Linking Habitat Selection to Correlates of Fitness in Herbivores: Role of the Energy Landscape

ELECTRONIC SUPPLEMENTARY MATERIAL

Linking Habitat Selection to Correlates of Fitness in Herbivores: Role of the Energy

Landscape

Ryan A. Long, R. Terry Bowyer, Warren P. Porter, Paul Mathewson, Kevin L. Monteith, Scott

L. Findholt, Brian L. Dick, and John G. Kie

Appendix S1. Description of statistical analyses used to evaluate relationships between behavior and fitness correlates of elk.

To quantify effects of behavior during the last third of gestation on birth mass of neonatal elk, we first averaged conditional parameter estimates for thermoregulatory costs across weeks between spring handling and parturition as a metric of the strength of selection for areas that reduced costs of thermoregulation and activity. We also averaged conditional parameter estimates for costs of thermoregulation and forage quality across diel periods prior to modeling, because they were highly correlated (r ≥ 0.86, indicating that patterns of selection were similar during daytime and nighttime hours). We then included our metric of costavoidance as a predictor variable in a multiple linear regression model (Neter et al. 1996) of birth mass; other predictor variables included conditional parameter estimates for selection of forage quality during spring, body mass (kg) and nutritional condition (percent ingesta-free body fat) of the dam during spring, sex and date of birth (Julian day) of the neonate, and interactions between sex of the neonate and date of birth, mass of the dam, and conditional parameter estimates for thermoregulatory costs and forage quality. We generally considered mass at capture to be equivalent to birth mass, because most neonates were ≤ 36 hrs old ( x = 19 hrs) at the time of capture. We estimated birth mass of older individuals (n = 3; age = 72-96 hrs) by subtracting 0.87 kg/d (Hudson and Haigh 2002) for each day of age after the first 24 hours of life. Prior to analysis, we used a correlation matrix to identify pairs of variables that could not be included in the same model because of collinearity (|r| > 0.6); relevant matrices are presented in Tables S1a and S1b below. In addition, we evaluated residual plots for each variable to assess adherence to assumptions of linear regression (Neter et al. 1996).

Prior to formal model selection, we fit a global model that included all uncorrelated predictor variables and interactions, and excluded variables that were clearly uninformative (i.e.,

85% confidence intervals overlapped 0; [Arnold 2010]) from further analyses. We then modeled all possible combinations of remaining predictor variables (Burnham and Anderson 2002), and recorded Akaike’s Information Criterion adjusted for sample size (AICc), ΔAICc, and the Akaike weight (wi) of each model (Burnham and Anderson 2002). In addition, we recorded the adjusted

2 R value of the best model (lowest AICc) in the set as a measure of predictive power, because

AICc alone does not facilitate a formal evaluation of model fit (Burnham et al. 2011, Grueber et al. 2011). We selected a 95% confidence set of models from the full set based on wi values, and used modelaveraging to produce final parameter estimates for each variable (Burnham and

Anderson 2002). We also calculated unconditional standard errors (SE; [Burnham and Anderson

2002]) for each parameter estimate, and concluded that the estimate differed from 0 if its 90% confidence interval (based on the unconditional SE) did not contain 0 (Long et al. 2009, Arnold

2010, Monteith et al. 2013). Akaike importance weights (Burnham and Anderson 2002) were used to evaluate the relative importance of each variable in the final model.

We used multiple linear regression (Neter et al. 1996) to model nutritional condition at the onset of winter, as well as change in nutritional condition between spring and winter, as a function of the energetic efficiency of behavior during summer and autumn (i.e., conditional parameter estimates for thermoregulatory costs and forage quality averaged across diel periods), and nutritional condition in spring. In addition, we included recruitment status (recruited = young alive at onset of winter; did not recruit = young died prior to winter), and interactions between recruitment status and conditional parameter estimates for thermoregulatory costs and forage quality, as candidate predictor variables in our models. Data on nutritional condition of adult elk in early winter were collected at different times for each study animal based on when the animal arrived at the winter feeding area. Consequently, we calculated the daily rate of change in condition over winter for all elk that were handled both at the beginning and end of winter in 2010-2011 or 2011-2012, and used that rate to estimate condition on 1 December of the appropriate year for each individual (e.g., [Herfindal et al. 2006]). We used the mean rate of change in condition of elk that were handled twice during the same winter to estimate condition on 1 December of individuals that were not handled twice. Our approaches to modeling nutritional condition and birth mass (i.e., evaluation of collinearity and adherence to assumptions, initial variable reduction, and model selection and averaging) were identical, with the exception of the different predictor variables considered in each model.

References

Arnold TW (2010) Uninformative parameters and model selection using Akaike’s information

criterion. J Wildlife Manage 74:1175-1178

Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical

information theoretic approach, 2nd edn. Springer-Verlag, New York, USA

Burnham KP, Anderson DR, Huyvaert KP (2011) AIC model selection and multimodel inference

in behavioral ecology: some background, observations, and comparisons. Behav Ecol Sociobiol 65:23-35

Grueber CE, Nakagawa S, Laws RJ, Jamieson IG (2011) Multimodel inference in ecology and

evolution: challenges and solutions. J Evolution Biol 24:699-711

Herfindal I, Solberg EJ, Sӕther BE, Hogda KA, Andersen R (2006) Environmental phenology

and geographical gradients in moose body mass. Oecologia 150:213-224

Hudson RJ, Haigh JC (2002) Physical and physiological adaptations. In: Toweill DE, Thomas

JW (eds) North American elk: ecology and management. Smithsonian Press, Washington

D.C., USA, pp 199-257

Long RA, Kie JG, Bowyer RT, Hurley MA (2009) Resource selection and movements by female

mule deer Odocoileus hemionus: effects of reproductive stage. Wildlife Biol 15:288-298

Monteith KL, Stephenson TR, Bleich VC, Conner MM, Pierce BM, Bowyer RT (2013) Risk-

sensitive allocation in seasonal dynamics of fat and protein reserves in a longlived

mammal. J Anim Ecol 82:377-388

Neter J, Kutner MH, Nachtsheim CJ, Wasserman W (1996) Applied linear statistical models, 4th

edn. McGraw-Hill, Boston, Massachusetts, USA Table S1a. Correlation matrix (Pearson correlation coefficients) of variables considered in models of birth mass of North American elk (Cervus elaphus) at the Starkey Experimental Forest and Range, Oregon, USA, 2011-2012.

Date of Dam Dam Cost Forage Sex birth mass condition coefficient coefficient Sex 1.00 -0.02 -0.07 -0.08 -0.32 -0.17

Date of birth -0.02 1.00 -0.13 -0.20 0.00 0.16

Dam mass -0.07 -0.13 1.00 0.14 -0.36 -0.23

Dam condition -0.08 -0.20 0.14 1.00 -0.18 -0.12

Cost coefficient -0.32 0.00 -0.36 -0.18 1.00 0.37 Forage -0.17 0.16 -0.23 -0.12 0.37 1.00 coefficient Table S1b. Correlation matrix (Pearson correlation coefficients) of variables considered in models of nutritional condition at the onset of winter, as well as change in nutritional condition between spring and winter, of North American elk (Cervus elaphus) at the Starkey Experimental

Forest and Range, Oregon, USA, 2011-2012.

Spring Cost Forage Recruitment condition coefficient coefficient status Spring 1.00 -0.32 0.07 0.23 condition Cost coefficient -0.32 1.00 -0.31 0.27

Forage coefficient 0.07 -0.31 1.00 -0.34 Recruitment 0.23 0.27 -0.34 1.00 status Appendix S2. Raw data used to fit models of fitness correlates described in the manuscript.

Fig. S2a. Raw data used to model birth mass of neonatal male (n = 14) and female (n = 15) North American elk (Cervus elaphus) at

the Starkey Experimental Forest and Range, Oregon, USA, 2011-2012, as a function of strength of selection by the dam for areas that

minimized costs of thermoregulation and activity prior to parturition (a), date of birth (b), and dam mass (c).

22 a b c

16 B i r 14 Females t Females Females h

Males m Males Males a 12 s s -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 130 135 140 145 150 155 160 165 170 190 200 210 220 230 240 250 260

( k g Energetic cost coefficient Date of birth (Julian day) Dam mass (kg) )

Fig. S2b. Raw data used to model ingesta-free body fat (IFBFat) at the onset of winter (1

December) of adult female North American elk (Cervus elaphus) that either recruited (n = 15) or did not recruit (n = 9) young at the Starkey Experimental Forest and Range, Oregon, USA, 2011-

2012, as a function of strength of selection for forage during autumn.

14 Did not recruit 13 Recruited 12 )

% 11 (

a 10 F

B 9 F I 8 7 6 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 Forage selection coefficient Fig. S2c. Raw data used to model absolute change in ingesta-free body fat (IFBFat) between spring and winter of adult female North

American elk (Cervus elaphus) that either recruited (n = 15) or did not recruit (n = 9) young at the Starkey Experimental Forest and

Range, Oregon, USA, 2011-2012, as a function of strength of selection for forage during autumn (a), and spring IFBFat (b).

12 a b 10 Did not recruit 8 Recruited 6 4 2 Did not recruit S 0 e Recruited a

s -2 o

n -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 1 2 3 4 5 6 7 8 9 a l

c Forage selection coefficient Spring IFBFat (%) h a n

( p p ) Appendix S3. Tabular results of modeling analyses described in the manuscript.

Table S3a. Ninety-five percent confidence sets of models of birth mass of neonatal elk (Cervus elaphus), ingestafree body fat of adult female elk at the onset of winter (winter IFBFat), and change in IFBFat between spring and winter (Δ winter IFBFat) at the Starkey Experimental

Forest and Range, Oregon, USA, 2011-2012. Predictor variables in models of birth mass were date of birth (dob; Julian day), mass of the dam (dmass; kg), sex of the neonate (sex), and conditional parameter estimates from a generalized linear mixed model (GLMM) that quantified the strength of selection for areas that reduced costs of thermoregulation and activity (energy).

Predictor variables in models of nutritional condition (winter IFBFat and Δ winter IFBFat) were

IFBFat in spring (springBC), recruitment status (recruit), conditional parameter estimates from a

GLMM that quantified the strength of selection for forage quality (forage), and the interaction between forage selection and recruitment status (forage*recruit). The value of Akaike’s

Information Criterion adjusted for sample size (AICc), ΔAICc, and the Akaike weight (wi) are presented for each model.1

Model Parameters AICc ΔAICc wi Birth mass dob+energy+dmass+sex 32.22 0.00 0.27 dob+dmass+sex 33.40 1.18 0.15 energy+dmass+sex 33.70 1.48 0.13 dob+energy+sex 33.72 1.50 0.13 energy+sex 33.95 1.73 0.11 dmass+sex 35.11 2.89 0.06 energy 35.91 3.69 0.04 dob+energy 36.01 3.79 0.04 dob+energy+dmass 36.68 4.46 0.03 Winter IFBFat recruit+forage+forage*recruit 5.35 0.00 0.55 springBC+recruit+forage+forage*recruit 5.75 0.40 0.45 Δ winter IFBFat2 springBC+recruit+forage+forage*recruit 5.75 0.00 0.99 1 Adjusted R2 of the best model in each set = 0.44, 0.76, and 0.89 for birth mass, winter

...IFBFat, and Δ IFBFat, respectively

2 The best model in the set for Δ winter IFBFat held >95% of the Akaike weight, so we

...present results for that model only Table S3b. Ninety-five percent confidence set of models of survival of neonatal elk (Cervus elaphus) to 16 weeks of age at the Starkey Experimental Forest and Range, Oregon, USA, 2011-

2012. Predictor variables in survival models were sex of the neonate (sex), birth mass (bmass), nutritional condition of the dam (condition), and conditional parameter estimates from a generalized linear mixed model (GLMM) that quantified the strength of selection for areas that reduced costs of thermoregulation and activity during the last third of gestation (cost1) or increased access to high-quality forage (supply1 and supply2). Numbers following cost and supply variables indicate whether a variable was allowed to influence survival during the first four weeks post-partum (cost1 and supply1) or from five to sixteen weeks post-partum (supply2) in the known-fate model in Program MARK. The value of Akaike’s Information Criterion adjusted for sample size (AICc), ΔAICc, and the Akaike weight (wi) are presented for each model.

Parameters AICc ΔAICc wi sex+bmass+condition+supply1+supply2+cost

1 102.93 0.00 0.16 sex+bmass+condition+supply1+supply2 103.64 0.71 0.11 sex+bmass+condition+supply1+cost1 104.56 1.63 0.07 sex+bmass+condition+supply2 104.60 1.67 0.07 sex+bmass+condition+supply2+cost1 104.80 1.87 0.06 sex+bmass+condition+supply1 104.87 1.94 0.06 bmass+condition+supply1+supply2 105.07 2.14 0.06 bmass+condition+supply1 105.35 2.42 0.05 bmass+condition+supply2 105.43 2.50 0.05 bmass+condition+supply1+supply2+cost1 105.64 2.71 0.04 bmass+condition 105.74 2.81 0.04 sex+bmass+condition 105.75 2.82 0.04 bmass+condition+supply1+cost1 105.93 3.00 0.04 sex+bmass+condition+cost1 106.19 3.26 0.03 bmass+condition+supply2+cost1 106.27 3.35 0.03 bmass+condition+cost1 106.62 3.69 0.03 supply1 108.84 5.91 0.01 sex+supply1 109.00 6.07 0.01