Population size structure - the distribution of the lengths / ages of fishes - is a rather amorphous concept. There are many ways fisheries biologists measure size structure and none of them are perfect but most are informative in their own way. And I'll get to those, in a bit...
Source: Creative Commons
I think that the first place to start the conversation is about survivorship curves. Survivorship curves are a way to think about how species survive over time - or conversely, when they are expected to die. We are a Type I species - we have high early survival and survival does not change significantly until relatively late in life. Type I species tend to be long-loved species that mature relatively late in life, produce few offspring and care for those offspring. Classic examples are humans and elephants. Type III species are rather the opposite in that they have high early life mortality (low survivorship) but produce a lot of offspring. Oysters, many invertebrates, trees, and others are classic examples. And type II species have the scariest of life histories - they have the same chance of dying at any point in their lives.
These curves are, of course, models and real life histories do not fit these models perfectly. Most species fit somewhere in-between these idealized curves. As population ecology is probably my favorite part of ecology and fisheries management, I have written about many of these topics previously and will give a list of links at the end of this post.
Size Structure
Size structure basically means how different sizes of a species are represented in a population. And generally, we want a diversity of sizes of fishes which indicate a healthy, stable population. Fishes do not perfectly fit one of the idealize curves and there is a great amount of variation among the fishes. Sturgeon are a great example of a Type III species - though they don't reproduce until quite old, a Type I species characteristic. Minnows (Cyprinidae) are typically a pretty classic Type II curve as are many other species that are food for a number of other, larger species (mice, small birds, etc.). And a bit surprisingly, Bluegill (Lepomis macrochirus) have a lot of Type I species characteristics. They - the parental males at least - have a long juvenile (non-reproductive) phase and care for their young more than most fishes (for more on Bluegill life history).
Survivorship curves affect size structure. One important note on the curves is that the X-axis is typically described as lifespan of the organism. Some fishes have a maximum age of only a year or 2 while others live for a decade or several decades. We expect sturgeon - at least those that make it to adulthood - to survive for a long time and thus, the population has an age structure with a large proportion of adult fishes. Stream trout rarely live much longer than 3 or 4 years - though there are exceptions. Trout are an interesting case and exhibit some characteristics of all survivorship curves - though fewer Type I characteristics. For more on the topic of survivorship curves.
Visualizations
There are a number of ways we try to understand the size distribution of a population and the first is typically some sort of visualization. I wrote about how to use online trout survey data in a previous post so I'll be more to the point here but to read further, Understanding Online Trout Surveys and Reports. There are a number of ways to visualize what a populations look like. I used data provided by Kirk Olson, our local fisheries biologist, from a stream reach I helped his crew electrofish last summer (2023). These data are from Brook Trout (Salvelinus fontinalis) captured in a stream in Monroe County, WI.
Histograms are a great way to visualize what a population looks like. From this population, you can see that the age-0 (that year's newly hatched fish) were rare - but they are hard to catch with electrofishing gear so I wouldn't put much stock in the sub-100mm bars. The large number of fishes between about 130 and 200 mm (about 5 to 8 inches) were - at that point in the summer - most likely fishes that hatched the year before (age 1+, hatched in 2022). The larger fishes are generally harder to discern their ages but there might be an age 2+ year class in the mid-200 mm size class. And maybe, the fishes around 300 mm (about 12 inches) are age 3+ Brook Trout. It is possible that there are some age 4+ fish in there but we'd have age the fish to know with any certainty (and even then there is a bit of an art to aging fish).
As seen above, you can change the bin size - that is how many of the X-axis units are grouped together - and the figures will look a little bit different. The bottom figure is a little coarser but pretty clearly shows that the majority of Brook Trout were in the mid- to high 100 mm size groups (6 inches = 152.4 mm, 8 inches = 203.2 mm). How to best display the data is a function of what you are looking to better understand and what the data look like.
In some ways, this cumulative distribution figure is more informative than the histogram. In other ways, it is a little harder to read and understand. It essentially shows the same thing as above - it should because it is the same data just displayed in a different way. On a cumulative distribution figure, changes in slope are important - steep slopes indicate a lot of individuals and small slopes indicate few fishes of that size were capture. A majority of the Brook Trout - around 70% were between about 130 and 200 mm as indicated by the steep slope in this area of the figure. Where the cumulative distribution figure shines is in comparing streams or stream reaches.
Above are three sites plotted together - the green line is the middle site which is used for the other figures above. What can we see in this figure? First, the middle and lower sites look pretty similar due to the upper site having so many more young-of-the-year (YOY) Brook Trout. Over 25% of the Brook Trout captured in the upper site were less than 100 mm (<4 in.). Large fishes are generally more susceptible to electrofishing and YOY numbers are more variable so if I really wanted to get a picture of the population, I might restrict my analysis to only fishes greater than 100 mm (>4 in.). The greater proportion of YOY Brook Trout in the upper site is probably truth - it may be closer to spawning sites and/or provide better rearing habitat. Another thing that is evident is that about 90% of the Brook Trout in the Upper site are less than 250 mm (about 10 inches) whereas in the other two sites, there are a lot more fishes over 10 inches.
What this method of visualization also allows for is statistical hypothesis testing. Neumann and Allen (2007) provide a much fuller discussion of how to statistically test for differences in distributions.
Since this is a cumulative distribution, this figure lacks information about sample size. In the lower site, 25 Brook Trout were measured, the middle site had 73 that were measured, and the upper site had 175 measured Brook Trout. (I mentioned measured as there are always a fish or two that are dropped or for some reason not measured.) Figures 5 and 6 below compare the three sites in slightly different ways.
The figure above are three histograms with 10 mm bins for each of the three sites. Because the Y-axes are all different, this figure is effective in comparing the general shapes of the distributions. For example, the lower site has a greater proportion of sub 200 mm (about 8 inches) Brook Trout. Average length in mm by sites were: lower = 194 (7.6 in.), middle = 190 (7.5 in.), and upper = 154 (6.1 in.). And the largest Brook Trout caught were: lower = 282 mm (11.1 in.), middle = 307 mm (12.1 in.), and upper = 290 mm (11.4 in.).
Lastly, Figure 6 shows the same data but with the Y-axis remaining constant. This histogram illustrates the differences in the number of fishes caught in the three sites. As mentioned above in association with Figure 4, YOY (under about 100 mm or 4 inches) are the fishes least likely to be captured by electrofishing. Unless specifically targeting YOY fishes, more likely using a method that captures them more effectively, YOY numbers are highly variable and those data are probably a bit suspect.
Stock Density Indices
Stock density indices are used to provide a single number that describes some quality of a population. Proportional stock density (PSD) is calculated by dividing the number of fish over quality length by the number of fish over stock length. As I had written in a post about what a trophy fish is, stock length is 20% of the world record length and quality fish are 36% of the world record length. For Brook Trout, a stock fish is 5 inches (130 mm) and a quality fish is 8 inches (200 mm).
Table 1. Proportion stock density (PSD) for Brook Trout from the three sites described above and relative stock density of Brook Trout greater than 10 inches (254 mm) listed as percentages.
Site | PSD | RSD >10 in. |
Upper | 32% | 3.2% |
Middle | 30% | 12.9% |
Lower | 24% | 12.0% |
The table above is pretty informative about Brook Trout in this stream. While the upper site has a lot of Brook Trout over 8 inches - 32% of those over 5 inches (130 mm) are over 8 inches (200 mm) - it has a really low percentage (3.2%) of Brook Trout over 10 inches (254 mm). If you wanted to catch a "quality" Brook Trout, one over 8 inches, the upper site would be great but you'd likely have to sort through a lot of small fish to have a chance at a larger one. The middle and lower sites give you a better chance at a larger Brook Trout.
A single number - like PSD or RSD - is never all that meaningful without more context. For Wisconsin streams, an average PSD value was 40.4% in a study by Fayram (2007) using data collected between 1995 and 2005. For Brown Trout, the average PSD was 53.6 and stock length was >150 mm (5.9 in.) and 230 mm (9 in.) for Brown Trout. So this Driftless Stream had slightly lower than average PSD values compared to other Wisconsin streams (from a couple of decades ago).
In general, a low PSD shows that fishes are not - for whatever reason - obtaining larger sizes. This may occur due to a number of reasons - high angler mortality of larger fishes, habitats incapable of supporting larger trout, being in a good juvenile rearing habitat, or a number of other reasons. And a high PSD is not necessarily a good thing. It may indicate a lack of spawning or poor juvenile survival. Where you are in a stream/watershed certainly has some effect on expectations. Downstream in more marginal trout waters, I would expect higher PSD values and in headwaters, I likely expect lower PSD values because there may not be sufficient water depth and habitat for larger trout. These are, of course, generalities and we all know exceptions to these generalities.
Age Structure
A post for another day - but other related measures of size structure or maybe more accurately, the health of a population - are relationships between length and weight. With the idea that streams with relatively heavy fish for their length - fat fishes - are healthier because they are able to provide more fish with sufficient food. Those of you that, like me, have been fishing "the coulees" for a number of years, remember "Timber fish". This was the name we gave to overly skinny trout that rarely got very long because there simply wasn't enough food to go around. Densities - while still quite high - have dropped significantly and Brown Trout have grown larger and fatter - a sign of a healthier fishery.
I titled this section "Age Structure" because in fishes, length and age are strongly correlated. There are many ways we show how age and population sizes are related. Determining the age of fishes is its own art and science and too much for this post but as I mentioned above, sometimes you can with some certainty, know the ages of fishes from histograms. Much of the time, this is an approximation - but then again, I'd argue that aging for many fishes is a pretty good approximation. But more on that later.
Why Size Structure Matters
Beyond the health of populations, for anglers, size matters. I'll give you the choice of two places to fish, one has Brown Trout that remain pretty skinny and rarely exceed 12 inches and another that has fishes where you have a decent chance of catching Brown Trout over 16 inches and those fishes are quite fat. Which are you choosing? And science shows us that anglers make those choices.
There are a number of factors that go into anglers' decisions where to fish (Hunt et al. 2019). At least in this meta-analysis (analyzing the results of other studies collectively - a way to assess what is known about a particular topic), distance and cost-related factors were the most important with most trips being close to home. Next most important were catch-related factors with catch rates being more important to most anglers than fish size.
The size structure of a population can tell us a lot about the stream. A lack of larger fish or at least larger fish in decent numbers may tell us that there is too much harvest of larger fish, that there is something preventing them from growing to larger sizes (water temperature, lack of food, etc.), or there is a lack of suitable adult habitat. A lack of small fishes - assuming you are using gear able to catch them - may indicate a lack of spawning in that area or nearby. Today (well, not today for you...), we sampled a reach of an uncategorized stream that will probably "become" a class 2 or 3 stream that had only 1 Brown Trout under 11 inches. This reach had a high number of forage fishes which allowed larger fishes to be successful but lacks resources - mostly a lack of macroinvertebrate growing riffles - for smaller trout to be successful. In a "healthy" stream, we expect to capture a number of different year classes.
A more full discussion of this will have to wait for another post as this one is long enough. Below are a number of related posts to keep you occupied in the meantime. Cheers!
Past Posts of Interest
Literature Cited / References
Fayram, A.H., 2007. Spatial and temporal variation in brook trout and brown trout proportional stock densities in Wisconsin streams. Fisheries Management and Ecology, 14(4), pp.239-244.
Hunt, L.M., Camp, E., van Poorten, B. and Arlinghaus, R., 2019. Catch and non-catch-related determinants of where anglers fish: a review of three decades of site choice research in recreational fisheries. Reviews in Fisheries Science & Aquaculture, 27(3), pp.261-286.