Length-weight relationships (LWRs) of fish are useful in determining their weight and biomass when only length data are available, and are useful in fishery management and conservation (Froese 1998, 2006). Moreover, LWRs have been used in the study of fish conditions and growth patterns (e.g., Ricker 1975).

Gobiids (Teleostei: Gobiidae sensu Gill and Mooi (2012)) of the Caspian Sea (i.e., the world's largest inland body of water, often described as the world's largest lake) include 43 species in 12 genera: 35 species are endemic to the basin, seven species are native to the overall Ponto-Caspian, and one species is exotic (Zarei et al. 2022). LWRs have already been reported for several gobiid species from the Caspian basin (e.g., Abdoli et al. 2009; Mousavi‐Sabet et al. 2016). This study provides LWRs for another four species: Benthophilus persicus Kovačić, Esmaeili, Zarei, Abbasi & Schliewen, 2021; B. baeri Kessler, 1877; Knipowitschia longecaudata (Kessler, 1877); and Hyrcanogobius bergi Iljin, 1928.

Using beach seining, scuba diving, and deepwater bottom beam trawls, the fish were collected (1996–2017) from the coastal waters of the southwestern Caspian Sea at Astara (38°25'27.4"N, 48°53'06.2"E), Bandar Anzali (37°30'27.9"N, 49°27'56.8"E), and Chaboksar (36°59'15.0"N, 50°34'01.7"E). Specimens were morphologically identified using Miller (2004) and Kovačić et al. (2021), fixed in 10% formalin, and deposited in the Zoological Museum of Shiraz University, Collection of Biology Department (ZM-CBSU).

Sex determination was achieved through external examination of the urogenital papilla morphology (Miller 2004; Kovačić et al. 2021). Specimens were measured to the nearest 0.1 mm total length (TL) and standard length (SL) using a digital caliper under a Zeiss Stemi sv6 stereomicroscope and weighed to the nearest 0.001 g (total weight, W). The parameters of the length-weight relationships W = aL^b were expressed by linear regression of the log‐transformed weight and length, where W is the total weight (g), L is the total length (cm), a is a constant being the initial growth index, and b is the slope of the log‐transformed linear regression. Prior to regression analysis, log-log plots of length and weight values were performed for visual inspection of outliers (Froese 2006). Additionally, 95% Confidence Intervals (CI) for a and b were estimated. The significance of the regression was tested by ANOVA. To examine the variation of the b values between sexes, a Student’s t-test was used to compare regression coefficients for male and female of the four species (Zar 1974). To test whether b values significantly deviated from the expected cube value of 3, Bailey’s t‐test was applied. Covariance analysis was applied to test for a significant difference in the b value between the sexes of the four species (Zar 1974).

A total of 410 specimens, including 199 Benthophilus persicus, 40 Benthophilus baeri, 135 Knipowitschia longecaudata and 36 Hyrcanogobius bergi were collected (Table 1). ANOVA showed a highly significant difference between sexes in three variables (TL, SL, and W) in B. persicus (p<0.001) (Table 2). Estimates for length‐weight parameters are given in Table 1. The slope (b) of LWRs ranged from 2.874 for B. baeri to 3.408 for H. bergi with r² values higher than 0.918. Covariance analysis using Student’s t-test revealed significant differences between b values of males and females in all four species. Furthermore, Bailey’s t-test in both sexes of the four species showed that b values significantly deviated from the expected cube value of 3.

The currently limited knowledge on Caspian endemic gobies is mainly due to sampling artifacts, since many species are known only from a few expeditions, and many, including those included in this study, appear to be ecologically restricted to difficult-to-sample deep-water habitats. In all four species, the allometric coefficient (b) of LWR is within the expected range of 2.5–3.5 (Froese 2006).

Studies have shown that factors such as season, habitat, sex, gonad maturity, diet, stomach fullness, health, and preservation methods may affect LWRs (e.g., Bagenal and Tesch 1978; Tesch 1971). In Benthophilus baeri and Knipowitschia longecaudata, the b values were larger in females, indicating that females are heavier than males of the same length, which might be explained by differences in gonadal development or nutritional status.

The LWRs provided here should be taken with caution and considered as preliminary since we cannot exclude shrinkage over time (i.e., over years in preservation fluid), and therefore, some of the estimates may deviate from those of freshly collected specimens. Additional data based on fresh specimens and measurements after fixation in formalin for 12–96 hours, as well as 10–50 days, would reveal the shrinking rate over time and enable calculating a correction factor.

The conservation status of Caspian gobiids and species of the South Caspian sub-basin, in particular, has been partially assessed (i.e., 64.9% as Least Concern and 35.1% as Data Deficient and Not Evaluated in the IUCN Red List) (Zarei et al. 2022). The IUCN Red List does not have information about B. persicus, and the other three species are under the Least Concern category; however, there is little data and the population trend is unknown. Increased sampling and more reliable metadata on their species distributions, combined with biological and ecological data are needed to determine their conservation status.