Evolutionary Ecology Research
online appendices for:

Alejandro Frid, Lawrence M. Dill, Richard E. Thorne & Gail M. Blundell. 2007.
Inferring prey perception of relative danger in large-scale marine systems.
Evolutionary Ecology Research, ar2178.pdf

Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F

Appendix A.

Measures of fish biomass during day (red) and night (blue) used as empirical inputs into Equation 1. Data were collected during March 2003 and 2004 in Prince William Sound (years pooled, see Methods). Panel A shows extreme outliers (11-280 X the mean) and Panel B shows values 10 X the mean. Regression lines are drawn with a distance weighted least square smother at tension = 1 (Wilkinson 2004).

Appendix B.

Characteristics of instrumented harbor seals and Pacific sleeper sharks at time of capture. Likely age classes of seal are estimated from length-age plots in Pitcher & Calkins (1979).

Species and identification	*Sex class	*Weight (kg).	† Length (cm)	Likely age class of seals (years)
seal af3	female	74.5	139	adult (>3)
seal af17	female	48.9	132	adult (≥3)
seal jf12	female	33.7	111	juvenile (1–2)
seal jf24	female	40.3	115	juvenile (1–2)
seal yf22	female	33.0	99	yearling (<1)
seal yf27	female	34.6	105	yearling (<1)
seal am1	male	157	101.0	adult (>3)
seal am8	male	86.4	149	adult (>3)
seal jm9	male	59.4	130	juvenile (1–2)
shark 2	unknown	231.4	250	-
shark 11	unknown	138.9	210	-
shark 21	unknown	120.4	200	-

*Seals were sexed and weighed directly while aboard a vessel. Sharks were handled in the water alongside the vessel and could not be sexed; their weights were estimated from the equation (Sigler et al. 2006), were W is weight and PCL is precaudal length.
† Precaudal length for sharks (Hulbert et al. 2006); standard length for seals.

 

Appendix C.

Assumptions about resources available to seals of length l (see Appendix B). Fish species
compositions for strata 55 m, 56-95 m, and >95 m were, respectively, Pacific herring only, equal proportions of
Pacific herring and walleye pollock, and walleye pollock only.

*Assumes maximum exploitable lengths of fish were 40 and 45 cm, respectively, for l115 and 130 cm.
**When including all fish sizes, mean mass at >95 m and 56-95 m is 711.35 g and 416.46 grams, respectively.
†Based on energy densities of 5.80 kJ g for Pacific herring (mean value for male and female adults during spring in Prince William Sound: Paul et al. 1998) and 4.08 kJ g for adult walleye pollock (value for Southeast Alaska during March: Vollenweider 2004), and 0.90 assimilation efficiency (Rosen et al. 2000).

Appendix D.

Dive data for all individual seals used as empirical inputs into the model. Panel sets are identified by diel period and dive cycle component. Individual panels within a set are identified by individual (see Appendix A). Regression lines are drawn with a locally weighted smoother at tension = 0.5 (Wilkinson 2004); axes are log10 scaled.

a) Preceding surface interval during day.

b) Preceding surface interval during night.

c) Patch residence during day.

d) Patch residence during night.

e) Travel time during day.

f) Travel time during night.

g) Travel rate during day.

h) Travel rate during night.

Appendix E.

Examples of per dive net energy gain and predation risk predicted under conditions of Experiment 8 (Table 3: ). Columns contrast a deep and a shallow diving adult female (af17 and af3, respectively). Red symbols represent day, and blue symbols represent night.

Appendix F: Sensitivity analyses

We conducted sensitivity analyses for four parameters whose values were based on either limited or no empirical data (see Methods). Values were changed one at the time, as described below. For all figures shown below, the panels represent computer experiments in the same order as Fig. 3.

Parameter k

Parameter k (see Equation 2) was given a value of 0.99 in the original experiments. Here we re-parameterised it as k = 0.95. As shown in the figure below, the re-parameterisation did not change conclusions derived from the original experiments (Fig. 3). (Y-axis values are unrealistic here, yet we are concerned only with the shape and fit of the regression line).

Parameter

In the original experiments, different levels of ε used different values of aε for scaling (see Equation 1). To assess whether aε differences might confound ε effects, here we used = 1 for both ε levels. As shown in the figure below, the re-parameterization did not change conclusions derived from the original experiments (Fig. 3). (Y-axis values are unrealistic here, yet we are concerned only with the shape and fit of the regression line).

Exploitable sizes of fish

Here we assume a 5-cm decrement in maximum sizes of exploitable fish, which leads to the following re-parameterization (compare it to Appendix C).

*Assumes maximum exploitable lengths of fish were 35 and 40 cm, respectively, for l115 and 130 cm.
† Based on energy densities of 5.80 kJ g for Pacific herring (mean value for male and female adults during spring in
Prince William Sound: Paul et al. 1998) and 4.08 kJ g for adult walleye pollock (value for Southeast Alaska during
March: Vollenweider 2004), and 0.90 assimilation efficiency (Rosen et al. 2000).

As shown in the figure below, the re-parameterization did not change conclusions derived from the original experiments (Fig. 3).

 

Twice the metabolic costs

We made many assumptions about metabolic costs. Rather than doing numerous sensitivity analyses to address them, we did one extreme re-parameterization: the doubling of metabolic rates. As shown in the figure below, the re-parameterization did not change conclusions derived from the original experiments (Fig. 3).

Literature cited

Anthony, J. A., Roby, D. D. and Turco, K. R. 2000. Lipid content and energy density of forage fishes from the northern Gulf of Alaska. - Journal of Experimental Marine Biology and Ecology 248: 53-78.

Hulbert, L., Sigler, M. and Lunsford CR 2006. Depth and movement behaviour of the Pacific sleeper shark in the northeast Pacific Ocean. - Journal of Fish Biology 69: 406-425.

Paul A.J., Paul J.M. & Brown E.D. (1998) Fall and spring somatic energy content for Alaskan Pacific herring (Clupea pallasi Valenciennes 1847) relative to age, size and sex. Journal of Experimental Marine Biology and Ecology 223, 133-142

Pitcher, K. W. and Calkins D.G. 1979. Biology of the harbor seal, Phoca vitulina richardsi, in the Gulf of Alaska. - Final report to OCSEAP, U.S. Department of Interior, BLM. Res. Unit 229. Contracat 03- 5-002-69. 72pp.

Rosen D.A.S., Williams L. & Trites A.W. (2000) Effect of ration size and meal frequency on assimilation and digestive efficiency in yearling Steller sea lions, Eumetopias jubatus. Aquatic Mammals 26.1, 76-82

Sigler, M. F., Hulbert, L. B., Lunsford, C. R., Thompson, N., Burek, K., Hirons, A. and Corry-Crowe, G. M. 2006. Diet of Pacific sleeper shark, a potential Steller sea lion predator, in the northeast Pacific Ocean. - Journal of Fish Biology 69: 392-405.

Vollenweider, J. J. Variability in Steller sea lion (Eumetopias jubatus) prey quality in southeastern Alaska. 2004. Fairbanks, Alaska, University of Alaska, Fairbanks.

Wilkinson, L. 2004. Smoothing. - In: SYSTAT Software Inc. (ed.), SYSTAT 11 Statistics. SYSTAT Sotware Inc., pp. 391-422.