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Population Energetics Model

Thus, DEE = DER_food when reserves are not required (body mass remains stable or increases as the result of carcass fat and protein synthesis). We used 4 steps to model food and habitat requirements of pintails: (1) estimate DEE by calculating EM from body mass and ambient temperatures (Kendeigh et al. 1977), then adjust EM to account for costs of free-living and tissue synthesis, energy provided by tissue catabolism, and allometric error; (2) estimate AME content of composite diets; (3) estimate population food requirements from the proportion of foods obtained from wetlands and rice fields, and the size and sex ratio of pintail populations; and (4) estimate area (ha) of wetlands and rice fields required to meet food requirements. We then used sensitivity analyses to assess the relative contribution of input variables and constants to model outcomes.

We estimated DEE and requirements for food and foraging habitat for pintails by sex (because of sex-specific differences in body mass) for 7 30-day periods between August and March 1980-81 and 1981-82. Each 30-day period extended between the median day of successive months. This procedure allowed us to account for tissue synthesis and catabolism between monthly means (Raveling 1979).

Calculation of Existence Metabolism

We estimated EM by using mean body mass for monthly periods (Miller 1986b) in Equations 5.28 and 5.31 in Kendeigh et al. (1977: 142-143). Equation 5.28 (EM = 4.469W^0.6637, where W = mass [g]) was derived under a 15-hr photoperiod at 30°C and represented late summer-early autumn weather in the Sacramento Valley. Equation 5.31 (EM = 17.719 W^0.5316) was derived under a 10-hr photoperiod at 0°C and represented midwinter weather. We estimated EM from corresponding mean monthly temperatures (National Oceanic and Atmospheric Administration 1980-82) measured in the central Sacramento Valley (Willows, California) by interpolating linearly through the 30°C and 0°C values at given monthly mean body masses (Wiens and Innis 1974).

Adjusting Existence Metabolism

Allometric Error.—Williams and Kendeigh (1982) showed that allometric equations for nonpasserine birds (Kendeigh et al. 1977) underestimated EM of Canada geese (Branta canadensis) by about 35%. We used feeding trial data for captive pintails (turkey starter diet; Miller 1984) and regressed metabolized energy intake (kJ/kg of initial body mass/day) on body mass change (kg/day) to estimate daily energy intake when body mass change was zero (maintenance level). The resulting equation follows:

where x is mass change in kg/day (r² = 0.87, n = 24 [3 M and 5 F hatching-year pintails, 3 trials each with food provided ad libitum, one-half ad libitum, and ad libitum again to cause ducks to lose and gain mass]). The EM of a 1-kg pintail determined with this equation is 852.3 kJ/day, which is 22% greater than the value of 697.1 kJ/day determined for a 1-kg bird with equation 5.31 of Kendeigh et al. (1977). Thus, allometric equations for nonpasserine birds apparently underestimate EM for pintails (i.e., allometric error), and we increased EM by another 25% to account for this difference.

Energy Costs and Contributions.—We accounted for metabolic cost of tissue synthesis during body mass gain by using conversion factors of 23.64 kJ/g for protein (ash-free lean dry mass) and 39.54 kJ/g for fat multiplied by 1.33 to account for 75% efficiency of synthesis (Ricklefs 1974:171; Raveling 1979, Bromley and Jarvis 1993). Energy contributed from tissue catabolism (DER_reserves) during mass loss is the sum of energy contributed from oxidation of fat (37.66 kJ/g) and protein (17.99 kJ/g; Ricklefs 1974:156, 160).

Energy From Food.—To estimate DER_food, we added energy required for tissue synthesis to adjusted EM during periods of body mass gain, and we subtracted energy produced by catabolization of fat and protein (DER_reserves) during periods of mass loss (Raveling 1979, Bromley and Jarvis 1993). The equations were

Mass gain:

and

Mass loss:

Energy Content of Composite Diets

Population Food Requirements

Pintail Populations and Food Requirements.—We used survey data from Sacramento NWR narrative reports, California Department of Fish and Game unpublished reports, and the annual midwinter inventory (Eggeman and Johnson 1989) to estimate mean monthly pintail populations in the Sacramento Valley during the winters of 1980-81 and 1981-82. We converted these population estimates to pintail use-days, assuming a 30-day month. We recognize these estimates may be biased (Conroy et al. 1988, Reinecke et al. 1992); however, the direction of bias is unknown for California, and we believe our model accounts for this potential error (sensitivity analysis). We divided the product of DER_food × percentage food obtained from rice and wetlands by corresponding composite AME values to determine food intake (FI) by individual pintails:

where FI_individual is food intake (g • pintail^-1 • day^-1). The product of individual food intake and pintail use-days yielded monthly estimates of population food intake from rice fields and wetlands:

where FI_population is food intake (kg/day) of the pintail population in the Sacramento Valley.

Food Density in Rice Fields and Wetlands.—Rice fields contained about 390 kg/ha dry mass of rice seed immediately after harvest, which occurs September-November (Miller et al. 1989), and <35 kg/ha dry mass of other seeds (M. R. Miller, U.S. Geological Survey, unpublished data). Thus, abundant rice seed was present when pintail populations increased in autumn. However, cut rice straw likely prevented complete use of rice seed by ducks (Baldassarre and Bolen 1984, Clark and Greenwood 1987); therefore, we used 276 kg/ha dry mass, which is the mean rice density in burned fields (Miller et al. 1989), to estimate amount of seeds available for consumption in harvested fields (Heitmeyer 1989).

We used the Sacramento Valley mean rice yield of 7,490 kg/ha dry mass (1980-81 and 1981-82 combined; Larson and Hettinger 1985) to estimate available seed in rice marsh managed for ducks on NWRs. Moist-soil plants and aquatic invertebrates (primarily Chironomidae) are abundant in Sacramento Valley wetlands (Heitmeyer et al. 1989), but wide variation is typical in densities of seeds (up to 2,200 kg/ha; Fredrickson and Taylor 1982, Reinecke et al. 1989) and invertebrates (6.4-96.6 kg/ha; Severson 1987). Therefore, we assumed 1,600 kg/ha dry mass of seeds and invertebrates were present in Sacramento Valley wetlands (Heitmeyer 1989). We further assumed that waterfowl consumed 75% of this amount, on average (Baldassarre and Bolen 1984, Clark and Greenwood 1987). Therefore, we used 1,200 kg/ha dry mass as the density of plant and animal foods available for pintails in wetlands during September-March. During August-September, when refuge rice marsh was available (Miller 1987), we estimated food in wetlands at 1,570 kg/ha dry mass (1,200 kg/ha in wetlands and 7,490 kg/ha in rice marsh weighted by area of wetlands [2,000 ha] and rice marsh [125 ha]).

Population Habitat Requirements.—Managers did not flood most wetlands until late autumn. For example, permanent or summer-flooded marsh increased from about 2,000 ha in August-September to 32,000 ha in October-March (Heitmeyer et al. 1989). We determined the area required to supply needed food by dividing population food requirements by estimates of available food density in rice fields and wetlands as follows:

Statistical Analyses

We conducted sensitivity analyses to determine if predicted areas of rice fields and wetlands depended more on (1) factors affecting DEE, including ambient temperature, body mass, tissue dynamics, corrections for free-living, and errors from allometric equations; (2) population size (use-days); (3) food density in rice fields and wetlands; (4) AME; or (5) proportion of food obtained from rice fields and wetlands. We varied each input variable or constant ±50% and constructed sensitivity curves. We also created curves to predict area of rice fields and wetlands required by varying food density in both habitats ±50% while keeping population size (use-days) constant at baseline, 50% of baseline, and 50% above baseline. To reflect historic abundance, we then varied use-days from half to twice baseline while holding food density in rice fields and wetlands constant at baseline, 50% of baseline, and 50% above baseline.