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Mar Biol (2017) 164:149 DOI 10.1007/s00227-017-3177-y

ORIGINAL PAPER

Shallow divers, deep waters and the rise of behavioural stochasticity

Xavier Meyer1 · Andrew J. J. MacIntosh2,3 · Andre Chiaradia4 · Akiko Kato5 · Thomas Mattern6 · Cédric Sueur1 · Yan Ropert‑Coudert5

Received: 13 February 2017 / Accepted: 31 May 2017 © Springer-Verlag GmbH Germany 2017

associated with bathymetry in local foraging areas; little penguins foraging in deeper waters produced more sto-chastic/less deterministic foraging sequences than those foraging in shallower waters. Corresponding data on fledg-ing success suggest that little penguins foraging in deeper waters also experienced reduced reproductive success. A principal component analysis further showed that our frac-tal scaling index, which specifically measured the degree to which sequences are long-range dependent (a determinis-tic phenomenon), correlated positively with foraging effi-ciency (prey encounter per unit time) and negatively with foraging effort (total time underwater). Our statistical mod-els showed that production of complex foraging sequences with high degrees of stochasticity appears to be energy intensive. However, we could not determine which strat-egy would have maximized foraging success, a variable we could not measure, under the conditions observed. We pro-pose that increasing stochastic elements in foraging behav-iour may be necessary under challenging environmental conditions, but it may not be sufficient to match fitness gains attained under more favourable conditions.

Introduction

Diversity in marine habitats induces variability in prey dis-tributions across time and space (Weimerskirch 2007). This has multiple and complex effects on the foraging behaviour of marine predators, including seabirds (Morrisson et al. 1990). For instance, seabirds require flexibility in their for-aging behaviour to catch mobile prey (Williams et al. 1992; Hull 2000). They use a variety of hunting tactics to pursue prey, including plunge diving, dipping and pursuit diving (Shealer 2002). Among diving seabirds, penguins occupy diverse habitats across their range and thus must adapt to

Abstract Little penguins (Eudyptula minor) have one of the widest geographic distributions among penguins, exposing them to variable ecological constraints across their range, which in turn can affect their foraging behav-iour. Presumably, behavioural flexibility exists to allow animals to adapt to prevailing environmental conditions throughout their foraging range. This study examined whether complexity in the temporal organization of forag-ing sequences corresponds to characteristics of the foraging area across four colonies geographically distributed along the entire species’ range. Complexity and fractal scal-ing in spatiotemporal patterns of foraging behaviour have been theoretically linked to foraging efficiency in hetero-geneous environments. Using fractal time series methods (detrended fluctuation analysis), we found that foraging complexity along a stochastic–deterministic gradient was

Responsible Editor V.H. Paiva.

Reviewed by: A. McInnes and an undisclosed expert.

* Xavier Meyer xavier.g.meyer@gmail.com

1 Université de Strasbourg, CNRS, IPHC UMR 7178, 23 Rue Becquerel, 67087 Strasbourg, France

2 Kyoto University Wildlife Research Center, 2-24 Tanaka-Sekiden-cho, Sakyo, Kyoto 606-8203, Japan

3 Kyoto University Primate Research Institute, Kanrin 41-2, Inuyama, Aichi 484-8506, Japan

4 Research Department, Phillip Island Nature Parks, P.O. Box 97, Cowes 3922, Victoria, Australia

5 Centre d’Etudes Biologiques de Chizé, CNRS, UMR 7372, 79360 Villiers-en-Bois, France

6 Department of Zoology, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand

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such diversity. Breeding penguins, like other central place foragers, are restricted to certain foraging zones and are constrained by a diverse set of physical parameters, such as sea ice (Watanuki et al. 1997), bathymetry (Chiaradia et al. 2007) and marine currents (Bost et al. 2009). For example, the foraging (diving) behaviour of rockhopper penguins (Eudyptes chrysocome) varies significantly among popu-lations breeding on three subantarctic archipelagos in the Indian Ocean (Tremblay and Cherel 2003). Similarly, gen-too penguins (Pygoscelis papua) exhibit extensive varia-tion in foraging behaviour between colonies, even within the same archipelago when they have variable access to the open sea (Lescroël and Bost 2005). These examples sug-gest that penguins at colonies across their geographic range are exposed to different ecological constraints, and this might explain the observed differences in their foraging behaviour.

Advances in bio-logging (see Ropert-Coudert and Wilson 2005; Ropert-Coudert et al. 2012) have allowed scientists to simultaneously measure a suite of foraging parameters at fine spatiotemporal scales. Foraging behav-iour can be examined in parallel to fitness indicators, such as reproductive success. A common approach to study-ing diving behaviour consists in analysing several diving variables, such as dive depths, durations and frequencies, or the numbers of undulations at the bottom phase of the dives (e.g. Ropert-Coudert et al. 2001). This approach to diving analysis have provided useful quantitative informa-tion on foraging behaviour, despite that inter-related met-rics can be difficult to interpret (Zimmer et al. 2011). Thus, novel analytical approaches using methods from the field of statistical physics have been developed that treat animal behaviour as part of an adaptive system aimed at mediating biological encounters (reviewed in MacIntosh 2014).

Optimal foraging theory stipulates that animals may adopt foraging patterns that maximize their rates of energy intake (MacArthur and Pianka 1966). More recently, it has been hypothesized that the super-diffusive and fractal prop-erties of Lévy movements, which are performed by animals as diverse as slime moulds, ants and humans, may reflect an evolved strategy that optimizes resource encounters, and thus energy balance, in heterogeneous environments (the Lévy flight foraging hypothesis—LFFH; Viswanathan et al. 1999, 2008; Bartumeus et al. 2005; Bartumeus 2007, 2009; Sims et al. 2010; Humphries et al. 2010). Debate still exists on whether these Lévy patterns actually reflect an underlying search algorithm or if they simply emerge from animal–environment interactions (Benhamou 2007; Sueur 2011; Pyke 2015; Reynolds 2015). However, the LFFH has fuelled numerous studies conducting spatial fractal analysis of animal movement data, and it seems clear that Lévy pat-terns do commonly emerge across a wide variety of taxa (Reynolds 2015).

While these studies have demonstrated Lévy patterns and thus fractal scaling in the step-length distributions of animal movements, another relatively novel approach is to investigate fractal properties in time-series of animal behaviour as a measure of complexity. In this case, behav-iour is modelled along a stochastic-deterministic gradient in which the degree of stochasticity or determinism (i.e. the complexity signature) can be linked to factors both intrinsic and extrinsic to the animal (MacIntosh 2014). Using this framework, several studies have shown that certain com-plexity signatures should optimize foraging efficiency with respect to biological encounters (Shimada et al. 1993, 1995; Cole 1995; Escos et al. 1995; Rutherford et al. 2004; Hock-ing et al. 2007; MacIntosh et al. 2011; Seuront and Cribb 2011). These complexity signatures are known to vary in animals experiencing stress, disease, a new environment, or a change in resources (MacIntosh 2014; Seuront and Cribb 2017). Thus, complexity signatures may generally have the capacity to act as behavioural indicators of animal condi-tion and performance (Rutherford et al. 2004; Asher et al. 2009; MacIntosh 2014; Cribb and Seuront 2016). Moreo-ver, balancing the stochastic and deterministic elements in behaviour sequences may be critical in the emergence and maintenance of behavioural flexibility (MacIntosh 2015; Reynolds et al. 2015). Methods that measure such com-plexity can thus complement classic methods used to inves-tigate diving behaviour and its flexibility in diving seabirds. Moreover, time series analyses can measure fundamental organizational/structural properties of behaviour, rather than using derived statistics such as means and durations of behavioural variables.

Here, we applied fractal time series analysis to diving sequences recorded using time-depth recorders attached to little penguins (Eudyptula minor) at four colonies across the species’ geographic range (Chiaradia et al. 2007). We tested whether observed complexity signatures correspond to distinct environmental conditions. Factors commonly expected to influence diving behaviour, such as bathymetry and primary production (Chiaradia et al. 2007; Afán et al. 2015), are known to vary across colonies. Chlorophyll-a concentration can be a reliable proxy of marine productiv-ity (Tynan 1998; Afán et al. 2015), while bathymetry pro-vides relevant information on physical processes or oceano-graphic features driving prey distribution (Hunt et al. 1998; Russell et al. 1999; Ladd et al. 2005; Benoit-Bird et al. 2013; Boyd et al. 2015). In our four studied colonies, lit-tle penguins feed predominately on similar types of small, schooling pelagic fish, mainly clupeiformes (Stahel and Gales 1987; Klomp and Wooller 1988; Cullen et al. 1992; Chiaradia et al. 2003, 2010, 2012, 2016; Fraser and Lalas 2004; Fleming et al. 2013; Poupart et al. 2017), which can be distributed from the surface to depths of 200 m (Kailola et al. 1993). We hypothesized that penguins would show

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increasing stochasticity in their foraging sequences while feeding in habitats characterized by deeper waters, where prey may be more difficult to locate and capture (Kokubun et al. 2010). Stochasticity should also increase in less pro-ductive waters where prey patches are expected to be more dispersed and less numerous (Kowalczyk et al. 2015a, b). In summary, we predict that penguins will show increased elements of stochasticity in their foraging behaviour in response to challenging environmental conditions.

Methods

Study subjects and colonies

The study was conducted on little penguins from four dif-ferent breeding colonies located across their entire geo-graphic range (Fig. 1). Data come from different years and have different sample sizes, concerning both the number of individuals sampled and the number of foraging trips recorded (Table 1). Data were collected at two colonies in Australia sampled in both 2001 and 2002 (Penguin Island: 32°18′S, 115°41′E; Phillip Island: 38°21′, 145°09′E), and two colonies in New Zealand, both sampled in 2000 (Oamaru: 45°07′S, 170°59′E; and Motuara Island: 41°06′S, 174°17′E) (see Fig. 1 and Table 1). Sampling at all colonies occurred during the guard stage with penguins rearing 1 or 2 chicks, with foraging trips lasting for 1 day only. Thus, birds from all colonies faced similar constraints on forag-ing trip duration and maximum foraging range.

Diving activity was monitored using three data log-gers of slightly different sizes at 2 s sampling intervals (Table 1). We acknowledge that loggers of different sizes may exhibit some influence on diving behaviour in little

penguins (Ropert-Coudert et al. 2007). We previously demonstrated that little penguins equipped with larger loggers produced more stochastic dive sequences than those with smaller loggers (Meyer et al. 2015). Unfor-tunately, as logger size varied as a function of the study design within each colony, we were unable to separate logger size effects from inter-colony effects in this study (see “Discussion”).

The four colonies differed in available foraging area, based on the proportion of water/land found within a 25–30 km radius of the breeding sites (Fig. 2). This radius corresponds to the mean maximum distance that a little penguin can travel in a 1-day trip, ca. 25–30 km (Collins et al. 1999; Hoskins et al. 2008; Pelletier et al. 2014). Phillip Island displayed the highest proportion of available foraging area (89%), followed by Penguin Island (65%), Motuara Island (62%) and Oamaru (51%) (Table 1, Chiaradia et al. 2007). Bathymetry grids in each colony’s foraging area were obtained from Geoscience Australia (2017) and Mitchell et al. (2012), and extracted using the package ‘rgdal’ (Bivand et al. 2016), ‘raster’ (Hijmans et al. 2016), ‘rgeos’ (Bivand et al. 2017) and ‘marmap’ (Pante and Simon-Bouhet 2013) in R statisti-cal software v.3.3.2 (R Development Core Team 2016). Grid resolution was 0.0025° (~250 m at the equator) for Australia and 250 m for New Zealand. Isobaths were defined every 10 m and used to categorize foraging area by depth (e.g. percentage of foraging area between 0 and 10 m, 11 and 20, 21 and 30, 31 and 40, and 41 and 50 m depths, etc.). To characterize the bathymetry around each colony, we then calculated a bathymetry evenness index (E), which can be represented by the following formula:

E =H

′/

H′

max,

Fig. 1 Location of the four Little Penguin colonies (black dots) in Australia and New Zealand.Map was created using Maptool in Seaturtle.org (2002)

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Tabl

e 1

Yea

r, sa

mpl

e nu

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rs,

sex,

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sed

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our

loca

tions

in

this

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dy (

Ada

pted

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m

Chi

arad

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t al.

2007

)

a The

dim

ensi

ons

are

give

n in

leng

th a

nd d

iam

eter

for

cyl

indr

ical

logg

ers

b The

dim

ensi

ons

are

give

n in

leng

th, w

idth

and

dia

met

er f

or r

ecta

ngul

ar lo

gger

sc F

orag

ing

area

is th

e ar

ea a

vaila

ble

for

fora

ging

in a

rad

ius

of 2

5–30

km

aro

und

the

colo

ny (

see

text

)d F

ledg

ing

succ

ess

at P

engu

in I

slan

d is

bas

ed o

n hi

stor

ical

dat

a (W

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et a

l. 19

95)

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n Is

land

Phill

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ra I

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d

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01 a

nd 2

002

2001

and

200

220

0020

00

Num

bers

of

peng

uins

[nu

mbe

r of

tr

ips]

8 [9

]21

[28

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[9]

4 [7

]

Mal

e/fe

mal

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411

/10

2/2

3/1

Log

ger

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2GT,

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le L

eona

rdo,

Ja

pan.

52

mm

× 1

5mm

a , 16

gLT

D 1

200-

100,

Lot

ek, C

anad

a.

62 m

m ×

18

mm

a , 17

gM

K7,

Wild

life

Com

pute

rs, U

SA.

65 m

m ×

12

mm

× 8

mm

b , 32

gM

K7,

Wild

life

Com

pute

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SA.

65 m

m ×

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× 8

mm

b , 32

g

Log

ger’

s pe

rcen

t of

the

Peng

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s fr

onta

l are

a (%

)3.

44.

91.

81.

8

Fora

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are

a av

aila

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(%)c

6589

5162

Mea

n de

pth

(m)

27.1

± 0

.10

65.7

± 0

.08

29.3

± 0

.12

108.

4 ±

0.5

5

Mea

n di

ve d

epth

(m

)6 ±

3.5

013

± 3

.90

5 ±

0.9

011

± 2

.70

E-i

ndex

0.80

0.57

0.91

0.90

Fled

ging

suc

cess

0.7d

0.5

0.8

0.5

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where H′ is the number derived from the Shannon diver-sity index:

where pi is the proportion of foraging area to the ith depth. H ′

max is the maximum possible value of H′ (if every foraging area depth was equally likely) and is equal to log2 S where S is the total number of depth categories. Evenness (E) varies from 0 to 1, expressing how depth is distributed across the foraging area. Foraging areas

H′=

R∑

i=1

pi log2 pi,

with equally distributed depths will be characterized by a higher bathymetry E than regions in which bathymetry is skewed toward a specific depth. For example, if a for-aging area is characterized by numerous depth catego-ries but a certain depth category (e.g. 50 m) dominates in the frequency distribution, E will tend toward 0. Alter-natively, if a foraging area is characterized by several equally distributed depth categories (e.g. 10, 20, 30, 40 and 50 m), E will tend toward 1.

Fledging success records for Phillip Island, Motuara Island and Oamaru were based on contemporaneous data (Chiaradia et al. 2007), while that for Penguin Island was

Fig. 2 Bathymetry and foraging area of a Penguin Island, b Phillip Island, c Oamaru and d Motuara Island. Each map created using the ‘marmap’ package (Pante and Simon-Bouhet 2013) in R statistical

software v.3.3.2 (R Development Core Team 2016) with the NOAA ETOPO1 1 arc-minute global relief model (Amante and Eakins 2009)

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based on historical data (Wienecke et al. 1995). Caution should be taken regarding Penguin Island historical data, therefore, as such data may not reflect the fledging success of the year of data collection.

Among the numerous parameters that could influence prey distribution and abundance, we restricted our analy-ses to those involving primary productivity. Following Berlincourt and Arnould (2015), we obtained chlorophyll-a concentrations by averaging chlorophyll-a data on an 8-day composite basis at a resolution of 0.1° in each for-aging area from satellite Orbiew-2 SeaWiFS measurements (National Oceanic and Atmospheric Administration 2015). Further details on colonies, field protocols and loggers can be found in Mattern (2001; Oamaru and Motuara Island), Ropert-Coudert et al. (2003; Penguin Island) and Chiaradia et al. (2007; Phillip Island). Finally, while it is known that the thermal structure of the water column plays a signifi-cant role in mediating the distribution of prey available to penguins (Ropert-Coudert et al. 2009; Pelletier et al. 2012; McInnes et al. 2017), this is a difficult parameter to calcu-late at a scale fine enough to match the behaviour of the birds, and was thus not included in our analyses.

Fractal analyses

We used detrended fluctuation analysis (DFA; Peng et al. 1992, 1995) to investigate long-range dependence (auto-correlation) in the sequential distribution of little pen-guin dives and surface times during foraging (MacIntosh et al. 2013; Cottin et al. 2014; Meyer et al. 2015). DFA is one of the more robust estimators of the Hurst expo-nent (Canon et al. 1997), a scaling exponent that meas-ures self-affinity across scales in time series data. The scaling exponent calculated by DFA (αDFA) measures the slope of the line on a double logarithmic plot of aver-age fluctuation as a function of scale (Taqqu et al. 1995; Cannon et al. 1997). Figure 3 illustrates the process of DFA using representative little penguins from the Phillip Island colony. Values of αDFA are bound between 0 and 1 for fractional Gaussian noises (fGn) and between 1 and 2 for fractional Brownian motions (fBm) (Eke et al. 2000; Delignières et al. 2005). Values in the range of 0.5–1 and 1.5–2 reflect persistence while those in the range of 0–0.5 and 1–1.5 reflect antipersistence in the time series for fGn and fBm, respectively. Values of 0.5 and 1.5 reflect Gauss-ian (white) noise and Brownian motion, respectively. Theoretically, αDFA is inversely related to the fractal dimension, which represents an index of structural com-plexity (Mandelbrot 1977). DFA was previously shown to produce reliable estimates of scaling behaviour in mul-tiple animal species (Alados and Huffman 2000; Kem-bro et al. 2009, 2013; MacIntosh et al. 2011), including

little penguin and Adélie penguin dive sequences (Mac-Intosh et al. 2013; Cottin et al. 2014). To avoid potential caveats when using DFA (Bryce and Sprague 2012), we first determined which scales should be included in our analyses following two different procedures described in Seuront (2010): the R2-SSR procedure and the compen-sated-slope procedure. In addition, we also used two other fractal methods, the box-counting method (Liebovitch and Toth 1989; Longley and Batty 1989) and another form of DFA, using a bridge-detrending method (DFAb, Cannon et al. 1997; Stroe-Kunold et al. 2009; Viswanathan et al. 2011). DFA was run using the R package ‘fractal’ (Con-stantine and Percival 2014) and box-counting with the R package ‘fractaldim’ (Sevcikova et al. 2014) in R statis-tical software v.3.3.2 (R Development Core Team 2016). Details of the analytical approach used, including DFA calculation, validation of scaling and its relationship to other fractal dimension estimates and illustrations are pro-vided in MacIntosh et al. (2013) and Meyer et al. (2015).

Fig. 3 Example of detrended fluctuation analysis (DFA) of forag-ing sequences from a little penguin from Phillip Island colony. a Integrated dive sequences (y(t)) generated by the accumulation of a binary time series of diving (+1) vs surface time (−1) across the entire length of the single-day foraging trip performed by one indi-vidual. b Log–log plots of the average fluctuation F(n) at each scale (window size) across the dive sequences on the y-axes as a function of scale (n) on the x-axes. The values of αDFA reflects the slope of the regression lines, with lower αDFA reflecting greater stochasticity. Note that only the points in black were used to fit the regression line to avoid biases introduced at small and large scales; these ‘best scaling regions’ were calculated using methods referred to in the text

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Statistics

All statistical analyses were conducted in R statistical software v.3.3.2 (R development Core Team 2016). We constructed linear mixed-effects models (LMMs, ‘lme4’ package in R, Bates et al. 2016) to investigate variation in αDFA across colonies. We set individual identity and trip date as crossed random effects to account for our re-sam-pling of a small number of individuals and the temporal variation in behaviour, respectively. Colony was set as a random effect to account for effects from other unmeas-ured variables related to the colony. Trip duration (in hours) was set as a covariate to control for the effects of sequence length on scaling exponents (MacIntosh et al. 2013). We included the following predictor variables in the model: bathymetry evenness index (E), chlorophyll-a concentration at the time of the trip and sex of the indi-vidual. Models were validated for residual homogeneity and homoscedasticity through visual inspection of the residuals (Zuur et al. 2009). To compare all colonies with one another, we did pairwise comparisons with Bonfer-roni correction.

We then ran a principal component analysis (PCA) to aid the interpretation of the relationships between αDFA and various other commonly presented foraging param-eters (see details about foraging parameters in Chiaradia et al. 2007), including (1) diving frequency (number of dives over the foraging trip), (2) foraging effort (total time spent underwater over the foraging trip; Takahashi et al. 2003), (3) trip duration, (4) mean dive depth (over the whole foraging trip) and (5) foraging efficiency esti-mated as follows (for details see Sala et al. 2012):

PCA provided information on relationships between parameters and their relative importance to the observed dimensions, as well as their similarities and differences with one another. PCA was run using the prcomp func-tion of the ‘stats’ package in R (R development Core Team 2016). Finally, we constructed separate LMMs to investigate whether αDFA covaried with the interaction between the proxy for foraging efficiency and colony, and the interaction between total time spent underwater, which we used as a proxy for foraging effort, and colony. This step was important because we were also interested in relating our complexity signatures to other diving parameters typically used to measure aspects of diving performance, particularly effort and efficiency. Because of model complexity and our focus on the interactions between colony and dive parameters, we analysed the relationship between our scaling exponents and each of foraging efficiency and foraging effort in two separate

Number of vertical undulations during a dive′s bottom phase

Total time spent underwater during foraging

models. Individual identity and trip date were again set as crossed random effects in these models.

Descriptive results are presented as means and stand-ard errors (SE), and the alpha level used for all statistical tests was set at 0.05.

Results

Fractal analysis of dive sequences

Detrended fluctuation analysis produced val-ues of αDFA ranging between 0.79 and 0.99 (mean ± SE = 0.89 ± 0.01, Fig. 4), indicating that binary dive sequences from foraging little penguins are best characterized as persistent, long-range dependent fractional Gaussian noise, as was shown previously for little and Adélie penguins (MacIntosh et al. 2013; Cot-tin et al. 2014; Meyer et al. 2015). In other words, dives and surface times of a given length are typically followed by dives and surface times of a similar length, with such patterns of fluctuation between behavioural states persist-ing across a range of measurement scales; observed best scaling regions included the scales 27–213, or 128–8192 s.

These results were confirmed by the bridge-detrend-ing method (DFAb) and the box-counting method (Db), in which the mean ± SE were αDFAb = 1.90 ± 0.02 and

Fig. 4 Results of fractal analysis of binary sequences of diving behaviour of little penguins, showing scaling exponents for each colony. Pairwise comparisons with Bonferroni correction showed significant differences between Phillip Island and Penguin Island (p value = 0.0002), Motuara Island (p value = 0.0001) and Oamaru (p value = 0.03). In contrast, pairwise comparisons showed no clear differences between Penguin Island, Motuara Island and Oamaru

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Db = 1.14 ± 0.03. The integrated dive sequences meas-ured via DFAb produced αDFAb in the range of 1.78–1.99, characteristic of fractional Brownian motion. Given the theoretical relationship of HfGn = HfBm − 1 (Seuront 2010), borne out almost perfectly in our analyses, this confirms that the original binary sequences were char-acteristic of fractional Gaussian noise. Furthermore, the Pearson correlation coefficient of 0.97 (p ≤ 0.01) between αDFA and αDFAb confirms their compatibility (Fig. 5). The relationship between scaling exponents estimated via DFA and those estimated via the box-counting dimension also fit with theoretical expectations (H = 2 − D; Seu-ront 2010), as Pearson correlations showed that Db was inversely related to both αDFA (r = −0.42, p = <0.01) and αDFAb (r = −0.40, p = <0.01).

Environmental parameters and behavioural organization

Mean chlorophyll-a concentrations were 0.49 ± 0.02 mg m−3 in 2000 around Motuara Island and 0.46 ± 0.02 mg m−3 in 2000 around Oamaru. Sur-rounding the Australian colonies, mean chlorophyll- a concentrations were 0.6 ± 0.04 mg m−3 in 2001 and 0.98 ± 0.15 mg m−3 in 2002 around Penguin Island and 0.44 ± 0.06 mg m−3 in 2001 and 0.68 ± 0.05 mg m−3 in 2002 around Phillip Island.

Our statistical model (Table 2) showed that αDFA increased with bathymetry evenness. The subsequent pair-wise comparisons between colonies showed significant

differences between Phillip Island and the other three colo-nies: Penguin Island, Motuara Island and Oamaru (Fig. 4). In other words, little penguins from Phillip Island exhib-ited greater stochasticity (i.e. lower values of αDFA) in the temporal organization of their foraging behaviour com-pared with penguins from the three others colonies, which themselves did not differ significantly from each other (Fig. 4). We observed no relationship between foraging sequence complexity and sex, trip duration or chlorophyll-a concentration.

Principal component analysis of foraging parameters and behavioural organization

The first two principal components in our PCA explained 72% of the variance in the data (Fig. 6a). The variables αDFA, foraging efficiency, foraging effort and mean dive depth all loaded into PC1, which explained 49.2% of the variance in the data. However, while αDFA (0.40) and forag-ing efficiency (0.50) loaded positively into PC1, foraging effort (−0.42) and mean dive depth (−0.52) loaded nega-tively. These results suggest that more efficient foraging sequences are also more deterministic (higher αDFA), while more stochastic sequences (lower αDFA) are associated with greater foraging effort. However, linear mixed-effects models examining the relationships between αDFA and both foraging efficiency and foraging effort showed significant interactions involving colony. First, the slope of the rela-tionship between αDFA and foraging efficiency differed sig-nificantly between Phillip island, where it was positive, and Oamaru, where it was negative (Table 3; Fig. 6b). A similar yet nonsignificant trend was also observed between Motu-ara and Oamaru (i.e. a positive and negative foraging effi-ciency, respectively), with birds from Penguin island exhib-iting an intermediary foraging efficiency. Second, the slope of the relationship between αDFA and foraging effort also differed significantly among colonies, with Oamaru pre-senting a negative relationship between these variables not observed at the other colonies (Table 3; Fig. 6c). Therefore, whether increasingly stochastic complexity signatures are

Fig. 5 Relationships between fractal-based dive parameters. Lower diagonal panels show correlation scatter plots, diagonal panels show densities plots and right diagonal panels give Pearson’s correlation coefficients. The Pearson correlation showed a significant correlation between the three methods (p = <0.01)

Table 2 Effects of bathymetry evenness index (E), chlorophyll-a concentration at the time of the trip, sex and trip duration on αDFA using linear mixed-effects models (LMMs) statistics

Bold text highlights significant effects

Variable β ± SE t-value p-value

Intercept 0.875 ± 0.060 8.336 <0.0002

E 0.158 ± 0.058 2.659 0.008

Chlorophyll-a −0.019 ± 0.040 0.458 0.65

Sex (female) −0.013 ± 0.009 1.440 0.15

Trip duration −0.0002 ± 0.005 0.036 0.97

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Fig. 6 a Principal component analysis showing relationships between αDFA (our scaling exponent) and various diving parameters along the first and second principal components, including (1) div-ing frequency (number of dives, Nb.d), (2) foraging effort (total time spent underwater, FEff), (3) trip duration (trpd), (4) mean dive depth

(Mn.) and (5) foraging efficiency (prey encounter per unit time, Fr_f). Other panels include representations of αDFA as a function of b forag-ing efficiency and c foraging effort. Green triangles, red circles, blue squares and purple crosses represent, respectively, individuals from Phillip Island, Penguin Island, Oamaru and Motuara Island

Table 3 Results of linear mixed-effects models (LMMs) examining the effect of foraging efficiency (prey encounter per unit time; foreffic in the model) and foraging effort (total time spent underwater; foreffort in the model) across colonies on αDFA

Date and bird ID were included in the LMMs as random effects. Bold text highlights significant effects

Model Variable β ± SE t‑value p-value

DFA ~ foreffic:colony + foreffic + colony + (1|date) + (1|ID)

Intercept 0.858 ± 0.094 9.131 < 0.0002

Foraging efficiency: Colony

Site 1 Site 2 −2.405 ± 1.342 −1.792 0.08

Motuara Island Oamaru

Motuara Island Penguin Island −0.854 ± 1.046 −0.817 0.42

Motuara Island Phillip Island 0.151 ± 1.271 0.119 0.90

Phillip Island Oamaru −2.557 ± 1.207 −2.117 0.04

Phillip Island Penguin Island −1.006 ± 0.859 −1.172 0.25

Oamaru Penguin Island 1.551 ± 0.963 1.610 0.11

DFA ~ foreffort:colony + foreffort + colony + (1|date) + (1|ID)

Intercept 0.737 ± 0.185 3.994 0.002

Foraging effort: Colony

Site 1 Site 2 −0.00001 ± 0.000006 0.397 0.08

Motuara Island Oamaru

Motuara Island Penguin Island −0.000006 ± 0.000006 0.397 0.29

Motuara Island Phillip Island −0.000006 ± 0.000006 0.395 0.26

Phillip Island Oamaru −0.000005 ± 0.000003 0.446 0.08

Phillip Island Penguin Island 0.0000005 ± 0.000002 0.446 0.81

Oamaru Penguin Island −0.000005 ± 0.000003 0.446 0.08

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increasingly efficient and/or increasingly energy-intensive or not, as was apparently the case at Oamaru, depends on the colony to which little penguins belong. The number of dives performed and trip duration both loaded positively into PC2 (0.67 and 0.58, respectively), which explained 22.8% of the variance in the data.

Discussion

Animal–environment interactions cause interspecific variation in behavioural organization among little penguins

The greater stochasticity observed in the foraging activity of penguins from Phillip Island corroborates our prediction that individuals from colonies surrounded by deeper waters had less deterministic foraging sequences than those from colonies surrounded by less variable depths and shallower waters. In deeper waters, penguin prey are presumably more dispersed and harder to catch as they may dive deeper outside of the penguins’ range. Under such conditions, stochastic elements in foraging sequences may increase to improve the probability of prey encounters. In contrast, shallower waters such as those surrounding Penguin Island and Oamaru may have more predictable prey fields, leading to more deterministic foraging sequences in little penguins. Given that fledging success was also significantly higher in these colonies than at Phillip Island, our results suggest that Phillip Island penguins might face more challenging for-aging conditions. However, strong inter-specific competi-tion for resources at Phillip Island may have contributed to these differences, given the exceptional size of that colony (approximatively 32,000 individuals compared to between 600 and 6000 individuals at the other colonies). Shifting to a more stochastic pattern of foraging may be a strat-egy that allows little penguins to cope with, if not thrive in, challenging environments. Indeed, our results indicate that under favourable conditions such as those at Oamaru, increasingly stochastic sequences may be associated with greater foraging efficiency, despite concurrent increases in foraging effort.

According to Reynolds et al. (2015), greater determin-ism in sequences of foraging behaviour may result from an underlying decision-based queuing process favouring exploitation over exploration, which is likely to occur when the prey field is more homogeneous or otherwise highly predictable. During periods of heavy prey exploitation within patches, penguins are physiologically constrained by oxygen reserves (Wilson 2003) and lactic acid build-up (Butler 2006). Patterns of alternation between dives and surface times are thus highly regulated in a way that would produce persistent and more or less periodic behaviour. If

the need for more exploratory modes of behaviour is lim-ited due to environmental homogeneity, such behavioural determinism may persist throughout the foraging trip. Con-versely, under less predictable environmental conditions, individuals are expected to increase their performance of exploratory dives, which would then be interspersed with foraging dives in an attempt to maximize prey encounters. For instance, greater stochasticity in foraging behaviour in deeper waters (e.g. Phillip Island) could be explained by greater heterogeneity in the vertical distribution of prey, as is commonly observed during El Niño years (Ropert-Coudert et al. 2009). As a consequence, birds may drasti-cally augment their target depths from one dive to the next, inducing variability in both dive durations and the subse-quent post-dive durations, which serve as recovery peri-ods from previous dives and for anticipating the next dive based on prey availability (Wilson 2003). Such alternation between foraging modes may ‘interrupt’ dive sequences and thus lead to reduced long-range dependence.

Behavioural organization along a stochastic–deterministic gradient allows flexibility under environmental variability

Diving behaviour is affected by resource availabil-ity (Mori and Boyd 2004), which can be summarized through its two major components: abundance of prey (Mori and Boyd 2004; Cook et al. 2008; Elliott et al. 2008; Doniol-Valcroze et al. 2011; Goundie et al. 2015) and prey distribution in the water column (Zamon et al. 1996; Boyd et al. 2015). In response to heterogeneity in the abundance and distribution of food resources, ani-mals are hypothesized to have evolved a scale-invariant foraging strategy that allows them to maximize the suc-cess of prey search (Viswanathan et al. 1999, 2008; Bar-tumeus et al. 2005; Bartumeus 2007; 2009; Sims et al. 2008; Humphries et al. 2010). Behavioural scale-invar-iance, through its super-diffusive and fractal properties, allows animals to reduce “overexploitation” by avoid-ing revisiting previously visited areas (Shlesinger and Klafter 1986). While the validity of the Lévy flight for-aging hypothesis remains under debate (Benhamou 2014; Pyke 2015; Reynolds 2015; Patterson et al. 2016), our study shows that the degree to which fractal properties in behaviour can vary within species depends on physi-cal characteristics of the environment that mediate the abundance and distribution of food resources. Indeed, a study on the fractal structure of behaviour time series in wild Japanese macaques (Macaca fuscata: MacIntosh et al. 2011) suggests that animals in more structurally complex environments (i.e. arboreal versus terrestrial) or those exploiting resources that are harder to obtain (i.e. mobile invertebrates versus immobile fruits) moved and

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foraged in a less deterministic manner. Moreover, con-trolled studies on fruit flies (Drosophila melanogaster: Cole 1995; Shimada et al. 1995) showed greater com-plexity in the distribution of dwelling times when chal-lenged with a new environment or inferior food quality. Furthermore, domestic hens (Gallus gallus domesticus: Rutherford et al. 2003) showed that vigilance time series become more stochastic when animals are moved to novel environments. Collectively, these results suggest that more stochastic behavioural sequences coincide with more structurally complex (e.g. uneven bathymetry) or otherwise less predictable (e.g. resource type, abundance and distribution) environments. Increased stochasticity in foraging patterns thus offers a possible mechanism to enhance fitness in, or to at least cope with, heterogeneous or otherwise more complex or challenging environments.

It is also significant that the relationship between forag-ing efficiency and sequence complexity changes from Phil-lip Island and Motuara Island on the one hand to Oamaru on the other, with Penguin Island in the middle. This apparent transitionary relationship fits with the breeding successes observed across colonies, with Oamaru having the highest and Phillip Island the lowest (Chiaradia et al. 2007). Such colony-level differences also reflect how the variable envi-ronments might set an observable complexity range, and how such variation relates to variation in foraging success. For example, more stochastic sequences at Oamaru corre-lated with increased foraging efficiency, despite the concur-rent increased effort required. However, foraging sequences at Phillip Island, where perhaps the opposite was true, were already far more stochastic than those at Oamaru.

All else being equal, foraging in shallow waters should allow little penguins to allocate a greater amount of under-water time to the bottom phase of dives, wherein they pre-dominantly feed (Ropert-Coudert et al. 2003, 2006). Simi-lar to other deep-diving marine vertebrates, such as blue whales (Balaenoptera musculus, Doniol-Valcrose et al. 2011) and Steller sea lions (Eumetopias jubatus, Goundie et al. 2015), little penguins exhibit higher foraging effi-ciency when performing shallow dives and also forage less efficiently in deeper waters with presumably more com-plex prey fields. Given that no associations were observed between the temporal organization of diving behaviour and primary productivity, a proxy for prey availability, the divergent bathymetric conditions are likely to be the main factor driving variability in the temporal patterns of little penguin diving behaviour. However, the thermal structure of the water column may also influence prey availability, but this could not be tested in the present study (see Rop-ert-Coudert et al. 2009; Pelletier et al. 2014; McInnes et al. 2017). Future work should be aimed at disentangling such potential confounds, but our current results indicate that even if increased stochasticity can enhance prey encounters

in more heterogeneous environments (e.g. Phillip Island), this may not be sufficient to match fitness gains attained under more homogeneous and favourable conditions (e.g. in Oamaru and Penguin Island).

Motuara Island: constraints on foraging area or different species altogether?

Interestingly, Motuara Island presents an intermediary case: greater determinism in the temporal organization of foraging sequences and high foraging efficiency. This was the case at Penguin Island and Oamaru as well, but in con-trast, Motuara Island also had a greater foraging effort and a poor fledging success similar to that at Phillip Island. We propose two mutually non-exclusive explanations for this discrepancy. First, the foraging area for little penguins at Motuara Island is restricted during the guard stage by Cook Strait’s strong currents (c.a. radius of 20 km). All penguins stayed within a limited shallow region of Queen Char-lotte Sound, just north of Motuara Island (Mattern 2001; Poupart et al. 2017). Thus, instead of extending their forag-ing ranges, penguins instead increased their foraging effort (i.e. longer dive times and greater depths) to increase their likelihood of prey encounters. This constraint on foraging area might have led to greater determinism through limita-tions imposed by the diving physiology of penguins.

Alternatively, a recent study (Grosser et al. 2015) sug-gests that the Eudyptula genus might include one species distributed across Australia and the south-eastern coast of New Zealand’s South Island (including Oamaru), and a second species distributed elsewhere in New Zealand (including Motuara). If this were the case, there may also be a species-specific component determining organiza-tional structure in dive sequences despite a very similar size and weight. Yet, even if this taxonomic split was con-firmed, this would not fundamentally change our results, because three of our colonies comprised the “Australian” species, yet these colonies experienced different conditions of bathymetry.

Sample size and logger effects as limitations of the study

As predicted, our results fit theoretical expectations derived from the literature on optimal search strategies under divergent environmental conditions. Nonetheless, we stress the need for caution due to the small sample size in two of the four colonies considered in this study: four individuals and nine trips at Motuara Island and four individuals and seven trips at Oamaru. Low statis-tical power can at once enhance the likelihood of both Type I and Type II errors (Button et al. 2013). Moreover, while we did not find an influence of sex in the present

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study, the numbers of sampled males and females were not always equal, especially at Motuara where the sex ratio of sampled individuals was biased in favour of males. Sex effects in the complexity signatures of little penguins at Phillip Island were previously described by Meyer et al. (2015), although in that case males produced more stochastic sequences than females, and thus can-not explain the difference observed here between Motu-ara and Phillip Island. Furthermore, loggers themselves are known to affect the swimming performance (Ropert-Coudert et al. 2007) and temporal organization of diving activity (Meyer et al. 2015) in little penguins. In the latter case, the authors showed that little penguins carrying log-gers that covered a larger cross-sectional area of the pen-guins (4.9 vs 3.4%) produce more stochastic sequences (i.e. the difference in αDFA between foraging sequences of little penguins carrying smaller versus bigger loggers is equal to 0.028 ± 0.013; Meyer et al. 2015). The present study shows that individuals from the colony equipped with the biggest loggers (Phillip Island) also produced the most stochastic foraging sequences among the four colonies studied, which is consistent with what this study would predict given differences in logger size alone. That said, the size of the effect of colony in the present study is much greater than that observed in relation to logger size in Meyer et al. (2015), so it is unlikely that this dif-ference reflects an artefact of our methodology. Further-more, the fact that we observed no differences between either Motuara Island or Oamaru and Penguin Island, where devices also differed significantly in size, indicates that logger size may not have had a significant influence on our results. Thus, while all of these factors may have played a role in our study, it is unlikely that they have confounded our findings.

Conclusion

Temporal fractal analysis of behaviour can provide new avenues to study seabird foraging behaviour in finer detail, and how such behaviour might change in response to changing environmental conditions. Our study sug-gests that the performance of complex foraging sequences characterized by higher degrees of stochasticity, which are predicted to outperform more deterministic sequences in heterogeneous environments, may in fact be more energy intensive and, therefore, may not be sufficient to match fitness gains observed in animals foraging under more favourable conditions. However, we were unable to directly test this possibility on an individual basis here, and thus we cannot currently determine whether links exist between complexity signatures, foraging success and fitness within colonies. These aspects should be a key

focal point for future studies investigating the adaptive value of foraging complexity in animals.

Acknowledgements The authors thank the staff and students of Phil-lip Island Nature Parks, in particular P. Dann, L. Renwick, P. Waziak, J. Yorke and the support of B. Cannell, D. Houston, Y. Naito and S. Ward. We thank the staff and rangers at Penguin Island and Oamaru Blue Penguin Colony. We also thank two anonymous reviewers for providing very valuable comments on earlier versions of this manu-script. This work was financially supported by grants from the Japan Society for the Promotion of Science, Phillip Island Nature Parks, Penguin Foundation, Australian Academy of Science, Murdoch Uni-versity, Otago University, Sasakawa Scientific Research Grant from the Japan Science Society and the Ministère de l’Enseignement Supé-rieur et de la Recherche (France).

Compliance with ethical standards

Conflict of interest The authors declare that they have no conflict of interest.

Funding XM received financial support from a PhD scholarship from the Ministère de l’Enseignement Supérieur et de la Recherche (France). The data were collected thank to grants from the Japan Soci-ety for the Promotion of Science (YRC-AK), Phillip Island Nature Parks (AC), Penguin Foundation (AC), Australian Academy of Sci-ence (AC), Murdoch University (YRC), Otago University (TM) and Sasakawa Scientific Research Grant from the Japan Science Society (YRC-AK).

Ethical approval The study was approved by the respective ethics committees of Phillip Island Nature Parks (Animal Experimentation Ethics Committee Number 6.2000), Murdoch University (no number) and Otago University (no number), and research permits were acquired from the Department of Natural Resources of Victoria (Wildlife per-mit No. 10001184), the New Zealand Department of Conservation (no number), and the Department of Conservation and Land Management of Western Australia (no number).

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