Scaling in Free-Swimming Fish and Implications for Measuring Size-at-Time in the Wild

<div><p>This study was motivated by the need to measure size-at-age, and thus growth rate, in fish in the wild. We postulated that this could be achieved using accelerometer tags based first on early isometric scaling models that hypothesize that similar animals should move at the same speed with a stroke frequency that scales with length^-1, and second on observations that the speed of primarily air-breathing free-swimming animals, presumably swimming ‘efficiently’, is independent of size, confirming that stroke frequency scales as length^-1. However, such scaling relations between size and swimming parameters for fish remain mostly theoretical. Based on free-swimming saithe and sturgeon tagged with accelerometers, we introduce a species-specific scaling relationship between dominant tail beat frequency (<i>TBF</i>) and fork length. Dominant <i>TBF</i> was proportional to length^-1 (r² = 0.73, n = 40), and estimated swimming speed within species was independent of length. Similar scaling relations accrued in relation to body mass^-0.29. We demonstrate that the dominant <i>TBF</i> can be used to estimate size-at-time and that accelerometer tags with onboard processing may be able to provide size-at-time estimates among free-swimming fish and thus the estimation of growth rate (change in size-at-time) in the wild.</p>