion). In he amewo k o op imal o aging heo y o one p eda o – wo p ey
sys ems, we ind ha he e a e anges o p ey densi ies in which he sea ch image use has a highe ne
ene gy in ake, and he e a e o he anges o p ey densi ies in which he andom sea che has highe ne
ene gy in ake. The damsel bug Nabis pseudo e us Remane (Hemip e a: Nabidae) is a gene alis p eda o
a he han an omni o e. This species has a wide ange o a h opod p ey (p edominan ly insec s and
mi es). Se e al aspec s o he biology o his species ha e been s udied, especially i s cannibalis ic
beha iou , which is a qui e impo an ea u e because N. pseudo e us is o en used as a biological
con ol agen agains lepidop e an pes s in g eenhouse c ops. Expe imen ally, we ound ha Nabis is a
sea ch image use in he abo e sense.
In his pape , we a e in e es ed in iden i ying he e ec o he sea ch image1–6 on op imal o aging. Acco ding o
Tinbe gen1, he sea ch image is a pe cep ual change ha imp o es he p eda o ’s abili y o de ec i s desi ed p ey
ype. Bond and Riley4 in oduced an accumula o model o isual sea ch ha includes disc iminabili y (i.e., he
ocus on isual ea u es ha a e cha ac e is ic o a pa icula i em), esponse bias (i.e., an inc eased p edisposi-
ion o espond o ood- ela ed s imuli), and a “cau ion” hypo hesis (i.e., a ibu ing imp o emen s in s imulus
de ec ion o changes in he amoun o e idence ha he animal acqui es be o e making a esponse). We use he
phenomenological de ini ion o a sea ch image p o ided by Dukas7, i.e., a “selec i e sea ch o a pa icula c yp ic
p ey ype, which in ol es an inc eased p obabili y o de ec ing ha p ey ype and a educed p obabili y o de ec ing
o he dis inc p ey ypes”. No e ha a sea ch image implies a ade-o be ween encoun e s wi h p e e ed and
non-p e e ed p ey ypes. In ou wo ds, he sea ch image use (SIU) can ind i s desi ed p ey wi h highe p ob-
abili y and i s undesi ed p ey wi h lowe p obabili y han a andom sea che . In he s anda d op imal o aging
models, he o age is a andom sea che (RS), i.e., i s p ey p e e ence does no a ec he encoun e p obabili ies
wi h he p ey ypes; in o he wo ds, he encoun e p obabili ies a e de e mined only by he p eys’ densi ies.
In p eda ion, he encoun e is one o he mos impo an s eps8,9. Finding he p ey is a complica ed s ochas ic
p ocess10, and he encoun e s a e de e mined a leas by wo main ac o s: he pe cep ion abili y o he p eda o 11
and he p ey densi ies12. He e, we will conside he case in which he p eda o inds i s desi ed p ey wi h a high,
densi y-independen p obabili y, bu he a elling ime13 o he p eda o will be longe a lowe p ey densi ies.
In a one p eda o – wo p ey sys em, he ques ion a ises: Which has highe ne ene gy in ake, he SIU o he RS?
We no e ha in g eenhouses, hese sys ems o en occu . The p ey p e e ence o he agen is impo an in
biological con ol. Fo ins ance, i he agen ’s p e e ed p ey causes less damage han he non-p e e ed p ey,
hen he economic e iciency o he agen is no op imal14,15. The basic pic u e is mo i a ed by he beha iou s o
1MTA-ELTE Theo e ical Biology and E olu iona y Ecology Resea ch G oup and Depa men o Plan Sys ema ics,
Ecology and Theo e ical Biology, Eö ös Lo ánd Uni e si y, Pázmány Pé e sé ány1/c, H-1117, Budapes , Hunga y.
2MTA Cen e o Ecological Resea ch, E olu iona y Sys ems Resea ch G oup., Klebelsbe g Kuno u ca 3, Tihany,
8237, Hunga y. 3Depa men o Ma hema ics, Szen Is án Uni e si y, Pá e K. u. 1.H-2103, Gödöllő, Hunga y.
4Depa men o P obabili y Theo y and S a is ics, L. Eö ös Uni e si y, Pázmány Pé e sé ány1/c, H-1117, Budapes ,
Hunga y. 5Depa men o Ma hema ics, Uni e si y o Alme ía. La Cañada de San U bano, 04120, Alme ía, Spain.
6Cen e o Ag ibusiness Bio echnology Resea ch, Alme ía Uni e si y, C a. Sac amen o s/n, ES-04120, Alme ía,
Spain. Co espondence and eques s o ma e ials should be add essed o J.G. (email: ga ayj@caesa .el e.hu)
Recei ed: 26 Sep embe 2017
Accep ed: 6 Feb ua y 2018
Published: xx xx xxxx
OPEN
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ce ain p eda o y insec s ha p ac ically o age con inuously wi h he excep ion o egg laying. Fo example, Nabis
pseudo e us Remane displays such beha iou 16. Nabis ea s all day; hence, he ime equi ed o lay eggs educes
he ime a ailable o p eda ion. The la e ac , in pa icula , will play an impo an ole in he calcula ion o he
nume ical esponse. The emale Nabis is e i o ial and uses isual and odou s imuli du ing hun ing16. Nabis
pseudo e us can be conside ed o be a non-omni o ous p eda o 17. The majo i y o s udied Nabidae species also
p ac ice plan eeding, bu hey a e no able o de elop in he absence o p ey18–20. The plan eedings only se e o
sea ch o wa e sou ces and seem o do li le o no damage o he plan 21. This p ac ice seems o help he p eda-
o o su i e du ing p ey sca ci y20. N. pseudo e us has a wide ange o p ey and has been ci ed as an impo an
p eda o o aphids22,23 bu is also a o acious p eda o o lepidop e ans and o he g oups o a h opods, including
hemip e ans and mi es24–27. N. pseudo e us is, om he ophic pe spec i e and acco ding o Hu d28, a s ic p ed-
a o wi h a wide ange o p ey a h opods. Se e al aspec s o he biology o his species ha e been s udied. Thus,
i is known, on he one hand, ha adul s and nymphs o N. pseudo e us exhibi a ype II unc ional esponse. In
gene al, o he Nabis species also p esen ype II esponses in hei nymph and adul s ages29. On he o he hand,
cannibalism in N. pseudo e us has also been documen ed and is an aspec o g ea impo ance in he biology o
his species29 because N. pseudo e us is also used as a biological pes con ol agen o lepidop e ans in g eenhouses
c ops30,31.
The pape is o ganized as ollows: In a Theo e ical s udy, we i s calcula e he nume ical esponse when ep o-
duc ion and a elling also equi e ime. We compa e he pe -uni ime ene gy in akes o RS and SIU. In he
Expe imen al s udy, based on ou labo a o y ials, we es whe he he Nabis uses sea ch images. The ma hema ical
de ails, he expe imen al da a and a new s a is ical me hod a e summa ized in he Supplemen a y In o ma ion (SI).
Theo e ical S udy
Assump ions. In a habi a o a ea M, he e a e H pe cep ion anges (PR-s), and in he habi a , he e a e wo
ypes o p ey: x is he numbe o A-p ey, y is he numbe o B-p ey, and we suppose ha x + y < H. Assume ha
he habi a is homogeneous12,32, i.e., in all PR-s, he p eda o -p ey in e ac ions a e he same. Fo example, we can
conside he ollowing si ua ion: A p eda o insec sea ches o p ey on a gi en plan , and he pe cep ion anges
a e he lea es.
Fo simplici y, we ha e assumed ha he p ey exhibi no an i-p eda o beha iou s, i.e., he p eda o can kill
any encoun e ed p ey. Speci ically, bo h o he p ey can nei he de end agains he p eda o no lee33, hey do no
ha e g ega ious beha iou 34, and he e is no e uge35. The abo e simpli ying assump ions imply ha he p ey ha e
no e ec on p eda ion; he e o e, we will ha e an op imal o aging model in which he p eda o maximizes i s
nume ical esponse. Each pe cep ion ange con ains, a mos , one p ey, so he p ey ypes a e andomly sepa a ed
in he PR-s in he home ange o he p eda o . The e is a s a iona y dis ibu ion o pe cep ion ange ypes, PR:X
(X = E (emp y), A, B), which does no change du ing ime T, e.g., one day.
The op imal o age p eda o has e i o y, hus, he e is no in e ac ion be ween wo p eda o s du ing hun -
ing36–38. Fo simplici y, we also assume ha he e is no nu i ional di e ence be ween he di e en p ey ypes
wi h he excep ion o ene gy con en 39. The sea ching p ocesses o he p eda o and he dis ibu ion o he p ey
a e independen . The a elling ime equi ed o ind a p ey depends on he densi y o he p ey, i.e., i is longe
a lowe p ey densi ies. An RS isi s he nea es pe cep ion ange, and he andom dis ibu ions o p ey ensu e
he andom encoun e s. An SIU uses a sea ch image and inds i s desi ed p ey ype wi h a densi y-independen
p obabili y. We will compa e he nume ical esponses o hese wo ypes o p eda o s.
Wha is he nume ical esponse i ep oduc ion also equi es ime? In op imal o aging heo y, a
widely used assump ion is ha he nume ical esponse equals he unc ional esponse weighed wi h a con e sion
coe icien . Howe e , i ep oduc ion (o iposi ion o o sp ing ca e) also equi es ime (simila o sea ching o
p ey and he handling o p ey), and ep oduc ion and hun ing exclude each o he , hen he nume ical esponse
and he unc ional esponse a e no V p opo ional. We emphasize he assump ion ha he ime du a ions o
he p eda o ’s ac i i ies do no o e lap, which is one o he basic equi emen s o he de i a ion o unc ional
esponses8,13. We no e ha , in he case o o sp ing ca e by emales, males and emales would ha e di e en unc-
ional esponses; e.g., emale c ocodiles s ongly de end he ne s agains e i o ial p eda o s, and hus, du ing
he ha ching pe iod, he emale c ocodile has a lowe unc ional esponse. Simila ly, male empe o penguins
(Ap enody es o s e i) do no hun du ing he ha ching season.
Fo Nabis, du ing he ime pe iod T, he p eda o ei he p eda es (TP deno es he o al ime du a ion o p e-
da ion du ing T) o lays eggs (TE is he o al ime du a ion o laying eggs du ing T). Rep oduc ion and p eda-
ion exclude each o he ; hus, we ha e T = TP + TE. The numbe o eggs, howe e , also depends on he collec ed
ene gy, so TP and TE a e no independen . Based on he ene gy balance o he ime pe iod T, in SI.1, we calcula e
he nume ical esponse:
=
−
+
W
EE
E E
s
s
s
()
()
() ,
CL
EE
whe e E(s) is he ene gy in ake in uni ime by a p eda o using o aging s a egy s, ECL is he cos o li ing o a
emale p eda o in uni ime, EE is he ene gy cos o one egg (including bo h he sea ching cos o a good place
o he egg and he ene gy cos o egg laying), and E is he ime du a ion o laying one egg, E > 1. Obse e ha he
nume ical esponse is a s ic ly inc easing unc ion o he ene gy in ake in he uni ime o p eda ion. Speci ically,
he nume ical esponse and he ene gy in ake will each hei maxima wi h he same o aging s a egy.
Sea ching ime and a elling ime. Ou basic assump ion is ha , ega dless o he PR ype ha he
sea ching p eda o inds, i will be he nea es one om ha ype. The sea ching ime τS has wo componen s: he
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i s is a elling ime τTX (X = E, A, B), which depends on he densi ies o A-p ey and B-p ey, and he second is
he local sea ching ime τLS in he PR. Fo simplici y, we assume ha τLS does no depend on he con en s o he
ocal PR. Thus, we ha e τS = τTX + τLS. In SI.2 we p o e he ollowing s a emen s. I ype PR:X has a densi y λX,
and is andomly dis ibu ed, hen he a e age dis ance be ween he nea es PR:X and he p eda o is he ollowing:
In one dimension ( o a p eda o mo ing along a s aigh line), he a e age dis ance is λ
1
2X
, in wo dimensions ( o
a p eda o mo ing along a plane), he a e age dis ance is
1
2X
1/2
λ, and in 3 dimensions, he a e age dis ance is
app oxima ely
λ.−
055396 X1/3
. We emphasize ha he dimension o he a elling mode o he p eda o has an
impo an e ec on he unc ional esponse40.
Now we a e in a posi ion o calcula e he op imal o aging s a egy o each o he wo ypes o p eda o s.
The andom sea che does no use a sea ch image. The RS is simila o a o age in he s anda d op i-
mal o ging model41. Because he p ey a e andomly dis ibu ed, he encoun e sequence o he RS is andom, i.e.,
he p ey p e e ence o he RS does no modi y he encoun e p obabili ies. Howe e , we ha e wo no el poin s:
he RS looks o he nea es PR, so i s a elling ime depends on he densi y o he PR. A e an encoun e wi h a
gi en p ey ype, he RS, as an op imal o age , accep s o igno es he encoun e ed p ey ype, so he sequences o
encoun e s and he sequences o killings may be di e en . Mo eo e , he RS’s nume ical esponse also depends on
he o iposi ion ime. As men ioned abo e, he nume ical esponse will each i s maximum wi h he same s a egy
ha maximizes he a e age ene gy in ake; hus, he RS applies he well-known ze o-one ule41, namely,
τ
ττ
τ
ττ
==
>−
<−
⁎⁎
ss
x
c
cc
H
xc
cc
H
1, and
0, i
1, i ,
AB
SB
AB BA
SB
AB BA
whe e cA, cB a e he ene gy con en s, and τA, τB a e he handling imes o A-p ey and B-p ey, espec i ely (Fig.1,
o ma hema ical de ails see SI.3). In he usual sense, we say ha A is mo e aluable han B, i
>
ττ
cc
A
A
B
B
. When he
mo e aluable p ey ype is abundan , he RS will only accep his ype and igno e he o he ype. In his case, he
encoun e sequence (a andom un o PR-s ha a e emp y o con ain A o B p ey) and killing sequence (only he
mo e aluable p ey) a e di e en . I he mo e aluable p ey ype is su icien ly a e, hen he RS oppo unis ically
accep s bo h p ey ypes. In his case, he encoun e and killing sequences a e he same, and bo h a e andom.
Sea ch image use . Fo simplici y, we assume ha he SIU can ind i s nea es desi ed p ey wi h a p obabil-
i y o 1; hus, he SIU canno ind an emp y PR. The SIU has wo sea ching modes; when looking o an A-p ey,
i canno encoun e a B-p ey, and ice e sa. Thus, his ype o p eda o has only a one-dimensional op imal
o aging s a egy; i looks o an A-p ey wi h a p obabili y s, and o a B-p ey wi h a p obabili y 1-s. Fu he mo e,
he e a e wo densi y-dependen a elling imes ha co espond o he desi ed p ey ype: τTA and τTB. In SI.4, we
calcula e he op imal o aging s a egy and ind ha
=> =<
⁎⁎
s
c
c
s
c
c
1, i ;and 0, i ,
A
A
B
B
A
A
B
B
whe e
τττ=++ ATALSA
and
τττ=++ BTBLSB
a e he densi y-dependen ime du a ions o ounds o killing
an A-p ey and a B-p ey, espec i ely. Thus, he SIU only accep he p ey ype ha ensu es a highe ene gy in ake
Figu e 1. Swi ching cu e σR sepa a ing he densi y anges in which he RS ea s only A ( igh side) and ea s A
and B (le side). Swi ching cu e σI sepa a ing densi y anges in which he SIU sea ches o A ( igh side) and
sea ches o B (le side).
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a e du ing he en i e ime pe iod T. Obse e ha he encoun e and he killing sequences o an SIU a e he same
and no andom because he p ey p e e ence de e mines he encoun e s (Fig.1).
We no e ha i he SIU can ind i s nea es desi ed p ey wi h a p obabili y less han bu su icien ly nea 1, hen
he SIU can also be oppo unis ic in he sense ha , i looking o B-p ey, i inds an A-p ey, he SIU may also kill
he A p ey. Obse e ha he ade-o o he sea ch image implies a ade-o be ween in en ional and oppo unis
because he SIU has a diminished chance o be oppo unis ic.
We emphasize ha he essen ial di e ence be ween he RS and SIU is ha hei encoun e sequences a e
di e en .
Does he sea ch image use o e pe o m he andom sea che ? Fi s , in Fig.1, we isualize ha he
di e en ypes o p eda o s ha e di e en op imal o aging s a egies, i.e., hei swi ching beha iou s a e di e en
( o calcula ions see SI.5).
Conside ing se e al ounds o p eda ion, he sequences o encoun e ed p ey ypes o he RS and SIU a e
di e en because he RS andomly encoun e s bo h p ey ypes acco ding o he p ey densi ies. In con as , he
SIU encoun e s i s p e e ed p ey ype wi h a highe p obabili y. Obse e ha in Fig.1, in he densi y ange o he
igh o σR, bo h he SIU and RS only consume he mo e aluable A-p ey; hus he killing sequences a e he same,
and despi e his, hei encoun e sequences a e di e en .
All hese elici he ollowing ques ion: Which ype o p eda o has highe ene gy in ake in uni ime a ixed
densi ies x and y? We ound ha he e a e wo p ey densi y anges in which he SIU collec s mo e ene gy han
does he RS. In ui i ely, when A-p ey is sca ce and B-p ey is abundan , he SIU kills mo e B-p ey, and he RS kills
e y ew A-p ey. Fu he mo e, i A-p ey is abundan , hen bo h p eda o ypes accep only A-p ey, bu he SIU
kills mo e A-p ey han does he RS. Mo eo e , he e is a ange o p ey densi ies in which he RS pe o ms be e
in e ms o ene gy in ake han does he SIU (Figs2 and 3).
The main in ui i e eason o he la e ou come is he oppo unism o he RS8,34: In he ange in which ER(x, y)
>EI(x, y), he SIU kills only one ype o p ey, whe eas he RS oppo unis ically exploi s bo h ypes o p ey.
Now we a e in he posi ion o p o ide some insigh in o ou main ques ion: Does he SIU o e pe o m he RS?
The answe is no necessa ily. E en wi hou se ing up a conc e e o m o he co esponding popula ion dynamics,
we ha e he ollowing wo main cases:
Fi s , assume ha he popula ion dynamics o he h ee-species sys em has a s able equilib ium. I he equi-
lib ium p ey densi ies lie in he ange in which he SIU has a highe ene gy in ake, hen he SIU o e pe o ms
he RS. I he equilib ium lies in he ange in which he RS has a highe ene gy in ake, hen he RS o e pe o ms
he SIU.
Second, assume ha he popula ion dynamics o he h ee-species sys em has no s able equilib ium, bu , e.g.,
he e is a cyclic coexis ence in which he cycle ouches all ypes o p ey densi y anges. Then, he op imal o aging
s a egy will be a mix; he p eda o uses ei he a sea ch image o a andom sea ch acco ding o he cu en p ey
ype densi ies.
Finally, we no e ha a special sensi i i y analysis e eals ha he densi y ange in which he RS o e pe o ms
he SIU, is obus agains changes in key pa ame e s. Indeed, Figs1–3 co espond o pa ame e choices
=c:1
A
,
=c:2
B
,
τ=:1
LS
,
τ=:1
A
, and
τ=:8
B
. In ou s udy, i is assumed ha A-p ey is mo e aluable han B-p ey; o -
mally,
=>
ττ
1
cc
A
A
B
B
. In SI.5, a simple calcula ion demons a es ha , i he gap be ween he alues o A-p ey and
B-p ey is su icien ly la ge, namely, <
τ
c4
13
B
B
, hen cu es γ1 and γ2 display a pa e n simila o ha in Fig.2.
Indeed, in his case, measu ing he size o he densi y ange in which ER > E, wi h he a ea o he ange be ween γ1
and γ2, indica es ha o
<
τ
c4
13
B
B
, his a ea emains s ic ly posi i e as illus a ed in Fig.4.
Figu e 2. In he ange be ween cu es γ1 and γ2, he RS collec s mo e ene gy in uni ime (ER) han he SIU
(EI). Cu e σI in Fig.1 would spli he ange ER > EI in o wo pa s.
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Expe imen al s udy: Resul s
We ha e demons a ed ha Nabis uses a sea ch image. Nabis is e i o ial, hus, emales can mainly cannibalize
hei own o sp ing. The e o e, when cannibalism is ampan , i is easonable o assume ha , o he e i o ial
cannibal p eda o , i is mo e bene icial o be an SIU ha ocuses on he non-conspeci ic p ey han a RS because
ilial cannibalism can dec ease he i ness o a emale. In a Pe i dish a ena, Nabis uses isual and odou s imuli
while sea ching and hun ing16. Nabis can ecognize i s ound possible p ey by ouching i wi h he an enna42.
Thus, we can de ine an encoun e by an an enna ouch o an i em by Nabis. Fu he mo e, we obse e ha Nabis
is an oppo unis ic p eda o in he sense ha i i encoun e s a p ey, i always kills ha p ey. The e o e, in ou
case, Nabis’ killing sequence and i s encoun e sequence a e he same; hus, we can use he killing sequence as he
encoun e s sequence. As we emphasized, he exis ence o a sea ch image can be de ec ed by he non- andomness
o encoun e sequences, i.e., we can say ha i he encoun e sequence is no andom, hen he o age uses a
sea ch image. Fi s , we examined he andomness o he encoun e sequence o Nabis. In SI.6, we in oduced a
new es o his pu pose, and we ound ha he Nabis encoun e sequence is no andom (P = 0.009). The Manly
p e e ence index (α) suppo s hese esul s. The alue o α indica es p e e ence when i exceeds 0.5, ejec ion
when i is lowe han 0.5 and indi e ence when i is exac ly 0.5. In ou ial, Nabis exhibi ed a clea p e e ence o
S. exigua la ae (he e ospeci ic p ey; α1 = 0.65 ± 0.14) and ejec ion o he conspeci ic nymphs (α2 = 0.35 ± 0.14;
Wilcoxon es P = 0.009).
Summa y. Al hough Nabis exhibi s mo e complex beha iou han ou heo e ical model, we ound ha he
cannibalis ic Nabis uses a sea ch image bu no wi h absolu e in en ion because i can also encoun e non-desi ed
p ey ypes; howe e , he i s encoun e sequence is no de e mined by he p eys’ densi ies, i.e., Nabis encoun e s i s
Figu e 3. Uppe hull o he ene gy su aces ER(x, y) and EI(x, y). The da k a ea indica es he ange in which he
RS has a highe pe -uni ime ene gy in ake han he SIU.
Figu e 4. The a ea o he densi y ange be ween cu es γ1 and γ2 is s ic ly posi i e o <
τ
c4
13
B
B
, which indica es
ha he highe e iciency o he RS is obus agains changes in he pa ame e s τB and cB.
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p e e ed p ey wi h a highe p obabili y han i s po en ial conspeci ic p ey. This inding co obo a es esul s on
he subjec ha ha e been published elsewhe e29.
Discussion
Some insigh in o he use o a sea ch image may be use ul om bo h he heo e ical and applied ecologi-
cal pe spec i es. In heo e ical ecology, one o he possible mechanisms o main aining di e si y is nega i e
equency-dependen selec ion, i.e., a e p ey expe ience highe su i al han mo e common ypes. Sea ch image
o ma ion has been in oked as a possible p oxima e explana ion o his mechanism43. Fo ins ance, Bond and
Kamil44 ound ha apos a ic selec ion by blue jays p oduces balanced polymo phism in i ual p ey.
Al hough we concen a e on Nabis, ou heo e ical model p o ides some gene al insigh . Fi s , because he
nume ical esponse eaches i s maximum a he maximum ene gy in ake, ou esul s a e also alid o cases
in which ep oduc ion ime cons ain has no e ec on he o aging p ocess. Thus, ou esul ha an SIU does
no necessa ily collec mo e ood han a RS is alid in gene al. Consequen ly, ou hypo hesis ha an op imal
o age mus use mixed beha iou , i.e., ei he ac s as an in en ional sea ch image use o an oppo unis ic andom
sea che (bu only one a a ime), acco ding o he densi y o i s p ey should be es ed.
Ano he possibili y is ha SIUs a e no pu ely in en ional (i.e., i hey eaches hei p e e ed p ey ype wi h a
p obabili y less han one). As we ound, Nabis alls in o his ca ego y because i s encoun e sequence is no an-
domly de e mined by p ey densi ies. In his case, oppo unism is also possible.
Fo an o e iew, we no e ha he mechanism o ou heo e ical model migh also be applied in he con ex s o
o he si ua ions o ood choice and is also ele an o he biological con ol o pes s when pe o med wi h a sig-
ni ican numbe o p eda o y species31,45,46. Mo eo e 47, such p eda o s may be classi ied acco ding o hei die o
by hei ole in ecological ood webs as “p eda o s” o “ ue omni o es”. In u n, he o me may be specialis and
gene alis p eda o y species48. Gene alis a h opod p eda o s a e ypically bi ophic; hey simul aneously occupy
he hi d and ou h ophic le els by eeding on bo h he bi o es and each o he 28. Mo eo e , mos gene alis
p eda o s a e cannibals49. In u n, ue omni o ous a h opods eed on bo h he bi o es and plan s46.
Acco ding o he abo e obse a ion, and in ela ion o biological con ol, he esul s ound in he p esen wo k
can be conside ed in one p eda o - wo p ey sys ems in wo si ua ions: (i) a one omni o ous p eda o - wo p ey
si ua ion and (ii) a si ua ion wi h a gene alis p eda o ha exhibi s cannibalism; his si ua ion would be a one
gene alis p eda o - wo p ey sys em (i.e., conspeci ic and he e ospeci ic p ey).
The i s assump ion can be ep esen ed by wo e en s. I he ue omni o ous Nesidico is enuis (Reu e )
(Hemipe a, Mi idae) and hei p ey Bemisia abaci (Gennadius) (Hemip e a, Aley odidae) and Tu a absolu a
(Mey ick) (Lepidop e a: Gelechiidae) a e p esen in g eenhouse oma o c ops, when bo h pes species a e p esen
in he c op, he biological con ol o he second species is poo 50. Ano he example is ep esen ed by he ue
omni o ous Mac olophus pygmaeus (Rambu ) (Hemip e a, Mi idae) in he same condi ions wi h pes species51,52.
In he second case, a gene alis p eda o ha exhibi s cannibalism can be ep esen ed by he species s udied he e
in he expe imen al pa , i.e., N. pseudo e us. In his case, i has been demons a ed ha , in he p esence o con-
speci ics, adul emales a e SIUs, which esul s in less e icien biological con ol o he pes species29 as has been
demons a ed in o he s udies53. Simila esul s ha e been epo ed in ela ion o cannibalism in he case o he
gene al p eda o mi e Typhlod omus py i Schue en (Aca i: Phy oseiidae), which a e agen s ha a e used agains
e anychid pes mi es o apples54. All o he abo e e e ences can only be explained i omni o es a e SIUs ins ead
o RSs.
The main p ope y o he sea ch image7 is ha he p ey p e e ence o he o age does a ec he encoun e
p obabili ies o i s p ey ypes. Thus, i an encoun e sequence is known, he applica ion o he me hodology
p oposed he e enables he de e mina ion o whe he he p eda o uses a sea ch image. We hope ou model and
me hodology will be use ul in he s udy o human isual o aging55–58 because, in human expe imen s, a clea
dis inc ion should be made be ween obse ing a a ge (a ixa ed gaze should co espond o encoun e ) and con-
sump ion ( inge apping should co espond o a kill)59.
In summa y, he SIU app oach e sus he RS app oach seems o be one o he c ucial ac o s ha should
be conside ed i omni o ous and gene alis species a e used o biological con ol in ag icul u al ecosys ems.
Especially, as men ioned abo e, because o he cu en end o biological con ol ha consis s o he use o gen-
e alis p eda o y species and, e en mo e igo ously, in cases in ol ing omni o ous species.
Me hods
In heo e ical pa , we use ma hema ical ools.
Expe imen al ial. The ial me hodology was adap ed om p e ious wo k16,29. Ma ed N. pseudo e us
adul emales we e used less han one week a e he inal nymphal ecdysis. They we e indi idually isola ed in
Pe i dishes and subjec ed o a s a ing pe iod o 24 h p io o es ing. The subjec s we e gi en a piece o sponge
mois ened wi h dis illed wa e . Six specimens o second-ins a S. exigua la ae we e u ilized as he e ospeci ic
p ey, and six specimens o second-ins a N. pseudo e us nymphs we e u ilized as conspeci ic p ey; he p ey we e
in oduced in o a choice a ena (Pe i dish), and hen a single N. pseudo e us adul emale was also in oduced.
Each adul emale p eda o was le o p ey on he la ae and nymphs o a pe iod o 4 h. Fi een eplica es we e
pe o med o each ea men . Two ypes o da a we e eco ded: a) he numbe o p ey killed was anno a ed a he
end o he ial (4 h), and b) he p ey-cap u e sequence o adul emales was also eco ded. Because di ec human
obse a ion may in e e e wi h he p eda ion beha iou o Nabis species60, we pho og aphed he ial a ena e e y
10 seconds using an Eos 550D (Canon® Inc, Tokyo 146-8501, Japan) digi al came a wi h an EFS 18–55 lens wi h
mac o unc ion (Canon®) ha was connec ed wi h a cable o a compu e . The Communica ion So wa e o he
Came a EOS U ili y, e sion 2.14 was used61. The pho og aphs we e collec ed in a ime-lapse manne using he
Image-P ocessing and Analysis in Ja a (ImageJ) so wa e, e sion 1.4962, which eco ded he iden i y o he killed
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p ey and he sequence o he p eda ion e en s. The adul p eda o s’ p e e ences o he di e en o e ed p ey we e
quan i ied wi h he Manly p e e ence index (α)63. As es ablished by Cock64, he Manly index is he only me hod
ha accoun s o he educ ion in p ey densi y ha occu s du ing he cou se o he ial as has been co obo a ed
in he e iew by She a and Ha ey65. The index equa ion is as ollows:
α=+,
i
N
N
N
i
i
i
i
j
j
whe e i = numbe o p ey i consumed, j = numbe o p ey j consumed, Ni = numbe o p ey i o e ed, and
Nj = numbe o p ey j o e ed. Compa isons o he p e e ence indexes we e pe o med using he Wilcoxon
signed- ank es .
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Acknowledgemen s
This wo k was pa ially suppo ed by he Hunga ian Scien i ic Resea ch Fund GINOP 2.3.2-15-2016-00057( o
JG.).
Au ho Con ibu ions
J.G., Z.V. and T.C. designed he s udy; T.F.M. calcula ed he nea es p ey in di e en dimensions; J.G., Z.V. and
M.G. analysed he heo e ical model; M.G. calcula ed he nume ical examples and made he igu es; T.F.M.
and I.L. c ea ed he new andomness es o he encoun e sequences o N. pseudo e us; T.C. designed and
di ec ed he expe imen on N. pseudo e us; J.R.G. pe o med he ials; T.C. calcula ed he p e e ence indexes o
N. pseudo e us; and J.G., Z.V., T.F.M. and T.C. collabo a ed in w i ing he a icle.
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Supplemen a y in o ma ion accompanies his pape a h ps://doi.o g/10.1038/s41598-018-21563-y.
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