RESEARCH ARTICLE
No E idence o T ade-O be ween Fa m
E iciencyand Resilience: Dependenceo
Resou ce-Use E iciencyon Land-Use
Di e si y
Helena Kahiluo o
1
*, Janne Kase a
2
1Lappeen an a Uni e si y o Technology, Saimaanka u 11, 15140 Lah i, Finland, 2Na u al Resou ces
Ins i u e Finland, 31600 Jokioinen, Finland
*[email p o ec ed]
Abs ac
E iciency in he use o esou ces s eam-lined o expec ed condi ions could lead o
educed sys em di e si y and consequen ly endange esilience. We es ed he hypo hesis
o a ade-o be ween a m esou ce-use e iciency and land-use di e si y. We applied s o-
chas ic on ie p oduc ion models o assess he dependence o esou ce-use-e iciency on
land-use di e si y as illus a ed by he Shannon-Wea e index. To al e enue in ela ion o
use o capi al, land and labou on he a ms in Sou he n Finland wi h a size exceeding 30 ha
was s udied. The da a we e ex ac ed om he Finnish P o i abili y Bookkeeping da a. Ou
esul s indica e ha he e is ei he no ade-o o a negligible ade-o o no economic
impo ance. The small dependence o esou ce-use e iciency on land-use di e si y can be
posi i e as well as nega i e. We conclude ha di e si ica ion as a s a egy o enhance a m
esilience does no necessa ily cons ain esou ce-use e iciency.
In oduc ion
E idence-basedpolicymay be wish ul hinkingin imes o u bulenceand mul i-dimensional
epis emic and on ological unce ain y. Robus s a egies [1], which wo k well e en i he in o -
ma ion is impe ec o inpu s o he sys em a y[2], may yield a mo e a o able cos -bene i
a io o socie alin es men s [3]. Enhancemen o sys em esilienceis one such obus s a egy
[2], and he e o e cu en lyan impo an complemen a ion o add o e iciency, o sus ainabil-
i y o a ming.
Resilienceis he capaci y o a sys em o ole a e dis u banceand eo ganizewhile e aining
i s unc ion,s uc u eand iden i y [4–6], and o shape change and lea n [7–8]. I a social-eco-
logicalsys em h ea ens esiliencea la ge scales, ans o ma ional change is equi ed [9]. In
he ace o inc eased u bulencein he globalclima e and ma ke s, he esiliencediscou sehas
eme ged in in e na ional en i onmen al and economic policy since he s a o he cu en
decadeiden i y, e.g.,[10–12]. Inc easing e o has also beenadd essed o ma hema ically
PLOS ONE | DOI:10.1371/jou nal.pone.0162736 Sep embe 23, 2016 1 / 16
a11111
OPEN ACCESS
Ci a ion: Kahiluo o H, Kase a J (2016) No
E idence o T ade-O be ween Fa m E iciency and
Resilience: Dependence o Resou ce-Use
E iciency on Land-Use Di e si y. PLoS ONE 11(9):
e0162736. doi:10.1371/jou nal.pone.0162736
Edi o : Gui-Quan Sun, Shanxi Uni e si y, CHINA
Recei ed: Feb ua y 26, 2016
Accep ed: Augus 26, 2016
Published: Sep embe 23, 2016
Copy igh : ©2016 Kahiluo o, Kase a. 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 S a emen : The hi d pa y o
hold he da a is Na u al Resou ces Ins i u e
Finland, and he pe son o con ac in his ma e is
A o La ukka (e-mail [email p o ec ed]).
Funding: This wo k was suppo ed by he Finnish
Clima e Change Adap a ion Resea ch P og amme
(ISTO) and by he Academy o Finland (h p://www.
aka. i), g an s 140870 and 255954. 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 .
model a ious aspec s o s abili y o complex sys ems, e.g.,[13–16]. Di e si y gene a es a a i-
e y o possible esponses o a iabili y [17–19] and o a ious h ea s [20] and ma e ial o
ans o ma ion [21], and as such is a p e equisi e o sys em esilience[20,22–26]. Di e si y
also implies he gene a ion o ‘pe pe ualno el y’ [26], which is c i ical o eo ganizing he sys-
em a e dis u bance[27].
E iciencyis a key economicconcep and has made a c ucialcon ibu ion o sus ainabili y
discou sesac oss disciplinesand sec o s[28]. Eco-e iciency, in e ms o he e icien use o
esou ces (‘mo e om less’), has long domina ed he in e p e a ion o sus ainabili y [29–30]
and has subs an ially in luencedsocie alde elopmen s a egies.Inc easing esou ce-usee i-
ciency, implying a small a io o esou ces o p oduc s o e enue, e.g., highe yields pe uni
a ea o land o o he na u al o economic esou cesin ag icul u alsys ems, is belie ed o p o-
mo e economicpe o mance, oodsecu i yand en i onmen al p o ec ion [31–32]. Ko honen
and Seage [33], Ulanowicz e al. [34] and Goe ne e al. [35] a gued o he complemen a i y
o he wo pe spec i es,i.e.,e iciencyand esilience,in sus ainable de elopmen .
In s able imes, sys em e iciencyis s eamlined o expec edcondi ions, o en c ea ing sys-
ems wi h less di e si y, as exempli iedby he de elopmen a a iousle els o ag icul u alsys-
ems in indus ialcoun iesin ecen decades[35–42]. Di e si y inc easess abili y o
p oduc ionin a iable ag icul u alen i onmen s [43], and land-use di e si y appea s o
inc ease a m esilience[44] also in e ms o economic e u ns [45–46]. Consequen ly, e i-
ciency may un coun e o sys em esilience[33], especially h ough loss o esponse di e si y
[18,20]. On he o he hand, basedon ecologicalmodels wi h economic ele ance, Tilman e al.
[47] concluded ha di e si y should enhance e iciencyin he use o limi ed esou ces.
The ela ionship o economic pe o manceand biodi e si y has been assessed [45–46],
especially om he iewpoin o ecosys emse ices[48–50]. Fu he , eco-e iciencyin e ms o
p oduc s ela i e o emissions has been ela ed o di e si y in wha -i scena ios o social-eco-
logicalsys ems [51]. Howe e , empi ical e idence o he dependencebe ween esou ce-useo
economic e iciencyand p oduc iondi e si y is sca ce o non-exis en . This knowledgegap is
also p ac ically impo an , because he cu en unde s andingo a ade-o ela ion be ween
economic e iciencyand di e si y in a ming in o ms ag icul u alpolicies.
Inspi ed by he model-baseds udy o Tilman e al. [47], we es ed in an empi ical case he
gene al belie ha di e si y educes e iciency, e.g., [44]. The aim o his s udy hus was o
in es iga e empi ically, whe he he e is ade-o be weendi e si y (c i ical o sys em esil-
ience) and e iciencyo esou ce-use (also equi ed o sus ainabili y) on a ms, and ha way
con ibu e o b idging he knowledgegap. We es ed he hypo hesis ha land-use di e si y is
nega i ely ela ed o a m e iciencyin e ms o e enue pe uni o land, labou and capi al.
We es ed his hypo hesis in he con ex o Finnish a ms, which du ing he wo las decades
inc eased apidly in specializa ionand size o achie e g ea e esou ce-usee iciency h ough
economieso scale[52–53], and o which esilienceis o pa amoun impo ance,due o he
no he nmos loca ionin he wo ld and he e o e a apid clima e change, as well as igh link-
ages o ola ile global oodma ke s.
Ma e ials and Me hods
Fa m da a
The empi ical da a analysed he e o igina e om he Finnish p o i abili y bookkeepingda a
used o compile he Finnish da a o he Eu opean Fa m Accoun ancy Da a Ne wo k (FADN),
which is main ained by he Eu opean Commission.Fo compa abili y and access, a iable de i-
ni ions simila o hose in FADN we e used o he accoun ing yea s o 1998–2008 ([54]; h p://
ec.eu opa.eu/ag icul u e/ ica/de ini ions_en.c m).FADN is used h oughou Eu ope o e alua e
Fa m Resou ce-Use E iciency and Land-Use Di e si y
PLOS ONE | DOI:10.1371/jou nal.pone.0162736 Sep embe 23, 2016 2 / 16
income om ag icul u alholdings and he impac s o he CommonAg icul u alPolicy (CAP).
Finland has ou FADN egions,bu he clima ic condi ions o ag icul u ein he no h clea ly
di e om hose o he sou h, and mos ag icul u alp oduc ion,accoun ing a ms and land-
use di e si y, is concen a ed in sou he n Finland. O he a eas we e hus excluded om he
analysis o emo e he bias ha could a ise h ough independen e ec so clima e on he e e-
nue and on he di e si y o ag icul u alland-use.In addi ion,a ailable ag icul u ala ea es ic s
land-use di e si y. Fo smalle a ms also o he easons o a ming ( ec ea ion, main enance o
land alue, li e s yle, emo ional easons such as he i agee c.) a e in a bigge ole which could
cause bias in o he conclusions i such a ms would be included in he analysis o he ade-o
be ween esou ce-usee iciencyand di e si y ( e lec ing he ela ion be weeneconomice i-
ciency and esilience),becausesuch ela ion has no ele ance o he a me s in hose cases.
The e o e, he u ilisedag icul u ala ea (UAA) below 30 hec a es(ha) was se as he lowe limi
o a m size in ou analysis. A e hese es ic ionswe e applied o emo e ob ious sou ces o
bias, we we e le wi h he empi ical da a o 3 268 a ms o ally o e he yea s (Table 1).
Land-use di e si y
The Shannon-Wea e index [hence o h, he Shannon index] [55], he mos commonly used
di e si y index, was used o illus a e a m land-use di e si y. Speci ically, he Shannon index
was used o desc ibe he numbe and p opo ional a ea dis ibu ion( ichness and e enness)o
eigh a m land-use ypes.A Shannon indexequal o ze o indica es ha he a m comp ises
only one land-use ype; he alue o he Shannon indexinc easesas he numbe o di e en
land-use ypes and/o hei e enness inc eases.The Shannon index gi es an equal weigh o
each obse a ionand is compa able among cases wi h di e en composi ions [56]. The Shan-
non index was calcula edacco ding o he ollowing eq (1):
H¼  XK
k¼1
wik
Wi
lnwik
Wi
; o i¼1;...;n a ms ð1Þ
whe e k=1,. . .,K e e ing o he numbe o land-use ypes; w
ik
is he a ea co e ed by land-
use ype ko a m i;W
i
ep esen s he o al a ea o a m i; and w
ik
/w
i
is he p opo ion o a ea
co e ed by land-use ype k. The Shannon index is exp essed in loga i hmic o m, and o
desc ibe he ue di e si y (‘land-use di e si y’), i needs o be con e ed (exp(H)).
Ag icul u alspecialisa ionis a ca ego ical a iable in he Finnish p o i abili y bookkeeping
da a (as in FADN); i consis s o ca ego ies ha a e bo h exhaus i e and mu ually exclusi e
such ha each obse a ionis assigned o one and no mo e han one ca ego y. The ollowing six
ag icul u alland-use ypes we e usedas independen classes o calcula ing he Shannon index:
ce eals (co esponding o FADN a iable SE035), o he ield c ops (SE041), ege ables,be ies,
lowe s and o namen al plan s (SE046-SE046), pe ennialc ops (SE054-55), odde c ops
and allow (SE071-73), and o he . Only on 69 a ms he class ‘o he ’ ep esen ed mo e han
10% o he ag icul u alland a ea, while89% om he o al 3 268 a m obse a ionso e yea s
did no ha e he class ‘o he ’ a all. This indica es ha no bias in he analysis was caused by he
lacking in o ma ion o he di e si y wi hin he class ‘o he ’. We hen calcula edPea son’s co -
ela ion coe icien s o he Shannon index and a m inpu /ou pu a iables, such as UAA,
labou , a m capi al and o al e enue.
Resou ce-use e iciency
Resou ce-usee iciencywas measu ed as a ela ion be ween he use o he majo a m esou ces
land, labou and capi al, and a m e enue, using Cobb-Douglas eg ession model. In addi ion,
‘ echnical e iciency’was measu ed wi h s ochas ic on ie models as he a io be ween he
Fa m Resou ce-Use E iciency and Land-Use Di e si y
PLOS ONE | DOI:10.1371/jou nal.pone.0162736 Sep embe 23, 2016 3 / 16
Table 1. Fa m inpu s (labou , capi al and land), o al e enue and land-use di e si y pe p oduc ion
line.
Va iable Mean S . De . Min Max
All a ms (3268)
Labou , h 3 347 2 144 159 16 608
Fa m capi al, €277 055 237 930 19 724 2 288 832
UAA, ha 71 40 30 655
To al e enue, €90 391 98 649 125 1 222 089
Shannon index 0.686 0.241 0 1.316
Ce eals,oilseeds and p o ein c ops (1140)
Labou , h 1 686 972 191 8 570
Fa m capi al, €180 394 137 295 19 724 2 288 832
UAA, ha 79 52 30 655
To al e enue, €38 702 34 329 125 419 030
Shannon index 0.675 0.244 0 1.316
Field c ops (453)
Labou , h 2 811 1 858 159 12 989
Fa m capi al, €227 728 164 551 34 528 983 156
UAA, ha 73 38 31 315
To al e enue, €75 594 66 440 2 112 454 462
Shannon index 0.869 0.177 0 1.256
Specialis dai ying (692)
Labou , h 5 623 2 037 1 982 16 608
Fa m capi al, €348 065 301 236 70 732 1788 464
UAA, ha 60 26 30 200
To al e enue, €123 574 67 223 29 736 393 392
Shannon index 0.648 0.174 0 1.076
Specialis g ani o es (284)
Labou , h 4 349 1 674 668 14 140
Fa m capi al, €482 851 354 022 65 385 2 069 981
UAA, ha 60 27 30 181
To al e enue, €215 821 161 085 48 569 669 621
Shannon index 0.502 0.252 0 1.054
Field c ops and g azing li es ock (283)
Labou , h 4 336 1 572 246 10 434
Fa m capi al, €255 716 152 461 50 305 924 458
UAA, ha 76 39 30 226
To al e enue, €64 566 42 936 13 624 173 232
Shannon index 0.781 0.214 0 1.207
Va ious c ops and li es ock (416)
Labou , h 3 342 1 208 980 8 091
Fa m capi al, €351 556 201 211 74 132 1 161 327
UAA, ha 70 27 30 201
To al e enue, €127 904 101 417 13 123 927 783
Shannon index 0.641 0.253 0 1.299
UAA = u ilised ag icul u al a ea; Shannon index = Shannon index o land-use di e si y; sample size in
pa en heses.
doi:10.1371/jou nal.pone.0162736. 001
Fa m Resou ce-Use E iciency and Land-Use Di e si y
PLOS ONE | DOI:10.1371/jou nal.pone.0162736 Sep embe 23, 2016 4 / 16
obse edou pu (he e o al e enue) o he maximum ou pu unde he assump ion o ixed
inpu s [57], i.e., he esou ce-usee iciencyo indi idual a ms ela i e o he maximum
esou ce-usee iciencyo he a ms. Use o he majo a m esou cesland, labou and capi al
was illus a ed by he ollowing inpu esou ces: he o al UAA o holding (ha; SE025), o al
labou inpu on holding in hou s (h; SE011), and a m capi al as he sum o he a e age o he
wo king capi al o li es ock, pe manen c ops, land imp o emen s, buildings,machine y and
equipmen , and ci cula ingcapi al (€; SE510). The o al e enue was calcula edas ou pu om
c ops and c op p oduc s, li es ockand li es ockp oduc s and o he ou pu (co esponding o
FADN a iable SE131), in €. Fo de ailed de ini ions o he a iables, see [54].
The Cobb-Douglas eg ession model
The Cobb-Douglasp oduc ion unc ionsee [58] is widely usedin econome ics o ep esen
he ela ion be weense e alinpu s and p oduc ion[59]. I allows he quan i y o one inpu o
a ec he p oduc i i yo ano he inpu . We included he Shannon index in he model,in anal-
ogy o inpu s [60]. The Cobb-Douglasmodel included h ee inpu s (land, capi al and labou ),
he Shannon index, and a single ou pu , o al e enue. The model can be exp essed as
yj¼A xb1
1jxb2
2jxb3
3jeoHjþεj;j¼1;. . . ;nð2Þ
whe e y
j
is he ou pu o a m jand x
1
,x
2
and x
3
a e he a ea (ha), labou (h) and a m capi al
(€) o a m j. The pa ame e H
j
is he Shannon index o a m j, and ε
j
is he e o e m, which
was assumed o be independen and no mally dis ibu ed.The emaining pa ame e s (A,β
1
,
β
2
,β
3
and ω) we e unknownand had o be es ima ed. The equa ion was modi ied o es ima -
ing he coe icien so he pa ame e s.Taking he na u al loga i hmo bo h sideso he equa-
ion leads o
ln yj¼ln A þb1ln x1jþb2ln x2jþb3ln x3jþoHjþεj;j¼1;. . . ;nð3Þ
By choosingY = ln(y
j
),X = ln(x
ij
)and H = H
j
, we ob ained a linea eg ession equa ion
Y¼b0þb1X1þb2X2þb3X3þoHþεð4Þ
whe e he unknown pa ame e s could be es ima ed.
Because he p oduc ionlines di e edin e ms o di e si y and e enue,we included he p o-
duc ionlines in he modelas dummy a iables.Dummy a iables a e a se ieso bina y a i-
ables ha iden i ywhe he o no each obse a ionis a membe o a speci icca ego y. The
yea s wi h a s a is icallysigni ican (α= 0.1) in e ac ion o Shannon index and p oduc ionline
we e no includedin u he analyses due o echnical and in e p e a ional complexi ies.
The s ochas ic on ie p oduc ion models
The Cobb-Douglas eg ession models used in he analyses abo e assume ha all a ms ep e-
sen equal echnicale iciency. Because his assump ion may no be alid, we also applied a
s ochas ic on ie p oduc ion unc ion,which adds o he model a new e m, echnical ine i-
ciency ha a e a ma hema ical ans o ma ion ep esen s he echnicale iciencyo each
a m.
We used wo mos common s ochas ic p oduc ion unc ions: he Cobb-Douglasand he
anslog p oduc ion unc ion.The anslog p oduc ion unc ionis mo e lexible,becauseall
secondo de c oss- e ms o inpu s and he Shannon index a e includedin he model, unlike
he Cobb-Douglasp oduc ion unc ion ha assumes all c oss- e ms o be ze o. The s ochas ic
on ie p oduc ionmodelincluded h ee inpu s (land, capi al and labou ), he Shannon index
Fa m Resou ce-Use E iciency and Land-Use Di e si y
PLOS ONE | DOI:10.1371/jou nal.pone.0162736 Sep embe 23, 2016 5 / 16

and a single ou pu , i.e., o al e enue.We also in es iga ed whe he he associa iono he o al
e enue and he Shannon index dependson p oduc ionline (Table 1) by including a sepa a e
in e cep e m o hem.
Thus, he Cobb-Douglasp oduc ion unc ioncan be exp essed as
lny ¼b0þXn
i¼1bilnxiþεð5Þ
and he anslog p oduc ion unc ionas
lny ¼b0þXn
i¼1bilnxiþ1
2Xn
i¼1Xn
j¼1bij lnxilnxjþεð6Þ
whe e yis he ou pu o a ms and nis he numbe o inpu s added wi h he Shannon index (x).
The pa ame e s β
0
,β
i
and β
ij
a e he unknownpa ame e s o be es ima ed. The ε= -u, whe e
is he sys ema ic e o componen , which is assumed o be independen lyand iden ically dis ib-
u ed, andom e o ha ing no mal dis ibu ionwi h mean being ze o and a iance beingσ
2
.u
is a non-nega i e andom a iable, whichis assumed o accoun o echnicaline iciencyin
p oduc ion,ha ing no mal dis ibu ion wi h mean being ze o and a iance beingσ
u2
(Fig 1).
Fig 1. The s ochas ic p oduc ion on ie [61–62]. Obse ed p oduc ions and on ie p oduc ions a e indica ed wi h xand o,
espec i ely. The on ie p oduc ion (FP), consis ed o obse ed p oduc ion, ine iciency e ec and andom noise, can lie abo e o below
he on ie p odu ion unc ion (PF), depending on he noise e ec .
doi:10.1371/jou nal.pone.0162736.g001
Fa m Resou ce-Use E iciency and Land-Use Di e si y
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Model compa isons
We de e minedwhe he he echnicaline iciency e m needs o be added, ela i e o he
Cobb-Douglas eg ession models, i.e., whe he s ochas ic on ie models (Cobb-Douglaso
anslog s ochas ic on ie models) would be equi ed ins ead o Cobb-Douglas eg ession
models (see abo e). The key pa ame e o es he need o he echnical ine iciency e m is
γ= σ
u2
/(σ
u2
+σ
2
), which ells he p opo iono a iance o he e iciency e m om he o e all
a iance. I hypo hesis H
0
:γ= 0 holds, he e is no need o an e iciency e m in he model.
Since γ[0,1] and he hypo hesis is one-sided,we usedc i ical alues om Kodde and Palm
(1986) o a likelihood a io es . The dis ibu ions o a echnical ine iciency e m we e com-
pa ed based on he in o ma ion c i e ia (AIC, Bayesian in o ma ion c i e ion (BIC)).
The likelihood a io es and BIC we e used o de e minewhe he he anslog p oduc ion
unc ionwould be mo e app op ia e han he Cobb-Douglasp oduc ion unc ionin he s o-
chas ic on ie models.The likelihood a io es s a is ic can be de inedby
D¼  2 ln½LðH0Þ ln½LðH1Þg ð7Þ
whe e L(H
0
)and L(H
1
)a e he alues o he likelihood unc iono he null hypo hesis (H
0
:β
ij
= 0)
and he al e na i e hypo hesis. Tes s a is ic Dis dis ibu ed chi-squa ed wi h deg ees o eedom
equal o he numbe o pa ame e s ha a e cons ained.BIC can be de ined by
BIC ¼  2 ln½LðHiÞþkln½Ng ;i¼0;1ð8Þ
whe e kis he numbe o ee pa ame e s and Nis he sample size.
To acili a e hein e p e a ion o he anslogp oduc ionmodels,all he a iableswe e
di idedby hei sample means be o e es ima ion. Consequen ly, he i s -o de coe icien scan
be in e p e ed as elas ici ieso he sample means [63]. The in e ac ion e ms show how he es i-
ma ed elas ici ies a y wi h a mo emen away om he sample means.
The s a is ical analyses we e pe o medusing SAS so wa e (SAS Ins i u e, Inc., Ca y, NC,
USA)and he REG, GLM, MIXEDand QLIM p ocedu es.The R 3.1.1 package ‘ on ie ’ ( e -
sion 1.1–0) was also used o es mo e complex models ha could no be applied using SAS (R
De elopmen Co e Team).
Resul s
Land-use di e si y in ela ion o a m inpu s and o al e enue
The Shannon index a ied by a m p oduc ionline (Table 1); he highes di e si y indiceswe e
ound o a ms wi h ieldc ops as he p oduc ionline, ollowed by a ms wi h ieldc ops and
g azingli es ock.The lowes Shannon index was measu ed o specialis g ani o e a ms.Only
i e a ms had i e di e en land-use ypes; he g ea es p opo ion o he a ms (55%) had
h ee di e en land-use ypes, and o y a ms had only a single land-use ype. The Shannon
index o a m land-use di e si y was weakly nega i ely co ela ed wi h o al e enue, while i
was weaklyposi i ely co ela ed wi h UAA (Table 2). Howe e , in p oduc ion-line-speci ic
analyses, he Shannon index was co ela ed wi h UAA only, i.e., weakly posi i ely co ela ed
wi h UAA o ce eals,oilseedsand p o ein c ops ( = 0.27, P<0.001) and ieldc ops ( = 0.28,
P<0.001) a ms.
Land-use di e si y in ela ion o a m esou ce-use e iciency
Cobb-Douglas eg essionmodel. When using he adi ionalCobb-Douglas eg ession
models,we ound no s a is ical suppo o he nega i e dependenceo esou ce-usee iciency
on land-use di e si y. The e was no s a is ically signi ican di e encein he dependenceo
Fa m Resou ce-Use E iciency and Land-Use Di e si y
PLOS ONE | DOI:10.1371/jou nal.pone.0162736 Sep embe 23, 2016 7 / 16
esou ce-usee iciencyon land-use di e si y among he p oduc ion lines; p- alues o he Shan-
non index a ied om 0.48 o 0.83 o e yea s. In he i es modelwhichincluded he h ee
inpu s (land, labou and capi al), he Shannon index and he p oduc ionlines, he es ima e o
he Shannon index a ied om -0.085 o 0.028 wi h he con idencein e al om [-0.323,
0.153] o [-0.206, 0.263], espec i ely. The models explained 80–86% o he o al a iance,
while he p opo iono land-use di e si y was less han one pe cen . In he yea 2000, he adi-
ional Cobb-Douglas eg ession model whe e he di e enceamong a ms in esou ce-usee i-
ciency is included in he expe imen al e o e m, was shown o be adequa e, bu in o he yea s
s ochas ic on ie p oduc ionmodels we e p e e ed (Table 3).
S ochas ic on ie Cobb-Douglasp oduc ion model. In he s ochas ic on ie p oduc-
ion models,whe e a new e m, he echnical ine iciencyo a ms was included, he null
hypo hesis, H
0
:γ= 0 ( he echnical ine iciencye ec in he model is ze o), was ejec ed
(P<0.002) o all he yea s (apa om 2000) (Table 3). The e o e, we concluded ha he e was
a echnical ine iciencye ec in he model o all he yea s (apa om 2000), i.e., he a ms di -
e ed om each o he in e ms o esou ce-usee iciency, and he e o e he s ochas ic on ie
models i ed o he da a be e han he eg essionmodels.The exponen ial dis ibu ion o
he echnical ine iciency e m was ound o be mo e app op ia e han he hal -no mal and
unca edno mal dis ibu ions, based on he in o ma ion c i e ia.Howe e , he di e ences
among he selec eddis ibu ionand he o he ones conside edwe e mino .
Acco ding o he BIC c i e ion, he Cobb-Douglass ochas ic on ie model was adequa e
o e e yyea . Simila ly o he eg ession model, he i es s ochas ic on ie p oduc ion
model showed no s a is ical suppo o he nega i e dependenceo esou ce-use e iciencyon
di e si y:p- alues o he Shannon index a ied om 0.58 o 0.99 o e yea s (Table 4). The
mean echnical e iciencysco e o a ms, 0.8, indica ed ha he a e age esou ce-use e iciency
o he a ms was 80%.
S ochas ic on ie anslogp oduc ion model. Based on he al e na i e compa ison
me hod,likelihood a io es , he Cobb-Douglass ochas ic on ie p oduc ion modelwas an
adequa e unc ional o m o he yea s 2004 and 2006 (Table 3). Fo he yea s 2001, 2002 and
2005, he mo e lexible anslog p oduc ion model was mo e app op ia e. In he yea s 2001,
2002 and 2005, a small posi i e, s a is ically non-signi ican ,dependenceo esou ce-usee i-
ciencyon land-usedi e si y was indica ed p = 0.406,p = 0.663 and p = 0.560, espec i ely)
(Table 5).
Acco ding o he anslog p oduc ionmodel, he coe icien so he in e ac ionso land-use
di e si y wi h UUA and capi al indica ed ha as land-use di e si y o a a m inc eases, he
esou ce-usee iciencyo UUA use ends o dec easeand he esou ce-usee iciencyo capi al
use o inc ease,in e ms o e enue [63]. The e was no s a is ically signi ican in e ac ion o
land-use di e si y and esou ce-usee iciencyin labou use (Table 5). The elas ici ieso inpu s
Table 2. Pea son co ela ion ma ix o land-use di e si y, o al e enue and inpu s (labou , a m capi al and land).
Shannon index To al e enue UAA Labou Fa m capi al
Shannon index 1
To al e enue -0.102*1
UAA 0.201*0.276*1
Labou -0.029 0.532*0.162*1
Fa m capi al -0.104*0.835*0.482*0.561*1
Shannon index = Shannon index o land-use di e si y; UAA = u ilised ag icul u al a ea; n = 3268. S a is ically signi ican co ela ions (P<0.05) a e ma ked
wi h as e isks.
doi:10.1371/jou nal.pone.0162736. 002
Fa m Resou ce-Use E iciency and Land-Use Di e si y
PLOS ONE | DOI:10.1371/jou nal.pone.0162736 Sep embe 23, 2016 8 / 16
o bo h Cobb-Douglasand anslog models could be in e p e ed simila ly, becauseall he a i-
ables we e di idedby hei sample means be o e es ima ion. The elas ici iesillus a e he
dependenceo esou ce-usee iciencyon land-use di e si y and inpu s. The small nega i e
elas ici ieso land-use di e si y in 2004 and 2006 indica ed ha a 10% inc ease in land-use
di e si y would esul in app oxima ely hal a pe cen agedec easein o al e enue. The posi i e
elas ici ies indica ed inc ease in o al e enue by inc easinginpu s (Fig 2). The con idence
in e alsindica e ha o al e enue could a maximum inc ease by 3% (yea 2001) o decline
by 3% (yea 2004) associa ed o 10% inc easeinland-usedi e si y (Fig 2).
The lack o s a is ical signi icancein he dependenceo esou ce-usee iciencyon land-use
di e si y, oge he wi h he nea -ze o alue o he coe icien o he land-usedi e si y, indica e
ha he e is ei he no dependenceo esou ce-usee iciencyon land-use di e si y o he depen-
dence is e y small.
Table 3. Compa ison o he Cobb-Douglas eg ession (H
0
) and s ochas ic on ie Cobb-Douglas (H
1
) and anslog (H
2
) p oduc ion models.
Log-likelihood alues o he models Compa ison o he models
Yea H
0
: Cobb-Douglas, λ= 0
a
H
1
: Cobb-Douglas
b
H
2
: anslog
c
H
0 s
H
1
:w2
1
d
H
1 s
H
2
:w2
10
e
H
1 s
H
2
:ΔBIC
2000 -123.7 -122.5 -107.1 2.4 30.8*27*
2001 -147.2 -130.2 -102.1 34.0*56.2*1
2002 -128.1 -119.7 -93.6 16.8*52.2*4
2004 -159.1 -154.9 -148.6 8.4*12.6 44*
2005 -172.4 -154.8 -135.5 35.2*38.6*18*
2006 -189.1 -140.8 -134.1 96.6*13.4 43*
Likelihood a io es (H
0 s
H
1;
H
1 s
H
2
) and Bayesian in o ma ion c i e ion (H
1 s
H
2:
ΔBIC) we e used in s a is ical in e ence o selec he adequa e model
o each yea . Based on he likelihood a io es , he Cobb-Douglas eg ession model is adequa e in 2000 and he s ochas ic on ie Cobb-Douglas
p oduc ion model in 2004 and 2006. Based on he Bayesian in o ma ion c i e ion, he s ochas ic on ie Cobb-Douglas p oduc ion model is adequa e o
e e y yea .
a
The log-likelihood alue o he Cobb-Douglas eg ession model wi hou he ine iciency e ec (λ).
b
The log-likelihood alue o he s ochas ic on ie Cobb-Douglas p oduc ion model wi h he ine iciency e ec .
c
The log-likelihood alue o he s ochas ic on ie anslog p oduc ion model wi h he ine iciency e ec .
d
Likelihood a io es o H
0
: The echnical ine iciency e ec is absen . The signi icance le el α= 0.05 (*).
e
Likelihood a io es o H
1
: ‘The Cobb-Douglas model is an app op ia e unc ional o m ‘. The signi icance le el α= 0.05 (*).
The di e ence o Bayesian in o ma ion c i e ion (BIC) alues o he s ochas ic on ie Cobb-Douglas and anslog p oduc ion models. Posi i e alues a o
Cobb-Douglas in e e y case; alues o e en indica e a e y s ong e idence agains anslog (*).
doi:10.1371/jou nal.pone.0162736. 003
Table 4. Maximum-likelihood es ima es o he land-use di e si y o he s ochas ic on ie Cobb-Douglas p oduc ion models.
Yea Coe icien o Shannon index S anda d E o o Shannon index P alue o Shannon index
2000 0.018 0.113 0.873
2001 0.018 0.101 0.860
2002 0.002 0.111 0.990
2004 -0.063 0.115 0.582
2005 0.055 0.102 0.592
2006 -0.037 0.097 0.701
The small coe icien o he Shannon index wi h no s a is ical signi icance indica es no o a mino dependence o esou ce-use e iciency on land-use
di e si y. Shannon index = Shannon index o land-use di e si y.
doi:10.1371/jou nal.pone.0162736. 004
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