www.ecole ol.o g Ecology and E olu ion 2016; 6: 7004–70147004
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© 2016 The Au ho s. Ecology and E olu ion
published by John Wiley & Sons L d.
Recei ed: 22 Ap il 2016
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Re ised: 1 Augus 2016
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Accep ed: 4 Augus 2016
DOI: 10.1002/ece3.2413
This is an open access a icle unde he e ms o he C ea i e Commons A ibu ion License, which pe mi s use, dis ibu ion and ep oduc ion in any medium,
p o ided he o iginal wo k is p ope ly ci ed.
Abs ac
Densi y dependence, popula ion egula ion, and a iabili y in popula ion size a e unda-
men al popula ion p ocesses, he mani es a ion and in e ela ionships o which a e a -
ec ed by en i onmen al a iabili y. Howe e , he e a e su p isingly ew empi ical
s udies ha dis inguish he e ec o en i onmen al a iabili y om he e ec s o popu-
la ion p ocesses. We ook ad an age o a unique sys em, in which popula ions o he
same duck species o close ecological coun e pa s li e in highly a iable (no h Ame ican
p ai ies) and in s able (no h Eu opean lakes) en i onmen s, o dis inguish he ela i e
con ibu ions o en i onmen al a iabili y (measu ed as be ween- yea luc ua ions in
we land numbe s) and in aspeci ic in e ac ions (densi y dependence) in d i ing popula-
ion dynamics. We es ed whe he popula ions li ing in s able en i onmen s (in no he n
Eu ope) we e mo e s ongly go e ned by densi y dependence han popula ions li ing in
a iable en i onmen s (in No h Ame ica). We also add essed whe he ela i e popula-
ion dynamical esponses o en i onmen al a iabili y e sus densi y co esponded o
di e ences in li e his o y s a egies be ween dabbling ( ela i ely “ as species” and go -
e ned by en i onmen al a iabili y) and di ing ( ela i ely “slow species” and go e ned by
densi y) ducks. As expec ed, he a iance componen o popula ion luc ua ions caused
by changes in b eeding en i onmen s was g ea e in No h Ame ica han in Eu ope.
Con a y o expec a ions, howe e , popula ions in mo e s able en i onmen s we e no
less a iable no clea ly mo e s ongly densi y dependen han popula ions in highly a i-
able en i onmen s. Also, con a y o expec a ions, popula ions o di ing ducks we e
nei he mo e s able no s onge densi y dependen han popula ions o dabbling ducks,
and he e ec o en i onmen al a iabili y on popula ion dynamics was g ea e in di ing
han in dabbling ducks. In gene al, i espec i e o con inen and species li e his o y, en-
i onmen al a iabili y con ibu ed mo e o a ia ion in species abundances han did
densi y. Ou indings unde sco e he need o mo e s udies on popula ions o he same
species in di e en en i onmen s o e i y he gene ali y o cu en explana ions abou
popula ion dynamics and i s associa ion wi h species li e his o y.
KEYWORDS
demog aphic s ochas ici y, densi y dependence, en i onmen al a iabili y, hie a chical Bayesian
s a e-space models, li e his o y s a egy, popula ion a iabili y
1Na u al Resou ces Ins i u e Finland,
Joensuu, Finland
2Na u al Resou ces Ins i u e Finland,
Helsinki, Finland
3USGS No he n P ai ie Wildli e Resea ch
Cen e , S . Paul, MN, USA
4Fishe ies, Wildli e, and Conse a ion
Biology, Uni e si y o Minneso a, S . Paul,
MN, USA
5Kuopio Na u al His o y Museum, Kuopio,
Finland
6En i onmen al Planning ENVIRO, Espoo,
Finland
7Depa men o In eg a i e
Biology, Uni e si y o Guelph, Guelph, ON,
Canada
8Depa men o Fo es Sciences, Uni e si y
o Helsinki, Helsinki, Finland
Co espondence
Hannu Pöysä, Na u al Resou ces Ins i u e
Finland, Joensuu, Finland.
Email: hannu.poysa@luke. i
ORIGINAL RESEARCH
En i onmen al a iabili y and popula ion dynamics: do
Eu opean and No h Ame ican ducks play by he same ules?
Hannu Pöysä1 | Jukka Rin ala2 | Douglas H. Johnson3,4 | Jukka Kauppinen5,* |
Esa Lammi6 | Thomas D. Nudds7 | Veli-Ma i Väänänen8
*Jukka Kauppinen passed away du ing he p epa a ion o he manusc ip .
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7005
Pöysä e al.
1 | INTRODUCTION
En i onmen al a ia ion and densi y dependence a e key phenom-
ena go e ning popula ion dynamics (Hixon, Pacala, & Sandin, 2002;
Mu doch, 1994; Royama, 1992; Sinclai & Pech, 1996; Tu chin, 1995),
and he ole o he la e in pa icula has been s udied ex ensi ely wi h
ecological ime se ies da a (e.g., B ook & B adshaw, 2006; Knape & de
Valpine, 2012; Sibly, Ba ke , Denham, Hone, & Pagel, 2005; Tu chin &
Taylo , 1992; Woiwod & Hanski, 1992; Zeng, Nowie ski, Tape , Dennis,
& Kemp, 1998; Zieba h, Abbo , & I es, 2010). Rela ionships be ween
hem and a ia ion in popula ion size ha e ecei ed less a en ion. I
has been sugges ed ha low empo al a iabili y in popula ion size
indica es densi y- dependen egula ion (e.g., Gas on & McA dle,
1994; Hanski, 1990). Howe e , he ew empi ical s udies ha ha e
add essed his ela ionship p o ided mixed esul s (see Hanski, 1990;
Hanski & Woiwod, 1993; Holyoak & Baillie, 1996a; Williams, I es, &
Applega e, 2003). I espec i e o he possible ela ionship be ween
densi y- dependen egula ion and empo al a ia ion in popula ion
size, bo h heo y (e.g., Kai ala, Ylika jula, Ran a, & Lundbe g, 1997;
Ran a, Lundbe g, Kai ala, & Laakso, 2000; Roughga den, 1975) and
labo a o y expe imen s (e.g., Ben on, Lapsley, & Becke man, 2002;
Laakso, Löy ynoja, & Kai ala, 2003; Pe chey, 2000) sugges ha en-
i onmen al a iabili y a ec s empo al a ia ion in popula ion size.
Theo e ical wo k indica es ha he ou come o his e ec depends
on he empo al au oco ela ion o he en i onmen and he espon-
si eness o he species o en i onmen al luc ua ions. In gene al, an
unde compensa ing popula ion (slow esponse o en i onmen al
change) su e s in slowly changing en i onmen s i a un o se e al
bad yea s occu s, whe eas an o e compensa ing popula ion ( apid e-
sponse o en i onmen al change) su e s in en i onmen s ha change
d ama ically om one ime s ep o he nex (see Ripa & Heino, 1999;
Roughga den, 1975; Schwage , Johs , & Jel sch, 2006).
Gene ally, empo al en i onmen al a iabili y, o en i onmen al
s ochas ici y, has been conside ed an impo an ac o a ec ing popu-
la ion dynamics, some imes masking any signal o densi y- dependen
egula ion (examples in Bonen an e al., 2009; bu see He ando-
Pé ez, Delean, B ook, Cassey, & B adshaw, 2014). Gas on and
McA dle (1994) easoned ha , in a iable en i onmen s, popula ions
may exhibi high empo al a iabili y ega dless o he ope a ion o
densi y- dependen egula ion. E en hough en i onmen al s ochas ic-
i y migh d i e popula ion dynamics, popula ions a e no necessa ily
in a nonequilib ium o un egula ed s a e (Sinclai & Pech, 1996; o a
concise e iew o he deba e abou popula ion egula ion and en i on-
men al a iabili y, see Tu chin, 1995). I has been gene ally acknowl-
edged ha bo h densi y dependence and en i onmen al s ochas ici y
a e impo an and o en in e ac in a ec ing popula ion dynamics (e.g.,
Bjø ns ad & G enle , 2001; Ross, Hoo en, DeVink, & Koons, 2015;
Tu chin, 1995, 1999), al hough hei ela i e oles a e less o en clea .
Depending on he ela i e s eng h o densi y dependence e sus
en i onmen al s ochas ici y, he e will be a con inuum o dynamics
anging om igh popula ion egula ion a ound a s able equilib ium
o o ally s ochas ic dynamics (Tu chin, 1995).
Conside ing he impo ance o en i onmen al s ochas ici y and
di e en popula ion p ocesses in a ec ing he abili y o a species o
espond o changes in en i onmen al a iabili y, in o ma ion abou
he ela ionships be ween hem om na u al sys ems is su p isingly
scan (see also Ben on e al., 2002). One o he ew examples o he
in luence o en i onmen al a iabili y on popula ion dynamics comes
om No h Ame ican p ai ies, whe e he numbe o we lands, a c i i-
cal esou ce o b eeding ducks, a ies d as ically be ween yea s (e.g.,
Ba , Ande son, Ande son, & Caswell, 1989). Such a ia ion a ec s
he local se lemen and numbe s o b eeding pai s (Johnson & G ie ,
1988), causes d ough - induced emig a ion o b eeding ducks om
p ai ies o less a iable mixed- p ai ie and pa kland egions (Johnson
& G ie , 1988; see also Be hke, 1993; Be hke & Nudds, 1995) and
d i es spa ial synch ony in b eeding numbe s o ducks (D e e , 2006).
Se e al ea lie s udies sugges ed ha en i onmen al a iabili y plays
a cen al ole in a ec ing he a iabili y o duck popula ions and he
s eng h o densi y- dependen popula ion egula ion. Fo example,
Nudds (1983) demons a ed ha duck popula ions a e mo e a iable
in mixed- p ai ie habi a s han in ela i ely mo e s able aspen pa k-
land habi a s o he Canadian p ai ies. In addi ion, Vicke y and Nudds
(1984) ound ha dabbling ducks, which occupy he mos empo ally
a iable we lands in he mixed- p ai ie habi a s, showed less e idence
o densi y- dependen egula ion han did di ing ducks, which use em-
po ally mo e s able we lands. This inding was accompanied by la e
wo k analyzing densi y dependence in ime se ies o No h Ame ican
ducks (Jamieson & B ooks, 2004). A gene al iew is ha dabbling
ducks espond mo e eadily o changes in we land condi ions han do
di ing ducks (bu see Lei ch & Kaminski, 1985) and, hence, exhibi less
densi y dependence in popula ion egula ion, a dis inc ion e lec ing
di e ences in li e his o y be ween dabbling and di ing ducks along a
“slow– as con inuum” sensu Sæ he (1987; based on he /K scheme
p esen ed by Pianka, (1970)) (Bailey, 1981; Gunna sson e al., 2013;
Johnson & G ie , 1988; Nummi, Holopainen, Rin ala, & Pöysä, 2015;
Pé on, Nicolai, & Koons, 2012; Vicke y & Nudds, 1984; Viljug ein,
S ense h, Smi h, & S einbakk, 2005).
Mu ay, Ande son, and S eu y (2010), howe e , did no ind sup-
po o he idea ha he s eng h o densi y dependence is associ-
a ed wi h species li e his o y in No h Ame ican ducks. Fu he mo e,
ecen analyses ha e eached mixed conclusions abou he p e alence
o densi y- dependen egula ion in No h Ame ican ducks al oge he
(see also Gunna sson e al., 2013). Sæ he e al. (2008) concluded ha
weak densi y egula ion is a gene al cha ac e is ic o he popula ion
dynamics o No h Ame ican mid- con inen al duck species. On he
o he hand, Mu ay e al. (2010) ound e idence o densi y- dependen
egula ion in all se en dabbling duck species and in h ee di ing duck
species s udied, bu a eanalysis o ime- segmen ed da a e ealed
ha densi y- dependen egula ion was weake in 1980–2005 han
i had been du ing 1955–1979 o bo h dabbling and di ing ducks.
Law ence, G amacy, Thomas, and Buckland (2013) in u n concluded
ha he e is li le e idence o densi y- dependen egula ion in many
No h Ame ican duck species. A simila conclusion was eached by
Roy, McIn i e, and Cumming (2016) o malla ds (Anas pla y hynchos
7006
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Pöysä e al.
Linnaeus, a dabbling duck) b eeding ac oss wes e n No h Ame ica,
anging om he highly a iable P ai ie Po hole Region o he mo e
s able wes e n bo eal o es s. In addi ion, hese au ho s ound ha
di e en en i onmen al ac o s a ec ed popula ion g ow h a es
in di e en egions. Ross e al. (2015) epo ed ha , i espec i e o
clima e- d i en a iabili y in en i onmen al condi ions, densi y depen-
dence was an impo an d i e o popula ion dynamics in scaup ( wo
species o di ing ducks, Ay hya spp.) in he no hwes e i o y egions
o Canada. Finally, Feldman, Ande son, Howe e , and Mu ay (2015)
ound ha , while he e ec o en i onmen al s ochas ici y on duck
popula ion dynamics was weak a he co e o he P ai ie Po hole
Region, i was s ongly in luen ial in pe iphe al si es, bu species
esponse a ied by si e.
To cla i y he ole o en i onmen al a iabili y in popula ion dynam-
ics, we need mo e empi ical s udies om sys ems in which masking
e ec s o spa ial co ela ion a e absen and whe e empo al shi s in
en i onmen al a iabili y do no domina e. The e is a undamen al
di e ence be ween No h Ame ican p ai ies and no he n Eu opean
bo eal a eas in he a iabili y o b eeding en i onmen s o ducks: The
numbe o we lands a ies d as ically be ween yea s on he p ai ies,
bu emains essen ially s able in no he n Eu ope (examples in Fig. 1).
Fu he , habi a condi ions in no h Eu opean lakes (e.g., s uc u e
o sho e ege a ion and wa e le el) show li le sho - o long- e m
a ia ion, excep ha caused by bea e dams (Holopainen, Nummi,
& Pöysä, 2014; Nummi & Pöysä, 1993; Suhonen, Nummi, & Pöysä,
2011). This being he case, e ec s on duck numbe s om such sho -
e m en i onmen al a ia ion, as desc ibed abo e o No h Ame ican
ducks, should be less impo an in no he n Eu ope han in No h
Ame ican p ai ies. Hence, because he same duck species, o close
ecological coun e pa s, occu in bo h No h Ame ica and Eu ope (see
Me hods), a compa ison be ween con inen s o e s a unique oppo u-
ni y o s udy whe he and how he magni ude o densi y e ec s migh
a y in compa ison wi h he e ec s o en i onmen al a iabili y on
popula ion dynamics.
We de eloped hie a chical Bayesian (Gelman, Ca lin, S e n, &
Rubin, 2003) s a e- space models (Dennis, Ponciano, Lele, Tape ,
& S aples, 2006; Mu shinda, O’Ha a, & Woiwod, 2011) o yea ly
dynamics o six species o dabbling ducks (Anas spp.) and wo species
o di ing ducks (Ay hya spp.) in each o Eu ope and No h Ame ica.
Hie a chical app oaches a e s ongly ecommended o es ima ing, o
ins ance, he impo ance o densi y- dependen egula ion o popula-
ions (Leb e on & Gimenez, 2013). We es ed wo p edic ions de i ed
om heo e ical wo k on he impo ance o en i onmen al a iabil-
i y in empo al popula ion dynamics and om he ea lie indings on
No h Ame ican ducks. Fi s , conside ing he d as ic di e ence in en i-
onmen al a iabili y be ween no he n Eu ope and No h Ame ica,
we expec ed densi y dependence o go e n duck popula ion dynam-
ics in no he n Eu ope and en i onmen al a iabili y in No h Ame ica.
Second, i species’ li e his o y s a egies u he media e popula ion
dynamical esponses o en i onmen al a iabili y, he e should be
less di e ence be ween dabbling (p esumed “ as species”) and di ing
(p esumed “slow species”) ducks in he ela i e impo ance o den-
si y dependence whe e en i onmen al a iabili y is lowe , ha is, in
no he n Eu ope e sus No h Ame ica. We also modeled he e ec
o demog aphic s ochas ici y on popula ion dynamics because i is an
impo an componen ha may a ec pa icula ly small popula ions
(e.g., Lande, 1993; Lande, Engen, & Sæ he , 2003). To ou knowledge,
no ea lie wo k has compa ed popula ion dynamics o a g oup o non-
cyclic species in such a se ing, ha is, he same species (o ecological
coun e pa s) be ween con inen s in con as ing en i onmen s ( o
species wi h cyclic dynamics, see S ense h, 1999). Hence, ou s udy
p o ides a no el app oach o add ess he impo ance o en i onmen-
al a iabili y in popula ion dynamics in gene al.
2 | METHODS
2.1 | Popula ion da a
The da a include 56 ime se ies (23–33 yea s) o b eeding numbe s
o eigh duck species om ou s udy a eas in Finland (all ha e s able
we land condi ions ypical o no he n Eu ope) and 16 ime se ies o
b eeding numbe s o eigh duck species om he Red e s Wa e owl
S udy A ea in Saska chewan, Canada (eigh ime se ies o 26 yea s,
da a om Vicke y & Nudds, 1984), and om he Woodwo h S udy
A ea in No h Dako a, USA (eigh ime se ies o 25 yea s, da a om
Johnson, 1995), ep esen ing a iable we land condi ions o No h
Ame ican p ai ies (Table S1). Th oughou he ex , one ime se ies
means he numbe s o b eeding pai s o one species a one si e. We
included eigh species pai s (i.e., he same species o ma ched spe-
cies [close ecological coun e pa s] om Eu ope and No h Ame ica)
o which we had ime se ies om bo h con inen s: Eu asian Wigeon
(Anas penelope Linnaeus; Eu ope) and Ame ican Wigeon (Anas
ame icana Gmelin; No h Ame ica); Malla d (Eu ope and No h
Ame ica); No he n Sho ele (Anas clypea a Linnaeus; Eu ope and
No h Ame ica); No he n Pin ail (Anas acu a Linnaeus; Eu ope and
FIGURE1 Examples showing he di e ence be ween no he n
Eu ope and No h Ame ican p ai ies in he a iabili y o duck
b eeding en i onmen s ( he numbe o we land basins/ponds
con aining wa e )
|
7007
Pöysä e al.
No h Ame ica); Ga ganey (Anas que quedula Linnaeus; Eu ope) and
Blue- winged Teal (Anas disco s Linnaeus; No h Ame ica); Eu asian
Teal/G een- winged Teal (Anas c ecca Linnaeus; Eu ope and No h
Ame ica); Common Pocha d (Ay hya e ina Linnaeus; Eu ope) and
Redhead (A. ame icana Ey on; No h Ame ica); Tu ed Duck (Ay hya
uligula Linnaeus; Eu ope) and Lesse Scaup (A. a inis Ey on; No h
Ame ica). In mos o he ma ched species cases, he species also a e
phylogene ically close ela i es (Gonzalez, Dű mann, & Wink, 2009);
Ga ganey and Blue- winged Teal a e no he closes ela i es bu a e
ecologically e y simila (e.g., Nudds, Sjöbe g, & Lundbe g, 1994). As
o he published ime se ies, we e e o he o iginal a icles o s udy
a eas and me hodological de ails (Johnson, 1995; Vicke y & Nudds,
1984).
All o he Finnish ime se ies a e based on g ound su eys ca ied
ou by one o us in he espec i e s udy egions, using he s anda d
me hods o moni o ing b eeding numbe s o ducks in Finland (cen-
sus me hods desc ibed in de ail in Koskimies & Väisänen, 1991). In
b ie , o ake in o accoun di e ences in he iming o sp ing mig a-
ion be ween species, 2–4 censuses we e ca ied ou in May in each
s udy egion; pai numbe s o a species we e in e p e ed using he
ield obse a ions om he census wi hin he ecommended species-
speci ic ime window (Kauppinen, 1983; Koskimies & Väisänen, 1991;
Pöysä, 1996).
The Finnish ime se ies a e om ou egions: (1) Hollola in sou h-
e n Finland (61°N, 25°E; wo isola ed lakes 7 km apa and a g oup
o wo lakes 0.1 km apa ; duck su eys ca ied ou by E. Lammi); (2)
Pa ikkala in sou heas Finland (61°N, 29°E; a g oup o 28 lakes, all
wi hin 6 × 7 km; duck su eys ca ied ou by H. Pöysä); (3) Pieksämäki-
Suonenjoki- Kuopio- Siilinjä i in Cen al Finland (he ea e , Kuopio,
62°N, 27°E; six isola ed lakes wi h mean dis ance o closes neigh-
bo 15.6 km, ange 11.3–45.1 km; duck su eys ca ied ou by J.
Kauppinen); and (4) Maaninka in Cen al Finland (63°N, 27°E; a g oup
o ou lakes wi hin 5 × 6 km; dis ance o nea es neighbo 0.9–3.2 km;
duck su eys ca ied ou by V.- M. Väänänen). Time se ies om isola ed
lakes we e conside ed as sepa a e da a, bu o neighbo ing lakes nea
each o he , and hence cons i u ing a unc ional uni om b eeding
ducks’ poin o iew, da a om wo o mo e neighbo ing lakes (g oup
o lakes) we e pooled o a gi en ime se ies. The lakes in he Finnish
s udy egions ep esen ypical lakes in he bo eal no he n Eu ope,
anging om oligo ophic lakes su ounded by o es and pea sho es
o eu ophic lakes su ounded by a able lands. Mo e in o ma ion abou
he Finnish s udy egions and lakes is gi en in Hea h and E ans (2000,
p. 252; Hollola), Pöysä (2001; Pa ikkala), Kauppinen (1993; Kuopio),
and Väänänen (2001; Maaninka).
Fo each species, we included only comple e ime se ies in which
ze o coun s (i.e., no b eeding pai s obse ed in censuses in a gi en
yea ) occu ed in ewe han hal o he o al yea s su eyed.
2.2 | Popula ion a iabili y
Fo desc ip i e pu poses, we examined o e all popula ion a iabil-
i y using he popula ion a iabili y measu e (PV; ange 0–1) in o-
duced by Hea h (2006). This measu e quan i ies a iabili y among all
combina ions (yea s) o obse ed abundances; PV = 0 means com-
ple e s abili y among yea s, while a alue o PV = 1 is app oached as
di e ences in popula ion size app oach in ini y ( o u he de ails, see
Hea h, 2006).
2.3 | Bayesian modeling o popula ion p ocesses
To model popula ion dynamics on a si e (i.e., communi y) le el, we
used hie a chical s a e- space o mula ion on mul ispecies da ase s.
Mul ispecies pe spec i e was used as i allowed he es ima ion o
posi i e o nega i e in e ac ions o di e en species in esponses o
en i onmen al luc ua ions (Mu shinda e al., 2011). We no e ha ,
e en hough we used a mul ispecies modeling app oach, in e speci ic
in e ac ions we e no conside ed in he models; using a simila mod-
eling app oach, Alma az, G een, Aguile a, Rendon, and Bus aman e
(2012) ound ha in e speci ic in e ac ions explained only a negligible
p opo ion o popula ion a iances o indi idual species in a wa e -
owl communi y in he Guadalqui i Ma shes, sou hwes Spain. The
au ho s concluded ha he e was no suppo o he inclusion o
any in e speci ic e ec in he s ochas ic communi y dynamics model
de eloped by hem. Fo an unde lying popula ion dynamical p ocess,
we assumed a Gompe z model, which has been widely applied in
modeling s udies o a ious animal popula ions (Alma az e al., 2012;
Dennis e al., 2006; Mu shinda, O’Ha a, & Woiwod, 2009; Mu shinda
e al., 2011). The ollowing model desc ip ion is based on he no a ion
o Mu shinda e al. (2011). Le Ni, indica e he s a e numbe o indi-
iduals o species i in a communi y a yea , and hen, he assumed
dynamics becomes he ollowing:
whe e i is he in insic g ow h a e, and ki deno es he na u al loga i hm
o ca ying capaci y o species i; εi, is assumed o be a andom p ocess
o e o s wi h o e all mean o ze o and a iance de e mined by demo-
g aphic s ochas ici y and en i onmen al a iabili y. On a loga i hmic
scale, equa ion (1) becomes he ollowing:
whe e ni, is he na u al loga i hm o Ni, . In he ma ix o m o equa-
ion (2),
𝛆
=(ε
1,
,ε
2,
,…,ε
S,
)
T
is he ec o o e o s o each species
(1, 2,…,S) in yea , assumed o be a mul i a ia e no mal dis ibu ion
(MVN) wi h mean a ec o o ze os and co a iance ma ix deno ed
as Σ ; ha is,
𝛆 =MVN(0, 𝚺 )
. The co a iance ma ix Σ can be u he
di ided in o demog aphic and en i onmen al a iance componen s:
whe e C is he en i onmen al co a iance ma ix, in which elemen s
on he main diagonal (Ci,i) co espond o species- speci ic esponses o
la en (unspeci ied) en i onmen al a ia ion (he ea e en i onmen al
a iabili y) and o - diagonal elemen s (Ci,j, i ≠ j) deno e he co espond-
ing join esponses o di e en species; be ween- species co a iances
wi h espec o en i onmen al a iabili y we e aken om hese
(1)
N
i, =Ni, −1exp
{
i
(
1−log Ni, −1
ki
)
+εi,
}
(2)
n
i, =ni, −1+ i
(
1−ni, −1
ki
)
+εi,
(3)
𝚺
=
D
+
C
7008
|
Pöysä e al.
co a iance ma ices. The demog aphic a iances o each species in
a communi y we e se o be in e sely ela ed o he s a e popula ion
sizes indica ed by he main diagonal o he ma ix,
diag(
D
)
=δ
2
i
∕N
i, −1
, he
o - diagonal elemen s being ze os. D accoun s o a popula ion- le el
demog aphic s ochas ici y e ec on species i om yea − 1 o yea .
In aspeci ic in e ac ion Ii (he ea e densi y dependence) o spe-
cies i is deno ed as ollows:
whe e Va (ni) is empo al p ocess a iance o species i. To al a i-
ance due o densi y dependence and en i onmen al a iabili y o
species i is hen: Ii + Ci,i. Fo ins ance, he p opo ion o he popula-
ion dynamics o a species i a ibu ed o densi y dependence is as
ollows:
The species- speci ic obse a ion model was speci ied wi h
Gaussian e o s. Le Yi, ep esen he obse ed coun o species i in
yea in a communi y, including measu emen e o . Taking he na u al
loga i hm, yi, = log(Yi, ), le us assume he ollowing ela ion:
Bayesian models equi e explici p io s o all unknown quan i ies.
We se he co a iance ma ix C o be he in e se o
Wisha (d ,𝛀)
p io , in which d is deg ees o eedom, ha is, he numbe o spe-
cies in a gi en communi y, and Ω is a d - dimensioned iden i y ma ix.
P io s o he es o he model pa ame e s we e de e mined as
ollows: i ∼ No mal(0, 1)B(0, ∞), in which B is di use bounda y
unc ion, gene a ing pos e io comp ising o he uppe 50% o he
no mal dis ibu ion ( alues > 0);
ki∼Uni o m(kmin i,kmax i)
, whe e
kmin i=Mean(ni)−2.576
⋅
SD(ni)
and
kmax i=Mean(ni)+2.576
⋅
SD(ni)
;
Uni o m (0, 10) was used o s anda d de ia ions τi and δi ( o uni o m
nonin o ma i e p io s, see Gelman, 2006; Ké y & Schaub, 2012).
In o de o sample om he join pos e io o he model pa ame-
e s, we used Ma ko chain Mon e Ca lo (MCMC) simula ions (Gilks,
Richa dson, & Spiegelhal e , 1996) implemen ed wi h OpenBUGS
e sion 3.2.3 (Thomas, O’Ha a, Ligges, & S u z, 2006). We used R
e sion 3.1.1 (R Co e Team 2014) and package R2OpenBUGS e sion
3.2- 2.2 (S u z, Ligges, & Gelman, 2005) o he p epa a ion o da a
as well as unning and summa izing he simula ions. Fo each model
pa ame e , we ini ialized ou simula ion chains and an 20,000 i e -
a ions, disca ding he i s 10,000 samples o each chain as bu n- in.
Ma ko chains we e hinned o e e y 20 h i e a ion. Con e gence o
he MCMC simula ions was good o each pa ame e as indica ed by
he low

R
alues (i.e., <1.1; Gelman e al., 2003; see Tables 1 and 2; see
also Table S2).
Bayesian analyses as desc ibed abo e we e pe o med sepa a ely
o each communi y; below hese a e called i s Bayes, he pos e io s
o which o m he basis o subsequen Bayesian analyses (nex sec-
ion); second Bayes we e pe o med in o de o compa e popula ion
pa ame e s be ween con inen s as well as guilds.
In o de o e eal he dis ibu ion o con inen e ec coe icien o
species- o species pai - speci ic popula ion dynamical pa ame e s, we
designed second Bayes model based on i s Bayes (abo e) pos e io
means and s anda d de ia ions. A simila p ocedu e was ollowed o
compa isons o guild e ec coe icien s sepa a ely o Eu opean and
No h Ame ican duck popula ion ime se ies. We used Bayesian mixed
model o mula ed as ollows:
whe e πx is second Bayes es ima e ep esen ing one o he pa am-
e e s Ci,i, Ii, o P op(Ii) (eqs. 3–5; see also Tables 1 and 2), he pa ame-
e s being speci ic o each species (i) and communi y. Each communi y
and species combina ion is indica ed by subsc ip x. Pa ame e αz is
andom e m ep esen ing a ia ion be ween communi ies, sub-
sc ip z indica ing communi y. The andom e m is speci ied as
α
z∼No mal(μ,σ
2
α)
wi h nonin o ma i e p io s
μ∼No mal(0, 10,000)
and
σα∼Uni o m(0, 10)
. Pa ame e β accoun s o he e ec o
con inen indica ed by dummy a iable cx (0 = Eu ope, 1 = No h
Ame ica); εx is esidual e o . Nonin o ma i e p io s we e se
as ollows:
β∼No mal(0, 10,000)
and
𝜀
x∼No mal(0, σ
2
ε)
, whe e
σε∼Uni o m(0, 10)
. The s uc u e o equa ion (7) is mixed model ha
includes bo h andom and ixed e ec s (Ke’ y & Schaub, 2012; Zuu ,
Ieno, Walke , Sa elie , & Smi h, 2009).
The obse a ion model is w i en as ollows:
whe e px is he pos e io mean ( o each x) o inspec ed popula ion
pa ame e aken om i s Bayes; s anda d de ia ions σp,x a e in o m-
a i e p io s based on co esponding i s Bayes pos e io s ( o in o m-
a i e p io s, see Ké y & Royle, 2016; McCa hy & Mas e s, 2005). The
compa ison o guilds based on da ase s om Eu ope was simila as
explained abo e ( o eq. 7), bu cx was eplaced by dummy a iable
indica ing di e en guilds (0 = dabbling, 1 = di ing), and o cou se,
e ms o con inen e ec we e omi ed. In No h Ame ican da ase s,
he e we e only wo communi ies. Thus, andom e m was changed o
a ac o ial dummy a iable, and an in e cep e m was included wi h
espec i e pa ame e s de ined simila ly as β abo e (eq. 7).
Second Bayes was pe o med wi h R package R2jags unning p o-
g am JAGS e sion 3.4.0 (Plumme , 2003). In second Bayes, ou simu-
la ion chains we e ini ialized and 20,000 i e a ions we e un, and he
i s 10,000 samples o each chain we e disca ded as bu n- in. Ma ko
chain hinning was se o e ain e e y 20 h i e a ion. Fo he s ep- by-
s ep speci ica ion o p ocedu es and he s uc u e o all models, see
Table S3.
3 | RESULTS
Popula ion a iabili y appea ed o be lowe in dabbling ducks han
in di ing ducks bu compa able be ween con inen s o bo h guilds
(dabbling ducks; Eu ope, 0.417 ± 0.021, n = 41; No h Ame ica,
0.442 ± 0.030, n = 12; di ing ducks; Eu ope, 0.576 ± 0.028, n = 15;
No h Ame ica, 0.569 ± 0.070, n = 4).
(4)
I
i=
(
i
k
i)2
Va (ni)
,
(5)
P op
(Ii)=
I
i
Ii+Ci
,
i
.
(6)
y
i,
|
ni, ∼No mal
(
ni, ,τ2
i
),
(7)
πx=αz+βcx+εx
p
x∼No mal
(
πx,σ2
p,x
)

|
7009
Pöysä e al.
All in all, he con ibu ion o en i onmen al a iabili y (Ci,i) o popu-
la ion dynamics was g ea e han ha o densi y dependence and also
g ea e in No h Ame ica han in Eu ope (Fig. 2, Table 1). In addi ion,
be ween- species (species pai s) co a iances in en i onmen al a iabil-
i y wi hin communi ies we e g ea e in No h Ame ican han in Eu ope
(see Fig. S1). The con ibu ion o densi y dependence (Ii) o popula-
ion dynamics was only somewha g ea e in Eu ope han in No h
Ame ica (Table 1), al hough i was gene ally low (Fig. 2; see also Fig. 3).
As a consequence, he p opo ion o a ia ion due o densi y depen-
dence in popula ion dynamics (P op(Ii)) was less in No h Ame ica han
in Eu ope (Fig. 2, Table 1); species- and si e- speci ic pos e io means
anged om 3.8% o 24.5% in No h Ame ica and om 3.6% o 54.7%
in Eu ope (Figs 2 and 3, “p op.in a”).
The con ibu ion o en i onmen al a iabili y o popula ion dynam-
ics was g ea e in di ing ducks han in dabbling ducks in bo h Eu ope
and No h Ame ica, bu he di e ence was no clea in he la e con i-
nen (Figs 2 and 3, Table 2). By con as , di e ences be ween dabbling
ducks and di ing ducks in he con ibu ion o densi y dependence
we e no clea in he Eu opean da a, no we e hey pa icula ly clea
in he No h Ame ican ime se ies (Figs 2 and 3, Table 2). Howe e ,
he p opo ion o a ia ion due o densi y dependence in popula ion
dynamics was g ea e in dabbling ducks han in di ing ducks in Eu ope.
Demog aphic s ochas ici y appea ed o be simila in he Eu opean
and No h Ame ican duck communi ies (see Fig. S2).
4 | DISCUSSION
Ou main indings can be summa ized as ollows. Fi s , con a y o
expec a ions, popula ions in he mo e s able en i onmen s o no h-
e n Eu ope did no show lowe a iabili y (PV) and showed only
sligh ly mo e densi y dependence- d i en dynamics han popula ions
li ing in he highly a iable en i onmen s o No h Ame ican p ai ies.
Second, he con ibu ion o en i onmen al a iabili y o popula ion
dynamics was highe in No h Ame ica han in Eu ope, a inding in
TABLE2 Guild e ec coe icien s based on second Bayes (see
Me hods) o he sepa a e con ibu ions o en i onmen al a iabili y
(Ci,i) and densi y dependence (Ii) o popula ion dynamics in duck
popula ion coun s and o he p opo ion o densi y dependence
(P op(Ii)) o he o al a iance explained by en i onmen al a iabili y
and densi y dependence o popula ion dynamics
Pa ame e
Guild e ec coe icien

R
pMean SD
Eu ope
Ci,i 0.034 0.022 1.0025 .948
Ii−0.003 0.007 1.0021 .661
P op(Ii) −0.068 0.034 1.0003 .980
No h Ame ica
Ci,i 0.098 0.095 1.0005 .855
Ii0.015 0.026 1.0017 .710
P op(Ii)0.062 0.067 1.0021 .828
Mean and s anda d de ia ion o he coe icien s a e gi en as well as

R
al-
ues desc ibing he con e gence o he MCMC simula ions. Righ mos col-
umn (p) gi es p obabili ies ha he coe icien de ia es om ze o;
p obabili ies we e de i ed om he pos e io dis ibu ion o each
coe icien .
FIGURE2 The sepa a e con ibu ions o en i onmen al a iabili y
(Ci,i; en . a ) and densi y dependence (Ii; in a) o popula ion
dynamics and he p opo ion o densi y dependence o he o al
a iance explained by densi y dependence and en i onmen al
a iabili y o popula ion dynamics (i.e., Ii/(Ii + Ci,i); p op.in a) in
dabbling duck (Dabbling) and di ing duck (Di ing) popula ion ime
se ies o no he n Eu ope (Eu ope) and No h Ame ican p ai ies
(No h Am.). The uppe whiske ex ends o he highes alue ha is
wi hin 1.5 × IQR, whe e IQR is he in e qua ile ange, o dis ance
be ween he i s and hi d qua iles, as indica ed by he hinge. The
lowe whiske ex ends o he lowes alue wi hin 1.5 × IQR. Da a
beyond he whiske ends a e ou lie s and plo ed as poin s. Da a
poin s exp ess species- and si e- speci ic alues
TABLE1 Con inen e ec coe icien s based on second Bayes
(see Me hods) o he sepa a e con ibu ions o en i onmen al
a iabili y (Ci,i) and densi y dependence (Ii) o popula ion dynamics in
duck popula ion coun s and o he p opo ion o densi y
dependence (P op(Ii)) o he o al a iance explained by
en i onmen al a iabili y and densi y dependence o popula ion
dynamics
Pa ame e
Con inen e ec coe icien

R
pMean SD
Ci,i 0.070 0.034 1.0010 .979
Ii−0.010 0.017 1.0012 .738
P op(Ii) −0.088 0.065 1.0019 .934
Mean and s anda d de ia ion o he coe icien s a e gi en as well as

R
alues
desc ibing he con e gence o he MCMC simula ions. Righ mos column
(p) gi es p obabili ies ha he coe icien de ia es om ze o; p obabili ies
we e de i ed om he pos e io dis ibu ion o each coe icien .
7010
|
Pöysä e al.
line wi h expec a ions conce ning he o e all impo ance o en i on-
men al s ochas ici y in popula ion dynamics. Thi d, popula ions o
p esumed “slow species” (di ing ducks) we e less s able and did no
show mo e densi y dependen - d i en dynamics han popula ions o
p esumed “ as species” (dabbling ducks). As a co olla y, he con ibu-
ion o en i onmen al a iabili y o popula ion dynamics was highe ,
and hence, he p opo ion o a ia ion due o densi y dependence in
popula ion dynamics was lowe , in “slow species” han in “ as spe-
cies” in Eu ope. These la e indings in p inciple con adic ou sec-
ond p edic ion conce ning he impo ance o li e his o y in media ing
popula ion dynamical esponses o en i onmen al a ia ion.
We es ic ed analyses o duck coun s by esea che s on he
g ound, yielding s udies om wo si es in No h Ame ica and ou in
Eu ope (Finland). This in i es c i icism ha hey migh no be ep e-
sen a i e o duck dynamics o hese wo guilds and hus whe he
ou indings can be gene alized o addi ional local popula ions o e
la ge spa ial scales. In he No h Ame ican p ai ies, he pa e ns o
popula ion dynamics a e ep esen a i e o he la ge p ai ie biome,
especially compa ed o egions whe e we land numbe s luc ua e
less, as con i med by many s udies o duck popula ion dynamics using
da a collec ed du ing ae ial su eys o e e y wide egions (Be hke
& Nudds, 1995; D e e , 2006; Sæ he e al., 2008). Co esponding
la ge- scale da a and analyses a e no a ailable om Eu ope. Howe e ,
da a om he Finnish wa e owl moni o ing p og am, ex ending o e
he en i e coun y (see Pöysä, Rin ala, Lehikoinen, & Väisänen, 2013),
make i possible o assess he ep esen a i eness o he Finnish s udy
si es a he na ional scale. To do ha , we co ela ed he annual si e-
speci ic pai numbe s (pooled wi hin each o he ou si es o his s udy)
o each species wi h he annual abundance indices om he na ional
moni o ing p og am (bo h da ase s om 1986–2009). We ound ha ,
in gene al, be ween- yea a ia ion in he si e- and species- speci ic
ime se ies co ela ed well wi h ha in he na ional abundance indi-
ces (mean co ela ion coe icien , = .466, ange −.170 o .810, n = 28
si e- and species- speci ic ime se ies). Fu he mo e, because he ducks
b eeding in Finland encompass a high p opo ion o he o al Eu opean
popula ion o many o he species s udied he e (see Hagemeije &
Blai , 1997), he popula ion dynamics o Finnish ducks should e lec
easonably well he dynamics o ducks b eeding in s able Eu opean
lakes. Thus, we a e com o able ha he long- e m da a om hese
si es a e ep esen a i e and ha he implica ion ha ou in e ences
FIGURE3 The sepa a e con ibu ions o en i onmen al a iabili y (Ci,i; en . a ) and densi y dependence (Ii; in a) o popula ion dynamics
and he p opo ion o densi y dependence o he o al a iance explained by densi y dependence and en i onmen al a iabili y o popula ion
dynamics (i.e., Ii/(Ii + Ci,i); p op.in a) in six species pai s o dabbling ducks ( i s six panels om he le ) and wo species pai s o di ing ducks
(las wo panels on he igh ) o no he n Eu ope (Eu ope) and No h Ame ican p ai ies (No h Am.). Same species o ma ched species [close
ecological coun e pa s] om Eu ope and No h Ame ica included ( o species, see Me hods). The uppe whiske ex ends o he highes alue
ha is wi hin 1.5 × IQR, whe e IQR is he in e qua ile ange, o dis ance be ween he i s and hi d qua iles, as indica ed by he hinge. The
lowe whiske ex ends o he lowes alue wi hin 1.5 × IQR. Da a beyond he whiske ends a e ou lie s and plo ed as poin s. Da a poin s
exp ess species- and si e- speci ic alues
|
7011
Pöysä e al.
gene alize o o he local popula ions ac oss b oad geog aphic scales
bo h in No h Ame ica and in no he n Eu ope.
Ou s udy did no p o ide suppo o he idea ha low popula-
ion a iabili y is associa ed wi h s ong densi y- dependen egula-
ion; popula ions o dabbling ducks appea ed o be less a iable, bu
did no show s onge densi y dependence. Compa isons wi h ea lie
s udies should be ca ied ou wi h cau ion because analysis me hods
ha e changed, especially in es ima ing densi y dependence (see Koons,
Gunna sson, Schmu z, & Ro ella, 2014; Leb e on & Gimenez, 2013;
Ross e al., 2015; Roy e al., 2016). Ne e heless, Holyoak and Baillie
(1996a) ound, among B i ish bi ds, ha annual a iabili y and he
s eng h o densi y dependence we e nega i ely co ela ed, a pa e n
hey a ibu ed o a ia ion in longe i y; ha is, sho - li ed species
end o ha e g ea e annual popula ion a iabili y han long- li ed spe-
cies. Simila ly, Sæ he , Engen, and Ma hysen (2002), Sæ he , G ø an,
Engen, Noble, and F eckle on (2011) ound ha species wi h la ge
clu ch size and lowe su i al ended o ha e mo e a iable popula ions
han low- p oducing long- li ed species. The species s udied by Holyoak
and Baillie (1996a) we e axonomically di e se and a ied conside ably
in e ms o li e his o y and body size, anging om 5–6 o 500–600 g
(see Holyoak & Baillie, 1996b); species included in Sæ he e al. (2002,
2011) a ied e en mo e. The ducks s udied by us cons i u e a much
mo e homogeneous g oup, emale body masses anging app oxima ely
om 280 o 1,050 g in dabbling ducks and om 680 o 910 g in di ing
ducks (Rohwe , 1988). Finally, Williams e al. (2003) did no ind a clea
connec ion be ween popula ion a iabili y and he s eng h o densi y
dependence in h ee game bi ds species in Kansas, USA. All in all, ou
esul s and p e ious indings oge he sugges ha he e may no be a
gene al ule abou he associa ion be ween popula ion a iabili y and
densi y- dependen egula ion in bi ds (see also Sæ he e al., 2016).
Ou esul s a e gene ally con a y o con en ional wisdom abou he
ela ion be ween li e his o y and cha ac e is ics o popula ion dynam-
ics in No h Ame ican ducks (see In oduc ion). The o iginal hypo hesis
was based on li e his o y ea u es, desc ibing he s abili y o habi a s
used by each species and he co ela ion be ween species densi y and
pond densi y (see Johnson & G ie , 1988). A key ea u e o pa icula
in e es in he p esen con ex is he idea ha he se ling pa e n o a
species is assumed o be ela ed o he s abili y o he habi a i selec s.
Species li ing in a iable en i onmen s will exhibi oppo unis ic
esponses o habi a change (i.e., “ as species”), whe eas species li ing
in mo e s able en i onmen s will exhibi s ong homing endency and
be less esponsi e (i.e., “slow species”). Hence, popula ions o he o -
me ype a e expec ed o be in luenced mo e by densi y- independen
ac o s and popula ions o he la e ype mo e by densi y- dependen
ac o s (Johnson & G ie , 1988). Resul s om se e al ea lie s udies,
discussed in Johnson and G ie (1988), p o ide some suppo o his
hypo hesis (Bailey, 1981; Pa e son, 1979; Vicke y & Nudds, 1984),
while mo e ecen s udies do no (Law ence e al., 2013; Mu ay e al.,
2010). Ne e heless, conside ing he d ama ic di e ence in en i on-
men al a iabili y be ween he Eu opean and No h Ame ican s udy
a eas (Fig. 1), ou esul s we e su p ising in ha Eu opean duck popu-
la ions, in gene al, we e no mo e s able, no mo e s ongly go e ned
by densi y dependence, han No h Ame ican popula ions. Equally
su p ising, in no he n Eu ope, popula ions o species gene ally con-
side ed “slow” (di ing ducks) we e no mo e s able and did no exhibi
mo e densi y dependen - d i en dynamics han popula ions o p e-
sumed “ as ” species (dabbling ducks). In o ma ion on homing a e in
Eu opean ducks is limi ed, bu ex ensi e cap u e– ecap u e and band
eco e y da a om one we land a ea in La ia sugges ha b eeding
emales o he wo di ing duck species included in ou analyses (i.e.,
Pocha d and Tu ed Duck) ha e e y high ideli y a es, as does he
No he n Sho ele , a dabbling duck (Blums, Nichols, Hines, & Mednis,
2002). Low demog aphic s ochas ici y in bo h con inen s (Fig. S2) also
sugges s high ideli y a es. Low homing a e may hus no explain he
ela i ely high popula ion a iabili y and weak con ibu ion o densi y
dependence obse ed in he Eu opean di ing ducks.
Ou inding ha popula ion coun s o ducks did no indica e pa -
icula ly high impo ance o densi y dependence co obo a es he ind-
ings o Law ence e al. (2013) and Sæ he e al. (2008), who analyzed
la ge- scale species abundance da a om No h Ame ican b eeding
duck su eys (see also Roy e al., 2016). Weak densi y dependence is
somewha unexpec ed, howe e , because he e a e bo h expe imen al
and obse a ional e idences o densi y dependence in c ucial demo-
g aphic pa ame e s, especially o Eu opean dabbling ducks ( e iew
in Gunna sson e al., 2013). On he o he hand, li le is known abou
densi y dependence o i al a es in he di ing duck species s udied
he e, and in o ma ion abou densi y dependence o i al a es o
No h Ame ica ducks in gene al is scan (see Gunna sson e al., 2013).
In e es ingly, using demog aphic and popula ion da a om 13 bi d spe-
cies o he han ducks, Sæ he e al. (2016) ound ha , e en hough
densi y dependence in su i al in luenced popula ion egula ion, en i-
onmen al s ochas ici y a he han a ia ion in he s eng h o densi y
dependence was he majo ac o a ec ing in e speci ic di e ences in
popula ion a iabili y. A any a e, ou esul s sugges ha ea lie ind-
ings om No h Ame ican ducks may no be gene ally applicable, a
leas no o Eu opean ducks. Because dabbling ducks and di ing ducks
b eed in he same s able en i onmen s in no he n Eu ope, en i on-
men al a iabili y, as measu ed as be ween- yea a iabili y in we land
numbe s, canno be he p ima y d i ing ac o o he di e ence in
popula ion a iabili y be ween he guilds. We ocused on only one
aspec o en i onmen al a iabili y and on b eeding g ounds, al hough
he cha ac e is ics add essed a guably a e c ucial o ducks. Ob iously,
he e a e o he in luen ial and a iable exogenous ac o s such as, o
ins ance, condi ions on win e g ounds (e.g., Kauppinen & Väänänen,
1999; Pöysä & Väänänen, 2014), whose ole in a ec ing duck popula-
ion a iabili y and dynamics should be add essed in u u e s udies (see
also Koons e al., 2014). In addi ion, due o demog aphic s ochas ici y,
popula ions may luc ua e conside ably e en in a seemingly cons an
en i onmen , especially a small popula ion sizes like hose in he p es-
en s udy (see Table S1). Howe e , he con ibu ion o demog aphic
s ochas ici y o popula ion dynamics was es ima ed o be ela i ely
weak and o simila magni ude in Eu ope and No h Ame ica.
In gene al, i espec i e o con inen and guild, en i onmen al a i-
abili y was mo e impo an han densi y dependence in d i ing popu-
la ion dynamics o ducks, accoun ing o be ween ca. 45% and 95% o
he o al a iance explained by hese wo a iance componen s. The
7012
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Pöysä e al.
e ec o en i onmen al a iabili y on popula ion dynamics depends on
he empo al s uc u e o he a ia ion and he esponsi eness o he
species o i (Roughga den, 1975; Ripa & Heino, 1999; Schwage e al.,
2006). In gene al, popula ion a iabili y should inc ease wi h espon-
si eness o he species. Howe e , i he en i onmen al a iabili y is
highly p edic able, he in luence o esponsi eness is educed; ha is,
bo h “ esponsi e” and “sluggish” species (sensu Roughga den, 1975)
a e able o ack he a ia ion in he en i onmen . On he o he hand,
in an unp edic able en i onmen , popula ion dynamics o a species is
go e ned mainly by i s esponsi eness o en i onmen al a ia ion (see
Roughga den, 1975). The b eeding en i onmen s o he No h Ame ican
ducks s udied he e exhibi a iabili y ha is wo h discussing in ligh
o hese ideas. The co ela ion in he numbe o May ponds be ween
consecu i e yea s was weak in Johnson’s (1995) s udy a ea (see Fig. 1;
au oco ela ion wi h a lag o 1 yea , = −.005), indica ing unp edic able
en i onmen on 1- yea ime scale (i.e., “whi e noise,” e.g., Roughga den,
1975; Ruokolainen, Lindén, Kai ala, & Fowle , 2009). Johnson (1995)
ound ha he numbe o b eeding pai s o ducks in he s udy a ea was
posi i ely co ela ed wi h May ponds in he same yea o all o he eigh
species included he e, bu signi ican ly so o only Blue- winged Teal and
No he n Sho ele . Lei ch and Kaminski (1985) ound in hei s udy a ea
in Saska chewan, Canada, ha he co esponding co ela ion was sig-
ni ican o all he species included he e, excep he Malla d, No he n
Sho ele , and No he n Pin ail. On he con a y, Sæ he e al. (2008)
ound ha he con ibu ion o he empo al a ia ion in pond numbe s
o annual changes in popula ion size o No h Ame ican p ai ie ducks
was gene ally small, excep o he Malla d. On he o he hand, hese
au ho s also ound ha popula ion a iabili y dec eased wi h dec eas-
ing en i onmen al a iabili y, due o lessening luc ua ion in pond num-
be s, in ou o he six dabbling duck species s udied; hese indings
we e associa ed wi h la i udinal g adien s in en i onmen al co a ia es
and duck popula ion dynamics in a complex way (see Sæ he e al.,
2008 o a comp ehensi e discussion; see also Feldman e al., 2015).
In sum, cu en knowledge o he esponsi eness o di e en species
o he annual a ia ion in pond numbe s does no allow gene aliza ions
abou di e ences be ween dabbling and di ing ducks in popula ion
dynamics. Mo eo e , in addi ion o he di ec esponse o b eeding
numbe s o a ia ion in pond numbe s, demog aphic esponses also a e
o be expec ed, and hei ole in d i ing popula ion dynamics may di e
be ween p ai ie- nes ing dabbling and di ing ducks (e.g., see discussion
in Pé on e al., 2012).
In conclusion, we compa ed basic popula ion dynamic cha ac e is-
ics o he same species o close ecological coun e pa s be ween wo
sys ems di e ing d as ically in a iabili y o an en i onmen al ac o
ecognized o be in luen ial in ea lie s udies o duck popula ions in
one o he sys ems. We ound ha basic dynamics ( empo al a ia ion
in popula ion size and densi y dependence) o he popula ions in he
sys em in which ha pa icula en i onmen al a iabili y is absen was
indis inguishable om he dynamics o he popula ions in he highly
a iable sys em. Fu he mo e, i espec i e o con inen and guild,
en i onmen al s ochas ici y was mo e impo an han densi y depen-
dence in d i ing popula ion dynamics o ducks. These indings lead
o a mo e gene al conclusion, joining he sugges ion by K ebs (2002),
ha we need mo e da a and s udies on popula ions o he same spe-
cies in di e en en i onmen s o e i y he gene ali y o ou explana-
ions abou popula ion dynamics.
ACKNOWLEDGMENTS
We hank Ma c Ké y o aluable ad ice in Bayesian analysis and wo
anonymous e e ees o use ul sugges ions o imp o e he manusc ip .
CONFLICT OF INTEREST
None decla ed.
FUNDING INFORMATION
None decla ed.
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