Understanding the origin of biodiversity has been a major focus in evolutionary and ecological biology for well over a century and several patterns and mechanisms have been proposed to explain this diversity. Particularly intriguing is the pattern of sexual dimorphism, in which males and females of the same species differ in some trait. Sexual dimorphism (SD) is a pattern that is seen throughout the animal kingdom and is exhibited in a myriad of ways. For example, differences between the sexes in coloration are common in many organisms  ranging from poeciliid fishes  to dragon flies  to eclectus parrots (see Figure 1).
Sexual dimorphism is also exhibited in ornamentation, such as the horns of dung beetles , the antlers of cervids , and the tail of peacocks . Many species also exhibit sexual differences in foraging behavior such as the Russian agamid lizard , and parental behavior and territoriality can be dimorphic in species such as hummingbirds [8, 9]. Another common pattern is that of sexual size dimorphism, such as is observed in snakes  and monk seals .
There are many mechanisms that drive the evolution of SD, the most accepted mechanism being sexual selection [12-14], which enhances fitness of each sex exclusively in relation to reproduction [15, 16]. This states that SD evolves in a direction such that each sex (especially males, see 17) maximizes reproductive success in two ways: by becoming more attractive to the other sex (inter-sexual dimorphism) or by enhancing the ability to defeat same-sex rivals (intra-sexual dimorphism), in both cases such that each sex increases the chances to mate and pass genes on to the next generation. Many researchers have argued that competition for mates is at the very heart of sexual selection because these rivalries greatly influence mating and fertilization success. Indeed, competition for mates has been shown to be the major factor impacting SD in several taxa . However the complexity of SD cannot be explained by a single mechanism.
Mate choice is an important proximate mechanism of sexual selection. Often the sex with the higher reproductive investment is the ‘choosy’ sex. Patterns then emerge, such as those consistent with the ‘sexy son’ hypothesis , where females prefer mates with phenotypes signifying fitness. The females prefer males that are phenotypically ‘sexy’ to ensure that the genes of their offspring will produce males that will have the most breeding success, propagating her genes successfully [16, 20]. Taken further, sometimes females prefer males that exhibit very extreme phenotypes within a population. Over evolutionary time these traits become increasingly exaggerated despite the potential fitness costs to the males themselves, termed Fisherian runaway sexual selection . Examples include the tails of male peacocks, plumage in birds of paradise and male insect genitalia [14, 21, 22].
Alternatively, ecological mechanisms, such as competition for resources, may exert distinct selective forces on the sexes resulting in the evolution of SD . Here, intraspecific competition in species-poor communities may allow divergent selection between the sexes (rather than between species), resulting in sexual niche segregatation [12, 24-26]. In this case morphological traits often change to minimize this intersexual competition. Other ecological hypotheses have been proposed to explain patterns of SD, such as the influence of sex-specific divergence in response to environmental gradients (i.e., intersexual niche packing: sensu 27]. For example, both sexes of fruit flies
2. Processes and patterns of sexual size dimorphism
Sexual size dimorphism is a frequent phenomenon where the size of males and females of the same species differ (see Figure 2), driven by one or more of the mechanisms mentioned above. When these processes occur in closely related species, distinct patterns of among-species size dimorphism can result, one of which is termed ‘Rensch’s Rule’ . Rensch’s rule is a pattern wherein the degree of sexual size dimorphism increases with body size in species where males are the larger sex, and conversely decreases in those species where females are the larger sex (see Figure 3).
Several hypotheses have been proposed to explain Rensch’s rule. One proposes that the combination of genetic correlations between male and female size with directional sexual selection for larger male size will cause the evolution of larger males relative to female body size [13, 32, 33]. Another argues that sexual size dimorphism evolves through intraspecific competition between the sexes when foraging is related to size [15, 26]. Finally, many researchers have hypothesized that this pattern is due to female fecundity, where the larger female will have bigger eggs and a greater capacity to reproduce successfully [15, 34, 35]. Examples of Rensch’s rule and support for all three hypotheses abound in nature in organisms as diverse as hummingbirds , hummingbird flower mites , water striders , turtles , salmon  and shorebirds .
Another such pattern is that of ‘adaptive canalization’, where the larger sex has less plasticity compared to the smaller sex. This is due to directional selection for a large body size and individuals with sub-optimal body sizes will have lower fitness [40, 41]. Alternatively, there may be condition-dependence, where the larger sex is under stronger directional selection for a large size and will be more affected by different environmental factors as compared to the smaller sex. This indicates that sexual size dimorphism should change with changing environments. These hypotheses and studies have led to much understanding of the patterns and processes underlying sexual size dimorphism.
3. Sexual shape dimorphism
In addition to sexual size dimorphism, males and females often differ widely in shape [42, 43]. Curiously, although shape can contribute meaningfully to various functions such as feeding, mating, parental care and other life history characteristics, patterns of sexual shape dimorphism have historically received considerably less attention than sexual size differences [12, 44, 45, 46]. Examining the size and shape of traits together provides a much more complete quantification of sexual dimorphism, as the two components are necessarily related to one another. As such, shape analysis allows a deeper understanding of mechanisms underlying SD, because different parts of the body can serve multiple functions and be under distinct selective regimes.
Shape is defined as the specific form of a distinct object that is invariant to changes in position, rotation and scale [46, 47], and many methods have been proposed to study shape. For instance, sets of linear distances may be measured on each individual (e.g., length, width and height) to represent shape (Figure 4A), as well as angles (Figure 4B) and ratios of these measurements.
Sets of linear distances do not always accurately capture shape because of shortcomings that limit their general utility. For instance, it is possible that for some objects the same set of distance measurements may be obtained from two different shapes, because the location of the measurements is not recorded in the distance measures themselves. For example, if the maximum length and width were taken on an oval and teardrop, the linear values might be the same even though the shapes are clearly different (see Figure 5). Additionally, it is not possible to generate graphical representations of shape using these measurements alone because the geometric distances among variables is not preserved and aspects of shape are lost . As a result of these shortcomings, other analytical approaches for quantifying shape have been developed.
A major advance in the study of shape is landmark-based geometric morphometric methods, which do not have these difficulties. These methods quantify the shape of anatomical objects using the Cartesian coordinates of biologically homologous landmarks whose location is identified on each specimen (Figure 6). These landmarks can be digitized in either two- or three-dimensions, and provide a means of shape quantification that enables graphical representations of shape (see below).
Geometric morphometric analyses of shape are accomplished in several sequential steps. First, the landmark coordinates are digitized from each specimen. Next, differences in specimen position, orientation and size are eliminated through a generalized Procrustes analysis. This procedure translates all specimens to the origin, scales them to unit centroid size, and optimally rotates them to minimize the total sums-of-squares deviations of the landmark coordinates from all specimens to the average configuration. The resulting aligned Procrustes shape coordinates describe the location of each specimen in a curved space related to Kendall’s shape space [49, 50]. These are then projected orthogonally onto a linear tangent space yielding Kendall’s tangent space coordinates [47, 51, 52], which can then be treated as a set of shape variables for further analyses of shape variation and covariation with other variables [e.g., 53, 54, 55].
In terms of sexual shape dimorphism, dimorphism, sets of both linear measurements and geometric morphometric methods have been utilized to identify patterns of shape dimorphism in numerous taxa, including fish , turtles , birds [58-61] and lizards [62, 63]. In addition to quantifying sexual shape dimorphism, identifying the potential mechanisms that generate these patterns is a current focus of many evolutionary biologists. For instance, one central hypothesis for the evolution of sexual shape dimorphism is that males and females diverge phenotypically due to intersexual competition for similar resources. Here, functional morphological traits diverge between the sexes such that the sexes partition resources. Under this scenario, SD is more strongly influenced by natural selection than sexual selection. For example, in the cottonmouth
By contrast, sexual shape dimorphism can be the result of sexual selection. For example, in the tuatara
Another study also rejects the hypothesis that differential niches maintain sexual shape dimorphism. Feeding, territory, and mate acquisition have been proposed as functions for the bill of the Cory shearwater
One study investigated the relative contributions of intersexual resource partitioning and sexual selection in the amagid lizard
Evidence supporting fecundity advantage is weak or not existent in many systems however. For instance, investigators examining the tortoise
Environmental conditions are also hypothesized to drive the evolution of different shapes between the sexes. Evidence for one environmentally-driven hypothesis is presented in a study looking at environmental gradients underlying SD and parallel evolution of a species of guppy
Although these and numerous other examples demonstrate the influence of environment on the evolution of sexual shape dimorphism, a recent study examined sexual shape dimorphism in the snapping turtle
Broadly, allometry (defined as a change in shape related to a change in size: 45) has also been suggested as having an influential impact on sexual shape dimorphism [80, 81]. In an example of evolutionary allometry, Gidaszewski
Exceptions continue to be found however. For instance, in a recent study examining sexual size and shape dimorphism in the bill morphology of two hummingbirds
Conserved genetics may be yet another factor driving patterns of sexual shape dimorphism. Sexual shape dimorphism has been studied in the piophilid fly
Although studies are currently underway, many questions about sexual shape dimorphism still remain. For instance, how frequently is sexual shape dimorphism exhibited and how is this related to ontogenetic and biomechanical influences? Worthington
Does sexual shape dimorphism follow well-known patterns of sexual size dimorphism, such as Rensch’s Rule? How much impact does allometry have in driving the evolution of sexual shape dimorphism? Although patterns such as these have been suggested as a component of sexual shape dimorphism, only recently have researchers begun to investigate these patterns. Is allometry in sexual shape dimorphism common? Berns and Adams  did not find a significant effect of allometry, whereas Worthington
As seen in the examples in this chapter, much of the evidence on processes underlying sexual shape dimorphism is incongruent. One area needing attention is that of the correlation between sexual shape dimorphism and fecundity advantage, as shape may impact egg carrying capacity as size does. More work is needed to assess genetics and sexual shape dimorphism, and studies continue to argue that sexual selection causes sexual shape dimorphism due to male-male combat and mate choice, while others argue for natural selection via environmental factors and interspecific competition. No doubt that all of these factors play a role in influencing the evolution of sexual shape dimorphism, but what are the patterns? Do vertebrates tend to follow one trend while invertebrates follow another? In closely related species, does body size impact the effect of condition dependent sexual shape dimorphism? Just how much can natural selection and sexual selection be teased apart?
We are just beginning to test the questions about the role evolutionary history plays in patterns of sexual shape dimorphism. How do phylogenetic relationships effect sexual shape dimorphism? What role does sexual shape dimorphism play in microevolutionary patterns and what are the mechanisms underlying these patterns? What might result when these patterns are scaled from micro- to macroevolution? One way to address these questions is to take a sequential comparative approach: first examining patterns of dimorphism in two closely related species, then scaling up to family, genera, and so forth. It is now also possible to ask if rates of evolution differ between species and if these rates differ more broadly between different sexually dimorphic traits. What effect do habitat and environmental gradients play in assessing rates and patterns of sexual shape dimorphism evolution? By examining the possible correlation between sexual shape dimorphism and habitat variables in a phylogenetic manner, it is possible to quantify hypotheses such as these. With the advent of new phylogenetic techniques, morphometric methods, and statistical testing, we can further examine the details of the evolution of sexual shape dimorphism.
I would like to thank D. C. Adams, A. Alejandrino, J. P. Chong, A. Kaliontzopoulou and C. P. Ceballos for comments on this chapter. I also thank the United States National Science Foundation for financial support through the Graduate Research Fellowship DGE0751279.