Evaluating Gain Functions in Foraging Bouts Using Vertical Excursions in Northern Elephant Seals

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Evaluating gain functions in foraging bouts using vertical excursions in northern elephant seals

Michelle S. Ferraro

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Sonoma State University

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MASTER OF SCIENCE

Biology

Dr. Daniel E. Crocker, Chair

Dr. Dorian S. Houser

Dr. Derek J. Girman

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By Michelle S. Ferraro

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111 Evaluating gain functions in foraging bouts using vertical excursions in northern elephant seals

Thesis by Michelle S. Ferraro

ABSTRACT

The marginal value theorem is used to model patch departure decisions in foragers using patchily distributed resources. A key component of these models is the decelerating energy gain function used to represent patch depletion. The form of within-patch gain functions have rarely been assessed in marine predators. We evaluated the gain functions in foraging bouts of northern elephant seals using a long-term dataset (2004-2012) that includes complete foraging trips from 205 individual female northern elephant seals on 303 migrations as revealed by TDRs and ARGOS satellite tags. Previous work has shown that the majority of putative prey capture attempts are associated with vertical excursions at the bottom of dives. We used vertical excursions to evaluate patch depletion across foraging bouts as defined using dive shapes. Rates of energy gain were measured using changes in mass and body composition across trips. Decelerating gain functions were fit in 83% of 77,820 bouts with the remainder showing accelerating functions. Despite wide variation for individual patches, mean deceleration constants did not vary with year or season. This suggests that average rates of patch depletion were relatively stable across the study period providing an opportunity for seals to develop and use optimal patch departure rules. The mean duration and number of dives in foraging bouts showed little annual or seasonal variation. However, the mean rate of vertical excursions during dives varied and predicted rates of energy gain across migrations. These results help to explain the relative consistency of individual diving behavior despite wide variation in geoposition and support the idea that the northern elephant seal foraging strategy buffers against short-term variation in prey abundance. These data suggest northern elephant seals are well-suited to provide a strong test of the marginal value theorem in predators foraging over a wide spatial and temporal scale.

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Table of Contents

Page

Abstract...... iv Introduction...... 1 Materials and Methods...... 6 Sample and Instrument Attachment...... 6 Track and Diving Analysis...... 8 Gain Function Analysis...... 9 Statistical Analysis...... 10 Results...... 11 Diving Behavior...... 11 Gain Functions...... 12 Foraging Success...... 14 Discussion...... 14 Conclusion...... 19

Appendix A-Tables...... 21

Appendix B- Figures...... 25

References...... 31

List of Tables

Table 1- Mean diving behavior for all records averaged by year and season. A minimum criterion for a foraging bout was defined as 3 consecutive foraging dives. A mean was calculated for each individual seal’s foraging trip and grand means and SD are presented for all years and seasons.

Table 2 - Grand mean and SD for VE on the bottom of dives, total vertical distance covered during VE for each dive (TVD), the vertical depth range covered by VE for each dive (bottom range) and the ratio of bottom time to dive duration (efficiency) averaged for each female by season and year.

Table 3 - Mean energy gain rate, deceleration constant and initial number of VE for all records by year and season. A minimum criterion for a foraging bout was defined as 3 consecutive foraging dives. A power function (y = α*xβ), where y is the cumulative number of VE, was fit to each bout using Matlab. α is the coefficient parameter estimate that is linked to the number of prey capture attempts on the initial dive and β is the exponent parameter estimate that represents change in PEE over a foraging bout. Table 4 - Relative percentages of accelerating and decelerating patches in all tracks, post- molting season, post-breeding season and age classes young (3-5 years old), prime (6-9 years old) and old (10+ years old).

List of Figures

Figure 1 - Example of decelerating gain function fit from seal 2004005 (A) and accelerating gain function from seal 2004004 (B) using time in minutes in a bout and cumulative number of VE.

Figure 2 - The number of dives associated with β values in the power function. Decelerating bout counts are shaded while accelerating are blank.

Figure 3 - Individual patches along the tracks of three different seals: 2009008, 2009014 and 2012010. Red positions indicate accelerating patches while yellow indicate decelerating patches. Latitude and longitude show no relationship with patch type.

Figure 4 - When a power function was fit to the cumulative number of VE in a foraging bout, the power exponent, β, predicted the mean number of dives in decelerating post- breeding (A) and post-molting (B) migration bouts.

Figure 5 - Mean rate VE during a dive (A) and the number of VE per minute of bottom time (B) affects daily energy gain rate. Each point represents the grand mean for all females in a migration season. Error bars are SE of the grand mean.

Figure 6 - Changes in energy gain rate of entire foraging migrations with the mean rate of VE during dives. Open circles and dashed line are means for individual post-molt females. Closed circles and solid line are means for individual post-breeding females.

vii

INTRODUCTION

Optimal foraging theory (OFT) has been successful in predicting the behavior of animals and understanding the basis of a variety of foraging decisions in nature including risk sensitivity (Barnard and Brown, 1985; Caraco et al., 1990; Cartar, 1991), diet choice

(Belovsky, 1978; Koselj et al., 2011; Krebs et al., 1977; Werner and Hall, 1974), patch departure rules (Goulson, 2000; Tome, 1988), and central place foraging (Lefebvre et al.,

2007; Lewison and Carter, 2004; Raffel et al., 2009). OFT assumes animals maximize fitness by optimizing currencies such as the long term average rate of energy intake under constraints specific to the ecology of a given species.

An extension of OFT, the marginal value theorem (MVT), applies to systems where energy or food is patchily distributed (Charnov, 1976). This model has been implemented widely in wildlife systems to predict when an animal is likely to leave a food patch based on the assumption that any food patch over time becomes depleted as an animal continues to forage (Astrom et al., 1990; Boivin et al., 2004; Cassini et al., 1990;

Laca et al., 1993; Pyke, 1978; Scrimgeour et al., 1991; Tome, 1988; Wajnberg et al.,

2000). Therefore, energy gain over time is assumed to display a decelerating function that eventually asymptotes (Pyke, 1980), and the rate of that deceleration within a food patch provides an indication of the quality of that food patch (Mori and Boyd, 2004).

Foragers should increase residence time in patches that take longer to deplete because these patches provide more energy per unit time (McNickle and Cahill, 2009; Shipley and

Spalinger, 1995).

Although the MVT has been successful in qualitative predictions in a variety of systems, quantitative predictions have rarely been able to accurately describe patch departure times during experimental validation (Jiang and Hudson, 1993; Laca et al.,

1993). Difficulties in quantitative predictions may be due to a number of factors such as limited sample sizes and time scales, elusive constraints and direct validation of the underlying assumptions of the model features within the study system, including the form of the gain function.

A gain function describes how energy intake rate changes over time spent foraging within a patch. The deceleration constant (β), derived from this gain function, roughly represents how the rate of prey encounter events (PEE) decreases as the prey in the current patch are consumed. As more prey are consumed the quantity of prey remaining in the patch dwindles, and the profitability to the predator of persisting in that patch declines. β, thereby has also been used as an index of patch quality in previous studies where patches that deplete more slowly are considered higher quality than those that deplete more rapidly (Mori and Boyd, 2004). The gain function, together with the time required to locate new patches, ultimately determines the optimal timing for patch departure and is thus a key assumption of a MVT model.

Gain functions can take on a variety of shapes including decelerating (Watanabe et al., 2014), sigmoidal (Ginnett et al., 1999), linear (Illius and Fryxell, 2002), piece-wise linear (Astrom et al., 1990), and asymptotic (Laca et al., 1993). Previous studies have shown that even slight changes in the shape of the gain function can result in dramatically different calculated patch residence times from MVT models, resulting in little resemblance to real world conditions (Astrom et al., 1990; Olsson et al., 2001; Searle et

3 al., 2005). This highlights the importance of empirical validation of the form of gain functions prior to attempts to fit MVT models. Unfortunately, direct characterization of gain functions in free ranging foragers is difficult and has been rare in previous studies

(Halsey et al., 2003; Olsson et al., 2001; Searle et al., 2005; Watanabe et al., 2014).

Conceptually, the marine environment provides excellent systems for testing

MVT models. Mesopelagic foraging meets many of the assumptions that are difficult to meet in model terrestrial systems such as foraging over large spatial and temporal scales in a highly patchy and ephemeral environment with low probabilities of patch revisitation

(Owen, 1981). Logistically, the use of these systems to test foraging models has been problematic because of these same features and because direct observation of foraging behavior while at sea is difficult (Robinson et al, 2010). In order to appropriately test foraging models, it is critical to be able to define foraging events and delineate patch use from behaviors associated with search and transit. Most problematic is the development of realistic gain functions that accurately reflect rates of patch depletion. Technological advances in satellite tracking and behavioral recording of marine predators have enabled the generation of large scale data sets of sufficient quality to provide robust tests of foraging models, given the ability to differentiate foraging behaviors from available sensor data (Naito, 2004).

To date, most investigations of optimal foraging in air-breathing marine predators have focused on individual dives and decisions related to time at depth and the allocation of time over the dive cycle. Several different models have been proposed to predict optimal depth and time at foraging depth (Houston and Carbone, 1992; Carbone and

Houston, 1996; Mori, 1998, 1999, 2002; Thompson and Fedak, 2001). A variety of

4 marine divers, such as grey seals, southern elephant seals, Steller sea lions and blue whales, terminate foraging dives prior to estimated aerobic limits and suggest that time spent in the foraging zone is moderated by patch quality indicating patch assessment and modulation of dive time (Cornick and Horning, 2003; Doniol-Valcroze et al., 2011;

Sparling et al., 2007; Thums et al., 2013). In contrast, use of MVT models to predict multi-dive use of prey patches and initiation of searching for new patches has been rare.

The multi-decade long research program on foraging in female northern elephant seals (NES) provides an extraordinarily large sample size with which to examine patch characteristics over large spatial and temporal scales (Robinson et al. 2012). In addition, there exist several measures of long term foraging success in NES including at sea changes in lipid mass, which impact rates of descent during food-processing drift dives

(Crocker et al., 1997), and direct measures of energy gain from changes in mass and body composition over foraging trips (Robinson et al., 2012; Hassrick et al. 2013). Body reserves accrued at sea during foraging migrations are the primary determinant of reproductive effort in NES and thus provide a relevant fitness proxy (Crocker et al.,

2001). NES also have low adult mortality at sea (Deutsch et al., 1994) which minimizes the potential importance of alternative currencies such as predation risk. Thus, NES provide an excellent system to assess patch departure decisions relative to dive characteristics and the resultant impacts on foraging success.

Female NES perform two extended foraging trips per year to renew their energy stores after molting or breeding and to accrue energy reserves for gestation and lactation

(Crocker et al., 2001). They feed on mesopelagic prey along oceanic fronts and in mesoscale eddies that occur in distinct patches in the Transition Zone and Subarctic Gyre

5 in the Pacific Ocean (Le Boeuf et al., 2000a; Robinson et al., 2010; Simmons et al.,

2010). NES display several characteristic dive shapes associated with foraging behavior

(Hassrick et al. 2007). Benthic foraging dives are flat-bottomed and reflect coastal foraging along the continental margin (Le Boeuf et al., 2000a), while dives that are categorized as pelagic foraging have a distinctive bottom time characterized by vertical excursions (VE). These VE are associated with dramatic changes in swimming speed that are consistent with pursuit of prey in the water column (Hassrick et al. 2007). It is hypothesized that these VE are prey capture attempts (Baechler et al., 2002; Bost et al.,

2007; Gallon et al., 2013; Le Boeuf et al., 2000a; Naito et al., 2013; Thums et al., 2008) and thus can be used as a proxy for PEE. Direct measurement of foraging events via stomach temperature sensors has shown that the vast majority of foraging occurs during

VE at the bottom of dives (Kuhn et al., 2009), and VE have also shown to be associated with feeding events in several other studies (Horsburgh et al., 2008; Thums et al., 2008).

A variety of other metrics have been used as proxies for prey capture attempts including jaw accelerometry (Foo et al., 2016; Gallon et al., 2013; Naito et al., 2013), stomach temperature (Horsburgh et al., 2008; Kuhn et al., 2009), and bottom sinuosity

(Heerah et al., 2014). Stomach temperature sensors have short recording lifetimes due to short sensor retention times (Austin et al., 2006; Kuhn et al., 2009). Accelerometers sample many times per second, which may limit the ability to record an entire foraging trip due to restricted memory capacity. In contrast, VE are easily derived from simple dive traces, are frequently available for entire foraging migrations, and can be used to examine large historical databases. Similar to jaw accelerometers, the use of VE as proxies for foraging success is limited by their inability to provide information about the

6 success of the associated foraging attempt. However, they are the best available proxy for variability in PEE and foraging effort. This approach assumes relatively consistent prey capture success while foraging.

NES make a series of successive pelagic foraging dives, termed bouts. The temporal structure of bouts of pelagic foraging dives has been shown to vary with ocean climate, influence foraging success over migrations, and be influenced by the age of foraging females (Crocker et al., 2006; Zeno et al. 2008; Hassrick et al., 2013). In the present study, we consider only large scale patch departure decisions on the level of dive bouts, including vertical transit to the surface between contiguous foraging dives as

'within patch'. We investigated the bout structure, within-bout gain functions and diving behavior of female NES foraging over a large spatial and temporal scale. The objectives of this study were to: (1) examine within-bout gain functions using VE as a proxy for

PEE; (2) examine variation in foraging bout and gain function characteristics with season, year, geoposition, and female age; and (3) examine the relationship of VE and patch depletion to foraging success.

MATERIALS AND METHODS

Sample and instrument attachment

The animal use protocol for this research was reviewed and approved by the

University of California at Santa Cruz Institutional Animal Care and Use Committee and followed the guidelines established by the Canadian Council on Animal Care and the ethics committee of the Society of Marine Mammalogy. Research was carried out under

National Marine Fisheries Service permits: #786-1463 and #87-143. A sample of 205 individual female NES from Año Nuevo State Reserve in San Mateo County, California, were tagged during haul-outs using 0.5 W ARGOS satellite transmitters (Wildlife

Computers, Belleview, WA, USA: SPOT4, SPOT5, MK10-AF; or Sea Mammal

Research Unit, St. Andrews, Scotland: SRDL-CTD) sampling at a 45 second repetition rate and time depth recorders (Wildlife Computers MK9, MK10; or Lotek, St. John’s,

NL, Canada: 2310) sampling at least once every 8 seconds between the years 2004 and

2012. These instruments recorded geographic location, movement, and diving behavior over the post-breeding and post-migration foraging trips. Diving behavior and foraging success in a subset of these females were analyzed previously (Robinson et al., 2012).

We sampled females in good health from ages 4 to 17. Out of 303 complete migration records, 249 of the records were from known-age females, whose age was determined from flipper tags applied at weaning. Females were chemically immobilized with a ~1mg/kg intramuscular injection of tiletamine hydrochloride and zolezepram hydrochloride (Telazol, Fort Dodge Laboratories, Fort Dodge, IA, USA) and immobilization was maintained with intravenous injections of 100mg ketamine hydrochloride into the extradural vein. Instruments were attached and recovered using standard procedures described previously (Robinson et al. 2012).

Body composition of each animal at deployment and recovery was assessed using the truncated cones method (Crocker et al., 2001; Gales and Burton, 1987; Webb et al.,

1998). Blubber thickness was measured with an ultrasound scanner (Ithaco Scanoprobe,

Ithaca, NY, USA) at 18 locations along the body coupled with 8 girth and length measurements. This method has been validated against water isotope measurements of

8 body composition (Webb et al., 1998). Mass was measured using a Dyna-Link scale

(capacity 1000 kg, accuracy ±1 kg, Dyna-Link MSI–7200, Measurement Systems

International, Seattle, Washington, USA) by suspending the seal in a canvas sling attached to a tripod. Mass at return of trip was corrected for time that elapsed between arrival at the rookery and instrument recovery (as well as the time elapsed between instrument deployment and the animal leaving the rookery) by using an equation based on serial measurements taken on females over the course of their fasting on shore. [mass change (kg d-1) =0.51+0.0076 * mass, n=27, r2 =0.79, p<0.01] (Simmons et al., 2010).

On average, seals were on shore 7 ± 5 days after deployment and 5 ± 4 days prior to recovery. We assumed adipose tissue was 90% lipid and lean tissue was 27% protein.

Gross energy content was calculated assuming 37.33 kJ g-1 and 23.5 kJ g-1 for lipid and protein respectively. For post-molting females, pup mass was added to the estimated weight at arrival with the assumption that pups were 13% adipose tissue (Crocker et al.,

2001).

Track and diving analysis

All tracks were truncated to arrival and departure dates and filtered for speed and turning angle to remove biologically improbable locations (maximum thresholds:

12km/hr and 160o). Tracks were also smoothed using a space-state model due to the frequency of low quality ARGOS location classes (the majority of classes were A and B).

The IKNOS Matlab dive analysis toolbox was used to zero-offset correct the raw data and calculate individual dive summary statistics sampling at 8 second intervals (Robinson

9 et al., 2012). This included information on bottom time, ascent and descent rate, dive duration, maximum dive depth and dive efficiency (bottom time/dive duration) for each recorded dive. All dives were required to be over 32s long and 15m deep to be considered for analysis. This eliminates variable surface behavior not associated with foraging.

The dives were classified into the four different types (transit, pelagic foraging, benthic foraging and drift dives) using a hierarchical classification program that uses a

Matlab dive typing algorithm to distinguish between individual dives (Robinson et al.,

2010). VE were defined by the IKNOS package as a change in vertical direction at the bottom of a dive over 8 second subsampling periods. We used VE as a proxy for PEEto calculate the gain functions for NES. Log-survivorship analysis generated a minimum foraging bout criterion of 2-3 dives within individuals (Crocker et al., 2006; Zeno et al.,2008; Hassrick et al., 2007). In this study, we defined a foraging bout as consisting of at least 3 or more dives and a bout was deemed finished when it was followed by two consecutive non-foraging dives (Crocker et al., 2006).

Gain function analysis

We used a power function model to fit dive bouts with more than four dives in order to calculate the gain function. The gain functions were calculated using only dive bouts that consisted of 4 or more dives due to the difficulty in accurately fitting nonlinear models with fewer than four data points. A power function (y = α*xβ) was fit to each bout using Matlab where α is the coefficient parameter estimate that is linked to the

10 number of prey capture attempts on the initial dive; and β was the exponent parameter estimate that represents change in prey encounter rates over a foraging bout. When β was less than 1, a bout was classified as decelerating. When β exceeded 1, a bout was classified as accelerating (Figure 1). The y in the power function indicates the total number of prey capture attempts, and the x variable represents the time in minutes since the start of the first dive in a bout. We calculated the gain functions along with their R2 values using this model.

Statistical analysis

Variation in power function parameters with season, year, female age, geoposition, and dive depth were analyzed using linear mixed effect models with individual seal as a random effect. Post-hoc comparisons were made using a student’s t- test to compare least square means from the mixed model. Model residuals were assessed for approximate normality and homoscedascity. A mixed model power function was fit to the relationship between number of dives in a bout and the deceleration constant, β. Due to the extremely large sample size, we filtered significant model effects based on effect size. Effect size was calculated for statistically significant fixed effects using a mixed model R2 (Edwards et al., 2008). Only effects with R2 greater than 0.1 were presented and discussed. We also used linear regression to examine the relationship between the mean number rate of VE over entire dives or bottom time and the mean energy gain rate for each annual migration in order to validate the use of VEs in NES as a measurement of foraging success through energy gain rate.

Mean bout and dive characteristics were calculated for all individual records and a grand mean was calculated by season and year including number of dives in a bout, bout duration, dive depth, VE per bout, VE per dive, VE per minute, VE per minute of bottom time, total vertical distance covered during VE for each dive, vertical depth range covered by VE during each dive and dive efficiency (bottom time/dive duration). All statistical analyses were performed in JMP 12.0, unless otherwise noted.

RESULTS

Diving behavior

In total, we analyzed 77,820 foraging bouts over 303 different migration trips in

205 individual female NES. The mean number of foraging bouts per migration was 2.3 times higher during the gestational post-molt trip than during the post-breeding trip

(Table 1). This difference was strongly influenced by the increased mean duration of the post-molt migration (2.9 times greater; 220 days vs. 76 days). Within seasons, the number of bouts per trip did not vary annually. The number of dives per foraging bout did not vary by season or year although this parameter had much greater variance among individuals during the post-molt migration (Table 1). Mean bout duration, dive depth and dive duration were invariant between seasons and years indicating stable dive behavior over large spatial and temporal scales (Table 1).

Mean prey encounter behavior over bouts was also remarkably consistent across seasons and years but showed marked variation at the level of individual bouts and dives.

VE per bout were highly variable in individual bouts but did not vary significantly

12 between years or seasons (Table 2). In contrast, the number of VE per dive was steadily increasing over the duration of the study during the post-breeding season but was consistent in the post-molting season (Table 2). Similarly, the rate of VE while diving varied between years during the post-breeding migration but has remained the same in the post-molting season. The rate of VE during bottom time varied annually in both foraging migrations. The general pattern was increasing rates of VE during the bottom of dives across the study period during the post-breeding migration and decreasing rates across years during the post-molt migration (Table 2). Both the total vertical distance covered during VE for each dive in meters and bottom range increased over the study period in both the post-breeding and post-molting migrations. For example, the range of depths covered during VE increased 63% over the study period in post-breeding females and 51% in post-molt females. The ratio of bottom time to dive duration or efficiency of foraging was relatively consistent across seasons and years except for increased efficiency during 2010 and 2011 in post-molt females (Table 2).

Gain functions

The fit of the power function to cumulative VE over individual dive bouts yielded an R2 ≥ 0.99 in 96.4% of bouts analyzed indicating that the power function was an appropriate model for patch depletion in NES. The majority of bouts (83%) were classified as decelerating with the remaining 17% yielding accelerating rates of VE

(Figure 2). These percentages were consistent across post-molt and post-breeding migrations and across age classes (Table 3). Similarly, the mean coefficient (α) that

13 represented the starting rate of VE for each bout did not vary between seasons or years.

Thus, when used as an index of patch quality, the power function suggested consistent overall patch depletion characteristics across years and seasons.

Deceleration coefficients (β) and initial coefficients (α) exhibited statistically significant but biologically insignificant associations with latitude and longitude (R2=

0.001 - 0.03, p < 0.05) across both migrations. This indicates that there were no important relationships between latitude, longitude and patch type or initial number of prey capture attempts. This finding was consistent with visual inspection of bout type along tracks which revealed no distinct pattern to the location of decelerating or accelerating bouts (Figure 3). Similarly, β and α had statistically significant but extremely weak relationships to dive depth and duration (R2 = 0.01-0.03, p < 0.0001).

There were no significant effects of season or year on the gain function

2 coefficients β or α, except for an exceptionally weak impact of year on β (R =0.02, F8,

380.9 = 2.16, p = 0.03). These findings remained consistent when patches were divided into decelerating and accelerating types. Deceleration coefficients had strong and consistent impacts on the number of dives within a foraging bout. The mean number of dives in a foraging bout increased exponentially as rates of patch depletion declined for

2 2 both foraging migrations (R =0.99, F1,79=3771, p<0.0001 and R = 0.99, F2,81=2925, p<0.0001 for post-molting and post-breeding respectively; Figure 4).

Foraging success

Foraging success over the entire migration was not affected by any bout or diving variable except the long term mean rate of PEE. At the level of each grouped foraging migration (e.g. post-molt, 2005), mean energy gain rate increased with the rate of VE

-1 2 min during the entire dive (R = 0.56, F1, 15 = 19.4, p < 0.001; Figure 5A) and with the

-1 2 rate of VE min during the bottom time (R = 0.26, F1, 15 = 5.4, p =0.03; Figure 5B). At the individual trip level, the rate of VE min-1 during the entire dive was also a significant

2 predictor of individual energy gain rate (R = 0.34, F1, 270 = 140.7, p < 0.0001; Figure 6).

However the slope of the relationship between VE rate and energy gain was significantly greater in post-breeding migrations (F1, 268 = 36.6, p < 0.0001; Figure 6). In contrast to the number of VE, the depth range of VE and the total vertical distance covered during

VE showed no association with foraging success (p > 0.05).

DISCUSSION

Consistent with MVT assumptions, female NES exhibited decelerating gain functions in the majority of their patches. This suggests the utility of NES to test MVT models of patch departure during pelagic foraging migrations and provides an empirical basis for describing rates of patch depletion. In addition, the deceleration constant derived from fitting a power function to cumulative VE was predictive of the number of dives in a foraging bout indicating that patch depletion characteristics influenced patch departure decisions. Foraging female NES follow the qualitative predictions of the MVT by modifying the number of dives, which have consistent durations (Table 1), in a bout in

15 response to prey patch quality, thereby spending more time in higher quality patches that take longer to deplete.

The proportion of patches with decelerating gain functions was consistent across years, seasons, and female age. This was reflected in similar mean foraging bout characteristics with similar numbers of dives and number of putative PEE within a foraging bout over seasons and years. Female NES exploit comparable proportions of decelerating patch types over their lifetime. In addition, the mean patch deceleration constant and the mean number of prey encounters on the initial dives in foraging bouts were similar over seasons and years. The stability of the seasonal and annual means of these features over nearly a decade of studies allows the potential for female NES to develop an adaptive long-term strategy to maximize energy gain. Due to consistent long- term mean rates of patch depletion in an ephemeral ocean, NES can potentially develop foraging rules to maximize energy acquisition and growth over long time scales. This may help to buffer against short term reductions in prey availability and support a capital breeding life-history strategy that prioritizes success over the scale of entire foraging migrations.

A subset of the gain functions were found to be accelerating (17%), highlighting the need to quantify gain functions when implementing MVT models (Searle et al.,

2005). The existence of patches that accelerate in putative PEE may reflect use of varied prey resources by NES. This pattern might be a result of high quality prey that satiate the predator before it has time to deplete the patches’ resources. The accelerating patches may also result from prey that aggregate more closely in response to the presence of a predator thus leading to higher encounter rates later in the bout. Alternatively, varied

16 mesoscale oceanographic features that lead to the aggregation of prey (Simmons et al.

2010) may limit the dispersal of prey fields and alter rates of PEE. There was no clear geospatial pattern to accelerating type patches, occurring intermittently across most foraging tracks with decelerating patches sometimes occurring during the same day. This pattern makes it difficult to use at-sea measures of foraging success, like drift rates, to assess the relative success associated with varying patch types. However, these accelerating gain function patch types occurred in all females’ records and may contribute significantly to overall foraging success.

The similarity of mean within-bout dive behavior (e.g. mean seasonal dive durations and depths) across the study period, despite widely variable characteristics of individual bouts and changes in physiological features that may influence breath-hold ability (Hassrick et al. 2010; Maresh et al. 2015), may reflect a consistent long-term foraging strategy that maximizes success over months of foraging. In contrast, mean rates of VE over dives and their associated features changed markedly over the study period and strongly impacted foraging success and body reserves when seals came on shore. Mean energy gain rates for the annual and seasonal foraging migration varied positively with rate of VE over the entire dive. This association was also evident at the level of individual female migrations. This result supports the use of VE as a proxy for

PEE in female NES which is consistent with previous studies on foraging seals (Baechler et al., 2002; Bost et al., 2007; Gallon et al., 2013; Le Boeuf et al., 2000a; Naito et al.,

2013; Thums et al., 2008).

Mean numbers of PEE over bouts and rates of VE during dives were much more variable in post-breeding migrations than in post-molt migrations. This difference was

17 reflected in the more variable rates of energy gain among post-breeding individuals.

Similarly the impact of VE on energy gain (i.e. the slope of the regression) was significantly higher during the shorter post-breeding migration. The greater stability of mean PEE and foraging success over the gestational post-molt trip may reflect the ability of the longer trip to buffer against short term variation in prey availability. However, it may also reflect differences in habitat use between the two migrations. Most females feed in the Sub-Artic Gyre during post-breeding migrations. During post-molt migrations, females use the additional foraging time to reach the Transition Zone

Chlorophyll Front (TZCF), an area associated with slower transit rates and greater area- restricted searching (Robinson et al., 2010; Simmons et al., 2010). The TZCF may present a more annually consistent aggregation of prey resources that are not attainable during the post-breeding migration. Previous investigations have shown the post- breeding migration to be more variable in duration in response to ocean climate (Crocker et al., 2006). This feature may allow females to compensate for more variable rates of success when recovering from the previous year’s breeding prior to implantation during the molt haulout.

Since mean dive behavior and bout structure were similar across seasons and years and prey encounter rates were largely predictive of foraging success, this suggests that female NES employ consistent diving rules when foraging and that individual differences in foraging success were most strongly affected by the quality of patches detected. However, some annual changes suggested alterations in foraging behavior required to pursue prey. In later years, there was a strong increase in the vertical depth range and the total vertical distance covered during VE during both foraging migrations.

This suggests increased foraging effort during the bottom of dives that is not reflected in our proxy for PEE. This change may have been due to a number of factors including changes in prey types, prey behaviors or physical forcing of oceanographic characteristics. Notably, dive efficiency, defined as the proportion of the dive in the foraging zone, increased in post-molting females in those same years and exhibited a similar trend during the post-breeding migration. This increase in efficiency may reflect increased aerobic breath-hold ability through metabolic and behavioral adjustments

(Hassrick et al., 2013, Maresh et al. 2015) and may be driven by seasonal changes in prey availability. While the source of this change is not known, the magnitude of the change and its consistency across large annual samples of females suggests an important alteration in prey or foraging behavior with changes in ocean climate.

Previous MVT studies have shown that many marine mammals optimize their average rate of energy intake on the level of dives by moderating their time at depth in relation to patch quality. Closely related southern elephant seals show increased bottom durations in dives where they encountered prey and when more prey capture attempts occurred (Gallon et al., 2013; Jouma'a et al., 2015) aligning with predictions from the

MVT. Further testing in sea lions and grey seals has shown that dive bottom durations increased with increasing prey encounter rates up to an asymptote indicating physiological constraints of dive times in these animals due to oxygen limitations

(Cornick and Horning, 2003; Sparling et al., 2007). Similar results were found on the level of a dive in a study on Australian fur seals where dives with more PEE had longer bottom durations (Foo et al., 2016). Therefore, marine divers spend more time at depth in response to increasing patch quality within the physiological constraint of their oxygen

19 stores. In contrast, this study focused on the choice of patch departure times on the level of the dive bout. Our results also conformed to predictions of the MVT, as divers performed more sequential dives in patches that depleted more slowly, a proxy for patch quality. Together these results suggests that foraging decisions for marine divers are complex and reflect hierarchical decisions where divers can optimize behavior at different levels relative to patch characteristics. Air-breathing marine predators make important foraging decisions by altering time spent at depth on individual dives and by altering swimming behavior while in transit to depth or the surface. In addition, predators make decisions about whether to return to detected and exploited patches on subsequent dives or to emphasize swimming behaviors that result in horizontal transit

(Hassrick et al. 2007) and search for new, unexploited patches. Finally, predators must manage time and distance of travel from breeding haulouts relative to life history constraints and capital vs. income breeding strategies. These features provide mechanistic associations between diving physiology, foraging ecology and life-history strategies that are adaptive over seasonal, annual and decadal changes in oceanographic features and may strongly influence the ability of species to respond to rapid changes in ocean climate.

CONCLUSION

As capital breeders, NES maximize reproductive effort and success by optimizing their average long-term rate of energy gain during foraging migrations and over their life- span. As a result of their long duration migrations and persistent mean decelerating patch

20 characteristics, they have the opportunity to acquire information that can form the basis for optimized patch departure decisions. Rates of patch depletion, as measured by putative PEE, strongly influenced patch residence times. Rates of prey encounter were a major driver of foraging success and thus may be the key criterion by which NES evaluate patch quality to inform decisions on patch departure. Empirical assessment of gain functions will enable stronger and more realistic tests of OFT models in future investigations. Most importantly, these findings provide insight into the advantages that select for capital breeding strategies, their association with foraging over wide spatial and temporal scales, and the ability to buffer reproductive success over short term variations in prey availability.

Table 1. Mean diving behavior for all records averaged by year and season. A minimum criterion for a foraging bout was defined as 3 consecutive foraging dives. A mean was calculated for each individual seal’s foraging trip and grand means and SD are presented for all years and seasons.

# Bout Dive Dive Bouts Bouts Season Year Females -1 SD dives SD duration SD depth SD duration SD analyzed trip -1 -1 bout (min ) (m) (min)

2004 4 651 162.8 49.2 13.5 7.0 285.0 154.4 460 66 20.7 2.1

2005 15 3587 163.8 35.1 14.3 4.2 330.2 113.3 545 61 22.5 2.0

2006 18 3819 170.9 38.8 15.5 4.8 332.3 100.1 520 56 21.4 1.6

2007 15 4206 190.5 25.3 11.9 3.8 261.6 89.3 563 34 21.4 1.3

2008 20 5229 190.6 26.1 11.6 4.7 253.5 109.7 553 33 21.6 1.5 Post- breeding 2009 14 2748 168.6 32.6 11.9 4.2 279.9 122.3 550 38 22.7 1.7

2010 20 4282 170.2 23.9 13.4 3.6 305.3 74.4 568 42 22.7 2.5

2011 18 3431 190.6 43.1 14.0 4.7 331.4 86.4 539 33 23.5 2.5

2012 19 3314 177.2 38.1 13.0 4.4 298.1 96.5 550 48 22.6 2.7 Mean ------176.1* 13.2 297.4 539 22.1*

2004 21 11622 422.0 95.0 12.5 11.1 292.9 77.2 520 45 23.5 2.3

2005 24 10930 410.2 87.4 13.1 11.9 305.1 104.3 528 47 22.7 2.7

2006 19 9206 378.6 131.3 11.7 10.8 259.6 83.7 526 27 22.0 2.5

2007 18 9563 398.9 103.0 12.5 10.6 295.9 91.4 535 47 23.7 2.7

Post- 2008 13 6618 402.7 99.2 14.2 11.6 362.1 115.7 546 25 25.2 2.5 molting 2009 10 3070 371.9 107.4 12.3 10.6 299.6 93.2 545 39 24.1 2.2

2010 18 7002 398.7 109.9 12.9 10.5 316.9 55.2 550 43 25.0 2.3

2011 14 6778 484.1 134.1 13.7 11.2 333.2 78.1 539 29 24.3 1.6 Mean ------408.4* 12.9 304.6 536 23.8*

Table 2. Grand mean and SD for VE on the bottom of dives, total vertical distance covered during VE for each dive (TVD), the vertical depth range covered by VE for each dive (bottom range) and the ratio of bottom time to dive duration (efficiency) averaged for each female by season and year.

VE Bottom VE VE -1 TVD Efficienc Season Year -1 SD 1 SD VE min SD bottom SD SD range SD SD bout dive -1 (m) y time (m)

2004 257 287 14.1a 1.6 0.66a 0.11 1.56a 0.22 273a 31 87a 11 0.43 0.02 2005 226 247 15.9a,b 1.9 0.71a 0.08 1.72a 0.24 288a 28 98a 14 0.41 0.02 2006 256 275 15.6a 2.2 0.70a 0.09 1.72a 0.26 286a 30 93a 15 0.41 0.03 2007 182 191 16.2b 2.1 0.73a,b 0.06 1.81b 0.15 285a 35 100a 23 0.40 0.02 Post- 2008 176 193 15.9b 1.0 0.73a,b 0.04 1.79b 0.26 290a 29 101a 9 0.40 0.02 breeding 2009 182 193 18.9c 1.3 0.85b 0.06 2.04b 0.21 290a 34 100a 14 0.39 0.03 2010 214 227 18.7c 1.5 0.80b 0.04 2.01b 0.25 320a 45 116b 26 0.39 0.03 2011 236 238 18.3c 1.6 0.78b 0.07 1.85b 0.19 374b 53 143c 22 0.42 0.03 2012 216 206 18.2c 1.6 0.80b 0.08 1.83b 0.13 379b 52 142c 22 0.44 0.03 Mean 216 16.9 0.75 1.81 322 110 0.41 2004 211 200 16.7 1.9 0.70 0.07 1.57a,b 0.36 312a 27 97a 13 0.41a 0.03 2005 223 219 17.2 1.9 0.74 0.06 1.69a 0.37 311a 45 99a 10 0.41a 0.03 a a a 2006 194 186 15.9 1.6 0.73 0.09 1.74a 0.34 287 46 92 11 0.38 0.03 2007 175 188 16.3 1.7 0.71 0.04 1.77a 0.35 327a 50 98a 11 0.40a 0.02 Post- a a a a molting 2008 242 310 17.1 1.0 0.71 0.03 1.71 0.34 329 28 99 7 0.41 0.02 2009 217 197 18.3 1.4 0.74 0.04 1.75a 0.33 334a 46 109a 19 0.41a 0.03 2010 231 201 16.9 1.5 0.68 0.05 1.44b 0.33 391b 59 139b 25 0.46a 0.02 2011 241 216 17.1 1.0 0.69 0.05 1.42b 0.17 417b 47 146b 18 0.46b 0.02 Mean 217 16.9 0.71 1.64 327 110 0.42

Table 3. Mean energy gain rate, deceleration constant and initial number of VE for all records by year and season. A minimum criterion for a foraging bout was defined as 3 consecutive foraging dives. A power function (y = α*xβ), where y is the cumulative number of VE, was fit to each bout using Matlab. α is the coefficient parameter estimate that is linked to the number of prey capture attempts on the initial dive and β is the exponent parameter estimate that represents change in PEE over a foraging bout.

Energy Season Year gain SD Β SD α SD (Mj day-1)

2004 12.8 7.2 0.813 0.053 2.98 0.95 2005 14.11,2 7.0 0.821 0.038 2.55 0.54 2006 14.53,4 7.5 0.808 0.059 2.73 0.68 2007 19.6 7.5 0.801 0.033 2.65 0.56 Post- 2008 16.7 7.3 0.799 0.045 2.77 0.47 breeding 2009 23.61,3 9.8 0.807 0.040 2.55 0.41 2010 22.32,4 8.1 0.813 0.036 2.57 0.39 2011 18.3 7.4 0.802 0.033 2.66 0.31 2012 19.5 6.9 0.776 0.101 2.86 0.65 Mean 17.9 0.804 2.70

2004 19.5 2.9 0.818 0.037 2.47 0.32 2005 19.2 3.3 0.817 0.039 2.65 0.55 2006 15.7 3.2 0.804 0.041 2.70 0.45 2007 15.2 4.5 0.807 0.046 2.66 0.49 Post- 2008 17.5 3.5 0.843 0.026 2.54 0.83 molting 2009 21.8 5.5 0.826 0.029 2.39 0.24 2010 16.3 3.5 0.832 0.035 2.52 0.35 2011 18.4 2.6 0.811 0.022 2.78 0.51 Mean 18.0 0.820 2.59

Table 4. Relative percentages of accelerating and decelerating patches in all tracks, post- molting season, post-breeding season and age classes young (3-5 years old), prime (6-9 years old) and old (10+ years old).

% decelerating % accelerating PM 81.0 ± 5.7 19.0 ± 5.7 PB 84.2 ± 5.8 15.8 ± 5.8 Young (3-5) 84.6 ± 5.1 15.4 ± 5.1 Prime (6-9) 81.8 ± 5.4 18.2 ± 5.4 Old (10+) 83.4 ± 5.3 16.6 ± 5.3 All migrations 82.8 ± 6.0 17.2 ± 6.0

Figure 1. Example of decelerating gain function fit from seal 2004005 (A) and accelerating gain function from seal 2004004 (B) using time in minutes in a bout and cumulative number of VE.

Figure 2. The number of dives associated with β values in the power function. Decelerating bout counts are shaded while accelerating are blank.

Figure 3. Individual patches along the tracks of three different seals: 2009008, 2009014 and 2012010. Red positions indicate accelerating patches while yellow indicate decelerating patches. Latitude and longitude show no relationship with patch type.

Figure 4. When a power function was fit to the cumulative number of VE in a foraging bout, the power exponent, β, predicted the mean number of dives in decelerating post- breeding (A) and post-molting (B) migration bouts.

Figure 5. Mean rate VE during a dive (A) and the number of VE per minute of bottom time (B) affects daily energy gain rate. Each point represents the grand mean for all females in a migration season. Error bars are SE of the grand mean.

Figure 6. Changes in energy gain rate of entire foraging migrations with the mean rate of VE during dives. Open circles and dashed line are means for individual post-molt females. Closed circles and solid line are means for individual post-breeding females.

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