Length-weight Relationship, Body Morphometrics, and Condition Based on Sexual Stage in the Rusty Crayfish, Orconectes rusticus Girard, 1852 (Decapoda, Cambaridae) with Emphasis on Management Implications

Invasive species can cause economic or environmental damage in that ecosystem [1]. The invasive nature of the rusty crayfish, Orconectes rusticus Girard can be understood by studying the relationship between length and weight [2]. Aggression is a key characteristic in competition to access to shelter, food, and mates [3]. Orconectes rusticus is known as an aggressive invader and displaces many native species of crayfish [1,4], destroys macrophyte beds [5], competes with fish for invertebrate prey, and decreases recruitment rates of sport fishes by eating eggs and removing macrophyte habitat [6-8].


Introduction
Invasive species can cause economic or environmental damage in that ecosystem [1]. The invasive nature of the rusty crayfish, Orconectes rusticus Girard can be understood by studying the relationship between length and weight [2]. Aggression is a key characteristic in competition to access to shelter, food, and mates [3]. Orconectes rusticus is known as an aggressive invader and displaces many native species of crayfish [1,4], destroys macrophyte beds [5], competes with fish for invertebrate prey, and decreases recruitment rates of sport fishes by eating eggs and removing macrophyte habitat [6][7][8].
The species was originally described from streams near Cincinnati in Hamilton County, Ohio, from the Ohio River basin, as well as the Whitewater and Maumee rivers in Indiana [2]. The range of O. rusticus include the Ohio River basin in Ohio, Kentucky, Indiana, West Virginia, and Tennessee, but it has extended its range to most of the Midwestern United States and Canada [9]. It was introduced widely by anglers through bait bucket release into lakes and streams where the species has outcompeted native crayfish species, especially in Wisconsin and Minnesota [7].
Sexual dimorphism within crayfish species can be determined by changes in specific characteristics between genders. Larger chelae cost more energy and are heavy; in many species chelae can be ornamental. Previous studies of O. rusticus morphometrics show that males had larger chelae and attained larger sizes than females, while female abdomen width was wider than males [10]. Length-weight relationships of crayfish enable understanding of each species growth and size at sexual maturity [11]. Growth of O. rusticus occurs during the spring molt. Males will molt from sexually inactive form II to sexually active form I with larger gonopods [12]. Male form I crayfish molt to form II by late summer and are sexually inactive until the following spring. Chelae typically grow in size during the spring since they are needed for copulation and amplexus. Relationships found for each sexual form can offer conclusions for sexual dimorphism between male form I, form II, and female.
The relationship of chelae length (ChL) to chelae width (ChW) is important for describing factors of aggressive behavior and competitive outcomes in rusty crayfish [10]. The chelae are used in antagonistic competition displays and in reproduction during amplexus [10,[13][14][15][16].
The objectives for this study were to evaluate patterns in growth and condition between the carapace length (CL)-wet weight (W wt ) relationship between male form I, male form II, female, and juvenile life stages. This study compared the carapace length (CL) to the postorbital length (POCL), carapace width (CW), carapace depth (CD), and abdomen width (ABW) measurements taken from males form I, males form II, and females. This study also compares the CL, ChL, and ABW of rusty crayfish within the native and the invasive ranges. Comparison of growth data from other tertiary burrowing crayfish species was compiled to evaluate patterns in growth.

Study area
The study area included portions of the native and introduced range of the rusty crayfish in the Midwestern United States. Portions of northern, central, and southeastern Indiana and the state of Wisconsin were sampled. Individuals of rusty crayfish were collected from sites throughout the native and introduced range in the state following standard methods [17]. Individuals were sampled from a range of counties (See supplemental materials) including introduced areas such as Hendricks, Shelby, Lake, LaGrange, Jay, Delaware, Franklin, Carroll, Grant, and Decatur, while native counties included Ripley and Madison.

Sample collection and analysis
Specimens (n=343) were measured for carapace length and weight based on gender. Individuals were identified as male Form I (n=32), male Form II (n=151), female (n=152), and juveniles (n=105). Males were classified as either reproductively active (form I) or inactive (form II) [18]. Form I males are sexually mature adults, and contribute to grow at a decreasing rate. Form I males are identified by an ischial hook on one pair of their periopods and a hardened, elongate and welldefined gonapod [18]. Form II males are not reproductively active. Form II males have less defined, blunt, and club-like gonopods. The annulus ventralis of females is an opening between the last pair of walking legs, located adjacent to a pair of seminal receptacles. Juveniles were identified based on size threshold of 15 mm. Specimens with a carapace length (CL) of fewer than 15 mm were classified as juveniles.
Each individual crayfish was measured for eight morphological characteristics including carapace length (CL), postorbital carapace length (POCL), carapace depth (CD), carapace width (CW), chelae length (ChL), chelae width (ChW), abdomen width (ABW), and wet weight [18]. A Neiko stainless steel 200 mm digital caliper was used to take the measurements to the nearest 0.01 mm. The CL was measured from the tip of the rostrum to the end of the carapace; POCL was measured from the spine adjacent to the orbit to the posterior terminus of the carapace; CW was measured laterally at the widest part of the carapace; CD was measured from the dorsum of the carapace to the ventrum along the sternum; ChL was measured from the posterior attachment of the chelae to the tip of the dactyl; ChW was measured at the widest point laterally along the palm; ChD was measured from the dorum of the palm to the greatest thickness ventrally. The ABW was measured laterally at the widest posterior point.
The individual net weight was taken using a Mettler Toledo PR503 balance and recorded to the nearest 0.001 g. A residual weight was recorded after the crayfish was removed from the balance. The wet weight was the adjustment from the net weight and the residual weight to account for the wet weight. Specimens with damaged or regrown chelae were not used for any chelae measurements.
Relationships between length-weight was determined using a linear regression analysis based on the equation y= mx + b. We used the logtransformed Fulton-Condition Index equation, log(W wt )=b*log(CL)+a, where a=intercept, b=slope of regression line, W wt =wet weight of samples (g), and CL=carapace length (mm). Sexual stages and species with slope greater than 3 have positive allometry, less than 3 have negative allometry, while a b value of exactly 3 is isometric. Positive allometry means that weight is gaining faster than length. Gender and trend lines determined best-fit regression models and residuals (R 2 ) graphed for carapace length (mm) and wet weight (g) [19]. Relationships between chelae (mm), abdomen, and carapace length were regressed with a best-fit regression model trend line. Significant differences in gender relationships were analyzed with Kruskal-Wallis with α= 0.05. Regression statistics were reported by sexual stage and the independent measure.
Morphometric relationships were found in other published papers and compared to this original O. rusticus data. No statistical analysis was done comparing O. rusticus to other species.

Morphometric relationship
The correlation between ChL and ChW showed that male form I have larger ChW and ChL (Table 2). Chelae width and length decreased as sexual form changes. Form II males had the second largest chelae, followed by females, then juveniles. Mean chelae length (ChL ± SD) and range were found for male form I, male form II, female, and juveniles as follows (   Male form I was significantly larger than Male form II for CD and ChL (P<0.05) (Figure 1). Male form I was significantly larger than B. A.

Range relationships
The crayfish collected from the Rusty Crayfish native range in Indiana (n=51; Ripley and Madison Counties) had significant larger CL, CW, CD, ChW, ChL, and ABW (P<0.05), and was also significantly heavier (P<0.05) compared to the Rusty Crayfish collected from their invasive range (n=291).

Condition factor
The condition factor for adult male and female were above 3.0 as shown in Table 1. This shows that the individual genders are in very good condition. The highest value (3.228) was observed for form I male, while the lowest value (3.005) was observed for form II male individuals. The slopes found for male form I, form II, female, and juvenile were 3.228, 3.005, 3.104 and 3.102 respectively. The slopes indicated positive allometric growth in each sexual form since each slope is greater than 3.0. In general, male crayfish from both forms were found to be larger compared to female crayfish. CL increased allometrically with weight for the entire population ( Table 1). The Log 10 transformed ANOVA test for CL vs. W wt showed significance of the slopes and intercepts at the P<0.05 level. The study showed that mean values for male form I were larger than form II males overall, despite the largest crayfish measured being a form II male. The male form II and female individuals had more similar results than either of those groups compared to the male form I and juveniles, but length-weigh relationship generally decreased from male form I, male form II, female, and lastly juvenile. All carapace length-net weight regressions were significant at the P<0.0001 level.
Orconectes rusticus had smaller CL and weighed less than other, published information for tertiary burrowers (   [20,21] and Great Lakes region, expanding into parts of Wisconsin, Michigan, and other northern states [22]. Length-weight and morphometric relationships are important to understand species growth. Invasive crayfish species have been found to be generally larger, while within species females are typically smaller than the males [10]. In northern Wisconsin lakes, two invasive species (O. rusticus and O. propinquus) had larger chelae than the native O. virilis [10]. The box and whisker plots (Figure 1) provide an analysis of sexual forms and differences in growth.
Carapace length (CL)-wet weight (W wt ) relationships for all genders (i.e., male, female, juvenile) and all male forms (form I and II) had positive allometric growth. As carapace length increased the net weight increased as well. For the chelae length (ChL)-carapace length (CL) growth relationships, all sexes and sexual forms grew positive allometrically. Based on the data collected, when comparing mean of ChW and ChL Male form I have larger chelae length than male form II and females. Chelae width (CW)-carapace length (CL) relationships show the same comparison as ChL when comparing gender and sexual forms. The increased growth and larger length of O. rusticus impacts sexual forms and is a factor in the reproductive dominance of the species. The positive allometric growth in male form I compared to male form II is essential in successful reproduction. Female length, weight, and growth rate (CL) is not significantly different from male form II.
Morphological differences can contribute to the displacement of native species [10]. Larger body size and larger chelae allow for better opportunities for predation, competition, and reproduction [10]. The current study shows that O. rusticus male form I are larger than male form II and females, which tend to be more similar in size. Garvey and Stein [10] reported that O. rusticus grew allometrically and this study validates their findings. Other native crayfish populations generally are at a competitive disadvantage, which was a finding emphasized by Garvey and Stein [10] compared to invasive crayfish. Typically, if an invasive species is larger than the native species it will most likely out-compete the native species and displace it [10]. Evaluating sexual dimorphism in crayfish is important because male and female interactions enable species to be influential in establishing populations within stable communities [23,24]. Predator pressure, sexual aggression, and habitat utilization are all size dependent attributes that selection for larger body and chelae size. O. rusticus growth patterns are consistent with the various sexual stages. Figure 1 shows a comparison of all measurements taken in the study for male form I, male form II, and female. The box and whisker chart shows the comparison of measurements within sex and between different sexes and sexual forms. Sexually active male form I will be larger and possess larger chelae than male form II. Male form I will be heavier than male form II because of the larger chelae growth rate.
Male form II and female are similar in size within their native distribution, but have a number of factors that can determine differences. Differences in length-weight may vary between populations and can be influenced by population density, food abundance, water level, temperature, or habitat quality, making it important to consider length-weight relationships within invaded habitats compared to native habitats for a species [25].
Sexual dimorphism is common in freshwater crayfish [26]. Orconectes rusticus shows strong sexual dimorphism patterns compared to other freshwater crayfish and have been seen using their generally larger size to establish populations in occupied invaded areas.

Range relationships
Orconectes rusticus collected in the native range had significantly larger CL, CD, CW, ChL, ChW, ABW, and weighed more than the O. rusticus collected from the invaded range in Indiana. Individuals collected in the invaded range may invest fewer resources into CL, ChL, and ABW than the populations in the native range, and instead use those resources on aggression, mobility, and competition.

Condition factor
Orconectes rusticus had positive size and growth rate in both genders. If the slope was greater than 3 than the growth as positive allometric, meaning that weight is gaining faster than length. If the slope is equal to 3 there is isometric growth, where length and weight are growing at the same rate. When the slope is less than 3, there is negative allometric growth and length is gaining faster than weight. O. rusticus, A. pallipes, P. clarkii, P. acutus, and P. fallax have positive allometric growth, while Procambarus alleni and O. limosus had negative allometric growth. Since O. rusticus is smaller and lighter than other tertiary burrowing crayfish (Table 4), the length of neither the carapace nor the weight give it an advantage over the other species. O. rusticus may utilize a combination of behavioral traits to gain a competitive advantage over these other tertiary burrowing crayfish.
Interspecific rates of growth, length, and weight comparisons among tertiary burrowing crayfish are shown in Table 4. Overall, O. rusticus shows similar growth as other tertiary crayfish. Males are larger than females and form I male is the largest overall. Compared to other crayfish species, O. rusticus as an invader is often successful due to larger size and aggression from possessing larger chelae [10]. The condition was also determined based on the slope value of the crayfish. Overall, O. rusticus had smaller mean CL and had a mean weight less than Orconectes limosus, Procambarus acutus, Procambarus fallax, and Procambarus clarkii.