Comparison and Validation of Two Linear Back-Calculation Models Used to Estimate Fish Growth

Abstract

Back-calculation, a useful tool in fisheries management, provides biologists with entire growth histories of fish from bony structures sampled at one point in time. Objectives of this study were to: assess and validate the Fraser-Lee and Weisberg back-calculation models using known growth histories of fish from scales and otoliths in laboratory and field settings, quantify the effect of scale measurement error on back-calculations for both models, and to compare the effects of different y-intercept values (i.e., correction factors) on back-calculated lengths in the Fraser-Lee model. In the laboratory, growth validations were conducted by simulating annuli using oxytetracycline hydrochloride (OTC) to mark the bony structures of bluegills (Lepomis macrochirus), bluegill X green sunfish hybrids (L. macrochirus X Lepomis cyanellus), and rainbow trout (Oncorhynchus mykiss) multiple times. In the field, smallmouth bass (Micropterus dolomieu) and walleyes (Stizostedion vitreum) were tagged in spring (i.e., at time of annulus formation) and later recaptured to assess growth. In the laboratory, OTC marking success of scales was not 100%; marking was lower for OTC-fed bluegills (46%) and OTC-fed rainbow trout (25%) than for OTC-fed hybrid sunfish (82%). Marking success was greatest for the hybrid-sunfish but differed by administration method; success was higher for fish fed OTC (82%) compared to OTC injection (74%). No back-calculations were performed with the rainbow trout because OTC marking success was low and the majority of scales were regenerated. For OTC-fed bluegills and hybrid sunfish, Fraser-Lee back-calculated lengths (BCLs) were within 6.0% of actual lengths except for a 13.9% deviation for OTC-fed bluegills at mark one. For OTC-fed hybrid sunfish, the bluegill standard intercept of 20 mm provided more accurate BCLs than the green sunfish standard intercept of 10 mm. For OTC-injected hybrid sunfish, neither the Fraser-Lee nor the Weisberg model consistently provided the more accurate BCLs when using scales. For all OTC marks in scales, Fraser-Lee and Weisberg BCLs were within 4.8 and 2.7% respectively, of the actual lengths. In comparison, BCLs with otoliths were generally less accurate and less precise than scales for both models. However, the Fraser-Lee model was generally more accurate and always more precise than the Weisberg model for otolith back-calculations. The effect of scale measurement error on BCLs for both the Fraser-Lee and Weisberg models was small; mean BCLs changed only 1.5 mm for the Fraser-Lee model and 1.6 mm for the Weisberg model as a result of a mean measurement error of 2.6 circuli. Each circulus corresponded to a measurement error in BCL of 1.73 mm for both models. The OTC marks did not correspond directly to circuli in OTC-fed bluegills and OTC-fed or OTC-injected hybrid sunfish thus raising questions about scale physiology. In all fish, the OTC marks cut across 3 to 5 circuli in the anterior region and 7 to 10 circuli in the lateral region of the scale. Marks from the OTC-injected hybrid sunfish appeared to 'bleed' in toward the scale focus and displayed fluorescence along the entire cross section, suggesting that the fibrillary layer of the scale was calcified. For wild caught fish in spring, the Fraser-Lee back-calculation model was more accurate and precise than the Weisberg model. Nearly all Fraser-Lee BCLs underestimated the actual lengths but no consistent bias existed for Weisberg model estimates. For the Fraser-Lee model, standard intercepts provided more accurate BCLs than biological intercepts (defined as the body length at scale formation) . Ratios of known body and known scale growth for marked and recaptured fish were not directly proportional (i.e., an isometric 1:1 ratio) and all simple linear regressions of known body growth ratios on known scale growth ratios were significantly different than the expected 1:1 ratio. However, the coefficient of determination (r^2 ) always decreased when all known growth ratios were used from fish recaptured multiple times compared to regressions with one randomly selected known ratio per fish. Lower r^2 values indicated the Weisberg Model assumption of independence for successive scale increments in fish may not be valid. The Fraser-Lee model is recommended over the Weisberg model for back-calculation because Fraser-Lee estimates were as accurate as the Weisberg model, were more precise and had a consistent bias towards underestimation.Department of Biology and the Wisconsin Cooperative Fishery Research Unit at the University of Wisconsin-Stevens Poin