Molecular Vision 2007;
13:2030-2034 <http://www.molvis.org/molvis/v13/a229/>Received 12 August 2007 | Accepted 20 October 2007 | Published 25 October 2007
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| Molecular Vision 2007;
13:2030-2034 <http://www.molvis.org/molvis/v13/a229/> Received 12 August 2007 | Accepted 20 October 2007 | Published 25 October 2007 |
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On the relationship between rabbit age and lens dry weight: improved determination of the age of rabbits in the wild
Vision Cooperative Research Centre, University of NSW; Biochemistry Department, La Trobe University, Bundoora, Australia
Correspondence to: R.C. Augusteyn, Vision CRC, 30 Melcombe Rd, Ivanhoe, Vic 3079, Australia; Phone: 03 9499 1838; email: raugustn@bigpond.net.au
Abstract
Purpose: Eye lens dry weights are commonly used for estimating the age of animals in the wild, but reported relationships are variable. The purpose of this study was to determine why different relationships have been reported using data available for the same species of rabbits.
Methods: Published results that relate lens weight to age for wild European rabbits from four locations in Australia and cottontail rabbits from two locations in the United States have been reexamined. In addition, the effects of variations in lens preparation have been tested with fresh eyes.
Results: It was found that, in previous studies, the logistic type relationship between lens weight and age was interpreted inappropriately through the use of age constants, which imply that lens growth commences before conception. Using gestational time as the constant yields a single formula for each species, and this is consistent with most of the published data. Variations in fixation and drying conditions may be responsible for small differences between different populations.
Conclusions: When using lens dry weights as a measure of age, it is recommended that eyes be fixed for at least four weeks and the fixed lenses be dried for two weeks at 85 °C or, preferably, three days at 100 °C. Any formula, relating age and lens dry weight for any species, must take into account the fact that lens growth commences during gestation not before or after.
Introduction
Determination of age is of paramount importance in the monitoring of animal populations in the wild. Where populations need to be culled, data can readily be obtained for body parameters such as weight, limb lengths, or tooth wear. These data are often used for estimating age [1]. However, many of these are dependent on the environment, nutritional history, and gender. Consequently, ages estimated from these parameters may be incorrect.
Use of the eye lens offers a more reliable means for estimating age. Lens growth is continuous throughout life [2-6] and is unaffected by nutritional factors [7,8] and independent of gender in most species including mice [9], rabbits [10], kangaroos [11], and dingoes [12]. Lens wet weight is the most convenient parameter to measure, but this may be subject to rapid postmortem changes due to the movement of water in or out of the lens [2,13,14]. Therefore, the dry weight of fixed lenses is generally used as a measure of age. This approach was first described for rabbits by Dudzinski and Mykytowicz [15] and has now been applied to many other species.
Dudzinski and Mykytowicz [15] were the first to report that the relationship between rabbit lens dry weight and age could be described using a form of the logistic equation
(1) Log(LDW) = log(a) - b/(A+c)
where A is the postnatal age, LDW is the dry weight of the lens, and a, b, and c are constants.
Several studies since then have examined the relationship between lens dry weight and age for rabbits in different locations and have interpreted the data using the same form of equation [10,16,17]. In each of these, the logarithm of lens dry weight was plotted as a function of reciprocal (Age + c) with c being varied until the best linear fit was obtained. The values reported for the three constants are presented in Table 1. The differences were variously attributed to variations in species, location, health, or nutritional status. Such differences seem surprising, especially for the same species, given that the lens, which has no blood supply or nervous connections, is well-shielded from environmental or nutritional influences. This suggested to us that some of the apparent differences may originate in the interpretation of data.
Equation 1 (above), used for fitting the lens weight data, is a linearized form of the logistic equation commonly used for describing asymptotic growth.
(2) A = Am * exp(-k/t)
where A is the parameter being measured, which in this case, is LDW; Am is the maximum, asymptotic value for this parameter (corresponding to the constant a in Equation 1), k is the growth rate constant, (b in Equation 1) and t is the elapsed growth time, ([A+c] in Equation 1).
Since t in Equation 2 represents postnatal growth, the age constant, c, must represent the time during prenatal life when a growing lens is present. This cannot be greater than the total gestational period, which is 30-32 days in the case of European rabbits. Thus, the values of 36, 41, and 57 reported for c (Table 1) cannot be correct. Furthermore, the constant Am (constant a in Equation 1), which represents the maximum dry weight the lens can attain at an infinite time, should be the same for genetically identical animals. If there were differences in lens growth between populations perhaps due to environmental or nutritional factors, these would only affect the growth rate constant, k (constant b in Equation 1).
In the present study, published data on the relationship between lens weight and age in two species of rabbits are reexamined, and it is concluded that a single set of constants can be used for all populations so far studied.
Methods
Data for dry lens weights (LDW) and postnatal ages (A) were obtained from the table published by Lord [15] and from graphs presented by various authors [10,16-18]. These studies encompassed 450 European rabbits (Oryctolagus cuniculus) at four sites in Australia and 266 cottontail rabbits (Sylvilagus floridanus) at two sites in the United States.
Published graphs were magnified a minimum of 10 fold, and x and y distances were measured to the nearest 0.1 mm. The distances were converted to weights and ages using factors determined from the magnification of the axes. Values obtained this way were accurate to within 1%. The data were plotted according to the linear form of the logistic equation, log(LDW) versus 1/(A+c). The age constant, c, was varied between 0 and 32, and the relationship was assessed using linear regression analysis. Data from Forestfield and Chidlow animals less than 45 days old were excluded from the statistical analysis of the set because of the uncertainty of their ages [17].
Fresh eyes were collected from four- to six-month-old animals culled as part of routine population monitoring by the Victorian Government. The eyes were placed on ice for transport to the laboratory and were used immediately. The time required for fixation was investigated by placing eight whole eyes in 10% formalin and measuring their weights (carefully blotted dry) at daily intervals for over two weeks. Drying time was investigated by weighing excised fixed lenses at various times during drying in a convection oven at 85 °C.
Results
Figure 1A,B present the lens dry weights as a function of age since conception for 450 European rabbits collected at four sites in Australia [10,17,18] and for 266 Cottontail rabbits collected in the United States [15,16]. With few exceptions, the data points are clustered closely together. This suggests that the different populations may be very similar.
The relationship between log(LDW) and 1/(A+c) was examined as in previous studies by varying the age constant, c, until the best linear fit was obtained. However, unlike previous studies, the values of c tested were restricted to 32 or below, corresponding to the European rabbit gestational period, or part thereof. For all populations, the best fit of the data was obtained with a value of 32. The corresponding constants determined for each population are presented in Table 2. The constants obtained using the published values for c are presented in Table 1. Comparison of the values for R2 in Table 1 and Table 2 indicate that, in most cases, the fit using c=32 is as good as that for the published fit.
The similarities of most of the logistic constants (Table 2) suggested that the four sets of data could be described with a single equation. Therefore, all data (450 points) were combined and reanalyzed. The resultant linearized logistic plot for the European rabbits is shown in Figure 2A together with the line of best fit. The constants from the plots of the combined data are included in Table 2. The goodness of the fit (R2>0.97) confirms that the four populations are indistinguishable.
The original logistic interpretations of the growth data for the four populations of European rabbits [10,17,18] are presented alongside in Figure 2B together with the lines of best fit, which yielded the constants listed in Table 1. Comparison of Figure 2A,B illustrates how much closer the various sets of data become when a uniform, biologically relevant value is used for the constant c.
Similar reanalyses were performed on the cottontail rabbit data, using the gestational period of 28 days for c instead of the published constant of 41 [16]. The new logistic constants for the two separate populations as well as the combined cottontail data are also included in Table 2. Again, it is clear that a single equation can describe both populations.
To identify possible reasons for the relatively small variations in weights between different populations, the change in weight during immersion in 10% formalin was monitored for eight eyes from rabbits aged three to six months. In all cases, the weight decreased slowly but continuously throughout 15 days, indicating that the eye was still equilibrating with the formalin. Typical examples are shown in Figure 3. The average rate of weight loss for the eight eyes examined was 7±1.2 mg/day.
The drying process was examined by monitoring the weights of fixed lenses during drying at 85 °C, the most commonly used temperature. As can be seen in Figure 4, although the majority of water was lost in the first day, water loss continued up to about 11 days. Between 8 and 11 days of drying, lens weights decreased by another 0.3%, corresponding to about 1 mg. By contrast, when lenses were dried at 100 °C, constant weight was achieved within 48 h.
Discussion
A reliable method for determining ages of animals culled in the wild is invaluable for population management. It was realized long ago that lens dry weight could be a very good indicator of age [15], and this has been adopted for many species. However, studies conducted on rabbits have led to the idea that there may be regional, seasonal, and subspecies variations in lens weight. If correct, this would diminish the value of the lens dry weight method. It would not be possible to determine ages or to compare different populations unless data for known-age animals were collected for each population being examined.
Our reexamination of the published data for four populations of European rabbits and two of cottontail rabbits, restricting the age constant to a value equal to or less than the gestational period, reveals that growth for each species can be described with a single logistic-type equation. For the European rabbit this is,
Lens dry weight = 276 * 10[-51.7/(A+32)]
For the cottontail rabbits, maximum lens dry weight is 277 mg and the growth rate constant is 46.3 using a gestation time of 28 days. Interestingly, the maximum dry weight attainable for the cottontails is the same as that for the European rabbit but the growth rate constant is substantially lower. This implies that cottontail rabbits grow more rapidly than the European rabbits and have a shorter lifespan. The shorter gestation period for the cottontail is also consistent with the observation that shorter gestation times are associated with shorter life spans [19].
According to the logistic model used in the present study, the age constant, c, corresponds to the prenatal time when a lens is present. From developmental studies, it has been established that lens induction occurs at Carnegie Stage 13, which is around 16 days before birth in the rabbit. Therefore, it might have been expected that the value of c would have corresponded to this time. This appears not to be the case. The logistic plots were obviously curved when 16 was used and the best fit (R2 = 0.99) was obtained when c = 32, the total gestational time. This was also found for kangaroo lens growth [11]. Interpreting the data with the Gompertz growth function and the biphasic growth model found for the human lens [6] yielded poor fits, indicating that the logistic fit remains the most appropriate at this time. Further studies are required to determine if another model for lens growth might be more appropriate.
Rearrangement of the above equation permits determination of animal age from lens dry weight. The Dudzinski and Mykytowycz [18] constants are used by Australian authorities in monitoring rabbit populations. In a field collection of approximately 230 rabbits, over 90% of lens dry weights lay in the range 100-200 mg. These were calculated to come from animals aged 90-339 days. Using the new constants, the ages were re-calculated to be 81-302 days, 10%-12% lower. For older animals, the differences were smaller. Thus, adoption of the revised formula derived in this work will not substantially alter age estimates. However, it does alter perceptions regarding the effect of external factors on lens growth.
The reported differences between rabbit populations in different localities were previously attributed to differences in environment or exposure to stress [10,17]. Such conclusions are not sustainable in view of the present reanalysis of the data. The differences between the data sets appear to reside mainly in the younger aged animals. This may in part be attributed to difficulties in determining their ages to the precision required for logistic analysis. A difference of a few days will have a significant impact on the value of reciprocal age for young animals and skew calibration curves.
Another possible reason for the variations lies in the experimental manipulations of the lenses. Fixation seems to have been somewhat arbitrary with whole eyes being fixed in 10% formalin for periods ranging from 48 h to six months. Our data indicate that the eye has not yet equilibrated with the fixative after 15 days of immersion. Because of its central location in the eye, the lens would be the last to stabilize. This would affect the amount of formalin bound to the tissue and may result in variations in the weight of fixed tissue.
The drying process used in the different studies was also variable with temperatures of 80 or 85 °C and drying times varying from 24 h to 14 days in a convection or in a fan-forced oven. Our data indicate that, in a convection oven at 85 °C, water is still being lost from the lens after 10 days. Similarly, Wheeler and King [17] demonstrated that lens weights continue to decrease up to seven days of drying. In general, if fixing or drying conditions were inadequate, this would be expected to produce the greatest differences in the weights of the large lenses. To avoid variations due to lens preparation, it is suggested that eyes should be fixed for at least four weeks and fixed lenses should be dried for at least two weeks at 85 °C or preferably for three days at 100 °C.
The major reason for the different interpretations of lens growth data can be attributed to the use of different and biologically inappropriate values for the constant c. The constant cannot be greater than the gestational period. This obvious fact had previously been recognized by several investigators who used the time since conception for lens age in studies on the Columbian black-tailed deer [20], coypus [21], house mouse [9], Norway rat [22], proghorn antelope [23], and a variety of laboratory animals [5]. Surprisingly, the earlier approaches appear to have been overlooked in subsequent studies on Australian bush rats [24], dingoes [12], blacktailed jack rabbits [25], snowshoe hares [26], blacktailed and mule deer [27], gray foxes [28], and root voles [29]. This makes it difficult to compare lens growth rates between different populations let alone between different species.
It is concluded that, contrary to previous reports, published data on the relationship between lens dry weight and age in rabbits provide no indication that lens weight differs with stress or environment. It is suggested that, when using the logistic equation, the time since conception be used as the independent variable.
Acknowledgements
The author is very grateful to Dr. Steve McPhee of the Victorian Government's Department of Natural Resources and Environment for his continued interest in and support of this research. This work was supported in part by the Cooperative Research Centre Scheme of Australia through the Vision Cooperative Research Centre.
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