Making It Fit:
Using Excel to Analyze Biological Systems

by
Robert Leaf and Brian R. Murphy
Fisheries and Wildlife Sciences Department
Virginia Polytechnic Institute and State University

Part I – The Age-at-Length Relation

… the islands are valued the world over for their spectacular coastlines and aquamarine waters, the industry of harvesting fish and other marine creatures for home aquariums is largely unregulated here, raising concerns over damage to the environment, the tourism industry and the aquarium fishery itself … a $50 permit allows collectors across most of Hawai‘i to net as many of a species as they want, wherever they want and whenever they want. That sometimes means harvesting hundreds of thousands per year of a single species from a single bay.

—Tara Godvin, The Honolulu Advertiser, Sunday, October 9, 2005

Dr. Latimer, an ichthyologist working in Honolulu, Hawai‘i, peered myopically at one of the tiny ear stones, the otolith, of the yellow tang (Zebrasoma flavescens) through his microscope. It was interesting for him to see the light and dark bands, called “annuli,” that were formed as the fish grows. They reminded him of the rings of a tree and, like the rings on a tree, these could also be used to estimate the age of a fish. He had studied this species for years, and had often seen them racing by when he was diving on the local coral reefs and rocky areas around the island. Dr. Latimer was interested in their ecology, but today he was counting rings on otoliths from a collection of fish to provide information for fishery managers. The necessity of determining the age-at-length relationship was crucial because yellow tang and other reef fishes in Hawai‘i are the target of a major fishery: hundreds of thousands of juvenile yellow tang and tens of thousands of Moorish idol (Zanclus cornutus), spotted surgeonfish (Ctenochaetus strigosus), and Achilles tang (Acanthurus achilles) are caught each year for the live aquarium trade, resulting in significant decreases in abundance (Tissot and Hallacher 2003). These fishes are shipped around the world to aquarium enthusiasts. In addition to determining the ecology of this species, Dr. Latimer’s agency was charged with describing important life-history characteristics in the hope that an understanding of the species would help improve management practices.

Dr. Latimer had had a long day. He was almost finished counting the rings of the otoliths for the collection of yellow tang he had collected. His next step was to figure out a way to present the data in a way that the managers could use. He knew that fishery managers generally fitted curved lines to these types of data, and he was puzzled about how to proceed. He was familiar with plotting straight lines (linear model) to data, but wondered if he could use the same principles of linear regression to plot curved lines.

Questions

1. Other than using the otolith, what alternatives are there for determining the age of a fish?

2. If we want to predict the length of a fish based on its age, how would we plot such a relationship on a graph with two axes (x and y)? How do we choose which value to appear on the vertical axis, and which to appear on the horizontal axis?

3. Consider the two panels (A and B) in Figure 3 below that include length and age (estimated from the number of annuli) data collected from a fish population. Discuss the criteria you would use to determine the “best-fit” line for each of the figures.

4. Why might you get such data? For example, when might you expect a straight line, and when might you expect a curved line? Justify your answers.

5. Draw a straight line through the points in Figure A and a curve through the points in Figure B. Both of these should start at or near the origin (0,0). Describe why you drew the line you did to determine the “best-fit” curve.

   Figure 3

   

References

• Tissot, B. N., and L. E. Hallacher. 2003. Effects of aquarium collectors on coral reef fishes in Kona, Hawaii. Conservation Biology 17:1759–1768.

Date Posted: September 11, 2009.

Image credits: Figure 1 used with permission from the Center for Quantitative Fisheries Ecology, Old Dominion University, Norfolk, VA. Figure 2 ©1997 Randall, J.E., Randall’s underwater photos, licensed under a Creative Commons Attribution-Noncommercial 3.0 Unported License.

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