Allometry is the relation of the body size of an organism to a specific anatomical feature, in this case, genitalia. Male genitalia of insects consistently display negative allometry, which is associated with stabilizing selection. Case in point illustrated by relatively small males displaying disproportionally large genitalia, while relatively larger males display disproportionally small genitalia. In contrast, male genitalia of mammals display positive allometry in relation to body size, and is thought to be the product of sexual selection. In this study, I investigated the relationship between genital size and body size in cephalopods, namely Octopus sp., and how they related to each other in terms of allometric slopes. Octopus sp. showed negative allometric slopes for ligula length and ligula width, and as such, male genitalia of Octopus sp. are associated with stabilizing selection. This study explores how stabilizing selection is associated with the one-size-fits-all hypothesis for male genitalia of Octopus sp. and how male genitalia are selected for in terms of desired receptor responses from females.
Key words: Negative allometry, stabilizing selection, sexual selection, cephalopods, one-size-fits-all.
Allometry, the variation of a specific trait (such as genital size) in proportion to body size as a result of growth. The allometric indicator is the natural log of the raw data where one allometric slope is favoured over another due to selection (or not being selected for. Positive allometry implies that for every unit of increase in body size, male genitals would increase by greater than one unit (an allometric slope greater than 1.0). This is generally the case for traits under sexual selection (e.g., Alatalo et al.,1988; Petrie, 1988, 1992; Green, 1992; Emlen and Nijhout, 2000). On the contrary, traits, which are not under sexual selection, show an allometric slope equal to 1.0 (isometry). They suggested that sexual selection favours males with genitalia of a standard size, which is suitable for the majority of female genital tract. Many studies have found negative allometry to be the case for male genitalia in insects, arthropods and vertebrates (e.g. Eberhard, 2009; Hosken at al., 2005; Ohno et al., 2003, Higgins, 2009; Tatsuta et al., 2001).
We examined the allometry of male genital traits (i.e. ligula length and width) and body size (inter ocular distance proxy) in order to observe how genital size relates to body size. We made these observations in order to determine if male genitalia are selected for, and if so, what pattern the allometric slope follows. Allometric relationships are important as it provides insights into species evolution and adjustment. Firstly, I hypothesized that ligula length and width is not uniquely acted upon by sexual selection what so ever, and thus genital size and body size will follow an isometric relationship. Secondly, I hypothesise that a positive allometric relationship will results between male genitalia and body size, and as a consequence, male genitalia will be increasing disproportionally to body size. Thirdly, I hypothesise that male genitalia of a standard size will be sexually selected for, and will result in negative allometry between male genitalia and body size.
Materials and methods
Male octopuses were purchased from Sydney fish markets in Sydney, Australia, and were kept on ice for the duration of the practical. Since the octopuses were already deceased and captive, no inferences can be made about the original habitat of the octopuses. The octopuses had been deceased for a few years and since we do not know their original place of capture, it may be possible for these octopuses to be from multiple locations. The possibility of multiple locations and the period since death should not present any problems for allometric estimations.
The octopus species is unknown, however specimens were clearly similar in terms of their dimensions. Therefore, I am lead to believe that all specimens are of the same species. In order to test my allometric hypotheses, the octopuses were placed under dissection microscopes, and the inter-ocular distance for each octopus was measured using plastic vernier callipers (See figure 3). The inter-ocular distance is used as a proxy for body size as opposed to the circumference of the visceral hump and is thought to be the distance from the inside corner of each eye, as opposed to the distance from the centres of the eyes (eg. O'Shea, 2002).
I used a microscope slide to gently flatten the ligula as it may have reduced in size during storage. This will allow for more accurate measurements. Again I used the plastic vernier callipers to determine the length and the longest width of the flattened ligula (See figure 3). The length of the ligula is measured from the very tip to the clearly defined start of the hectocotylus arm, where the arm width is at its narrowest. The general shape of the ligula was similar for each individual specimen.
The natural log of the lengths and widths were taken prior to analysis. Taking the natural log of raw data equalizes measurement error and minimizes the effect of outliers (Voight, 2002).
Graphs of the non log-transformed data were generated using Microsoft Excel. Figure1 explored variation in intra-occipital length versus the ligula width. Figure2 explored variation in intra-occipital length versus ligula length.
Using VassarStats, I was able to perform a regression analysis on the log-transformed data for ligula width and body size, as well as ligula length and body size. I was also able determine the variation in genitals that can be explained by body size (R^2 regression). Outliers exceeding more than two standard deviations from the mean were excluded. The allometric slope was determined and thus allowed us to determine the nature of the allometric relationship. Furthermore, plotting our data over a 1:1 line of isometry, I was able to determine to what extent the nature of the allometric relationship was.
Ligula width was statistically significant in relation to male Octopus body size (t = 5.97, df = 116, P < 0.0001). Therefore, we are able to reject the null hypothesis, as there is an association between ligula width and body size. We hence tested the degree of variation between the ligula width and the Octopus body size only to discover a weak association (See Figure 1). The regression line slope was indicative that for every one unit that body size was grander, ligula width increases ~ 0.60 units (See figure 1). The true value of our slope digresses from isometry and a slope value less than one unit increase in ligula width per unit increase in body size is symptomatic of negative allometry (See figure 1). Confidence limits place 95% certainty on the true value of the slope between 0.40 and 0.80. An upper confidence limit is indicative of a negative allometry, however, a positive relationship still exists.
Ligula length was typically significant relative to male octopus body size (t = 6.7, df = 116, P < 0.0001). Furthermore, there exists a weak correlation in variation for ligula length explained by body size proxy (See figure 1). Therefore it is plausible for a relationship other than isometry to exist. Albeit ligula length allometry was significant, the slope was less than 1 (See figure 1). Thus evidence of a negative allometry exists, therefore for every unit increase in Octopus body size, formulates an increase less than one unit in ligula length (See figure 2). With 95% certainty, the true slope lies between 0.41 and 0.76. With the upper confidence limit less than 1, there is undeniably a negative allometry, however, a positive relationship between inter ocular length and ligula length still exists.
For both ligula length vs. proxy and ligula width vs. proxy correlations, the allometric slopes significantly digress from 1.0 (See Table 1).
Minor deviations occur between allometric slopes for body size & ligula width and body size & ligula length. Nevertheless, this contrast is statistically insignificant.
I was able to successfully determine that a negative allometry exists in Octopus sp. male genitalia. An outcome of uniform negative allometry is especially notable when taken into consideration that the ligula of Octopus sp. was chosen for ease of measurement and not in light of the specific function of the structure. Negative allometric slopes imply that relatively small male octopuses display disproportionately large genitalia, while relatively large males pose disproportionately small genitalia.
Consistent negative allometry in male genitalia is likely to indicate an exact fit between male and female genitalia. Which is consistent with the lock-and-key hypothesis.
The lock-and-key hypothesis suggests that in an effort to avoid cross-species mating, males have developed complex genitalia, which are unique to each species. Usami et al. (2003) used Japanese Carabid beetles in order to provide support for the lock-and-key hypothesis. Their results indicated that many different species did not attempt to mate. Two species did attempt to mate, however their genitalia were too diverse to allow for copulation. If species isolation was the causation behind genital divergence, then species, which have evolved in isolation, should not display a deviation in genitals. Cixiid insects display intricate and different genitalia despite evolving in isolation from other species.
Since sexual selection does not place a pressure on male genitalia in terms of a positive allometric variance, and a selective advantage implies to males who are able to stimulate females, there must exist a strong variance in shape of male genitalia. Fertilisation success is directly related to variation in genital morphology (Hosken et al., 1998).
Usually male weapons such as horns and tusks show an obvious positive allometric slope (Kodric-Brown et al. 2006). In contrast, male genitalia typically display negative allometric slopes (Eberhard, 2008). Hence it is clear that male genitalia are independent of a sexually selective demand for positive allometry. In addition, male genitalia are usually not a good indicator of 'fitness' as they are inexpensive to develop and maintain. Thus reducing selective pressure on male genitalia, hence a reduction in need for positive allometry.
My findings provide support for the "one-size-fits-all" hypothesis originally argued by Eberhard et al. (1998), which implies a selectable advantage on males, which are able to stimulate particular receptors in order to obtain a desired female response. Therefore, there must be a consist relativity between male and female genitalia, and a standard size in male genitalia. This standard size in male genitalia would presumably have to be suitable for the majority of female octopuses of the particular species. Therefore, sexual selection may pressure a preference for negative allometric slopes in male genitalia, in order to cause desired receptor stimulation in females. Eberhard et al., 1998; Gage, 1998 provide examples to support the assumption that female structures, which interact with male genitalia, are negatively allometric as well.
There are three primary selective mechanisms: directional, disruptive and stabilizing. These selective mechanisms have implications for genital allometry. For example, positive allometry is associated with directional selection whereby genital size increases at a greater rate than body size. In contrast, stabilizing selection is associated with negative allometry.
Stabilizing selection reduces genetic diversity as a species stabilizes on a specific attribute. Therefore, extreme phenotypes are selected against, gradually allowing a particular trait to become more prevalent. For example, industrial melanism has caused many species of insects to evolve and develop colour changes, allowing them to blend in with the polluted background.
My findings of negative allometric variance in male genitalia appear to contradict the findings of Miller and Burton 2001; Lu¨pold et al. 2004 in terms of male genital allometry. Their study on mammals (B. suillus) provides evidence of positive allometric variations, however, this relationship was only relevant during mating season. While it interesting for a contrast to occur between mammals and cephalopods, positive allometry does indeed have its advantages. Inferences of the time of year that tested octopuses were captured cannot be made, therefore it is a possibility that genital size displays positive allometry according to the time of year as Miller and Burton 2001; Lu¨pold et al. 2004 were unable to replicate their findings at any other time of year.
In carrying out this study, many assumptions were made. Following a regression assumption is essential as our data must follow a mean and must be normalized to be significant. Furthermore, we must assume that inter ocular distance as a proxy is proportionate and relative to body size. Finally, we must assume that inter ocular distance is not a sexually selected trait that is selected for. Thus we assume females are not attracted to males with greater or smaller distances between their eyes.
It may be of interest for further research to investigate allometric variation throughout the course of the year at several intervals including mating season.
I would like to thank the collectors for the octopuses, the demonstrators for answering any questions and for the guidelines. I would like to thank Kate Umbers for explaining exactly what was expected and for taking us through the practical. I would finally like to thank Darrell Kemp for all his work, answering all of my questions, helping wherever possible and for the guidelines of this article.