TITLE PAGE - acumen - The University of Alabama
TITLE PAGE - acumen - The University of Alabama TITLE PAGE - acumen - The University of Alabama
What explains the large discrepancy between the estimates of Cooper (1975), Culver (1982) and this study? Since the general approach and methods in the two studies were similar, the differences between conclusions must be related to the data used to drive the size-at-age models. Below potential factors related to the data are discussed, particularly with respect to: (1) the size distribution of crayfish used to estimate growth rates, (2) the size thresholds used to define life-history stages (e.g. size-at-maturity, age-at-first-reproduction) and (3) the general limitations of using iterative growth models to estimate size-at-age. Differences in the size distribution of crayfish used to estimate growth rates The morphology of a growth model is influenced by the distribution of size-classes included in its construction. In many species, smaller size-classes show greater mass-specific growth per unit time than larger size-classes. Growth models that include a wide range of sizeclasses will typically show an early period of exponential growth, followed by an abrupt plateau. However, growth models become more protracted and almost linear when smaller size-classes are underrepresented, which can ultimately cause inaccurate estimates (i.e. overestimates) of life span, time-to-maturity and age-at-first-reproduction. In Cooper’s (1975) original size-at-age models, only 12 of the 56 individuals were less than 30 mm TCL, and only two of the 26 individuals used to produce size-at-age models based on Cooper’s (1975) data were less than 30 mm TCL (23 mm OCL). When comparing the distribution of individuals used to estimate growth rates (Fig. 1) with the actual size distribution of O. australis sampled from Shelta Cave (Fig. 4), it is clear that there was a strong bias to large individuals in Cooper’s full set of recapture data, even though smaller individuals (e.g. 12 to 30 mm TCL) were well represented in the population. Unlike the growth models for Shelta Cave, all 85
available size-classes were well represented in this study’s models from the three new Alabama cave sites, which produced distinct periods of exponential growth in each model. Differences in size thresholds used to define life-history stages While methods used to distinguish ovigerous females were consistent among studies (presence of ova or attached young), those used to set thresholds for female size-at-maturity differed significantly. Cooper (1975, p. 202) conservatively identified mature female crayfish as those displaying “late stage (3-4) oocytes and, usually, cement glands”. Mature females were identified in this study using the presence of cement glands alone, which is a reliable indicator of maturity in female surface crayfish (see Reynolds, 2002). Applying the definition from this study to Cooper’s (1975) data for Shelta Cave resulted in a reduction of female time-to-maturity by 5 to 16 years. Limitations of iterative growth models The asymptotic relationship between size and age is an inherent limitation to size-at-age estimates made using iterative growth models. If the models are interpreted literally, the largest individuals in a population are not significantly different from an infinitely old crayfish, such as in the model for Hering Cave (Fig. 3). In such cases, size is no longer an accurate predictor of age because annual growth increments become vanishingly small or stop altogether. Additionally, iterative models do not account for anomalies, such as individuals that are much larger than average at birth or those that have exceptionally fast growth rates (Weingartner, 1977, p. 208). Presumably, it is factors such as these that are the “flies lurking in the ointment of growth records” to which Cooper was referring (1975, p. 314). To avoid such drawbacks, iterative models must be interpreted within the context of population structure and dynamics. For example, Hering Cave’s growth model cannot estimate the age of the largest male or female. 86
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available size-classes were well represented in this study’s models from the three new <strong>Alabama</strong><br />
cave sites, which produced distinct periods <strong>of</strong> exponential growth in each model.<br />
Differences in size thresholds used to define life-history stages<br />
While methods used to distinguish ovigerous females were consistent among studies<br />
(presence <strong>of</strong> ova or attached young), those used to set thresholds for female size-at-maturity<br />
differed significantly. Cooper (1975, p. 202) conservatively identified mature female crayfish as<br />
those displaying “late stage (3-4) oocytes and, usually, cement glands”. Mature females were<br />
identified in this study using the presence <strong>of</strong> cement glands alone, which is a reliable indicator <strong>of</strong><br />
maturity in female surface crayfish (see Reynolds, 2002). Applying the definition from this study<br />
to Cooper’s (1975) data for Shelta Cave resulted in a reduction <strong>of</strong> female time-to-maturity by 5<br />
to 16 years.<br />
Limitations <strong>of</strong> iterative growth models<br />
<strong>The</strong> asymptotic relationship between size and age is an inherent limitation to size-at-age<br />
estimates made using iterative growth models. If the models are interpreted literally, the largest<br />
individuals in a population are not significantly different from an infinitely old crayfish, such as<br />
in the model for Hering Cave (Fig. 3). In such cases, size is no longer an accurate predictor <strong>of</strong><br />
age because annual growth increments become vanishingly small or stop altogether.<br />
Additionally, iterative models do not account for anomalies, such as individuals that are much<br />
larger than average at birth or those that have exceptionally fast growth rates (Weingartner, 1977,<br />
p. 208). Presumably, it is factors such as these that are the “flies lurking in the ointment <strong>of</strong><br />
growth records” to which Cooper was referring (1975, p. 314). To avoid such drawbacks,<br />
iterative models must be interpreted within the context <strong>of</strong> population structure and dynamics. For<br />
example, Hering Cave’s growth model cannot estimate the age <strong>of</strong> the largest male or female.<br />
86
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