Since my whole project on growth is based on measurements, a critical element to consider is measurement error. (See Wang et al, 1995 and Francis, 1988 for general overview). For gastropods, errors can take several forms as a result of :
- damage to the shell,
- epibionts making an accurate measurement difficult,
- different operators measuring differently, or
- retrospectively estimating shell length at the assumed size of tagging from striae on the shell surface
The last of these is the main focus of this blog post, so let me deal with the other three first.
1 Shell damage Removing snails from the rocks or handling them in the boat can chip off the fragile new growth at the margin which has not yet been consolidated with a strong nacreous layer. Sometimes a snail is damaged by attempted predation and is missing a semi-circular piece of shell. An example of this is shown in Figure 1 below.
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Figure 1. Lunella torquata with shell repair of naturally-occuring damage at the growing margin. The tag is attached to the repaired section. Note the clean shell (rapid growth?) after barnacles colonised the shell.
In these instances, whether for tagging or just measuring for a length frequency distribution, the estimated maximum length was recorded. I didn’t do any work to document the scale or scope of these “broken edge” errors. They are included in the overall measurement error estimate from the GROTAGPLUS growth analysis program. Kienzle et al (2022) reported that measurement error for Lunella from this program was around 0.2mm. The R Documentation for the program notes that fitting the model for separate sexes improves the accuracy of measurement error estimation.
The empirical calculations from multiple tag recaptures outlined below also include these errors, noting that I arbitrarily corrected for large, obvious broken edges during measurement of tagged and recaptured snails.
2 Epibionts Barnacles, tubeworms and other epibionts were removed from the back of the shell using a serrated knife prior to measurement, virtually eliminating this as a source of error in tagging and recapture. Nearly all shells had relatively clean growing margins which is where the tags were attached. Some heavily encrusted snails were just not used for tagging but were included in length frequencies, so there is more potential error in that dataset but since those numbers are larger, errors are less significant.
Figure 2. A heavy infestation of barnacles on Lunella torquata. There was still a small clean margin to attach the tags. The barnacles at the rear (left hand side) were removed prior to measuring
Figure 3. Turbo militaris showing encrusting worm tubes and an oyster but still with a clean shell margin enabling easy tagging.
3 Operator error I did all the measuring in this study so there is no chance of errors arising from different operators. I had previously measured thousands of abalone, sea urchins, scallops and turban snails so I assumed there was no “learning curve” which might result in later measurements being more accurate than those done early in the study.
There are two things that I didn’t do but should have: get one or more other operators to a) measure a sample of actual lengths at tagging and recapture, and b) estimate length-at-tagging (L1) from recaptures. These would have provided other measures of measurement and estimation errors.
4 Estimation error As outlined in an earlier blog post about recaptures, the length at tagging was estimated by measuring the maximum dimension from the back of the shell to the shell striae at the location of the front of the tag(s).
Multiple recaptures, (where a tagged snail was recaptured, measured, re-tagged, released and recaptured a second time, or a third or fourth time) enabled several estimates of estimation error. The Turbo militaris snail shown below was captured once and then recaptured three times, resulting in three entries in my recaptures database with three separate recapture ID’s – one with estimated L1 and actual L2, one with estimated L1, estimated L2 and actual L3, and one with estimated L1,L2,L3 and actual L4. By matching tag colours and lengths, I could confidently identify the multiple recapture history of most individual snails (but some guesses will be wrong). This occurred only 18 times for Lunella torquata (at two sites) but 135 times for Turbo militaris, because there was little movement by the population out of Mahon Pool.
In Figure 4, below, the shell striae at the red tag indicate the length at first tagging (estimated L1). The striae at the yellow tag indicate the length at first recapture and thus the first re-tagging (estimated L2 for 1st tagging period at liberty and estimated L1 for 2nd tagging period at liberty). The striae at the blue tag indicate the length at the second recapture and thus the second re-tagging (estimated L1 for 3rd re-tagging, estimated L2 for 2nd re-tagging). This snail thus yields 7 estimates of measurement error:
- actual L3 from 2nd recapture vs estimated L3 from 3rd recapture (blue tag)
- actual L2 from 1st recapture vs estimated L2 from 2nd recapture (yellow tag)
- actual L2 from 1st recapture vs estimated L2 from 3rd recapture (yellow tag)
- estimated L2 from 2nd recapture vs estimated L2 from 3rd recapture (yellow tag)
- estimated L1 from 1st recapture vs estimated L1 from 2nd recapture (red tag)
- estimated L1 from 1st recapture vs estimated L1 from 3rd recapture (red tag)
- estimated L1 from 2nd recapture vs estimated L1 from 3rd recapture
Figure 4. Turbo militaris from Mahon Pool showing three taggings (red,orange,blue) and indicating three recapture lengths (orange,blue,untagged edge).
The tables below show measurement error estimates for the 135 multiple recaptures of Turbo and the 18 multiple recaptures of Lunella.
Turbo militaris Mahon Pool | Number | Average estimated error (mm) |
Recaptured twice | 89 | 0.55 |
Recaptured 3 times | 42 | 0.79 |
Recaptured 4 times | 4 | 1.04 |
L1 error estimates | 201 | 0.73 |
L2 error estimates | 228 | 0.64 |
L3 error estimates | 49 | 0.64 |
L4 error estimates | 4 | 0.63 |
Actual measurements vs estimated lengths | 216 | 0.59 |
Estimated lengths vs estimated lengths | 233 | 0.70 |
Table 1. Differences between estimates of shell length at various tagging events for Turbo militaris at Mahon Pool.
This table and the corresponding Figure 5 below show that measurement errors for Turbo militaris were mostly less than 1mm.
Figure 5. Turbo militaris – Distribution of differences between actual length measurements and subsequent, retrospective estimates of those lengths (blue) and differences between estimates of length from one recapture and subsequent re-estimation of those lengths from further recaptures (orange).
Lunella torquata Mahon Pool & Little Bay | Number | Average estimated error (mm) |
Recaptured twice | 16 | 0.51 |
Recaptured 3 times | 2 | 0.77 |
L1 error estimates | 21 | 0.26 |
L2 error estimates | 20 | 0.70 |
L3 error estimates | 2 | 2.75 |
Actual measurements vs estimated lengths | 20 | 0.93 |
Estimated lengths vs estimated lengths | 23 | 0.28 |
Table 2. Differences between estimates of shell length at various tagging events for Turbo militaris at Mahon Pool.
Figure 6. Lunella torquata – Distribution of differences between actual length measurements and subsequent, retrospective estimates of those lengths (blue) and differences between estimates of length from one recapture and subsequent re-estimation of those lengths from further recaptures (orange).
As for Turbo, the estimated measurement errors for Lunella were mostly less than 1mm.
Finally, these error estimation analyses also produced recapture rates using multiple recaptures. For Turbo militaris, 377 snails were re-tagged on 11 occasions (all at Mahon Pool). The 135 multiple recaptures is a 36% recapture rate. For Lunella torquata, 156 snails were re-tagged on 30 occasions (132 at Little Bay, 24 at Mahon Pool). The 18 multiple recaptures is an 11.5% recapture rate. Compare these with the overall recapture rates from all taggings reported in earlier blog posts of 50% for Turbo at Mahon Pool and 19%,15% and 8% for Lunella at Little Bay and Mahon Pool.
References
GROTAGPLUS : Flexible maximum likelihood estimation of growth from multiple tagging datasets. R documentation : fishmethods package (version 1.12-1)
Francis, R. I. C. C. (1988). Maximum likelihood estimation of growth and growth variability from tagging data. New Zealand Journal of Marine and Freshwater Research, 22(1), 43–51. https://doi.org/10.1080/00288330.1988.9516276
Kienzle M, M Broadhurst and G Hamer, 2022. Bayesian estimates of turban snail (Lunella torquata) growth off south-eastern Australia. Fisheries Research : 248, 106218.) https://doi.org/10.1016/j.fishres.2021.106218
Wang YG, MR Thomas, IF Somers. 1995. A maximum likelihood approach for estimating growth from tag–recapture data. Canadian Journal of Fisheries and Aquatic Sciences https://doi.org/10.1139/f95-025