There are many ways that biologists estimate populations and capture-mark-recapture (CMR) might be the most commonly used. CMR is often simplified to mark and recapture but the capture part is just as important. As the name suggests, it is pretty simple. An organism is captured, given an identifiable mark, and then, at a later date, recapture attempt(s) are made. And while on its face, it is pretty simple, however, the devil is in the details. How long do we wait between samples? What if the marks are "lost" (i.e. they are shed, they heal, or are in other ways unidentifiable)? How do things change if we capture, mark, and recapture more than once?
The basics are pretty simple - the population is estimated based on the relationship between the number of marked and unmarked individuals that are captured in a second (or more) sample. As with any model, there are assumptions that, if violated, may produce a biased estimate of the population. In science, bias means that there are factors that alter a result - if these biases are known, they can be corrected. The assumptions of CMR are:
The population is closed - that is, there is no movement into or out of the sample area between samples. (and no births between the samples)
Marked individuals mix randomly into the population.
Marks are not lost between sample periods.
The mark does not negatively effect the individual. (No mortality between samples, the tagging does not make them more or less likely to be recaptured.)
All individuals are equally likely to be captured.
These assumptions essentially come down to the simple idea that the populations at first capture and the recapture are the same and that the process of capturing and marking individuals does not have a negative effect on the population.
The simple equation - the Lincoln-Peterson index - is that the population size (N) is a function of the number of individuals captured and marked in the first sample multiplied by the number of individuals captures in the second sample, then this is divided by the number of individuals in the second sample that had a mark from the first sample. You will see a lot of different variable names for these factors but the relationship is always the same.
Even more complex marking programs - like US Fish and Wildlife Service and US Geological Survey's duck banding program, National Oceanic and Atmosphere Administration's cooperative tagging program (saltwater fishes), or programs operated by states like the Wisconsin Department of Natural Resources fish tagging studies - use the same basic relationship but with more marking and recapture events, the math gets more complex. Because of this, there is software that does the math for researchers.
Initial Capture and Marking
Fish and wildlife tend to have specific and traditional non-lethal capture methods depend upon the habitat they live in. Gear - as we call the equipment used to capture fishes - are generally divided into active and passive gears. Passive gears are put in place and allowed to "soak" for a period of time. These are a number of different nets like gill nets and trammel nets, pots, things like the commonly used crayfish / minnow traps, longline fishing, and other gears that are left in place to catch fishes. Active gears are things like trawls, seines, active hook and line fishing, electrofishing, and other gears where operators are actively moving the gear to catch fishes. There is a bit of gray area with some nets that are put in place and fishes are driven into the nets. For more on gear types: link.
What mark is given and if a batch or individual mark is used depends upon the objectives of the study along with other considerations such as time and money - considerations for nearly every experiment. A batch mark - all individuals from a sample receive the same mark - is sufficient for CMR studies. The choice of mark is usually based on what others have used and have sound to be useful for that species (for more: All about Fish Tagging). Sometimes, a sample of fishes are reserved and put into a closed population - like a hatchery pond - to measure how effectively and for how long after tagging the marks are still visible. This is because the denominator of the equation - the number of recaptures in the second sample - has a very strong influence on the population estimate. If a number of fishes lost their mark and were not counted as recaptures, the denominator will be artificially low and the population artificially high.
No matter how fishes or other animals are marked, one of the most important things is that they in good health before and after being marked. Marking organisms that do not survive between their initial capture and subsequent recapture attempts biases the sample. If 100 organisms were marked but 10% died between the samples, two variables would be affected.
The number individuals captured and given a mark - part of the numerator - would be 90 rather than 100.
The potential number of recaptures is reduced which likely reduces the denominator of the CMR equation. The equation is particularly susceptible to issues of small sample size and biases in the number of recaptures.
Recapturing
One of the most significant decisions about recapturing fishes is when to resample. There needs to be sufficient time for tagged individuals to mix back into the population but not so long that the populations are different between the initial capture and subsequent recaptures. This is a bit of the art in the science of CMR.
There are a number of considerations that provide a better population estimate. With many animals, we talk about them being potentially trap happy or trap shy. That is, they are likely to be recaptured because their capture often involves a food reward (e.g. a baited trap) or capture was a stressful experience and some individuals are more likely to avoid another trap experience.
Another concern is the mark must remain visible or readable. As mentioned above, many studies of tag retention have been done and for larger studies, researchers often incorporate a survival and mark retention experiment into their study (link to Google Scholar search).
Lastly, another issue - and a place where model assumptions are often violated - is that we are often treating populations as closed (no immigration or emigration) when they, in fact, are open. An early idea in fisheries has been that fishes are restricted in their movements (Gerking 1959). This idea has been tested and has held up for some fishes (Petty and Grossman 2004, Rodríguez 2002) but not others (Gowan et al. 1994, Gowan and Fausch 1996). Gowan et al. (1994) argue that the restricted movement paradigm - a term they coined - was mostly because methods used to estimate movement are biased against finding movement. If a three hundred meter reach is sampled and 500 fish are tagged and 300 are recaptured in a subsequent survey, the standard assumption is that most fishes didn't move. However, the inherent issue is that 200 tagged fishes were not recaptured and we don't know what happened to that 40% of the population. Did they die? Move just out of the sample reach? Move far out of the sample reach? Or did they avoid recapture? There really is no way to know (unless they are recaptured in other sample reaches.
We can avoid some of the issues inherent in using CMR in open systems - that is places were fishes are free to move outside of our potential sample area. Timing is an important part of this - we want to target our sampling around times when fishes are expected to be relatively restricted in their movements. For example, having mark and recapture events in the later part of spring or the summer is generally a time we expect trout to move less. Avoiding major dispersal events - movements to spawn, to find overwintering refugia, or other events - is key when dealing with open populations. We want to sample at times when we expect no or at least few deaths and no births. And we can use block nets to prevent movement in and out of the reach but this adds a lot of effort and is rarely done except over short time spans.
Dealing with Multiple Mark-Recapture Events
Much of the time, scientists are not using a single mark and a single recapture event but instead are sampling - capturing and marking fishes - over multiple samples. Many of these larger studies - think duck banding - are long-term, continuous experiments. And because of this, they violate all of the assumptions of simple CMR. However, when we know what the effects of those assumptions violations are, we can correct for them mathematically.
I will not dig too deep into the mathematics of multiple captures - it gets complicated - which is why software and statistical experts are used to make sense of it. Think about all the considerations get even more complex in open populations - which migratory bird populations certainly are. The U.S. Geological Survey Bird Banding Laboratory has it covered with decades of experience and many experts in statistical ecology.
Bird banding - waterfowl in particular - are some of the most complex CMR surveys but they have also resulted in much of what we know about how and why populations change over time or in response to specific conditions. In the fisheries world, many state agencies use angler recaptures as part of their study designs (list of ongoing Wisconsin studies). And many coastal states have cooperative programs where anglers in addition to biologists tag the fishes that they catch. These programs are associated with the National Oceanic and Atmospheric Agency (NOAA) and the US Fish and Wildlife Service (USFWS) and state agencies (typically). Some examples of state and federal tagging programs are:
Additionally, countries have come together to manage tagging programs such as the Pacific Island Fisheries Group and non-profit agencies like the Bonefish and Tarpon Trust and Littoral Society are involved in tagging programs. And these cooperative programs are important because fishes do not respect international boundaries (Larkin et al. 2023).
Population Estimates
This is generally the ultimate goal of CMR - to estimate the population size. Yes, there are other data we can often gather from fish tagging studies - like mortality, movement, and growth - but most of the time, understanding the population is the goal of the tagging program. You'll have noticed throughout, it is always referred to as an estimate. Censusing populations is rarely possible so we have to sample and use those samples to provide estimates of the population.
Because these are estimates, they come with an inherent error. However, we can reduce that error by designing our study to violate the assumptions of CMR as little and possible and understand what the effects of violating assumptions will be. And, as with almost all studies, increasing effort and sample size will provide a better estimate. Often multiple reaches of the same stream or lake are sampled to give a better estimate of spatial variability. When you see that there are 1,500 Brown Trout per mile in a particular stream, it does not mean that each mile has 1,500 trout. As an aside, I do wish that state agencies would include measures of variability with their population estimates. A stream that averages 1,000 fish per mile with a large amount of variation is quite different from a similar population estimate with much lower variability. The first one tells me that I would expect fish to be concentrated in some areas with other reaches having much fewer than 1,000 fish per mile.
The Wrap-Up
Fish tagging and capture studies have been important in helping us better understand fish demographics (births, deaths, immigration, and emigration) and how populations change over time. And these studies will continue to inform managers about a host of factors like responses to barrier removal (i.e. Easterly et al. 2020), stocking (i.e. Leonard et al. 2013), water quality and habitat improvements (i.e. Landsman et al. 2011), harvest (i.e. Deroba et al. 2007) and regulations (i.e. Barker et al. 2002), and in long-term research (Sass et al. 2022). Tagging and CMR studies are one of the backbones of population ecology, not only in fisheries.
Links
Literature Cited / References / Reading List
Barker, R.J., Taylor, P.H. and Smith, S., 2002. Effect of a change in fishing regulations on the survival and capture probabilities of rainbow trout in the upper Rangitikei River, New Zealand. North American Journal of Fisheries Management, 22(2), pp.465-473.
Deroba, J.J., Hansen, M.J., Nate, N.A. and Hennessy, J.M., 2007. Temporal profiles of walleye angling effort, harvest rate, and harvest in northern Wisconsin lakes. North American Journal of Fisheries Management, 27(2), pp.717-727.
Easterly, E.G., Isermann, D.A., Raabe, J.K. and Pyatskowit, J.W., 2020. Brook trout (Salvelinus fontinalis) movement and survival after removal of two dams on the West Branch of the Wolf River, Wisconsin. Ecology of Freshwater Fish, 29(2), pp.311-324.
Gerking, S.D., 1959. The restricted movement of fish populations. Biological Reviews, 34(2), pp.221-242.
Gowan, C. and Fausch, K.D., 1996. Mobile brook trout in two high-elevation Colorado streams: reevaluating the concept of restricted movement. Canadian Journal of Fisheries and Aquatic Sciences, 53(6), pp.1370-1381.
Gowan, C., Young, M.K., Fausch, K.D. and Riley, S.C., 1994. Restricted movement in resident stream salmonids: a paradigm lost?. Canadian Journal of Fisheries and Aquatic Sciences, 51(11), pp.2626-2637.
Landsman, S.J., Nguyen, V.M., Gutowsky, L.F.G., Gobin, J., Cook, K.V., Binder, T.R., Lower, N., McLaughlin, R.L. and Cooke, S.J., 2011. Fish movement and migration studies in the Laurentian Great Lakes: research trends and knowledge gaps. Journal of Great Lakes Research, 37(2), pp.365-379.
Larkin, M.F., Kroetz, A.M. and Boucek, R.E., 2023. Bonefish do not respect international borders: the Florida–Bahamas connection. Marine Biology, 170(11), p.149.
Leonard, J.B., Stott, W., Loope, D.M., Kusnierz, P.C. and Sreenivasan, A., 2013. Biological consequences of the coaster brook trout restoration stocking program in Lake Superior tributaries within Pictured Rocks National Lakeshore. North American Journal of Fisheries Management, 33(2), pp.359-372.
Petty, J.T. and Grossman, G.D., 2004. Restricted movement by mottled sculpin (Pisces: Cottidae) in a southern Appalachian stream. Freshwater Biology, 49(5), pp.631-645.
Rodríguez, M.A., 2002. Restricted movement in stream fish: the paradigm is incomplete, not lost. Ecology, 83(1), pp.1-13.
Sass, G.G., Shaw, S.L. and Renik, K.M., 2022. Celebrating 75 years of Wisconsin’s Northern Highland fishery research area: the past, present, and future. Fisheries, 47(2), pp.55-67.