From Descriptive to Accurate Horseshoe Crab Size Variations in Wild Populations

Horseshoe crabs have survived until Holocene, but their persistence beyond the Anthropocene is challenged by drastic environment changes that entail impoverishments and the resultant unusual growth sizes. Previously, allometry via morphometric ratio was introduced to classify horseshoe crabs into normal-abnormal growth. However, the descriptive size and weight analysis indicated a considerable portion of Tachypleus gigas with normal allometry. This error was caused by the median sorting of values. Therefore, the same data was treated with correlation before generating a linear equation. By being sexual dimorphs, these arthropods actually have gender-specific morphology indicators which could generate a functional allometry. Since the assessed arthropods were mature, the 19 % yield of smaller female T. gigas was possibly due to degradation effects from poor diets or stress. Yet, for this population, an added risk was female-only harvest. Perhaps, close sizing to male counterparts could be perceived a survival strategy by the female T. gigas . More evidence is needed to strengthen this opinion but for now, this assessment method is novel for accurate allometry assessments in the species with sexual dimorphism. Overall, capture fisheries could have negative impacts and when made severe by sex-specific harvest, the unaccounted practices could collapse sustaining populations.


INTRODUCTION
A rapidly growing human population is creating demands for food. However, sustainable practices in the wild stock supply chains are challenged by both climate and human activities [Pramanik et al. 2021]. Further challenges are caused by abrupt environmental changes due to human practices of the Anthropocene. Waste is a major concern for pollutant-introduction routes. Aside from being able to leach into water systems, pollutants have various retention periods and remain in the environment, unless it is metabolically detoxified or stabilized by free ions in the sediment. In the case of gravitational settling, waste or pollutants become bioavailable for uptake, from which, the internal metabolites of an organism become stimulated to manage the body burden (or stress). While not all aquatic organisms choose to evade stressful environments [Ariffin et al. 2022], the decisions to become a generalist could build up a body burden.
Hence, energy allocation is a metabolic strategy adopted by aquatic organisms, mainly fish, to survive under harsh conditions in polluted environments or during food scarcity. Energy compensation was theorized as practical for cryptic species until its grow-out (or filial) occupies the predator categories in food chains [Sastraprawira et al. 2020]. Yet, in some cases, energy-storing or energy conservativeness results in slower growth rates in juvenile fish, which then becomes detrimental to the persistence of the entire population [Post and Parkinson 2001]. In fact, energy conservation strategies are also responsible for exclusivity and vigor (or natural selection) in confined fish populations, especially in the temporary holding tanks [Jaffar et al. 2019].
Meanwhile, the ability to allocate energy is a strategy also discovered in Tachypleus gigas. Horseshoe crab embryos use energy allocation to manage stress from the external environment ]. When applied, energy allocation that manages stress compensates for the growth of the horseshoe crabs, which means the life stages related to molt cycles could either become delayed or collectively, the entire population would possess unique morphology measurements. Size-to-weight variations (or allometry) could indicate unhealthy growth in T. gigas [Vijayakumar et al. 2000]. Unfortunately, a similar approach was inconclusive to detect unhealthy sizing in small populations of T. gigas [Tan et al. 2012], which could be due to the samples originating from a single population. Descriptive analysis was introduced for size and weight variations, but for T. gigas, its telson length was an imperative inclusion [Sahu and Dey 2013].
However, for a population of T. tridentatus, its allometry was negatively skewed and indicated the population to be less healthy [Chatterji and Pati 2014]. The samples from the same area had a combination of both negative and positive allometry [Mohamad et al. 2016], which indicates that descriptive analysis is not reliable to assess the length-weight variations of horseshoe crabs (T. gigas or T. tridentatus). The major drawback in past assessments is the methodology, where the morphometrics of male and female crabs are compiled together, the pool of data is small (<40 crabs), or the comparison itself is biased towards the size range of earlier horseshoe crab populations. Thus, the allometry analysis is considered inaccurate and does not indicate the morphology sizing for the assessed horseshoe crab population.
A later examination on T. tridentatus was integrated with statistics and descriptive analysis and the use of Spearman's correlation to select suitable size indicators [Mohamed et al. 2021]. The findings were conclusive that male and female horseshoe crabs have unique size indicators aside from the agreement that telson length was part of the inclusion criteria. Now, with the objective to develop accurate gender-specific allometry for a large number of samples, the present work compared the differences between conventional (descriptive) and statistical outputs c.a. [Mohamed et al. 2021

Data collection
The horseshoe crabs, T. gigas were retrieved from Sungai Merlimau (Jasin, West Peninsular Malaysia), a river mouth where horseshoe crabs arrive for their monthly spawning activity. This arthropod arrives into the shallow river banks to deposit their eggs in burrows confined at the water edge, most likely medium to high shores. It is this lunar tide, regardless during the full or new moon where horseshoe crabs are seen as amplexus. Fishermen constantly use this opportunity to maximize the catch-per-unit effort. The 8-inch gill nets (300×1 m) were set during dawn (4.00-7.00 am) tide rise and retrieved 2.5-3 hours later. Removing each entangled horseshoe crab is tedious and would require roughly 5-10 mins/ crab. For each crab, the 9-point morphology (total length, interorbit distance, opisthosoma length, prosoma width and length, carapace length, telson length and weight) was measured by using a measuring tape (±0.1 cm; Figure 1) and portable scale (±0.01 g). All horseshoe crabs were returned to the water after the exercise.

Descriptive analysis
The conventional method of morphometrics involves allometry, a descriptive method that uses length-length and length-weight ratios. The standard values for morphology indicator were developed from available literature c.a. [Razak and Kassim 2018] for Malaysia, [Chatterji and Pati 2014] India and, [Mashar et al. 2017] Indonesia. The deviation from standard values gives rise to negative (small carapace size or small size-to-weight value), normal (balance growth, size-to-weight ratio = 0.0±0.1) and positive allometry (large carapace size or large size-toweight value). These values are output from the distribution curve made on the x-axis with a random range of values or standard deviation in the y-axis of the linear equation. In addition, comparative size classifications from other horseshoe crab populations were also introduced to show the inconsistencies that arise from using the conventional allometry method.

The accurate analysis
Morphology, presented as body measurements for all male and female T. gigas were plotted in Microsoft Excel before being prepared for export into Primer v.7. The square root (√Xi) data was transformed before Bray-Curtis cluster analysis to generate the resemblance matrix. Then, Pearson's correlation is employed to reorganize the values into functional allometry for T. gigas. The indicators of morphology for each horseshoe crab gender group were identified with the highest correlation value. This morphometric group was then assessed for its mean (x̄), standard deviation (σ), normal distribution (y = mx + c), and regression (r 2 ). Then, the x-axis and y-axis values were replaced with the new range of x̄ and σ. This method omits methodological errors in classifying the horseshoe crab morphometrics because findings are specific for each gender and exclusive

Revised allometry
The 9-point morphometry was used to classify horseshoe crabs into size-size indicators for their growth. The male T. gigas achieved p = 0.791 for the correlation values that involve opisthosoma width, prosoma length, telson length, and body weight values. It was p = 0.620 for prosoma width and the total length and p = 0.469 for carapace length, opisthosoma length and interorbit distance. The morphology of the female crab was indicated with better correlation values where p = 0.973 was achieved for opisthosoma width, telson length, and body weight and p = 0.971 for interorbit distance. For other morphology aspects, correlation values were reduced to p = 0.839 for prosoma width, total length, and carapace length and p = 0.812 was indicated for prosoma length and opisthosoma length.
Alongside regression (r 2 = 0.726-0.769), the opisthosoma width, telson length, and body weight were identified as relevant to both genders. However, the prosoma length and interorbit distance were unique indicators for the allometry of the male and female T. gigas (Table 2).
By reprocessing the descriptive allometry into the linear equation, there were marked differences for all 5-morphometric points ( Table 3). The large proportion of male T. gigas recorded with normal allometry (24-28 crabs) for opisthosoma width, prosoma length, telson length, and body weight were actually reclassified with Note: Abbreviations follow the order M -male, F -female, PL -Prosoma length, OW -opisthosoma width, TEL -Telson length, BW -Body weight, IO -interorbit distance. The r 2 represents a goodness-of-fit measure for linear regression. Note: Abbreviations follow the order PL -prosoma length, OW -opisthosoma width, TEL -telson length, BW -body weight, IO -interorbit distance. The denominator (n) represents the number of Tachypleus gigas associated to the census for each of the statistical-selected (Pearson correlation, ρ) morphometric indicators. Denominators for the allometry census (negative, normal and positive) were used to arrange the Tachypleus gigas size into a classification limit for the adult body condition.
positive allometry (10-24 crabs), and concerning telson length measurements, 15 crabs were indicated with negative allometry. Similarly, the large proportion of female crabs described with normal allometry (109-134 crabs) was actually vastly having negative (60-122 crabs) and, if not, substantially having normal (9-52 crabs) or positive allometry (1-74 crabs). The findings are conclusive towards better allometry assessments, because the samples from Pahang, Sarawak, and Melaka were previously missing some morphometric points (Table 4). In fact, the descriptive analysis that used mean and standard deviation as median values did not produce a conclusive range that supports the actual condition (or health) of the T. gigas. Comparatively, the revised range was constructed with a linear equation. Through this equation, the range of 83-93 mm for male opisthosoma width classified the T. gigas with a narrow body layout (Table  4). This example adds support for the need of data transformation before statistics is used to indicate the most-associated morphology for a population. Only then should a linear equation be produced to generate an accurate version of allometry. Despite an imbalance in sample yield for this population, the findings are conclusive that prosomal length and interorbit distance are useful to develop accurate allometry for the male and female T. gigas, respectively. In contrast, the first attempt was made on T. tridentatus from three localities with sample sizes <40 per population [Mohamed et al. 2021]. Still, it should not be misunderstood that statistically-validated allometry has neglected the application of descriptive analysis.  Chatterji and Pati [2014] suggested observing molt cycles, which means the samples having carapace dorsal spines are juvenile crabs. Instead, another consortium of researchers was persistent that size is the best criterion to identify juvenile crabs and this criterion is useful to separate adults from juveniles in a sample pool [Mohamad et al. 2016;Razak and Kassim 2018]. Hence, the developments concerning sample size and size classification itself were rather insufficiently justified. Conversely, the examination of molt cycles is efficient but, a second inclusion criterion is needed. The first is the visibility of eggs in the thin prosoma sheet of the female crab, and the second is the swelling of the genital pore of the male crab. This method of examination adopted from Mohamed et al. [2021] allowed smaller horseshoe crabs that were sexually mature to be part of the allometry assessment.

DISCUSSION
The samples from Sungai Merlimau recorded 6 female T. gigas of smaller size (c.a. opisthosoma width, interorbit distance and telson length) class. In contrast, another 26 crabs were slightly larger but below the normal range for these indicators. Crossreferencing with bodyweight suggests that mass increase exceeds the body size simply because eggs (white-yellow) that are visible in their prosoma were the baggage that added to their body weight. These 32 female T. gigas were gravid with eggs ready for fertilization, which indicated them to be sexually mature. Thus, it is clear that 19 % of the female T. gigas in this captured population resort to survival strategies that reduce the risk of them being captured. Comparatively, 6 % of T. tridentatus captured in Sabah were similarly recorded with this strategy [Mohamed et al., 2021]. Though an indication, more assessments would be better to denote the connections between the 8-inch fishing gear and the chances of capturing both male and female T. gigas. The chances of capturing the entire amplexus increase when both male and female crabs have almost relative sizes. Yet, it is unclear if the smaller female-only opts to form an amplexus with large male crabs. However, the authors are certain that imbalances in operational sex ratio are forcing a survival strategy that was theorized to exist with the Limulus polyphemus [Smith and Brockmann 2014; Hare and Simmons 2019]. This is the first record where T. gigas, similar to the T. tridentatus of Sabah, were reported to practice survival strategies to sustain their population. It was assumed that male mimicry was the strategy utilized where the female grew to appear monomorphic to the male crab.
The classic method of size classification would use median values and then re-class the size and weight of horseshoe crabs in the order of (positive and negative) binomial bulges. However, this method produces inconsistent results (Table 4), which means a definite morphometric indicator could not be established. For instance, ichthyologists used baseline fish measurements and successfully developed length-weight mathematical assessments [Jisr et al. 2018]. Moreover, the carapace width of porcelain crab could indicate age and readiness to reproduce [Hamasaki et al. 2020]. However, horseshoe crabs are neither crustaceans nor fin-fish and have 16-17 molt stages before maturing into the adult [John et al. 2018]. With this, the accurate allometry assessment introduced for T. tridentatus [Mohamed et al. 2021] also indicated opisthosoma width, telson length and body weight as inclusive morphometric-indicators for the T. gigas. Nevertheless, by using a larger sample size, it was found that prosoma length and interorbit distance are additional morphometric indicators for the allometry of T. gigas. Overall, baseline or benchmark measurements are no longer required in any processes that evaluate the growth or health of horseshoe crabs. In addition, the accurate size class projection for a population also reduces the baseline errors that arise from using random sampling.

CONCLUSIONS
The novelty of this work arises from using a larger sample size because the prosoma length and interorbit distance were exclusive for the male and female T. gigas, respectively. By using statisticalvalidated allometry, this work discovered the presence of female T. gigas that were diminished in size which not only suggested that male mimicry is taking place in populations with weak operational sex ratio but, depending on fishing gear, the chances of capturing both, male and female horseshoe crab also increases. Thus, the strategy adopted by the female crabs by appearing monomorphic to the male could be a new research exploration by the scientific community to realize the impacts of sex-based capture in marine species.