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Figure 1. Location of the study site in west-central Minnesota.

Collection of Field Data

Our study wetland, Sagebraten, is located on a USFWS Waterfowl Production Area (WPA) in west-central Minnesota (Figure 1) and has a surface area of 3.71 ha and a maximum depth of 2.46 m. We established two sampling strata consisting of deep (water depth > 1.25 m) and shallow (depth < 1.25 m) water. We used an area-density method to estimate the population size of fathead minnows (Duffy 1998), and this technique requires estimation of the surface area of both strata. A Topcon® total station was used to generate data for a basin-morphometry map for the study site in mid-July, and the area of each depth-stratum was determined using Surfer software (Golden Software 1997).

Fathead minnows were sampled every two weeks from 19 May through 14 August 1997 using square-shaped pop nets (Dewey et al. 1989) with a sampling area of 1 m² and fitted with 0.5 mm (bar measure) mesh. On each date 15 samples were taken at random locations at wadeable depths in each stratum and the total number of fish captured per set was determined. We then determined the average number of fish per m² for each stratum from the 15 samples, and estimated the total population size by summing the average density multiplied by area for each stratum.

A substantial portion (39%) of our study wetland was too deep to be sampled without use of a boat, and considerable error can be introduced into the population estimates if densities vary between the sampled and unsampled area of the deep stratum. Therefore, we sampled this deeper water on 15 July to determine if densities were significantly different than those observed in shallower water of the deep stratum. Fifteen samples were taken and compared to 15 samples taken on the same day in shallower water of the deep stratum. As no difference was found between the two depths (T-test; t=2.2, 28 df, P=0.35), we concluded that the shallower samples accurately estimate densities for the entire wetland.

Use of bioenergetic models requires estimating the growth of fish during the time period being modeled, which is usually done by identifying and tracking the growth of individual cohorts. However, standard techniques cannot be used to identify cohorts in fathead minnow populations, as they are fractious spawners and produce multiple cohorts throughout the summer (Duffy 1998). Thus, we used size-frequency data to identify and track the growth of cohorts throughout the sampling season. On each sampling date the total length and wet-mass were determined for 300 randomly selected minnows. Modal lengths were identified, and fish within + 20% of a mode were associated as a cohort (Duffy 1998). The average weight of fish in each cohort was determined on each date, and growth of individuals in each cohort was determined by the increase in average weight between one sampling date and the next.

We analyzed the diet of fathead minnows by collecting 15 adult (total length > 40 mm) and 15 juvenile (total length < 40 mm) fish on each sampling date and immediately preserving them in 10% buffered formalin. In the lab, the anterior 1/3 of each stomach was removed, and it's contents enumerated and identified to the lowest feasible taxonomic group. Lengths of prey were determined and converted to biomass with length-mass equations of McCauley (1984) and Smit et al. (1993). The percent of total diet by weight was then determined for each prey type. Results for fish collected in each month were pooled, giving an average diet composition for the months of May, June, July and August. We were unable to determine diets of fish < 30 mm in length, but Held and Peterka (1974) found that fish < 20 mm in length fed mainly on cladocerans and copepods. Therefore, we assumed all YOY fathead minnows fed exclusively on copepod prey (cladocerans were rarely found in stomachs of fish or in the water column during our study) during the first two weeks of the model (when their total lengths ranged from 13-19 mm) and utilized the observed diet data after two weeks (when their total length was > 19 mm).

Metabolic rates of fish are temperature dependant, making water temperature data necessary for bioenergetic models. We measured water temperature during the sampling period with temperature-data loggers (Hobo Inc., Procasse, MA). The data logger was deployed 50 cm off the bottom at 1 m depth, and recorded water temperature every 4 hr. The average daily water temperature was then incorporated into the bioenergetics model.

Physiological Variables and Bioenergetic Modeling

Use of the bioenergetic model to estimate nutrient dynamics in fish requires constructing energy and nutrient budgets. The energy budget of fish is based on the energy mass-balance equation

In a similar fashion, consumption, allocation to growth, and excretion of both phosphorus and nitrogen can be estimated with the mass-balance equation

We used sensitivity analysis to determine how errors in the physiological parameters would effect model estimates. Sensitivity was assessed with the equation

All modeling was performed with Fish Bioenergetics 3.0 © (Hanson et al. 1997). All calculations were performed on a daily interval, and models for each cohort were combined for total population estimates. The model was used to estimate consumption rates of prey, nutrients contained in the fish population, nutrients released via fish mortality, and nutrient consumption, allocation to growth, and excretion.