Analysis of band pair formation in elasmobranch vertebrae with implications for fisheries management

Sharks, skates, and rays are particularly sensitive to over-exploitation due to their life history traits (slow growth, late age at maturity, small litter size, and extended longevity). It is important to know the age of sharks, skates, and rays because it has implications for our ability to assess the status of populations and to manage fisheries. They are aged most often using the concentric bands that alternate in appearance: opaque and translucent in their vertebral centra. An opaque and translucent band together (a band pair) is assumed to represent one year of growth and is counted to estimate an individual’s age. However, counts of these bands are being shown to underestimate age in a growing number of instances. An alternate explanation to annual band-pair deposition suggests that the number of band pairs may vary with body size and vertebral centrum morphology and not age. I examined centrum morphology and band-pair counts along the vertebral column within and among species. I measured the morphology of 80 centra from various-sized individuals of both sexes of five batoid species and counted the band pairs in every fifth centrum along the vertebral column from a subset of these individuals. Centrum morphology and band-pair count both varied along the vertebral column in all individuals of all species except young of the year. This evidence that the number of opaque and translucent bands does not reflect age reinforces the need to understand the differences between these two band types. In the second study, the bulk chemical composition of opaque and translucent bands was examined using energy-dispersive X-ray spectrometry, focusing on 11 elements across 12 elasmobranch species. I found that there was no difference in chemical composition between opaque and translucent bands in the little skate, Leucoraja erinacea, (p = 0.954) or across the 12 species (p = 0.532). Vertebral centra are composed mostly of oxygen, calcium, and phosphorus. The evolutionary significance of optical differences between opaque and translucent band types requires further research. Validation of age estimates from band-pair counts has only been successful for individuals at or prior to sexual maturity. Therefore, I investigated the rate of formation of band pairs in mature individuals. Mature male and female little skates were injected with oxytetracycline and maintained in captivity for 13 months to assess centrum growth and the frequency of band-pair deposition. Of 41 individuals analyzed, 63% did not deposit a full band pair over the 13-month period, meaning that a majority of individuals did not exhibit deposition of an annual band pair. Such potentially inaccurate age estimates are still used in the construction of stock-assessment models that dictate how elasmobranch fisheries are managed. To reconcile the fact that the data for stock assessment models is biased I examined the effect of intentionally biased age data on stock assessment model output in the final part of the study. Length-at-age data for little skate and winter skate were biased ±10% and ±25% of the lifespan for (1) all ages and (2) mature ages only. For each species, these eight scenarios and an unbiased (normal) scenario were modeled with the von Bertalanffy growth model and applied to a statistical catch-at-age model. The effects of biased age data were subtle and had the largest effect on estimating spawning stock biomass. As age underestimation is identified in more elasmobranch species, research on the implications of biased age estimates that are incorporated into stock assessment results will be crucial until an alternate method to estimate elasmobranch age is found.

between opaque and translucent bands in the little skate, Leucoraja erinacea, (p = 0.954) or across the 12 species (p = 0.532). Vertebral centra are composed mostly of oxygen, calcium, and phosphorus. The evolutionary significance of optical differences between opaque and translucent band types requires further research.
Validation of age estimates from band-pair counts has only been successful for individuals at or prior to sexual maturity. Therefore, I investigated the rate of formation of band pairs in mature individuals. Mature male and female little skates were injected with oxytetracycline and maintained in captivity for 13 months to assess centrum growth and the frequency of band-pair deposition. Of 41 individuals analyzed, 63% did not deposit a full band pair over the 13-month period, meaning that a majority of individuals did not exhibit deposition of an annual band pair.
Such potentially inaccurate age estimates are still used in the construction of stock-assessment models that dictate how elasmobranch fisheries are managed. To reconcile the fact that the data for stock assessment models is biased I examined the effect of intentionally biased age data on stock assessment model output in the final part of the study. Length-at-age data for little skate and winter skate were biased ±10% and ±25% of the lifespan for (1) all ages and (2) mature ages only. For each species, these eight scenarios and an unbiased (normal) scenario were modeled with the von Bertalanffy growth model and applied to a statistical catch-at-age model. The effects of biased age data were subtle and had the largest effect on estimating spawning stock biomass. As age underestimation is identified in more elasmobranch species, research on the implications of biased age estimates that are incorporated into stock assessment results will be crucial until an alternate method to estimate elasmobranch age is found.

LIST OF TABLES
Chapter 1   Table 3.1 Differences in ten growth variables in males versus females at the end of the 13-month experimental period for Leucoraja erinacea analyzed using t-tests. LT is total length and WT is total weight. Asterisk indicates significant difference. ........... 72 Table 3   .6 (a) Monthly growth rate for males (black circles, n=20) and females (grey circles, n= 21). Male linear regression: y = 0.021x -33.775; p < 0.01; adj r 2 = 0.42.

Introduction
The vertebral centra of elasmobranchs have characteristic concentric bands that alternate in appearance: opaque and translucent (Ridewood 1921;Dean and Summers 2006). A band pair composed of one opaque and one translucent band has been assumed to represent one year of growth and has been used to estimate age in elasmobranch fishes (Ridewood 1921;. The basis of this method was the fact that more band pairs in the vertebral centra are formed in larger individuals (Ridewood 1921). Later studies showed a positive relationship between somatic growth and centrum size and seemingly seasonal alternation of opaque and translucent bands Cailliet and Goldman 2004). However, a growing body of research shows that band-pair deposition slows and/or stops in older animals, so that the number of band pairs does not necessarily accurately reflect age throughout the entire lifespan of an individual Natanson et al. 2015;. In some species a direct relationship between the number of band pairs and somatic growth has been suggested   . The results of this study have led to the conclusion that band-pair deposition is related to growth in girth of the fish, such that band-pair deposition is only coincidentally related to age, and only at some life stages ).
It has been further suggested that differences in deposition patterns are correlated with body type and swimming mode among species ).
An additional assumption critical for ageing elasmobranchs using vertebral centra is that all centra along the vertebral column have the same number of band pairs at a given point in time. If this assumption is true, then band-pair deposition could be related to age; if it is false, then band-pair deposition cannot be related to age. Several studies Huveneers et al. 2013;  shark, porbeagle, shortfin mako, common thresher shark, blue shark, and dusky shark).
Variation in the number of band pairs among centra along the column of larger fish has been found to be directly correlated with the girth of the fish where the centra were taken. As the sharks grow in girth (which is most pronounced in the abdominal region), the variation in the number of band pairs among centra along the column increase . Regardless of species, larger centra have more band pairs indicating that band-pair deposition is a structural requirement of the individual and not related to time .
The goal of the present study was to investigate whether centrum morphology and the number of band pairs in a centrum varies along the vertebral column in several batoid species. To accomplish this, we measured centrum dimensions and counted the band pairs in individual centra along the columns of various-sized individuals of both [large]) six winter skates and six barndoor skates (two small, two medium, and two large of each), nine Atlantic stingrays (three small, three medium, and three large), and ten round rays (two small, four medium, and four large) were collected for analysis of centrum morphology (Table 1).
For analysis of the number of band pairs among central along the vertebral column, a subset of little skate individuals (one male and two females of similar sizes; three small, three medium, and three large), a subset of Atlantic stingray individuals (two females of similar sizes; two small, two medium, and two large) and a subset of round ray individuals (one male and one female of similar sizes; two small, two medium, and two large) were used from the analysis of centrum morphology. All individuals (one male and one female of similar sizes; two small, two medium, and two large) of winter skate and barndoor skate were analyzed for the number of band pairs.
Total length (TL), measured as the straight-line distance from snout tip to tail tip, and disc width (DW), measured as the straight-line distance from wing tip to wing tip, were measured to the nearest 0.1 cm. Sex and maturity status were determined by visually inspecting gonad condition (Ebert 2005).

Centrum Morphology
The vertebral column was extracted from fish starting with the first vertebra behind the synarcual cartilage and ending at the 80 th vertebra. Centra posterior to the 80 th centrum were too small to successfully separate without damage, especially in small individuals in all species. The 80 th centrum was underneath the first dorsal fin in little skate, just rostral to first dorsal fin in both barndoor and winter skates, beneath the barb in the round ray, and just caudal to the barb in Atlantic stingray. Caudal centra were particularly difficult to separate in little skate, and only centra through approximately the 60 th centrum from two individuals could be accurately measured.
One round ray sustained tail damage and no centra beyond the 48 th centrum were available.
Each vertebral centrum was measured to the nearest 0.1 mm in three dimensions: dorso-ventral diameter (DVD), medio-lateral diameter (LD) and rostrocaudal length (LEN), using Vernier calipers following . Each measurement was divided by TL for the skate species and DW for the stingray species to standardize data across sizes. By convention, TL is used to measure size of skates, while DW is used to measure the size of stingrays. These standardized data were plotted against centrum number for each individual, noting the centrum number at the transition from abdominal cavity to tail.
To assess if centrum morphology was similar within a species, by sex, by size, or varied by individual it was analyzed using multiple generalized additive models

Band-pair Counts
To determine if band-pair number varied along the vertebral column of an individual, every fifth centrum was assigned a random ID number and processed histologically to visually enhance the band pairs (as per Natanson et al. 2007). Every fifth centrum was chosen for analysis to evenly sample the vertebral column. This analysis included the centrum attached to the synarcual, 4-9 abdominal centra, and 7-12 caudal centra, depending on species. Centrum sections were viewed under a dissecting microscope (Nikon SMZ1500 ® , Melville, NY, USA) using reflected light and images were captured with a digital camera (Nikon DSR12, Tokyo, Japan) and image processing software (NIS Elements,v. 4.40,Nikon,Tokyo,Japan). The birth band was identified as the first fully-formed band beyond the focus and was associated with an angle change in the corpus calcareum of the centrum (Cailliet and Goldman 2004). Two band-pair counts were made for each individual by a primary (KCJ) and a secondary reader. To assess repeatability of counts, precision was determined using the coefficient of variation (CV) within and between readers (Chang 1982), with a target value of <10%. Bias as a result of either systematic or random error was assessed using the Evans-Hoenig's (1998) test of symmetry. Within reader precision and bias were compared between the first and second count of each reader while between reader precision and bias was compared between the second band-pair counts of both readers. If the second band-pair counts differed by three or more band pairs between primary and the secondary reader, the centrum was examined together and a consensus count was reached. Final band-pair counts were assigned from the primary reader's second count or the consensus count if appropriate. The final band-pair count was plotted by centrum number for each individual. The mean band-pair count and 95% confidence interval (CI) of the mean was calculated among vertebral centra for each individual to test if band-pair count varied significantly among centra along the vertebral column. Band-pair counts that fell outside of the 95% CI indicated significantly different counts within an individual.
A mixed-effects model was used to determine if there was a correlation between band-pair counts and the three centrum measurements (DVD, LD, and LEN) for each species with individual included as a random effect.

Centrum Morphology
Centrum morphology varied along the vertebral column in all species. The transition between abdominal and caudal centra occurred at the 24 th to the 47 th centra in the study species (Table 1) In the barndoor skate LEN followed a similar trend to that in little and winter skate except that, starting at approximately the 45 th centrum, LEN was greater than DVD or LD ( Figure 3). The centra in Atlantic stingray and round ray had similar morphologies, which differed from the skate species examined. In Atlantic stingray and round ray DVD and LD increased from the head, were constant along the   abdominal cavity, and both measurements were smaller in the caudal centra (Figures 4 & 5). Atlantic stingray and round ray centra were slightly ovoid (greater LD) along the abdominal cavity. LEN increased from the head until the transition from abdominal to caudal vertebrae after which LEN quickly decreased, but the decrease was less dramatic than that seen in the skate species. In both ray species LEN was constant along the tail.
For each species, the centrum morphology along the vertebral column was best described by individual variation ( Figure 6). The best-fit GAMs modeled each individual with its own intercept and smoothing function for all species and measurements rather than by sex or species. The only exception was the LEN measurements in Atlantic stingrays, which was best modeled by each individual with its own intercept, but the same smoothing function for all individuals (Table 2).

Band-pair Counts
Counting every 5 th vertebral centrum from one to 80 should result in 17 vertebral centra analyzed for band pairs from each individual. The number of centra counted was sometimes less than 17 (range 11-17) due to damage that made some centra unusable (Table 1). The within-reader CV was 6.86 -14.88% for primary reader and 6.37 -12.54% for the secondary reader (Table 3), while the between-reader CV ranged from 10.08 -21.35% (Table 3). The number of centra per species with counts that differed by three or more band pairs, and thus were examined by both readers for a consensus, ranged from 9 -16 (Table 3). Between-reader CV was calculated before centra were re-examined by both readers for a consensus;

Evans-Hoenig (1998) Bias test
post-consensus CV values would be lower. The Evans-Hoenig (1998) test of symmetry detected within-reader bias for primary reader only for barndoor skate data and within-reader bias for the secondary reader was detected only for Atlantic stingray data and between-reader bias was detected only for barndoor skate data (Table 3).
Detailed examination of barndoor skate data revealed that the number of band pairs was undercounted on the second count of the primary reader relative to the first count for centra with >12 band pairs. The analysis of between-reader bias for the barndoor skate data showed that the secondary reader undercounted band pairs in the two smallest individuals compared to the primary reader. The secondary reader for Atlantic stingray overcounted on the second count relative to the first count for centra with three and four band pairs. abdominal centra had higher band-pair counts than caudal centra. The two smallest Atlantic stingray specimens examined were YOYs and did not have any band pairs in any centra along the vertebral column, this explains why the band-pair counts were not significantly different among centra for these two individuals ( Figure 4).
Dorso-ventral diameter, medio-lateral diameter, and length had significant correlations with the band-pair counts of little skate, barndoor skate, and round ray (Table 4). Atlantic stingray had significant correlations with DVD and LD, but not with LEN. Winter skate did not have any significant correlations with any centrum measurements.

Discussion
The rationale for the use of skeletal hard parts like vertebral centra to estimate age is that band pairs are deposited as the hard part and the individual increase in body size relative to a consistent time period ). Vertebral centra, which vary in morphology within an individual, vary in the number of band pairs within an individual. Variable band-pair counts among centra along the vertebral column has now been observed in 15 species representing 9 elasmobranch families Huveneers et al. 2013;; current study). The presence of variation in band-pair counts among vertebral centra within an individual suggests that the mechanism that regulates the formation of band pairs does not result in annual band-pair formation for all centra in any given individual. An increase in centrum size (and subsequent increase in the number of band pairs) with somatic growth is required if centra are to be used to estimate age.
However, in the case of centra, this makes them unreliable as a tool for ageing fish. In Table 4. Linear mixed-effects model comparing band-pair counts with the three centrum measurements with individual included in the model as a random effect. Asterisk indicates significant correlation.  .

Species Measurement Estimate S.E. df t-value p-value
The prevailing hypothesis is that band pairs are deposited to provide structural support within the vertebral column. This hypothesis was suggested as a result of the observation that band-pair deposition patterns were obviously not annual in the Pacific angel shark , which has now been observed in a variety of species over the years Chidlow et al. 2007;Huveneers et al. 2013). Recently, this hypothesis has gained further support; band-pair deposition has been found to be more closely linked with somatic growth and the structural needs of the elasmobranch skeleton than with age .
A complimentary assumption to annual band-pair deposition was the assumption that every centrum has the same number of band pairs, so any centrum could be used to estimate age. This assumption is only occasionally addressed in age and growth studies in which vertebrae from different regions of the vertebral column are compared Officer et al. 1996;Piercy et al. 2006;). When differences in band-pair counts between more anterior and more posterior centra were detected, it was suggested that band pairs in smaller, caudal centra were more difficult to interpret (Brown and Gruber 1988;Officer et al. 1996;Natanson et al. 2006;Piercy et al. 2006). This study did not find it difficult to interpret band pairs in smaller centra, instead the observed variation in band-pair counts along the vertebral column in five species disproves the assumption that every centrum has the same number of band pairs.
To establish if band-pair counts accurately estimate age, counts must be  (Table 3) driven by low band-pair counts, particular the two medium specimens that had band-pair counts between one and four. The CV is much larger when comparing one and two band pairs (47.14%) versus 10 and 11 band pairs (6.73%). In theory the precision should be higher for fewer band pairs, but the band pairs of some centra are more difficult to interpret than others regardless of position along the vertebral column. Whether the difficulty in interpretation stemmed from the centrum itself or processing error, no centra were removed from the study based on readability. Instead, if band-pair counts differed by three or more band pairs, the centrum was examined by both readers together and a consensus band-pair count reached. Using all centra regardless of readability highlights the variation among centra.
Centrum morphologies in these five batoid species were roughly similar to the centrum morphology of sharks, which also exhibited species-specific patterns . Centrum morphology increased in size from behind the cranium to a peak or plateau in the abdominal cavity and in most cases decreased after While rough similarities exist across and within species, individual variation was the best descriptor of centrum morphology for batoids. Centrum morphology was not statistically similar by size class (small, medium, or large), sex, or within a species. This suggests that the conditions that an individual experiences influences the growth of the vertebral centra. For instance, in Atlantic salmon, Salmo salar Linnaeus 1758, different vertebral centra grew at different rates when exposed to different photoperiod regimes (Fjelldal et al. 2005). Besides Fjelldall et al. (2005), there is a dearth of research exploring variable centrum growth. Therefore, we rely on research on the plasticity of fish growth and suggest that factors affecting individual body growth (food availability, temperature, population density, and genetics [McDowall1994]) may also affect growth of vertebral centra.  suggested that for sharks, "centra are functionally linked to body shape". This finding is based on the positive correlation of body girth measurements to centrum size and is supported by Thomson and Simanek's (1977) five categories of body and tail type, in which species of similar body shapes and swimming styles also had similar centrum morphology. While batoids possess vastly different swimming styles than many sharks, the Atlantic angel shark uses a swimming mode that is an intermediate between caudal fin propulsion and paired fin propulsion (Wilga and Lauder 2004). These dorso-ventrally flattened sharks also demonstrate a relationship between body shape and centrum morphology , so it is reasonable to assume that this relationship extends to batoids. The body girth measurements used by  did not translate to a batoid body plan (James, unpub. data) so a different approach will have to be used to investigate the relationship between body shape and centrum morphology.
The paradigm of annual band-pair deposition within vertebral centra of elasmobranchs has been repeatedly called into question over the years . Here we demonstrate that centrum morphology and band-pair count vary along the vertebral column of an individual, supporting the idea that band pair number is related to somatic growth and/or the structural needs of the individual ). Thus, we are unable to accurately determine the age of elasmobranchs based on band-pair counts and caution should be applied when using band-pair counts as a proxy of age without validation (Beamish and MacFarlane 1983). Unfortunately, validation throughout the entire lifespan has not been achieved for any elasmobranch species. Therefore, two tasks now must be accomplished: investigating the impact of inaccurate ages on stockassessment model results and determining an alternate method to age elasmobranchs.
Campana, SE (2001) (Clement 1992;Dean and Summers 2006). The mechanism of formation of tessellated cartilage has been well-studied (Kemp and Westrin 1979;Clement 1992;Dean et al. 2009;Dean et al. 2015;Seidel et al. 2016), but the formation of areolar cartilage and the associated unmineralized cartilage in vertebrae has not received the same attention.
The alternating pattern of areolar cartilage and unmineralized cartilage in the vertebral centra has been the subject of extensive research. Early investigators attempted, with marginal success, to use the species-specific mineralization patterns to establish taxonomic relationships (Hasse 1879; Ridewood 1921). Haskell (1949) and  noted that the mineralization pattern manifested as opaque and translucent bands in horizontal section and suggested that the bands might be related to time. This launched the field of elasmobranch age and growth; vertebral centra are still the preferred method to estimate age for elasmobranchs.
The mineralization pattern in vertebral centra has also been attributed to species-specific mechanical and structural needs (Kemp and Westrin 1979;Dingerkus et al. 1991;Clement 1992;Egerbacher et al. 2006;Porter et al. 2006;Porter et al. 2007;. Furthermore, the alternation of opaque and translucent bands has been proposed to behave as a viscoelastic composite that can withstand the stresses experienced during swimming (Porter et al. 2006;Huber et al. 2013). Several authors have suggested that the formation of the mineralization pattern is directly related to somatic growth rather than to age ).
Despite the varied areas of research into the vertebral centra mineralization pattern, the basic chemical composition of the opaque and translucent bands has not been conclusively determined. The goal of most examinations of the chemical composition of band pairs has been to verify age estimates from counting translucent and opaque bands.  were the first to use energy-dispersive Xray spectrometry (EDS) on elasmobranch vertebrae and that study related Ca and P peaks to length-frequency age estimates in the spiny dogfish (Squalus acanathias). (1987)  were calculated from the three measurements of each band type. Correlations between elements were assessed using correlation coefficients (r).

Cailliet and Radtke
Differences in element concentrations were analyzed in the following groupings: band type (opaque vs translucent), species, species by band type, body plan (batoid or shark), and body plan by band type. Homogeneity of multivariate dispersion was tested with betadisper and differences among groups were tested with PERMANOVAs using adonis from the R package vegan (Oksanen et al. 2016; R Core Team 2014). PERMANOVAs were appropriate when the homogeneity of multivariate dispersion was not different, the groups had balanced designs (same sample size), or for unbalanced designs when the group with the larger sample size had the greater dispersion (Anderson and Walsh 2013).

Results
Of the eleven elements analyzed, Ca, P, and O were found in the highest concentrations in the majority of sampled material ( Figure 2; Table 1). Five elements (Al, K, Mg, Si, and Sr) combined comprised less than 6% in any sample. Sulfur ( Figure 2d), Na, and Cl each comprised more than 10% in a few samples, but never more than 21%.
Elements were highly correlated. Six element pairs had r values greater than 0.8 (Table 2). There were negative correlations between O and P, O and Ca, S and P, and S and Ca and positive relationships between P and Ca and between Na and Cl.
Multivariate dispersions were unequal for all comparisons (p < 0.001) except between band types (p = 0.344). Nevertheless, testing differences among groups was

Discussion
There was no chemical difference between band types (opaque and translucent) within L. erinacea and across species. This is at odds with previous research that detected peaks and troughs of Ca and P that corresponded with opaque and translucent bands  However, in many cases the element concentrations were highly variable within each band type and among individuals both within and between species ( Figure   2). Variability of elements is evident in other chemical analyses of elasmobranch vertebrae, but not always discussed. For instance,  tracked Ca and P from focus to centrum edge and some troughs had similar values as peaks for both elements.  found Ca peaks that varied 3.5x (~400,000 to ~1,400,000 Ca counts) within an individual and varied by 46.7x (~30,000 to ~1,400,000 Ca counts) among individuals. Christiansen (2011) also detected highly variable Ca peaks in C. carcharias centra using LA-ICP-MS; 1.6x (~1,250,000 to ~2,000,000 normalized Ca concentrations) within individuals and 2.6x (~700,000 to ~2,000,000 normalized Ca concentrations) among individuals. Additionally, Christiansen (2011) did not detect differences in amount of Ca between opaque and translucent bands.  showed consistent relative magnitudes of peaks and troughs but had two instances of two Ca and P peaks for one opaque band. The variation of each element among bands of the same type along a centrum (opaque vs. opaque) may preclude detecting differences among bands of different types (opaque vs. translucent).
Chemical differences ( The suggested difference between opaque and translucent bands within elasmobranch vertebrae is different amounts of mineralization between the two band types: opaque and translucent but results on which band type is more mineralized directly conflict. Some studies document higher amounts of Ca and P in the opaque band ) while other studies claim the translucent bands are hypermineralized . The direct sampling of opaque and translucent bands separately in this study shows that Ca and P are present throughout both band types. Therefore, the optical differences between the band types are not based on a difference in basic chemical composition. Perhaps the difference between band types is structural rather than chemical. Opaque and translucent refer to whether light passes through a substance or is reflected; therefore, the crystalline structure may differ between opaque and translucent bands. This warrants further research as opaque and translucent bands are used to estimate age, but the fundamental difference between the two is still unknown.
sharks through annuli as shown in cross-sections of vertebrae.

INTRODUCTION
In fishes, accurate age-based characteristics, such as age at sexual maturity and longevity, are crucial for the construction of stock assessment models in order to correctly estimate population productivity. Age is generally determined by counting growth zones in a hard structure that grows in proportion to body size or weight. Sizeat-age data compiled from individuals across the entire size range of a species are used to estimate these age-based characteristics.
Vertebral centra are the most commonly used structure for age determination in elasmobranch fishes. The centra have characteristic band pairs, each of which is composed of one opaque and one translucent band (Figure 1; Lagler, 1952;. The assumption has been that one band pair is deposited per year , but  and  showed that band-pair deposition is correlated with somatic growth, but not age, in two species, the Pacific angel shark Squatina californica Ayres 1859 and the basking shark Cetorhinus maximus (Gunnerus 1765). Furthermore, no predictable temporal pattern of band-pair deposition (annual or otherwise) could be identified in several other elasmobranch species Chidlow et al., 2007;Huveneers et al., 2013).
Age validation studies (confirming the accuracy of age estimates with a determinate method; Cailliet, 1990) support the assumption of annual band-pair deposition for a part of the lifespans of only some species, and other studies have shown that band-pair deposition slows and/or stops at older ages . 1825)   (Pierce & Bennett, 2009). Leucoraja erinacea is an interesting example because three independent experimental studies have documented annual band-pair deposition in juveniles and in some adults Cicia et al., 2009;Sagarese & Frisk, 2010). However,  noted two mature, ovipositing females that only deposited a partial opaque band in one year of captive growth. That study concluded that "annual banding may not occur when the females are reproductively active" . This result, in combination with the documented decreased frequency of band-pair deposition in larger/older elasmobranch species, suggested that reproductive state may affect band-pair deposition.
Instead of age, a proportional relationship between somatic growth and frequency of band-pair deposition has been suggested in several shark species . The relationship between somatic growth and total centrum growth over a period of time has long been established  and is the basis for using hard parts, like vertebral centra, as indicators of age .  suggested that centra grow (and therefore band pairs are deposited) in proportion to increases in body mass as dictated by structural needs. As an individual approaches maximum total length, body growth and centrum growth decrease; therefore, the frequency of bandpair deposition may also decrease .
The goal of the present study was to investigate the frequency of band-pair deposition and centrum growth in sexually mature individuals. Leucoraja erinacea was used as a model organism based on its use in previous research and its resilience in captivity. Annual band-pair deposition was confirmed in juvenile L. erinacea Sagarese & Frisk, 2010), but not in reproductive, mature females.
Here, monthly growth rate, total centrum growth, and frequency of band-pair deposition were compared over a period of 13 months in sexually mature (ovipositing) females and sexually mature males using a chemical marker. The characterization of centrum growth in adults is critical to assess the validity of using band-pair counts for accurate age estimates and their subsequent use for stock assessments and fisheries management. locations, were used to identify individuals. Water temperature in holding tanks was maintained at ambient Narragansett Bay temperatures, but was not allowed to go below 5˚C or above 20˚C to acknowledge the normal thermal range for the species (1-21ºC; Bigelow & Schroeder, 1953). Temperature, dissolved oxygen, and pH were monitored daily.

Forty
Skates were acclimated for at least two weeks. On 4 December 2015, each skate was injected intramuscularly in the thickest part of the pectoral fin muscle with 25 mg kg -1 body weight of oxytetracycline (OTC). Skates were fed every other day by offering 2-g pieces of herring or squid to each individual until food was refused. Food consumption was recorded at each feeding for each individual and egg deposition was recorded daily. At the end of 13 months (4 January 2017) skates were euthanized via overdose with tricaine methanesulfonate (400 mg L -1 water) and measured (LT) and weighed (WT). Monthly growth rate (g month -1 ) was calculated as .
Sexual maturity status was determined by visually inspecting the condition of the gonads (Ebert 2005).
Two adjacent abdominal vertebral centra ( Figure 1) were extracted from each skate. One centrum used for oxytetracycline analysis (hereafter referred to as the OTC section) was embedded in TAP® Clear-Lite casting resin (TAP® Plastics, Dublin, CA, USA), and sectioned horizontally through the focus (Figure 1) (Natanson et al., 2007) and photographed with reflected light using the camera system described above. The total centrum growth measured from the image of the OTC section was divided by the length of the corpus calcareum (CC) then superimposed on the image of the histology section to determine into which band type the OTC was incorporated, and the number of band pairs located distal to the OTC mark (new cartilage deposition; Figure 2). The number of band pairs distal to the OTC mark was compared between sexes and with respect to each of seven growth variables (food consumption, monthly growth rate, centrum growth, change in LT, final LT, final WT, and total band-pair count, detailed below) using logistic regressions (R Core Team 2017).
Band pairs were counted in captured digital images of the histology sections.
The birth band was identified as the first fully-formed band beyond the focus that was associated with an angle change in the CC. Two readers counted the band pairs in each centrum twice, without knowledge of fish size or sex. Precision, to assess repeatability of counts, was determined using the coefficient of variation (CV; Chang, 1982).
Coefficients of variation <10% were interpreted as reflecting acceptable within and between reader precision. Bias, as a result of either systematic or random error, was assessed with the Evans-Hoenig (1998)  were assigned from the primary reader's second count (KCJ) or from consensus between readers if the band-pair counts differed by more than two band pairs.
Food consumption per individual was summed for the entire experimental period (13 months). Ten growth variables: food consumption, monthly growth rate, total centrum growth, change in LT, initial LT, final LT, initial WT, final WT, total band-pair count, and band pairs distal to OTC were compared between sexes using ttests (R Core Team 2017). Food consumption and monthly growth rate and food consumption and total centrum growth were compared in males and females using analyses of covariances (ANCOVAs; R Core Team 2017).

RESULTS
Forty-one skates (21 females and 20 males) were used for analysis; three fish were eliminated due to procedural error and mortality. During the experimental period water temperature ranged from 5 to 21 °C, pH ranged from 7.8 to 8.2, and dissolved oxygen ranged from 2.4 to 11.9 mg L -1 . Total fish length did not differ significantly between the sexes at the beginning or end of the 13-month experimental period, but females had a significantly higher mean mass than males both at the beginning and the end of the experimental period (Table I).
All but one female was observed laying at least one egg during the experimental period. A total of 1395 eggs were laid during the experimental period representing a mean of 65.2 eggs per reproductively active female per year. Peak egg deposition occurred between June and October 2016. The total number of eggs laid per month increased with increasing temperature over the experimental period (Figure 3). Upon Table I. Differences in ten growth variables in males versus females at the end of the 13month experimental period for Leucoraja erinacea analyzed using t-tests. LT is total length and WT is total weight. Asterisk indicates significant difference.  dissection, the one female that had not been observed to lay eggs was determined to be sexually mature based on the presence of well-developed shell glands, ovaries, and uteri, but no eggs were present in either ovary. In the remaining females, each ovary had 1-6 eggs, ≥ 10 mm in diameter.

Females
A mean of 2192 g of food (± SE = 82 g) was consumed per individual during the experimental period. Females consumed significantly more food than males (Table   I; Figure 4a), but the mean monthly growth rate was not significantly different between sexes (Table I; Figure 4b).
Total band-pair counts ranged from 4 to 15 for all 41 individuals, but the number of band pairs was not significantly different between males and females ( Table I). The within-reader precision of the primary reader was good (CV = 8.57%), while the within-reader precision of the secondary reader was greater than 10% (CV = 12.03%). Comparing the second counts between readers, between-reader CV was 21.08% with 22 centra differing by more than two band pairs. These 22 centra were re-examined by both readers to determine a consensus. The between-reader CV value without these 22 centra was acceptable at 9.05%. The Evans-Hoenig test of symmetry detected within-reader bias for the primary reader (χ² = 13.45, d.f. = 4, p < 0.01), and between-reader bias (χ² = 30.33, d.f. = 8, p < 0.001). Within-reader bias was not detected for the secondary reader (χ² = 3.12, d.f. = 3, p > 0.05).
All 41 individuals had a fluorescent OTC mark. Six individuals (15%; 1 female, 5 males) did not have an OTC mark across the corpus calcareum (CC; where band pairs are visible), therefore the number of band pairs distal to the OTC mark and  Table II). Sixty-three percent of individuals had OTC in the ultimate band, having formed only 0.5 band pairs (11 females and 11 males), and 34% had formed one band pair (9 females and 3 males). One male (#10) had formed 1.5 band pairs during the 13-month experimental period (Figure 2; Table II) and was excluded from subsequent statistical analyses, because its category (1.5 band pairs) represented a sample size of one. Skates that deposited a full band pair were smaller in size (final LT) and their centra grew more during the experimental period (Table III).
The number of band pairs deposited (0.5 or 1) was not significantly different between males and females (Table I), or with reference to any of the following growth variables: food consumption, monthly growth rate, change in LT, final WT, or total band-pair count (Table III).
The relationship between total food consumption and monthly growth rate was significantly different between sexes (F = 12.015, d.f. = 1, p < 0.01). Monthly growth Figure 5. Locations of oxytetracycline in Leucoraja erinacea centra. Oxytetracycline was expected to be across the corpus calcareum (A), but also occurred on the outer edge of the corpus calcareum (B), diffuse in the corpus calcareum (C), diffuse in the intermedialia (D), at the focus (E), and in the arch tissue surrounding the centrum (F). Centra belong to specimens #23 and #99. 699.5 813.0 † Numeric or alphabetic code for individual skates; ‡ OTC, in which band the oxytetracycline mark was and subsequent band types present distal to this mark; O, Opaque band; T, Translucent band; -, no oxytetracycline detected in the corpus calcareum. Table III. Differences between the number of band pairs present distal to the oxytetracycline mark (0.5, 1) and seven growth variables in males and females at the end of 13-month experimental period for Leucoraja erinacea analyzed with logistic regressions. Asterisk indicates significant difference. rate showed a positive correlation with food consumption in males but was not related to food consumption in females (Figure 6a). The relationship between food consumption and total centrum growth was significantly different between sexes (F = 6.226, d.f. = 1, 0.05 > p > 0.01). Total centrum growth showed a positive correlation with food consumption in males, but was not related to food consumption in females ( Figure 6b).

DISCUSSION
The current study adds more evidence to the growing body of literature showing that elasmobranchs do not demonstrate annual band-pair deposition after sexual maturity (e.g. throughout their entire lifespan). A recent review of elasmobranch age validation studies concluded that age was likely underestimated in 30% of elasmobranch populations examined . Age validation studies on several shark species show annual band-pair deposition up to the approximate age of sexual maturity, followed by band-pair deposition that is not annual . The present study shows that adult L. erinacea of both sexes do not always have annual band-pair deposition. This corroborates the finding by  of two adult female L.
erinacea that did not deposit a full band pair in one year. In fact, many adult males do not deposit a full band in one year either suggesting a link between maturation and decreased frequency of band-pair deposition.
The frequency of band-pair deposition was variable among sexually mature individuals in this study, so it is not surprising that the band type (opaque or translucent) in which OTC was deposited was not synchronous among individuals.
Oxytetracycline appeared either in a translucent band (74% of individuals) or an opaque band (26% of individuals), despite the fact that all individuals were injected on the same day. This could be explained by the timing of injection (December), which seems to be a transition period between deposition of opaque and translucent bands in L. erinacea Waring, 1984). On the other hand,  suggested that opaque bands are formed in fall/winter in L. erinacea. Nevertheless, synchronous seasonal switching of band types is not likely occurring in L. erinacea since OTC appeared in both band types among individuals and the rate of band-pair deposition was variable. The inconsistencies in previous studies Waring, 1984; Kinney et al., 2016) is likely the result of bandpair deposition not being annual in older individuals .
The absence of an OTC mark in vertebral centra is well documented in captive and wild mark-recapture experiments in elasmobranchs (e.g. Smith, 1984;Sagarese & Frisk, 2010). In this study, OTC failed to mark the CC of six individuals (15%). In , two out of 13 (15%) L. erinacea failed to incorporate OTC into their vertebral centra. Other studies of captive elasmobranchs had an OTC mark failure rate as high as 81.03% (Sagarese & Frisk, 2010). Mark-recapture studies of wild animals had OTC mark failure rates from 6.38% (Walker et al., 2001) to 66% (McFarlane & Beamish, 1987). Smith (1984) attributed the absence of OTC to insufficient mineralization of the vertebral centra directly after injection. Oxytetracycline deposited outside of the CC was common in the current study indicating active mineralization at these different sites (e.g. outer edge of CC) at the time of injection.
Oxytetracycline was also present diffusely in both the intermedialia and throughout the CC in several individuals. Holden & Vince (1973)  is not actively mineralizing. Additionally, one individual in the current study which was not used for analysis was injected with OTC at two different times (approximately 8 months apart), but only one OTC mark was seen in the centrum. In other growth studies of captive elasmobranchs, multiple injections of OTC sometimes resulted in fewer than expected OTC marks Huveneers et al., 2013).
The higher energetic cost of reproduction for females is well documented in many invertebrate and vertebrate taxa (Haywood & Gillooly, 2011). Female skates in this study consumed 1.5 times more food per individual than males (Figure 4a), which suggests a direct link between food consumption and reproductive output, given the energy needed for egg production. While females likely allocated food to egg production, there were no statistically significant differences between sexes in body or total centrum growth, or number of band pairs. Therefore, the physiological mechanism regulating centrum growth or number of band pairs is likely not different between males and females.
The inability to accurately age elasmobranchs throughout their lifespan using current techniques raises concerns for current stock-assessment practices. The systematic under-ageing of larger, older individuals will lead to biased growth parameters with implications for stock assessments . Some stockassessment methods used for teleosts do incorporate ageing bias and imprecision (Methot, 1990;Punt et al., 2008), and conclude that increases in the variability of assessment results that are particularly sensitive to the magnitude of the biases . The discussion of the implications of age underestimation in elasmobranchs has started. Harry (2017) addressed the potential effects of age underestimation on growth and mortality, highlighting complicated and conflicting consequences. As age underestimation is identified in more elasmobranch species, the effects of biased growth parameters on stock assessment results must be better understood and an alternate method to estimate elasmobranch age must be found.

Introduction
Elasmobranchs, the sharks, skates, and rays, have been a successful evolutionary lineage for 450 million years. Their biggest threat has only arrived relatively recently with the development of global fisheries targeting them (Catarci 2004;Vannuccini 1999). Elasmobranchs are characterized by slow growth, late age at maturity, small litters, and extended longevity; these traits make them particularly sensitive to over-exploitation (Cortes 2002;Holden 1973;Stevens et al. 2000).
Achievement of sustainable elasmobranch fisheries requires correct evaluation of the status of elasmobranch populations, which requires knowledge of their life history characteristics (Cortes 1998;Heppell et al. 1999). There is large variation among elasmobranch species in productivity and resilience, the ability to respond to perturbations. This ability ranges from populations that are relatively fishing-resilient to populations that are unable to recover after moderate exploitation (Cortes 2002;Smith et al. 1998). Such variation requires substantial knowledge of life-history characteristics in order to provide the data necessary to determine population status and potential for recovery after exploitation.
Accurate stock assessments require a knowledge of life history characteristics including age at first reproduction, years reproductively active, and growth rates, to determine a population's status. These characters are traditionally determined through estimates of length-at-age, which require the species to have a hard structure that records growth over time in a reliable and permanent way .
Several hard structures exhibit growth patterns useful for ageing elasmobranchs, and the most effective for many species is an analysis of the vertebral centra ). These structures grow via accretion, producing detectable band pairs composed of one opaque and one translucent band that may be counted and have been used as a proxy for age ).
The validity of using band pair counts for age has been brought into question over the years starting with species for which band pair formation was related to somatic growth, growth of the body, rather than time or age ). An increasing number of studies demonstrate underestimation of age for larger, older individuals Natanson et al. 2015;). Indeed, for many of these studies annual band pair deposition is validated up to the approximate age at maturity Natanson et al. 2015;). This systematic under-ageing of larger, older individuals needs to be accounted for in stock assessments. Alternatively, the overestimation of age may occur if band pair deposition occurs more frequently than annually. For instance, juvenile shortfin mako sharks (Isurus oxyrinchus) in the Pacific Ocean deposit two band pairs a year for approximately the first five years . Thus, the effects of ageing errors need to be addressed for elasmobranch stock assessments.
Age bias was intentionally introduced to age-at-length data of two skate species as a case study. Leucoraja erinacea, little skate, and L. ocellata, winter skate, are sympatric species that are targeted by trawl for the lobster bait fishery and wing fishery, respectively, in addition to being bycatch in other fisheries (NMFS 2007).
They are managed as a part of the Northwest Atlantic skate complex which includes seven skate species, but fisheries assessment does not currently incorporate age structure of the population. Nevertheless, little and winter skate provide an interesting case study particularly as a data-poor example. This study is the first to investigate the effect of ageing bias on the stock assessment outputs on elasmobranch species.

Simulated Bias
Length-at-age data for L. erinacea and L. ocellata were obtained from Frisk and Miller (2006). Ageing bias was applied to the length-at-age data to simulate minor and major underestimation and overestimation of all ages and of mature individuals only. Minor bias is a deviation of 10% of the maximum age from true age while major bias is a deviation of 25% of the maximum age from true age. The maximum age of L.
erinacea was 12 years (Frisk and Miller 2006); the 10% and 25% bias were one year and three years respectively. The maximum age of L. ocellata was 20 years (Frisk and Miller 2006); the 10% and 25% bias were two and five years respectively. These age biases were applied over all ages, and for mature ages only by adding or subtracting the bias (in years) from the length-at-age data. Leucoraja erinacea matures at eight years old and L. ocellata matures at 12 years old (Frisk and Miller 2006 where L is the length at age a, L∞ is the asymptotic length, k is the growth coefficient and t0 is the theoretical age at length zero (Ricker 1979;von Bertalanffy 1938).
Maximum age, age at maturity, and von Bertalanffy parameters changed with each bias scenario (Figure 1; Table 1). In several cases the maximum age group was truncated to a younger age because the biased von Bertalanffy parameters created ages with zero frequency in the length-at-age matrix. For example, the negative 10% bias for little skate estimated that 49-cm TL individuals were 9 years old and 50 cm TL individuals were 11 years old; therefore, the maximum age group for negative 10% for the little skate was 10 rather than 11 years.
Indices of relative abundance and length-frequency data were used from the National Marine Fisheries Service (NMFS) groundfish spring (for L. erinacea) and fall (for L. ocellata) surveys from 1994 to 2014. Total catch (kg) and lengthfrequencies were used from fishery-dependent data provided by Dr. Sosebee. The simulated von Bertalanffy parameters (Table 1) were used to estimate ages for the total catch and survey length-frequency data. These ages were used in combination with the indices of relative abundance and total catch to test the sensitivity of a statistical catch-at-age model to various ageing bias scenarios.

Statistical Catch-at-age Model
The model developed for this study was an age-structured statistical catch-at age model. The predicted number of fish ( ) was modelled as a cohort where A is the age-plus group: The model estimated the number of fish at age in the first year of simulation and fish recruitment at age zero. The total mortality on fish was given by where M was assumed known for each species and set equal to k. The fishing mortality F each year t is the product of estimated fully selected fishing mortality E and fishing selectivity: where is the fully selected fishing mortality parameter. The fishing selectivity (s F ) at age a was estimated following a logistic form where γ F and A50 F were estimated parameters on a logit scale Selectivity was scaled so it is at its maximum at the maximum age class.
Predicted fishing catches in numbers (C) were calculated following the Baranov equation: The predicted survey abundance (I) was calculated as follows where ψ is the fraction of the year elapsed when the survey takes place: The catchability (q) is estimated on a logit scale with logit_q being estimated within the model:

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The survey selectivity (s surv ) was assumed to be follow a logistic curve: The spawning stock biomass (SSB) was calculated within the model as follows where w SSB is the observed weight in the SSB, mat is the proportion of mature fish at age and ϕ is the fraction of year elapsed when the spawning takes place: The model is fitted to annual observations of total catch and survey abundance indices and corresponding age compositions for each species independently. We assumed log aggregated catch and log aggregated survey indices were normally distributed with given variance. Catch and survey index age compositions were assumed to be multinomially distributed for little skate and logistic-normally distributed for winter skate.
The model was developed in the R package (R Core Team 2017) Template Model Builder (TMB) (Kristensen et al. 2016). The estimated outputs from the various model scenarios were qualitatively compared.
The statistical catch-at-age successfully estimated parameters and standard error estimates for most bias scenarios. For little skate, the -25% and +25% bias for all ages did not successfully estimate parameters and standard errors. For winter skate, the +25% bias for all ages and +25% bias for mature ages only did not successfully estimate parameters and standard errors. These four models were left out of 105 subsequent analyses. The model had difficulty estimating some parameters for some scenarios, particularly recruitment at the end of the time series (little skate scenario +10%; winter skate scenario +10%) and age at 50% of selectivity for either the survey or fishing (little skate scenarios -10% mature only, -25% mature only; winter skate scenarios -25%, -10% mature). These models were included.

Results
The no-bias scenarios qualitatively fit the total catch data well for both species ( Figure 2); however, the qualitative fit to the survey data was worse than for total catch data ( Figure 3). The intentionally biased scenarios were similar to catch and survey data (Figures 2, 3). For winter skate, the last five years of the time series were not modeled well by any scenario; in general total catch data were overestimated and survey data were underestimated (Figures 2b, 3b). The direction of bias (positive or negative) did not result in a consistent over-or under-estimation of catch or survey data.
Estimates of SSB had high variability throughout the time series with most bias scenarios overestimating SSB for little skate and underestimating SSB for winter skate compared to the no-bias scenario (Figure 4). For little skate, the more extreme bias scenarios deviated most from the no-bias scenario (Figure 4a). For winter skate, the end of the time series had similar declining trends in SSB values for all the scenarios except -25% (Figure 4b).

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Estimates of F were predictable by bias scenario for little skate: when all ages were biased, a positive bias did not affect the estimated F (was similar to the no-bias scenario) while a negative bias decreased the estimated F, when only mature ages were biased, a positive bias decreased F while a negative bias increased F (Figure 5a).
For the winter skate, estimates of F were overestimated by most of the bias scenarios, particularly in the last five years of the time series (Figure 5b).

Discussion
Intentionally biased age estimates introduced variability into stock assessment results, mostly into estimates of SSB. The variability was not predictable and does not align with similar research on teleosts .  simulated a fish population and applied two ageing error scenarios, relatively accurate and substantial underestimating of age, to determine the effect of ageing error on the estimation of a time series of recruitment via a sequential population analysis. Both scenarios reduced the estimated inter-annual variability in recruitment by up to 50% and 66%, respectively . Another simulation study generated three ageing error scenarios to examine the effect of ageing error on predicted stock trends. It found that, in general, ageing error resulted in prediction of similar stock trends no matter the bias, but spawning stock biomass estimates were more variable and fishing mortality was consistently underestimated . In contrast to , the bias scenarios applied here did not have similar stock trends, particularly SSB, among scenarios.  (Figure 3). While the gold standard of stock assessment is to incorporate as much life history data as possible, for little and winter skate, the fishery-independent survey is providing sufficient information on the stocks to manage them appropriately.

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With the increasing instances of age underestimation, uncertainty in ageing accuracy needs to be accounted for in elasmobranch stock assessments. The biased age scenarios affect stock assessment results. In this case study, the effects were subtle and not always predictable. In fisheries where age structure and accurate catch data are known, these simulated bias scenarios could be very informative to the range of resiliency of a population to mitigate the uncertainty around age estimates.

CONCLUSIONS
The banding pattern in elasmobranch vertebrae which alternates opaque and translucent, has been used to estimate elasmobranch age for over 35 years (Haskell 1949;. However, there are still outstanding questions about how and why these bands form and whether they accurately reflect the age of the individual. An increasing number of studies show exceptions to a pattern of annual band-pair formation, so that band-pair counts cannot accurately reflect age, and this is particularly true for older individuals . Many of these studies validate annual band-pair formation up to the approximate age of maturity, but the ages of older, mature individuals are underestimated Natanson et al. 2015;).
This dissertation addressed several questions regarding opaque and translucent bands in elasmobranch vertebrae, whether they accurately reflect age, and how inaccurate ages may affect fisheries management.
Elasmobranch vertebral centra fit the criteria for an appropriate ageing structure because they are a permanent record of growth and grow in proportion to body size ). However, not all centra within individuals are the same size (Figures 1.1-1.5). There are two explanations for variation in the alternating opaque and translucent banding pattern between centra and along the column of an individual: (1) the widths of the opaque and translucent bands are thinner in smaller centra, but every centrum along the column of an individual contains the same number of bands or, (2) band width is approximately the same among centra, but smaller 121 centra contain fewer bands. The second possibility aligns with the hypothesis that band pair number is related to somatic growth and/or the structural needs of the individual rather than to age . This hypothesis poses a problem for age and growth estimates because band-pair counts that vary along the vertebral column of an individual cannot accurately reflect a single age estimate. Variable band-pair counts have been documented in several species of sharks . In this dissertation, band-pair counts were found to vary along the vertebral column in five batoid species (Figure 1.1-1.5). This finding extends the issue from sharks to all elasmobranchs. Since different centra have different numbers of band pairs within an individual, the mechanism of band-pair formation cannot be directly linked to an annual cycle.
Sexual maturation may be a key transition point in the timing of deposition of opaque and translucent bands. Species with successful validation of annual band-pair formation have only been validated up to the approximate age at maturity Natanson et al. 2015;.  showed that two captive adult female L. erinacea did not deposit a full band pair in one year. In this dissertation, 63% of adult male and female L. erinacea held in captivity for 13 months did not deposit a full band pair. While it was expected (based on  that only sexually mature females would exhibit decreased frequency of band-pair deposition, this trend in both sexes suggests a link between maturation and decreased frequency of band-pair deposition.

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The inability to accurately age elasmobranchs throughout their lifespan using current techniques raises concerns for current stock-assessment practices. The systematic under-ageing of larger, older individuals will lead to biased growth parameters with implications for stock assessments . The only research on ageing bias to date has been on teleosts, where incorporating ageing bias into stock assessments increases the variability of assessment results, which are particularly sensitive to the magnitude of the biases . In this dissertation, intentionally biased age estimates also introduced variability into stock assessment results but, the direction of bias (negative or positive) did not have a predictable effect (i.e. consistent over-or under-estimation) on the estimated parameters. If age estimates are inaccurate at any point in the lifespan of a fish, the consequences will be seen in the stock assessment of the population.
The explanation of the difference between opaque and translucent bands is that they have different amounts of mineralization, but results conflict on which band type is more mineralized. Some studies document higher amounts of Ca and P in the opaque band  while other studies claim the translucent bands are hypermineralized . Previous research correlated peaks and troughs of Ca and P to opaque and translucent bands, but the peaks and troughs are variable with some troughs having similar values as other peaks . In this study, bulk chemical composition did not differ between band types (opaque and translucent) within L. erinacea and among 11 other 123 elasmobranch species. The variation of each element among bands of the same type (opaque vs. opaque) along a centrum may preclude the detection of differences between different band types (opaque vs. translucent). Nonetheless, this dissertation showed that the optical differences between band types was not based on a difference in basic chemical composition, but a satisfactory explanation for the difference between the two band types is still unknown.
The results of this dissertation have wide-ranging impacts on the fields of age and growth and fisheries management. The major conclusion here is it is unlikely that band pairs are deposited annually throughout the entire lifespan of the fish, therefore an alternate method to estimate elasmobranch age must be found. The mechanism that controls band-pair deposition may approximate an annual cycle for a portion of the lifespan (e.g. up to sexual maturity). In this case including uncertainty in band pair counts particularly for sexually mature individuals may mitigate the effects that inaccurate ages have on stock assessments. The next step is to confirm the mechanism behind band-pair deposition so it can be predicted. If band-pair deposition is based on somatic growth then age can be predicted based on body size and annual growth. In the meantime, the effects that inaccurate ages have on stock assessments must be explored and incorporated into fisheries management.