# Length-Weight Relationship of 20 Cryptobenthic Fish in Coral and Rocky Reefs in the Gulf of California, Mexico

Authors: Marina Soledad Irigoyen-Arredondo; Xchel G. Moreno-Sánchez; Emigdio Marín-Enríquez; Jose Manuel Ayala-Galaz; Daniel Stiven Ortiz-Oyola; Fausto Valenzuela-Quiñonez; Damien Olivier
Journal: Journal of Applied Ichthyology
 (2023)

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## Abstract

We present the length-weight relationships (LWRs) in 20 cryptobenthic reef fish species in the Gulf of California (Mexico). Nine of these species had no LWR records yet. However, the other species had LWRs based onin-formalin specimens collected more than 20 years ago. This conservation method has likely affected LWRs parameters. Our study showed higher estimations of the parameter a obtained on fresh specimens than in-formalin individuals. On the other hand, parameter b was not affected. Therefore, the biomass estimates using previous LWRs were strongly underestimated. Ergo, the similitude in parameter b between the two conservation methods highlights that the shape of the LWRs is conserved and did not change over the last 20 years. Finally, we compared the LWRs of shared species in the region’s two main types of shallow reefs, i.e., coral and rocky reefs. We found that the body fitness was not affected by reefs type, which means that both habitats seem to offer similar living conditions for shared species.


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## Body

## 1. Introduction

The cryptobenthic reef fishes (CRFs) are small size species (∼less than 50 mm) living hidden in the interstices of the reef’s substratum [1]. Although highly abundant and playing essential roles in reefs’ trophodynamics and productivity [2–4], CRFs are generally understudied because of their discrete nature. The Gulf of California (GC, Mexico) supports a rich and abundant ichthyofauna with approximately 300 reef fishes’ species [5, 6], of which about one-third are CRFs [7]. While some studies have investigated biogeographic patterns of CRFs in this region [8, 9], their ecology is still poorly known (but see [10, 11]).Length-weight relationships (LWRs) allow for estimating fish biomass thanks to more accessible fish body length data and are essential for fisheries management and conservation for regulating catches [12]. Moreover, LWRs can be used as conditions factors to compare the fitness of individuals [13] that may vary on temporal and spatial scales [12]. Because of their small size, CRFs have a high metabolism, and unfavorable conditions (scarcity or less nutritional prey, higher predation pressure, pollution, etc.) may have rapid negative effects on their fitness and, in turn, on their productivity [1]. CRFs may represent ∼60% of consumed reef fish biomass and represent a cornerstone for ecosystem functioning and trophodynamic relationships [4]. Therefore, a less suitable environment for CRFs may affect the equilibrium and functioning of the reef. For example, divergent prey availability between the southern Arabian Gulf and the Gulf of Oman modified LWRs of CRFs with lower fitness in Arabian Gulf, characterized by more extreme environmental conditions [14]. Therefore, knowledge about species LWRs and their spatial and temporal comparison may estimate the individual’s living conditions and help understand the health status and functioning of the reefs.To our knowledge, a single study estimated the LWRs in 17 CRFs species in the GC (La Paz Bay) on individuals collected more than 20 years ago [15]. Additionally, a LWRs study was conducted in the mangrove swamp of La Paz Bay and included a single CRF species [16]. Balart et al. [15] used weights of specimens preserved in formalin, likely affecting the LWRs estimations.We estimated the LWRs in 24 CRFs species using fresh weight in the present study. Nine of them have not been recorded in Fishbase yet. Then, by comparing the shared species between our research and the anterior of Balart et al. [15]; we investigated the effect of conservation methods on LWRs estimation. Finally, we compared the LWRs between rocky and coral reefs to test whether both habitats offer similar ecological opportunities for shared species.


## 2. Materials and Methods

We sampled CRFs assemblages from August to November 2020 in two coral and two rocky reefs in La Paz Bay (Figure1) at 2 to 6 m depth. We injected clove oil and ethanol (ratio 1 : 3) inside a leak-proof bag covering a one-meter squared quadrant. Anesthetized fish were collected by divers using hand nets, placed in tagged plastic bags, and preserved on ice until transport to the laboratory, where specimens were preserved at −20°C. We collected CRFs on 70 quadrants (16 on the reef “El Faro” and 18 for each other three reefs). All fish were identified to species level using specialized keys [5]. The total length (TL) of fish was measured using digital calipers with 0.1 mm precision and weighted using an electronic scale with 0.01 g precision.Figure 1
Geographic location of the four reef sites where cryptobenthic fishes were collected in La Paz Bay, Gulf of California. Coral and rocky reefs are orange and blue-colored, respectively. CAL: Caleritas, CRU: Las Cruces, FAR: El Faro, PME: Puerto Mexía.First, we explored the length-weight relationships for each species to delete high-leverage points (FigureS1). We then calculated LWRs using Froese’s equation (2006) as given as follows:(1)W=a∗Lb+ε,or in its logarithmic form as given as follows:(2)logW=loga+b∗logb+ε,where W is the total weight of the fish (g), L is total length (mm), a is the intersection point with the y axis, b is the slope of the curve, and ε is an error term, assuming that ε∼N0,σ. The LWR models were adjusted using nonlinear least squares with the nls function in R software [17]. Because the sampling size was highly heterogeneous among species (Table 1), we plot the relationships between each models’ coefficients of determination (r2) against sampling sizes. Finally, we plot the logarithmic values of parameter a against parameter b values to detect questionable LWRs due to narrow size range, not enough data, or outliers to the respective model [12].Table 1
Characteristics of the sample and estimated length-weight relationship (LWR) parameters for the 24 studied species. References are indicated when LWR had been studied in previous studies.
SpeciesAnterior studiesTrue crypticNMax sizeSize range (cm)a95% CI ab95% CI br2Body shape(1 = yes, 0 = no)Acanthemblemaria crockeri (Beebe & Tee-Van, 1938)A122861.43–3.370.0140.013–0.0162.7382.625–2.8520.93ElongatedApogon retrosella (Gill, 1862)A0112101.15–6.160.0210.018–0.0243.2123.127–3.2980.98FusiformAxoclinus nigricaudis (Allen & Robertson, 1991)—1384.51.21–30.0180.015–0.0212.8942.710–3.0840.98ElongatedAxoclinus storyae (Brock, 1940)—1231.13–2.280.0190.014–0.0272.9592.501–3.4520.93ElongatedBarbulifer pantherinus (Pellegrin, 1901)A1365.21.18–2.410.0160.011–0.0213.2982.908–3.7150.91ElongatedChriolopis zebra (Ginsburg, 1938)—1724.40.91–2.780.0130.011–0.0163.2333.011–3.4670.96ElongatedCirrhitichthys oxycephalus (Bleeker, 1855)A017104.42–6.270.040.016–0.0982.8682.347–3.4030.91Short & deepCoralliozetus micropes (Beebe & Tee-Van, 1938)—11141.61–2.030.0140.004–0.0412.8461.078–4.7410.6ElongatedCoryphopter usurospilus (Ginsburg, 1938)A11366.51.36–3.760.0120.011–0.0143.4313.312–3.5520.96ElongatedCrocodilichthys gracilis (Allen & Robertson, 1991)A186.42.4–3.880.0160.010–0.0262.772.394–3.1650.99ElongatedDoryrhamphus excisus (Kaup, 1856)A11671.69–4.590.0020.001–0.0023.1812.865–3.5240.98Eel-likeEnneactes reticulatus (Allen & Robertson, 1991)A12394.91.22–4.020.0320.027–0.0372.4592.313–2.6060.83ElongatedGobiosoma chiquita (Jenkins & Evermann, 1889)B1276.51.09–2.340.0140.009–0.0213.3652.861–3.9400.95ElongatedLythrypnus pulchellus (Ginsburg, 1938)A1934.50.7–20.0190.016–0.0233.0442.718–3.3860.85FusiformLythrypnus rhizophora (Heller & Snodgrass, 1903)—1353.40.74–2.180.0190.014–0.0243.3332.905–3.7740.91FusiformMalacoctenus hubbsi (Springer, 1959)—11992.29–4.860.0180.009–0.0323.0922.671–3.5520.97FusiformParaclinus mexicanus (Gilbert, 1904)—116240.86–3.340.0160.015–0.0182.9962.886–3.1080.96FusiformParaclinus sini (Hubbs, 1952)A12261.74–30.0110.007–0.0163.533.142–3.9340.96FusiformPycnomma semisquamatum∗ (Rutter, 1904)—1386.31.25–3.30.0160.011–0.0233.2042.833–3.5800.91ElongatedStarksia spinipenis (Al-Uthman, 1960)A11351.79–2.980.0150.011–0.0223.3572.994–3.7430.98FusiformStathmonotus sinuscalifornici (Chabanaud, 1942)—1246.50.88–3.080.0060.003–0.013.162.57–3.850.93ElongatedStegastes rectifraenum (Gill, 1862)A01413.50.98–4.040.0420.030–0.0572.8852.646–3.1500.99Short & deepThalassoma lucasanum (Gill, 1862)A06151.12–2.910.0240.013–0.0372.842.398–3.4130.99FusiformTigrigobius puncticulatus (Ginsburg, 1938)A16051.07–2.610.0180.015–0.0223.0592.803–3.3190.92ElongatedA: Balart et al. [15]; B: Moreno-Sánchez et al. [16]; ∗ new maximum length record; N = number of specimens; a = is the intersection point with the y axis, b = is the slope of the curve, r2 = coefficients of determination, a and b parameters and associated (upper-lower) 95% confidence interval (CI).Based on the 14 species in common between our study and the collection of Balart et al. [15], we compared a and b parameters between the two studies and how potential differences may affect the estimated biomass. Finally, we selected seven species abundant in both coral and rocky reefs, and we compared their length, weight, and LWRs between the two habitats. Length and weight comparisons were run with student t-tests (Table S1) in R software [17].


## 3. Results and Discussions

The LWR models generally provided a good fit to the data asr2 was higher than 0.9 for 21 of the 24 species and below 0.7 for Coralliozetus micropes (Table 1). Although the lowest r2 had a small sampling size and narrow size range, these two parameters do not seem to have affected the fitting of the models (Figure 2(a)). All the parameter b values fell in the acceptable 2.5–3.5 range (Table 1), with values outside this range generally indicating wrong estimates due to sampling size or too narrow range size [18]. The parameter a values were also included in the 95% range values found on teleosts [12]. The relationship between the logarithmic values of parameter a and parameter b indicates some outliers (Figure 2(b)). These divergences do not seem related to the representativity of the studied size range but the body shape of the species. The two non-CRFs species Cirrhitichthys oxycephalus (Bleeker, 1855) and Stegastes rectifraenum (Gill, 1862) have a short and deep body shape. These two species have higher values of parameter a for a given parameter b value than most studied species with elongated or fusiform body shapes (Figure 2(b)). On the contrary, Doryrhamphus excisus (Kaup, 1856) has an eel-like body shape and lower parameter a value (Figure 2(b)). Our observed body shape effect reflects what was observed on teleosts [12].Figure 2
(a) Relationship between the coefficient of determination (r2) of LWR models and sample size and relative size range. (b) Relationship between parameter a (log-scale) and parameter b. For each species, the relative size range and the body shape are indicated.
(a)(b)We found a high difference in parameter avalues when estimations were made on fresh or in-formalin specimens, but parameter b showed complete overlap (Figure 3(a)). That means that the preservation in formalin affected the intercept of the LWRs models (in log scale, equation (2)) but not the slope. That provides a substantial underestimation of the biomass (Figure 3(b)). However, the shape of the LWRs (slope value) seems unaffected. Hence, LWRs based on in-formalin specimens will poorly estimate weight or biomass values but can be helpful for comparing the slope, and therefore, the body condition of individuals preserved with the same method. As we found no difference in parameter b with the collection made ∼20 years ago, the LWRs showed temporal stability, indicating that reefs’ environmental conditions did not significantly change in the last two decades or that species were able to adapt.Figure 3
Comparison of LWR based on fresh (green) andin-formalin (purple) specimens. (a) Comparison of parameters a and b. (b) Effect of LWR difference on weight and biomass estimations. For example, the estimated weight of Acanthemblemaria crockery along the full simulated range size of the species is shown according to the two conservation methods. The biomass per quadrant of fish assemblages considering the 14 species in common between the present study (fresh specimens) and the anterior study (in-formalin specimens, [15] is also shown. Data are represented by site and reef types are indicated (coral and rocky). Three biomass values are shown: (i) the estimated biomass based on LWR parameters using in-formalin specimen (purple); (ii) the estimated biomass based on LWR parameters using fresh specimen (green); and the true (weighted) biomass (grey).
(a)(b)From the abundant species in both coral and rocky reefs, we found that only the gobiidChriolepis zebra (Ginsburg, 1938) had a higher length and weight in coral reefs than in rocky reefs (Figure 4(a), Table S1). However, the LWRs did not differ between the two habitats (Figure 4(b)), meaning that body conditions are similar. A less favorable habitat could affect the fitness of species [14]. Although coral reefs generally host less fish diversity than rocky reefs in the eastern tropical Pacific due to a more homogeneous seascape [19], they seem to offer similar living conditions for shared species.Figure 4
Comparison of length, weight and LWR between coral (orange) and rocky (blue) reefs of seven abundant species in the two habitats. (a) The differences between rocky and coral means are sketched with their 95% CI. The only significant difference (CI not crossing zero) is highlighted in orange with higher length and weight in the coral reefs. (b) The LWRs are sketched for the seven species in function of the habitat.
(a)(b)



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*Source: 1122004-2023-01-10.xml*