Evaluating gain functions in foraging bouts using vertical excursions in northern elephant seals by Michelle S. Ferraro A thesis submitted to Sonoma State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE m Biology Dr. Daniel E. Crocker, Chair Dr. Dorian S. Houser Dr. Derek J. Girman Date l ~_ Copyright 2016 By Michelle S. Ferraro ii Authorization for Reproduction of Master's Thesis Permission to reproduce this thesis in its entirety must be obtained from me. Permission to reproduce parts of this thesis must be obtained from me. DATE: 'ff 2 fol/ C, Signature Street Address City, State, Zip 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. CbaIT: Signature MS Program: Biology Sonoma State University Date: 4 /1 Ce, J t ~ IV 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 v 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). vi 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 1 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). 2 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