Conditional Ulam stability and its application to von Bertalanffy growth model

<abstract><p>The purpose of this paper is to apply conditional Ulam stability, developed by Popa, Rașa, and Viorel in 2018, to the von Bertalanffy growth model $ \frac{dw}{dt} = aw^{\frac{2}{3}}-bw $, where $ w $ denotes mass and $ a &gt; 0 $ and $ b &gt; 0 $ are the coefficients of anabolism and catabolism, respectively. This study finds an Ulam constant and suggests that the constant is biologically meaningful. To explain the results, numerical simulations are performed.</p></abstract>

Estimation of Fishing Mortality Rate and Exploitation Status of Yellowstrip Scad (Selaroides leptolepis) in Tomini Bay using Von Bertalanffy Growth Model Approach

Highlight ResearchThe fishing area of S. leptolepis in this study was confirmed to be located in Tomini BayThe fish samples were gathered randomly from fishers’ catch using purse seinesThe growth curve for the male and female fish data were both plotted following the trend of the Von Bertalanffy equationThis study estimates the growth parameters, mortality, and exploitation rates of the male and female fish separately.AbstractComprehensive data is required for implementing sustainable fisheries management. Population dynamic and stock assessment aspects of Selaroides leptolepis species in Tomini Bay have not been entirely reported. This study aimed to determine the fishing mortality rate and exploitation status of S. leptolepis in Tomini Bay by calculating Von Bertalanffy growth model parameters (L∞, K, t0) then plotting them into Pauly's empirical equation. The sampling was conducted monthly from April to September 2020 at Gorontalo City Fishing Port. Samples were collected randomly from five commercial fishing vessels shortly after the fishermen landed their catch at the fishing port. All fish samples were confirmed to be obtained by the fishermen from Tomini waters. The growth parameters of the samples were analyzed using FiSAT II based on Von Bertalanffy mathematical model. While the mortality and exploitation values were calculated manually using Pauly's equation. The study showed that the growth parameter values of S. leptolepis in Tomini Bay were 245.47 mm, 0.49/year, and -3.04/year for males, while 227.80 mm, 0.63/year, and -2.72/year for females separately for L∞, K, and t0. The total, natural, and fishing mortality rates were 3.06/year, 0.61/year, and 2.45/year for males and 0.99/year, 0.74/year, and 0.25/year for females. The analysis results showed that the female's natural mortality (M) was higher than the male. In contrast, the fishing mortality (F) and total mortality (Z) of male fish exceed the female. The exploitation value of males (E=0.80) was greater than that of females (E=0.26).

Age and growth of large scale scraper (Capoeta aculeata) in the Gizehrud River, Tigris basin

The large scale barb, Capoeta aculeata is a little known species native to Iran. Its age and growth were studied in 377 specimens collected monthly from the Gizehrud River in Lorestan Province (Tigris basin) during May 2014–May 2015. Sex ratio was 1M:2.1F. The maximum age of both female and male specimens was 6+ years. The most common age group of both male and female fish was 4+. The fork length ranged from 12.2 to 20.8 cm (17.4 ± 1.2SD) and weight from 32 to 188 g (93.6 ± 21.8SD). The estimated length-weight relationship of male specimens was W = 0.0161FL3.012, (r2 = 0.82) and that of female specimens W = 0.0248FL2.87, (r2 = 0.79). This relationship showed that growth of both Capoeta aculeata sexes was isometric. The estimated von Bertalanffy growth model for males was Lt= 20.9[1-e-0.57(t+0.2)] and for females Lt = 20.3[1-e-0.56(t-0.8)]. The growth performance index was estimated at 5.4 and 5.5 for males and females, respectively, indicating a similar growth rate for both sexes.

Trends in Growth Modeling in Fisheries Science

Growth models estimate life history parameters (e.g., growth rates and asymptotic size) that are used in the management of fisheries stocks. Traditionally in fisheries science, it was common to fit one growth model—the von Bertalanffy growth model—to size-at-age data. However, in recent years, fisheries science has seen an increase in the number of growth models available and the evaluation of multiple growth models for a given species or study. We reviewed n = 196 peer-reviewed age and growth studies and n = 50 NOAA (National Oceanic and Atmospheric Administration) regional stock assessments to examine trends in the use of growth models and model selection in fisheries over time. Our results indicate that the total number of age and growth studies increased annually since 1988 with a slight proportional increase in the use of multi-model frameworks. Information theoretic approaches are replacing goodness-of-fit and a priori model selection in fisheries studies; however, this trend is not reflected in NOAA stock assessments, which almost exclusively rely on the von Bertalanffy growth model. Covariates such as system (e.g., marine or fresh), location of study, diet, family, maximum age, and range of age data used in model fitting did not contribute to which model was ultimately the best fitting, suggesting that there are no large-scale patterns of specific growth models being applied to species with common life histories or other attributes. Given the importance and ubiquity of growth modeling to fisheries science, a historical and contemporary understanding of the practice is critical to evaluate improvements that have been made and future challenges.

Size, growth and mortality of riverine golden perch (Macquaria ambigua) across a latitudinal gradient

Effective fisheries management requires fish size, growth and mortality information representative of the population and location of interest. Golden perch Macquaria ambigua is long lived, potamodromous and widespread in the Murray–Darling Basin (MDB), Australia. Using a sample spanning 13 river systems and 10° of latitude, we examined whether the maximum size of golden perch differed by latitude and whether growth and mortality varied between northern and southern MDB regions. The length, weight and age ranges of golden perch sampled (n=873) were 52–559mm, 2–3201g and 0+ to 26+ years respectively, and maximum length and weight were unaffected by latitude. Length and age–length distributions represented by age–length keys varied by region, with greater variability in age-at-length and a larger proportion of smaller individuals in northern MDB rivers, which generally exhibit greater variability in discharge. Growth and mortality rates were similar between regions, and an MDB-wide von Bertalanffy growth model (L∞=447, k=0.32 and t0=–0.51) and instantaneous mortality rate (Z=0.20) best described the data. An MDB-wide length–weight equation also provided the best fit (W=6.76×10–6 L3.12). Our data suggest that the MDB can be treated as one management unit in terms of golden perch maximum size, growth and mortality parameters.

Age and growth of a newly described barb, Capoeta coadi (Cyprinidae), in Beheshtabad River, Tigris basin

The Coad barb, Capoeta coadi Alwan, Zareian and Esmaeili, 2016, is a newly described endemic fish in Beheshtabad River, Tigris basin of Iran and little is known about its life-history. Life history characteristics were examined in 426 specimens collected monthly from Beheshtabad River (central Iran) during May 2013 to May 2014. The sex ratio was 1M:0.7F. Based on scale and opercular readings, the maximum ages of the population were 8+ years for females and 7+ for males. The most frequent age groups were 3+ and 4+ in males and females, respectively. Size varied from 8.94 to 42.95 cm in fork length and weight between 10.3 and 1255.5 g. Length–weight relationship implied that the growth was negatively allometric for both sexes. The von Bertalanffy growth model was estimated as Lt =35.97[1‑e‑0.205( t+0.586)] and Lt = 49.31[1‑e ‑0.162( t‑0.208)] for males and females, respectively. The growth performance index was estimated as 5.58 and 5.97 for males and females, respectively, indicating a faster growth rate for females.

SOME POPULATION PARAMETERS AND EXPLOITATION STATUS OF FOURFINGER THREADFIN (Eleutheronema tetradactylum Shaw, 1804) IN TARAKAN WATERS, NORTH KALIMANTAN

Information on exploitation status of fourfinger threadfin (Eleutheronema tetradactylum Shaw, 1804) is important for sustainable gillnet fisheries management in Tarakan, North Kalimantan waters. In an attempt of providing scientific data and information on the exploitation status of this species, a research work was conducted from January to November 2016 in Selumit landing place. Fish sampling was done by trained enumerator on bottom gillnet catches landed through semi-regular observation. A total of 1964 specimens were collected and measured. The results showed that the size ranged between 16-70 cmFL with an average of 37.72 ± 0.36 cmFL. The length at first captured (Lc) of about 38.5 cmFL, was smaller than the length at first mature of female (Lm) of 39.6 cmFL. The growth pattern was negative allometry. By applying von Bertalanffy growth model, it was found that growth model for this species was L(t)=75,8(1-e0,3(t+0,035)). Exploitation rate (E) was 0,47. It showed that the exploitation status of fourfinger threadfin in Tarakan Waters was still sustainable.