Fractal patterns are found everywhere in nature, e.g., in the shapes of clouds, mountains and coastlines, or in plant structures such as those produced in the Romanesco broccoli (Brassica oleracea var. botrytis) [1]. Such patterns are also known to emerge in spatial and temporal sequences of animal movement, which exhibits self-similarity across a range of measurement scales [2–7]. Three approaches have used fractal geometry in the field of animal movement ecology: (1) measuring step length distributions (sensu the Lévy flight foraging hypothesis) [5, 8–11], (2) spatial fractal dimension estimation [12–16], and (3) fractal time series analysis of behavior sequences [17, 18]. These studies highlight how highly irregular patterns of behavior may reflect an optimal strategy to facilitate resource encounters in heterogeneous environments.

Fractal time series analyses of animal behavior measure the structure of behavior as it occurs through time, which is linked to the concept of behavioral organization [17, 19]. Borrowing from the field of complexity science, such studies have adopted the term ‘complexity’ to refer to the correlation structure of the time series, which behave as nonlinear systems [20]. Complexity in diverse biological phenomena is considered to be adaptive because it is error-tolerant, making it possible to buffer changes arising from both intrinsic (e.g., reproductive state and hormones) and extrinsic factors (e.g., environmental perturbations) [21]. On a temporal scale, physiological or behavioral changes can impact the complexity observed in time series data collected from diverse systems [18]. These deviations from normal behavioral patterns in nonlinear systems, known as ‘complexity loss’, were first observed in physiological systems producing heart rate variability [22], stride patterns [23] and neural activity [24]: pathological systems produce times series with altered complexity signatures. Complexity loss has now also been observed in various forms of animal behavior, such as not only foraging and movement but also vigilance, postural behavior and even social behavior, when animals are confronted with some or another stressor [6, 25–30]. For example, Spanish ibex (Capra pyrenaica, [25]) and Japanese macaques (Macaca fuscata, [6]) infected by parasites have showed a decrease in behavioral sequence complexity. Similarly, Adélie penguins (Pygoscelis adeliae, [30]) treated with corticosterone implants also exhibited reduced dive sequence complexity in comparison with untreated (control) birds. Moreover, Indo-Pacific bottlenose dolphins (Tursiops aduncus, [29]) exposed to the presence of motor boats also showed a decrease in the complexity of their dive sequences. Thus, complexity loss, as far as it has been detected in altered behavior sequences, is predicted to reduce an animal’s fitness long term.

Altered complexity signatures may reflect changes toward either greater stereotypy or greater randomness, depending on the nature of the disruption [17, 18, 26]. Kembro et al. [31] for instance showed increased stochasticity in the movement behavior of mosquito larvae exposed to lethal and sub-lethal doses of essential oils. Similarly, greater stochasticity was also observed by Rutherford et al. [26] in behavioral patterns of hens exposed to novel housing conditions. The contrasting responses to the presence of stressors appear to depend on the specific type of stressor faced by individuals, with greater stochasticity expected in cases of acute stress and greater stereotypy expected in cases of chronic stress [18, 27]. The concept of complexity loss was thus extended to allow for the fact that changes in both directions can equate to suboptimal complexity signatures, as both reflect a departure from optimal patterns of behavioral organization that can be detrimental over the long term [18]. We could easily hypothesize about the potential benefits of increased complexity in the vigilance behavior of animals exposed to novel environments in which the location of potential resources, but also potential threats, cannot be a priori known. However, we would predict a return to normal, i.e., more deterministic behavior patterns over time, as animals familiarize with their surroundings, whereas the same might not be said of an animal exposed to a truly chronic stressor.

Here, we re-examined published datasets that found an effect of either external devices [32, 33] or flipper bands [34] on the foraging activities of penguins to determine whether hydrodynamic handicaps can induce altered complexity signatures in foraging (diving) sequences of two species of penguin: the Adélie penguin and the little penguin (Eudyptula minor). Indeed, previous studies of Adélie and little penguins have revealed short-term impacts of back-attached diving recorders on diving activities through comparisons of diving parameters in groups of birds equipped with devices of different sizes [32, 33]. These experiments offer a good framework to test whether the attachment of such devices, which imposes a known hydrodynamic handicap [34, 35], would also induce organizational changes in patterns of foraging behavior. Thus, we predicted the existence of variation in the organizational complexity of foraging behavior in relation to logger size (large vs small loggers) and logger position (higher vs lower on the penguin’s back). Since large loggers and those positioned higher on the back should increase drag relative to smaller loggers and those positioned lower on the back [34, 35], we assumed that the organizational properties of foraging sequences in birds under the latter conditions were more similar to those in birds under unburdened, control conditions. Following the results of Fallow et al. [36], predictions about the impact of flipper bands should differ between short-term (acute stressor) and long-term (chronic stressor) attachment experiments on little penguins. Thus, we predicted short-term effects on the organizational properties of foraging sequences but not long-term effects.

We studied little penguins from the Penguin Parade colony at Phillip Island, Victoria, Australia (38°30′S, 145°09′E) and Adélie penguins in Dumont d’Urville, Adélie Land (66°39′S, 140°00′E).

Fractal analyses showed values of α _DFA ranging between 0.74 and 0.94 (mean = 0.86, SE = 0.008) for little penguins during the logger experiment and values of α _DFA ranging between 0.74 and 0.97 (mean = 0.88, SE = 0.008) for little penguins during the flipper band experiment. Adélie penguins exhibited higher mean values of α _DFA ranging between 0.91 and 0.98 (mean = 0.94, SE = 0.005). These values indicate that dive sequences are long-range dependent and resemble persistent fractional Gaussian noise, as shown previously [30, 37]. The likelihood ratio test showed no difference between statistical models with and without interaction terms (p = 0.16), so we present results from the more parsimonious models without the interaction terms in which the main effects can be better interpreted.

We observed a significant difference between dive sequences produced by little penguins carrying loggers of different sizes (Table 1; GLMM: α _DFA, df = 21, t = 2.22, p = 0.04; mean α _DFA large logger = 0.85 ± 0.008; mean α _DFA small logger = 0.94 ± 0.008): little penguins carrying larger loggers exhibited lower values of α _DFA, reflecting greater stochasticity in dive sequences than those carrying smaller loggers. Figure 1 illustrates this difference as well as the process of DFA using representative little penguins equipped with a small and large logger, respectively. Logger position, on the other hand, was not significantly associated with complexity in dive sequences, although little penguins carrying loggers in middle positions showed a tendency toward lower α _DFA values compared with those carrying loggers in lower positions (Table 1; GLMM: α _DFA, df = 21, t = 1.79, p = 0.09; mean α _DFA middle position = 0.85 ± 0.015; mean α _DFA low position = 0.87 ± 0.008). In addition, our statistical model showed that males displayed higher values of α _DFA than females (Table 1; GLMM: α _DFA, df = 21, t = −4.87, p = 0.0001; mean α _DFA male = 0.89 ± 0.007; mean α _DFA female = 0.84 ± 0.009), whereas trip duration had no effect (Table 1; GLMM: α _DFA, df = 21, t = −0.05, p = 0.96).

Experiment	Variable	Est	SE	df	t value	p value
Little penguin logger size	Intercept	0.8733	0.1973	21	4.42	0.0002
	Size (large vs small)	0.0285	0.0128	21	2.22	0.04
	Position (middle vs low)	0.0232	0.013	21	1.79	0.09
	Trip duration	−0.0006	0.0132	21	−0.05	0.96
	Sex (male vs female)	−0.0623	0.0128	21	−4.87	0.0001
Adélie penguin logger size	Intercept	0.9628	0.0129	7	74.58	0
	Size (large vs small)	0.0053	0.0084	7	0.64	0.54
	Trip duration	−0.0008	0.0003	7	−2.46	0.04
Little penguin flipper band short-term	Intercept	1.0824	0.344	11	3.15	0.01
	State (non-banded vs banded)	−0.024	0.0265	11	−0.91	0.38
	Trip duration	−0.013	0.0226	11	−0.57	0.58
Little penguin flipper band long-term	Intercept	0.7463	0.3493	14	2.14	0.05
	State (non-banded vs banded)	0.011	0.025	3	0.44	0.69
	Trip duration	0.0076	0.0234	3	0.33	0.76

Italicized text highlights significant p values.

Est estimate, SE Standard error, df degree of freedom.

We did not observe any effects of flipper banding on α _DFA values in either the short-term (Table 1; GLMM: α _DFA, df = 11, t = −0.91, p = 0.38; mean α _DFA non-banded = 0.88 ± 0.021; mean α _DFA banded = 0.86 ± 0.013) or long-term (Table 1; GLMM: α _DFA, df = 3, t = 0.44, p = 0.69; mean α _DFA non-banded = 0.86 ± 0.018; mean α _DFA banded = 0. 88 ± 0.014) experiments. Our covariate, trip duration, was also not associated with values of α _DFA in either experiment, respectively (Table 1; GLMM: α _DFA, df = 11, t = −057, p = 0.58; GLMM: α _DFA, df = 3, t = 0.33, p = 0.76).

Finally, logger size had no effect on the α _DFA values estimated for Adélie penguin diving sequences (Table 1; GLMM: α _DFA, df = 7, t = 0.64, p = 0.54; mean α _DFA large logger = 0.938 ± 0.008; mean α _DFA small = 0. 937 ± 0.008), but longer trip durations were negatively associated with α _DFA values (Table 1; GLMM: α _DFA, df = 7, t = −2.46, p = 0.04), i.e., the longer the trip the greater the stochasticity of the dive sequence.

We demonstrate here that the size of back-mounted recording devices is associated with variation in the temporal organization of foraging behavior in little penguins. Unlike most previous studies of fractal time in animal behavior, which demonstrated alterations toward more stereotypical sequential patterns in the presence of various stressors (i.e., complexity loss), we show here that dive sequences were more complex, exhibiting greater stochasticity, in birds with larger loggers. The hydrodynamic handicaps imposed by large loggers, and by extrapolation perhaps loggers in general though studies of this nature necessarily lack true controls (i.e., birds without loggers), thus seem to add an extra element of noise into the diving sequences of little penguins. However, the lack of effects of logger position in little penguins, logger size in Adélie penguins and, surprisingly, flipper bands in little penguins suggests that animal-attached devices do not universally induce such organizational changes in seabird foraging behavior, despite having clear effects on other dive parameters and potentially, for flipper bands at least, fitness outcomes [49–51].

The use of back-mounted recording devices on penguins and other marine animals increases drag, which should increase swimming energy expenditure at a given velocity [35, 52]. With increasing energy expenditures, air-breathing marine predators such as penguins may need to reduce dive durations as oxygen stores are depleted more rapidly than when they are not handicapped, and/or increase post-dive duration periods at the surface to replenish oxygen stores in provision of future dives. This may in part explain our results for little penguins; because of the increased foraging effort observed in little penguins with large loggers, evidenced by the greater numbers of dives per foraging trip, hourly dive rates, total time spent underwater and at least in males longer foraging trips [32, see also 53], the between-dive durations were less variable (the mean standard deviations for individuals equipped with large loggers vs small loggers were 72.88 ± 10.11 vs 105.13 ± 9.08 s, respectively), leading to more randomized sequences of behavior. All else being equal, surface durations are much freer to vary (diverge from a random distribution) than are dive durations due to the physiological constraints of diving activity (i.e., oxygen depletion, CO₂ and lactic acid accumulation [54]). Given the small differences in body size between sexes [55], the sex differences observed here could be explained by variation in dietary preference, e.g., males having a different diet than females or perhaps feeding on same species but larger prey. Unfortunately, we do not have any dietary information for the birds we monitored, though dietary differences between sexes have been shown to be minimal in little penguins [56].

Alternatively, rather than reducing dive durations and other frequency-based dive parameters, Adélie penguins equipped with large loggers are known to compensate for this handicap by reducing swim speeds, thereby maintaining similar per dive energy expenditures as birds equipped with small loggers [33]. Both strategies would reduce achievable dive depths and time spent with prey, thus limiting foraging efficiency [32, 33], but such limitations would likely be far less detrimental to Adélie penguins, which feed on densely packed, slow-moving prey (krill [57, 58]). This effect should be stronger on little penguins that indeed showed organizational changes in their dives as they feed on fast-moving prey (fish [55]). At a given position, the drag caused by back-mounted devices, and resultant effects on dive profiles, should depend primarily on the ratio of logger to body size. In the present study, large loggers accounted for a significantly larger cross-section of the frontal area of little penguins (4.9%) than the much larger Adélie penguins (only 1.4%). Small body size already disadvantages diving seabirds, so little penguins may not have the option to decrease swim speeds to compensate for the extra drag as Adélie penguins seem to do [33], and must instead make organizational changes to their dive profiles. Interestingly, we detected an effect of trip duration on the sequential organization of foraging behavior in Adélie penguins and the direction of the effect may seem counterintuitive when comparing with the results of [37]. However, MacIntosh et al. [37] conducted their analysis on little penguins during the guard stage where birds are restricted to a 1-day trip. It is possible that variation in trip duration and the associated variation in foraging effort in Adélie penguins [59] may have cause this statistical effect to appear. Future studies should investigate this as variable trip lengths could potentially influence the conclusions driven from the use of the DFA method. For the present analysis, we note that the effect should be limited as the estimate value only changes by 0.0008.

Despite that logger position was not significantly associated with foraging sequence complexity in little penguins, we hesitate to reject this possibility outright for two reasons: (1) that the results showed a statistical trend and (2) that the difference exhibited consistency with the effect of logger size in that the sign of the difference was the same, i.e., toward greater stochasticity in the middle position, which we predicted would impose a greater hydrodynamic handicap than loggers placed lower on the back. Still, that the effect of logger position was weaker than that of logger size also mirrors the original study, in which the former had little impact on the dive parameters examined [32]. However, penguins with small loggers positioned middle on their backs did dive to significantly greater depths than those with large loggers on the same position and displayed a tendency toward increased dive durations as well, while no difference was observed when the loggers were positioned lower [32]. As discussed above, resultant changes in the sequential distributions of dive and between-dive times may account for the tendency toward greater stochasticity observed here in penguins equipped with loggers in the middle of their backs as well, however marginal these differences may be. Since the change in drag is expected to be less dramatic for the two logger positions than the two logger sizes [32], the weaker influence of position on dive sequence complexity is not surprising.

What is perhaps most surprising in our study is the lack of effect of flipper bands on observed dive sequences. Using the same dataset, Fallow et al. [36] highlighted the immediate effects of flipper banding on the diving behavior of little penguins using conventional measures; notably, dive durations increased significantly while dive efficiency, defined as bottom phase duration/(dive duration + post-dive duration), decreased significantly in newly banded birds. Apparently, these differences are not necessarily associated with organizational changes in dive sequences. One major difference between the previously observed flipper band and large logger effects is that increased logger size induced significant increases in overall diving effort, defined as the cumulative time spent underwater during the trip, and total numbers of dives performed, neither of which differed in the flipper band experiment [32, 36]. Indeed, dive durations and between-dive durations increased in the flipper band experiment, meaning that the sequential distribution and variance of both dive and surface durations may not have changed, leaving the global structure of the foraging trip unchanged as well. This also suggests that global structural changes in the organizational complexity of dive sequences need not be associated with other changes in foraging behavior, e.g., those induced by flipper bands, that are known to significantly affect survival and reproduction (e.g., [49–51]).

While variation in performance outcomes (e.g., body mass gain) was not measured in the original study [32], the alterations in the organizational structure of foraging sequences we observed in little penguins equipped with large loggers, and potentially those placed in positions that further increase drag, can theoretically affect the overall performance of birds in their ability to detect and capture prey. Emergent fractal patterns in the movement behavior of numerous animal species are thought to reflect an underlying strategy aimed at maximizing prey encounters, particularly with heterogeneous prey fields [5, 8–11]. Observed complexity signatures under normal conditions are thus predicted to reflect theoretical optimal behavior patterns [14, 25], while deviations from such theoretical optimal patterns have been associated on numerous occasions with pathological or otherwise challenging intrinsic conditions, such as intense parasitic infection [6, 25], increased physiological stress [30], anthropogenic disturbance [29] and even advanced reproductive state [6, 25]. While increased complexity might approximate an optimal solution to some imposed stressors, e.g., the increased vigilance sequences observed in hens moved to novel enclosures [26], these tendencies toward stochasticity also appear to be associated with decreased energetic efficiency. Thus, hens in novel environments also significantly increased their total vigilance behavior, which would interfere with normal feeding patterns [26]. Here, little penguins carrying large loggers were probably forced to compensate with more frequent dives and longer foraging trips, presumably to achieve baseline energy gains. These compensatory behavior patterns are unlikely to be optimal in the long term.

Hydrodynamic handicaps caused by carrying externally attached devices exhibited variable influence on the organizational properties of penguin foraging sequences. Relative drag caused by back-mounted devices is likely an important component of dive sequence complexity for smaller species, decreasing variability in the alternation between diving and surface intervals and thus creating greater stochasticity in patterns of foraging behavior. It is also important to remember that there was no true control in this experiment, since all birds were equipped with loggers of variable sizes and positions. Given our results, it seems likely at least for little penguins that unequipped birds might exhibit a different set of fractal properties altogether, with even less noise in their dive sequences. This might even have confounded our flipper band experiment, for which there was a true control, if the effects of loggers interacted in some way with or overshadowed the effects of flipper bands, but this cannot be tested. Ultimately, we show here that increased noise in dive sequences, as opposed to the more commonly observed increased stereotypy [6, 25, 29, 30], is a potential outcome of coping with an added stressor. Further application of fractal tools to temporal sequences of behavior is needed to examine how animals cope with various realizations of environmental change, particularly organisms used as indicator species for environmental change.