Introduction

This is a report for preliminary estimates of natural mortality for marsh-resident juvenile fish species collected during summer 2020 at the Point aux Pins peninsula, Mississippi Sound, coastal Alabama. Here I synthesize the choice of input parameters and methods used to estimate daily mortality rates for juveniles of hardhead catfish Arius felis, silver perch Bairdiella chrysoura, blue crab Callinectes sapidus, white trout Cynoscion arenarius, spotted seatrout Cynoscion nebulosus, gulf killifish Fundulus grandis, pinfish Lagodon rhomboides, and white shrimp Litopeaneus setiferus.

The length-converted catch-curve

I chose the length-converted catch-curve (LCCC) to derive estimates of mortality for the species analyzed herein. Over the course of this document, I will be referring to the mortality estimates as natural mortality (M), as there’s no fishing pressure targeting any of the species at this life stage in the region. The framework used to run the LCCC was the “i-LCCC” (improved length-converted catch-curve, see de Barros 2023 for freely available code), which further advances mortality estimation by (1) bootstrapping the input abundance-at-length data to estimate uncertainty coming from sampling errors and fitting the linear regression over the log-transformed abundances, and (2) allowing to estimate mortality with size distributions with a maximum size larger than the asymptotic length (Linf).

The catch curve relies on the following framework:

Numbers-at-age decrease over time according to the instantaneous rate of total mortality (Z):

\[N_{t} = N_{t-1}e^{-Z(t)}\]

\[ln[N_{t}] = ln[N_{t-1}] - Zt\]

Simply assuming that catch (C) is related to numbers-at-age (i.e. the observed proportions-at-age from the sample reflects the expected population age distribution) allows us to estimate Z by tracking catch-at-age through time. The rate of decline = Z:

\[ln[C_{t}] = ln[C_{t-1}] - Zt\]

In the length-converted catch-curve, age is estimated from the observed length composition using growth parameters. Assuming growth follows a von Bertalanffy function, we can estimate relative age (aL), which is the expected age an individual would be at a given length:

\[a_{L} = t0 - (1/k) ln(1-L/L_{\infty})\]

Input parameters

The length converted catch-curve requires growth parameters as input to transform observed size frequencies into relative ages. It is ideal to use estimated growth parameters from the study site, but plotting length frequencies over time (Figures 1, 2, 3, 4, 5, 6, 7, and 8) show that it is only possible to track cohorts through modal class progression for the spotted seatrout and pinfish, therefore making the estimation of absolute growth rates for most species unfeasible. Despite ELEFAN (ELectronic LEngth Frequency ANalysis) being more robust to data which cohort tracking is harder, it is likely that growth parameter estimates will end up being trapped in multiple local maxima during the estimation given the absence of pretty much any distinguishable cohorts in the datasets of the remaining species, likely a result of continuous recruitment (see Schwamborn et al 2019). Given those mentioned caveats, I have chosen to survey the literature for growth parameters for all species. When multiple estimates are available at the literature, I simply chose the one coming from a study from closest location to the study site. Growth curves were also inspected to make sure estimates are not highly uncertain or doubtful. Estimates of absolute growth for juveniles were given priority, and von Bertalanffy growth parameters were collected if the later were unavailable. If the surveyed studies did not report uncertainty in parameter estimates, I assumed a coefficient of variation of 20% around the mean estimates, which is pretty close to a standard deviation of 0.2. Input parameters are summarized in Table 1 below.

Table 1. Growth parameters for each study species

Species Absolute Growth K (year-1) Linf (mm) t0 (year-1) Reference Location
Arius felis NA 0.25 (0.023) 410 (2.81) -1.24 (0.29) Flinn et al (2019) Louisiana
Bairdiella chrysoura NA 1.32 116 -1.02 Sirot et al (2015) Yucatan, Mexico
Callinectes sapidus 0.513 (0.317) NA NA NA Hayes et al (2022) Northern GoM
Cynoscion arenarius NA 0.325 336.85 -1.745 Nemeth et al (2006) Florida Gulf Coast
Cynoscion nebulosus NA 0.36 597.5 -0.955 Bohaboy et al (2018) Alabama
Fundulus grandis NA 2.43 87.27 -0.022 Vastano et al (2017) Louisiana
Lagodon rhomboides 0.5421 (0.07) NA NA NA Estimated locally Study site
Litopeaneus setiferus 0.77 (0.05) NA NA NA Baker and Minello (2010) Texas

Below are plots of the catch per size class for each species, and data seem suitable for estimating mortality through catch-curves. For the hardhead catfish, in particular, there appears to be two cohorts, which are going to be referred to as early and late juveniles. In fact, according to growth parameters extracted from Flinn et al (2019), those appear to be young-of-year and one year olds, respectively. Further estimation is gonna be executed separately for early and late juveniles.

Catch-curves

Hardhead catfish (late juveniles)

Silver perch

Blue crab

White trout

Spotted seatrout

Gulf killifish

Pinfish

White shrimp

Estimating mortality with size composition

A modified version of the Baranov catch equation in its continuous formulation will essentially estimate a snapshot of the “true” underlying population modified by selectivity when fishing mortality is negligible (Branch, 2009) (Figure 26):

\[C_{a,t} = S_{a}N_{a-1,t-1}e^{-M}\]

\[N_{a,t} = N_{a-1,t-1}e^{-M}\]

I have wrote a Bayesian model to estimate mortality rates using the predicted age composition of the catch after accounting for selectivity. The benefit of this method over the catch curve is that it uses all data points rather than just the fully-selected sizes/ages, and therefore can potentially improve model fit. A disadvantage of this model is that mortality is always confounded with migrations out of the study area, specially when dealing with juvenile fish exhibiting ontogenetic shifts in habitat use. Although one option to tackle this would be using dome-shaped selectivity with decreasing probabiliy of selection for older size classes (e.g. double logistic, double normal), parameter estimation for those models is difficult for the same reason: selectivity is confounded with mortality. I have chosen to estimate logistic selection for the sake of simplicity. Results corresponding for ths method can be found on Figure 4 and Table 2.

Table 2. Posterior distributions (means and 95 % C.I.s) of mortality estimates for the study species across methods.

Species Catch curve Catch composition
Arius felis 0.006 (0.003 - 0.011) 0.0048 (0.004 - 0.0055)
Bairdiella chrysoura 0.022 (0.019 - 0.024) 0.036 (0.032 - 0.042)
Callinectes sapidus 0.066 (0.018 - 0.103) 0.054 (0.048 - 0.062)
Cynoscion arenarius 0.028 (0.008 - 0.036) 0.026 (0.022 - 0.029)
Cynoscion nebulosus 0.031 (0.025 - 0.041) 0.016 (0.0125 - 0.019)
Fundulus grandis 0.024 (0.016 - 0.026) 0.018 (0.015 - 0.022)
Lagodon rhomboides 0.02 (0.013 - 0.026) 0.21 (0.018 - 0.024)
Litopeaneus setiferus 0.028 (0.025 - 0.03) 0.018 (0.017 - 0.02)

References

Baker, R., & Minello, T. J. (2010). Growth and mortality of juvenile white shrimp Litopenaeus setiferus in a marsh pond. Marine Ecology Progress Series, 413, 95-104.

Bohaboy, E. C., Patterson III, W. F., & Mareska, J. (2018). Stock assessment of Spotted Seatrout (Cynoscion nebulosus, Sciaenidae) in Alabama. University of Florida, Gainesville and Alabama Department of Conservation and Natural Resources, Marine Resource Division, Dauphin Island.

Branch, T. A. (2009). Differences in predicted catch composition between two widely used catch equation formulations. Canadian Journal of Fisheries and Aquatic Sciences, 66(1), 126-132.

de Barros, M. (2023). iLCCC. RPubs. Available at https://rpubs.com/matheusdebarros/1034241

Flinn, S., Midway, S., & Ostrowski, A. (2019). Age and Growth of Hardhead Catfish and Gafftopsail Catfish in Coastal Louisiana. Marine and Coastal Fisheries, 11(5), 362-371.

Hayes, C. T., Alford, S. B., Belgrad, B. A., Correia, K. M., Darnell, M. Z., Furman, B. T., … & Darnell, K. M. (2022). Regional variation in seagrass complexity drives blue crab Callinectes sapidus mortality and growth across the northern Gulf of Mexico. Marine Ecology Progress Series, 693, 141-155.

Nemeth, D. J., Jackson, J. B., Knapp, A. R., & Purtlebaugh, C. H. (2006). Age and growth of sand seatrout (Cynoscion arenarius) in the estuarine waters of the eastern Gulf of Mexico. Gulf of Mexico Science, 24(1), 7.

Schwamborn, R., Mildenberger, T. K., & Taylor, M. H. (2019). Assessing sources of uncertainty in length-based estimates of body growth in populations of fishes and macroinvertebrates with bootstrapped ELEFAN. Ecological Modelling, 393, 37-51.

Sirot, C., Darnaude, A. M., Guilhaumon, F., Ramos-Miranda, J., Flores-Hernandez, D., & Panfili, J. (2015). Linking temporal changes in the demographic structure and individual growth to the decline in the population of a tropical fish. Estuarine, Coastal and Shelf Science, 165, 166-175.

Vastano, A. R., Able, K. W., Jensen, O. P., López-Duarte, P. C., Martin, C. W., & Roberts, B. J. (2017). Age validation and seasonal growth patterns of a subtropical marsh fish: The Gulf Killifish, Fundulus grandis. Environmental Biology of Fishes, 100, 1315-1327.