Understanding how many fish are born in a given year—a measure known as year-class strength, meaning the number of fish that survive from a specific spawning year—is essential for making smart decisions about managing fish populations. But figuring this out can be tricky due to natural ups and downs in reproduction, changing death rates, and varying levels of fishing. A new study by Dr. Ji He from the Michigan Department of Natural Resources and Dr. Charles Madenjian from the United States Geological Survey has shown that two main ways of estimating these fish numbers produce very similar and trustworthy results. The study is published in the journal Fishes.
Dr.He and Dr. Madenjian compared two methods in using decades of fish survey data. Both approaches use a type of statistical model called a linear mixed-effects model, to separate the effects of fish age, year of capture, and year of borth . “Using data collection from multiple years and the linear mixed-effect model allowed us to consider how fish production, fish behavior, and fishing pressure can vary from year to year.” explained Dr. He.
The first method, known as longitudinal analysis, uses repeated-meaasures at a few consecutive ages and does not rely on the pattern in how fish numbers decline with age. Among many possible ways to fit the data, one model stood out as the best according to a statistical rating system known as the Akaike Information Criterion. This model first focused on the birth year of the stocked and wild fish. Another model, preferred by a different statistical tool called the Bayesian Information Criterion, first focused on fish age instead. Even though these models looked at the data in slightly different ways, they came up with nearly the same results and explained the data similarly well.
The second method, called catch-curve regression, uses a wide range of fish age and the pattern in how fish numbers decline with age. This method is often used to estimate mortality with the assumption that all potential differences in year-class strength are negligible between age groups from a year-specific data collection, Dr.He and Dr. Madenjian did not use the unrealistic assumption. Rather, they incorporated the estimates of year-class strength with the estimate of mortality in a generalized application of the catch-curve regression by using data from multiple years of a given time-period, with similar environmental conditions and the fishery practices and management. For each of two different time periods, the best model based on the AIC or BIC comparison was again not the same but provided similar results. “Year-class patterns and trends estimated with birth year as a fixed factor from the best model based on Akaike’s criterion were consistent with those estimated with birth year as a random factor from the best model based on Schwarz’s criterion,” Dr. Madenjian said.
Dr.He and Dr. Madenjian’s findings are especially important because of the long standing challenge to understand recruitment dynamics in fish populations. Fish recruitment is typically indexed as fish abundance at a single age, but it is difficult to maintain a survey-based recruitment index, particularly with large and rapid changes in the ecosystem, such as the lake trout story in Lake Huron. Dr. He and Dr. Madenjian’s study highlights an alternative and likely more effective approach. As Dr. Madenjian pointed out, “Annual collection of biological data can be fully explored for reliable reconstruction of year-class strength,” The longitudinal analyses and the generalized application of catch-curve regression were carried out in the published study using basic, freely available statistical software, specifically the R “nlme” package, indicating that both methods are accessible for front-line fishery biologists and managers without needing specialized resources. “Both methods can provide robust estimates of year-class strength,” Dr. He added, “although when a fish year-class lived through two time periods with large difference in adult mortality, the first method is more accurate than the second method.”
Journal Reference
He J.X., Madenjian C.P., “Comparing Year-Class Strength Indices from Longitudinal Analysis of Catch-at-Age Data with Those from Catch-Curve Regression: Application to Lake Huron Lake Trout,” Fishes, 2025. DOI: https://doi.org/10.3390/fishes10070332
Image Reference
Greg Kennedy, USGS Great Lakes Science Center, Ann Arbor, MI
