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H Frederik Nijhout, Kenneth Z McKenna, The Origin of Novelty Through the Evolution of Scaling Relationships, Integrative and Comparative Biology, Volume 57, Issue 6, December 2017, Pages 1322–1333, https://doi.org/10.1093/icb/icx049
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Synopsis
Morphological novelty is often thought of as the evolution of an entirely new body plan or the addition of new structures to existing body plans. However, novel morphologies may also arise through modification of organ systems within an existing body plan. The evolution of novel scaling relationships between body size and organ size constitutes such a novel morphological feature. Experimental studies have demonstrated that there is genetic variation for allometries and that scaling relationships can evolve under artificial selection. We show that an allometry equation derived from Gompertz growth kinetics can accurately reconstruct complex non-linear allometries, and can be used to deduce the growth kinetics of the parts being compared. The equation also shows the relationship between ontogenetic and static allometries. We discuss how changes in the non-linear kinetics of growth can give rise to novel allometric relationships. Using parameters for wing and body growth of Manduca sexta, and a population simulation of the allometry equation, we show that selection on wing-body scaling can dramatically alter wing size without changing body size.
Introduction
Morphological novelty is often thought of as the evolution of an entirely new body plan or the addition of new structures to existing body plans. Novelty within an existing plan can come about by invoking developmental pathways in novel circumstances. Good examples are the evolution of eyespots in butterflies, whose development is controlled by the distal-less transcriptional regulator, which normally functions in developmental systems to specify the outgrowth of morphological features such as legs and antennae (Carroll et al. 1994; Brunetti et al. 2001). Another example is the evolutionary origin of horns in scarabeid beetles whose growth is controlled by insulin signaling and could therefore arise by expression of the insulin receptor and response pathway in novel locations (Emlen et al. 2006). These are novel phenotypes without prior homology to another morphological feature but whose origin relies on the expression of old pathways in novel locations and in a different morphological and developmental context.
Less dramatic novelties can come about by changes in the relative sizes of body parts. Many insects, for instance, have evolved almost grotesquely enlarged appendages, usually thought to evolve under sexual selection for competition among males or attraction of females. The long eyestalks of diopsid flies are an example of this (Wilkinson and Reillo 1994), as are mandibles in stag beetles, and the relative sizes of cephalic and thoracic horns in beetles (Emlen and Nijhout 2000). The wings of bats are another example of novelty through a change in form and function of a pre-existing body part.
If the evolution of novel scaling relationships between body size and organ size, or among organs or appendages, or along the different dimensions of an organ or appendage, can be thought of as novel morphological features, then morphological novelty can arise through evolutionary changes in the relative growth of body parts (Fig. 1). Insects provide excellent examples of evolutionary novel allometries (Emlen and Nijhout 2000).
Experimental studies have demonstrated that there is genetic variation for allometric relationships and that allometries and scaling relationships can evolve under artificial selection (Weber 1990; Emlen 1996; Frankino et al. 2005). A natural question that therefore arises is how changes in the growth kinetics of body and body parts lead to altered scaling relationships? Understanding how body parts grow and how their growth kinetics leads to allometric relationship is therefore critical to a mechanistic understanding of the evolution of novel scaling relationships. It would also provide new insights into evolutionary novelty itself.
Growth kinetics and the ontogenetic allometry equation
(where α is the scaling factor and β is the allometric coefficient), to analyze allometries. Like the polynomial, Huxley’s equation is fundamentally an empirical equation in the sense that it is not based on any a priori biological principles. It is just an equation that often fits the data reasonably well. The Huxley equation arose from the observation that when morphometric data are log-transformed, or when data in the arithmetic domain are plotted on double-logarithmic axes, their relationships are often approximately linear.
Huxley (1932) pointed out that his power equation would emerge naturally if one assumed that the two structures being compared grew exponentially. In brief: if structure A grows exponentially as dA/dt = a*A, and structure B grows as dB/dt = b*B, then their relative growth is dA/dB = a*A/b*B. A solution of this differential equation is A = cBa/b, where c (the scaling factor α in Huxley’s equation) is an arbitrary scaling constant, and the ratio of the two growth constants (a/b) is the exponent β of Huxley’s equation above (the allometric coefficient). When researchers who study allometry attempt to interpret the parameters of the Huxley equation, they simply assume that the allometric coefficient is the ratio of the growth constants of the two body parts, but seldom attempt to identify and understand their actual form of their growth trajectories (for exceptions see Nijhout and Wheeler [1996] and Shingleton et al. [2008]).
Problems with the Huxley equation
Two examples of ontogenetic allometries in the rat are given in Fig. 2A and B. It is clear that these are quite nonlinear (and will be so even after log-transformation [not shown]). A best-fitting Huxley equation curve is shown in both figures. Clearly, power law equations do not fit the data well. A log transform of the data will make it look like a slightly better fit, but that obscures some biologically significant deviations from the Huxley law. Note that the r2 values look reasonable, but that is not the point. The point is that the regressions do not follow the data correctly, no matter what the r2, and the regression obscures important bits of the underlying biology that give the data distributions their particular shapes. For instance, the data show that the mandible begins to grow in height before it begins to grow in length, and the spleen stops growing before the heart does; such observations lead naturally to questions about how the timing of growth of those parts is controlled, questions that would never arise from fitting the Huxley equation.
Although some biologists are happy enough with a nice-fitting curve, many proceed to interpret the cause of a scaling relationship as being due to differences in the relative growth rates. This is incorrect for two reasons. The Huxley derivation assumes (1) that the two structures grow exponentially and then suddenly stop, and (2) that they grow for exactly the same amount of time. Both assumptions are unrealistic. Most biological structures grow with sigmoidal kinetics, slowing their growth rate as they near their final size, and no two structures grow for exactly the same amount of time (Miller and German 1999; Stewart and German 1999; Nijhout et al. 2006).
If the sizes of two structures differ due to differences in duration of growth, this could not be deduced from Huxley’s equation. Moreover, few allometries are truly linear after log transformation (MacLeod 2010). Indeed, almost all allometries illustrated by Huxley (Huxley 1932) in his seminal work on relative growth are nonlinear, typically curving at one or the other extreme. Allometries in social insect castes, and beetle horns, legs and wings, are highly nonlinear; usually sigmoidal (Kawano 1995; Wilson 1971; Feener et al. 1988; Emlen and Nijhout 2000). The literature is replete with examples of non-linear allometries in which the nonlinearity is either ignored (presumably it is thought of as noise), or analyzed by piecewise linear regressions (Boag 1984; Cane 1993; Knoops and Grossman 1993) and interpreted as being due to size-specific or age-specific differences in the relative growth rates of body parts.
Realistic growth kinetics and the resulting allometry equation
In both insects and mammals, bodies and body parts grow with sigmoidal kinetics that can typically be fit to the Gompertz equation or the logistic equation. Both types of growth kinetics produce sigmoidal growth trajectories, where the growth rate is initially nearly exponential but gradually declines to zero as final size is reached. In rats, for instance, the body, internal organs and skeletal elements grow with Gompertz kinetics (German and Meyers 1989; Miller and German 1999; Stewart and German 1999; Reichling and German 2000), and in Manduca, both body and wing imaginal disks do (Nijhout et al. 2006, Nijhout unpublished). The scaling relationships among two such growing parts cannot be captured by the Huxley equation (Fig. 2, and see Nijhout and German [2012]).
This equation is obviously not as pretty and simple as Huxley’s equation, but it is based on biologically realistic assumptions about how body parts grow, and we have shown that it accurately describes real allometries (Nijhout and German 2012).
A stress test of the allometry equation
A stress test for the utility of this equation is shown in Fig. 3. Here, we deduce the allometry among two traits growing with exceptionally different kinetics. Part X grows rapidly to its maximum size, while part Y does not begin to grow appreciably until part X has almost stopped growing (Fig. 3A). Such largely asynchronously growing structures are exemplified by body and imaginal disks in holometabolous insects, where the imaginal disk that will form the appendages do most of their growth after the larva has stopped feeding and the body has stopped growing (Nijhout and Grunert 2010). The allometry among these two traits is extremely nonlinear (Fig. 3B, solid curve).
The challenge now is how to deduce the growth kinetics of the parts X and Y from the allometry alone, since the allometry is usually all that an experimenter will have. To do this, we digitized 12 points on the solid curve in Fig. 3B and used a nonlinear fitting algorithm (using JMP; SAS) to fit Equation (2) and find the values of the parameters (a, aa, b, bb, c, cc, t, tt). When those values were introduced into two Gompertz equations they yielded the curves shown by dotted lines in Fig. 3A. And when those two curves are plotted against each other to yield an allometry we obtained the dotted curve in Fig. 3B. As can be seen, in both cases the approximation is excellent. This illustrates the usefulness of the new allometry equation to correctly represent even highly complicated and nonlinear allometries, and our ability to correctly deduce growth parameters, including duration of growth of the two parts (parameters t and tt), from the allometry.
Another example of the utility of considering sigmoidal kinetics is illustrated in Fig. 4. Here, we take a well-known study on phenotypic integration in terns (Cane 1993). The ontogenetic allometry of two homologous bones in leg and wing is patently non-linear (Fig. 4, left panel), and the author analyzed it by piecewise regression using Huxley’s equation. The regressions are shown by the dashed lines and the numbers next to the regressions are the allometric coefficients. The analysis implies that the relative growth of these two parts changes abruptly and dramatically at several life stage transitions. In Fig. 4 (right panel), we show the predicted allometry (the solid chair-shaped curve) derived from Equation (1) that assumes that both parts grow with Gompertz kinetics. The fit is good and shows that no special assumptions need to be made about abrupt and arbitrary changes in growth: the growth of both structures simply followed sigmoidal trajectories, throughout.
How does one determine whether (or not) to use Equation (2) to describe an allometric relationship? The important thing to note is that the biological problem is not to find an equation gives the best statistical fit to the data, but to use an equation that fits the underlying biology. Drawing a bivariate regression though a set of data points is, in effect, a hypothesis about the mechanism by which the two things being plotted are related to each other. A linear regression implies, or should imply, a hypothesis that the underlying mechanism is linear. Using the Gompertz-derived allometric equation is an (empirically testable) hypothesis that the two features being compared grow with Gompertz kinetics. If they do not, then a different allometric equation needs to be used. For allometric equations derived from linear, exponential, Gompertz, and logistic growth kinetics, that also include development time as a parameter, see (Nijhout 2011).
Effect of parameters on shape of the allometry
The empirical Huxley equation has two parameters, one describing the slope of the line (on logarithmic axes) and the other the elevation of the line, and evolution of allometry is assumed to be through changes in the slope or changes in elevation of the allometry line (Frankino et al. 2007; Shingleton et al. 2007, 2008). In the more realistic allometry Equation (2) things are not so simple. The allometry Equation (2) has eight parameters: four kinetic parameters for each of the two structures being compared. Evolution of the allometry could be due to changes in any one, or any combination, of those parameters, so it is useful to know how each of them affects the shape of the allometry. It turns out that because the system is nonlinear, the effect of any one parameter will depend on the values of all the others. This is illustrated in Fig. 5. Here we show how different values of parameter b affect the shape of the y-yy allometry, and how the effect of parameter b on the allometry depends on the value of parameter a. The allometric relationships are very non-linear. The shape, the elevation, and the local slope of the allometric relationship between structures y and yy depend on the values of all the parameters. The shape of the allometry is not captured by simply calculating a best fitting linear slope and intercept (Nijhout 2011).
Thus, rather than being a simple 2-variable problem, the evolution of allometry actually occurs in a high-dimensional space. The universe of possibilities is very large. Which parameters will change when the relative sizes of two parts are under selection will depend on the correlations of the parameters with the trait under selection. That correlation, in turn, depends on the amount of variation in a given parameter and on how much variation in the trait depends on variation in that parameter. The degree to which a trait depends on the value of a given parameter can be found by doing a sensitivity analysis and can be visualized graphically by the slope of the graph that relates the value of the parameter to the value of the trait. An example is given in Fig. 6. Here, we plot the value of trait y as a function of parameters b and c over a range of values of b and c.
At low values of c the slope of b is steeper than at high values of c, so other things being equal, one would expect a higher correlation of b with the trait when c is small than when c is large. Conversely, at high values of b the relationship between c and the trait is negative (higher values of c correspond to lower values of yy), whereas at low values of b it is weakly positive. So, other things being equal, one would expect either a negative or a positive correlations of c with the trait, depending on the value of b. Of course, these relationships will also depend on the values of all the other growth parameters. Understanding, and taking account of, the growth kinetics of the morphologies being compared, gives a richer and deeper understanding of the mechanisms that give allometries their shapes. It is the kinetics of those underlying mechanisms that evolve when allometries evolve.
Evolution of novelty
The evolution of novelty can come about by a significant change in the growth trajectory of a body part. In insects, growth is controlled systemically by hormones, primarily ecdysone and for some tissues by insulin-like growth factors as well (Nijhout and Grunert 2002; Emlen et al. 2006; Nijhout et al. 2007; Shingleton et al. 2007; Nijhout et al. 2014). Growth in a novel location could come about by the novel expression of the ecdysone or insulin receptor in an area where it was not formerly expressed, whereas increased growth in a particular location could be due to an increased expression of receptors for these hormones. This would result in the origin of a new structure (such as a horn in a beetle (Emlen et al. 2006; Moczek and Rose 2009; Snell-Rood and Moczek 2012), a disproportionate increase in a structure, or, if the spatial pattern of receptor expression is altered, growth in a different shape-altering direction. Such a change in the regional pattern of growth of a body part would result in a change in its shape, and lead to a change in allometry. The exaggerated traits shown in Fig. 1 are examples of changes in form due to localized changes in growth patterns.
Evolution of allometry
Evolutionary changes in growth patterns and growth kinetics will lead to changes in all three of the generally-recognized modes of allometry: (1) Ontogenetic allometry, which follows the change in the relative sizes of two body parts during embryonic and postembryonic development in an individual; (2) Static allometry, which is the collection of the endpoints of many individual growth trajectories of two body parts (Fig. 7), and measures variation within a species; and (3) Phylogenetic allometry, which describes the scaling of homologous parts among different species.
These three kinds of allometries describe fundamentally different things, yet biologists have for decades used the same Huxley power equation to describe all three. There is, in principle, no reason why these different kinds of scaling relationships should be described by the same equation; indeed, several authors have noted the non-correspondence between them (Cheverud 1982; Pelabon et al. 2013). Nevertheless, it is almost universal practice to use the Huxley equation to describe ontogenetic, static, and phylogenetic allometries because in many cases it provides a reasonable fit to log-transformed data. The Huxley power equation says nothing, however, about the biological processes that lead to the allometry except that the variation is probably due to a large number of variables that act multiplicatively (hence approximating a log-normal distribution). In order to understand the biological underpinning of all three kinds of allometry, it is necessary to have a quantitative theory of growth that explains how the kinetics of growth can lead to particular scaling relationships. In the present paper, we discuss the causes of, and relationships between, ontogenetic and static allometry.
Equation (2) can be used to predict the effect that a particular evolutionary change in growth kinetics will have on the ontogenetic allometry. And, conversely, as shown above, given the allometry, the equation can be used to deduce what aspect of growth kinetics changed during the evolution of a morphological novelty.
Deducing the effect that a change in growth pattern will have on the static allometry is more difficult. This is because static allometry plots individual variation in the sizes of the body and its parts at a common time in development, so in order to understand static allometry it is necessary to understand how individual variation in those final sizes comes about (Nijhout and Wheeler 1996; Nijhout 2011). Equation (2) can be viewed as an ontogenetic allometry equation if we allow only t and tt to vary but fix all other parameters, and as a static allometry equation if we fix t and tt and allow the other parameters to vary to produce variation in y and yy. The same cannot be done with the Huxley power equation, because time plays no role in that equation. Any or all of the growth parameters (such as the growth exponent, the rate of damping of growth and the duration and timing of growth) can be subject to individual variation, because they are affected by genetic and environmental factors. When variation in size is due to an environmental variable such as temperature or nutrition, the resulting allometry is sometimes referred to as an environmental allometry or a norm of reaction (Schlichting and Pigliucci 1998). The effect of nutrition, for instance, would primarily be manifest in the growth exponent, and not in any of the other parameters. So by varying the growth exponent (parameter b for the body) one could study the potential effect of this particular environmental variable on variation in overall size and on the resulting allometry.
In most cases, the cause of individual variation in overall size is not known. Presumably there is individual variation in many and perhaps all the growth parameters, and that would produce a natural distribution of sizes. Not all parameters contribute equally to variation in size, and, as we will see below, the effect that variation in a given parameter has on variation in size depends on the values of all the others. In other words, the shape of the allometry, and how the growth parameters contribute to the shape of the allometry is a systems property, not a property of the parameters because their effect is context-dependent.
Selection and the evolution of allometry
It is likely that the growth and size of different parts of the body are at least partially independently controlled and are subject to (at least partially) independent genetic and environmental variation. Several artificial selection experiments in insects have demonstrated the independent variability of the body and appendages. For instance, experiments with the butterfly Bicyclus anynana demonstrated that the relative size of wings can change under selection (Frankino et al. 2005, 2007). In this study, two lines were developed: one strain was selected for increased relative wing size and one strain was selected for decreased relative wing size. After several generations, both lines significantly diverged from the control line, showing considerable increase and decrease in the relative size of wings, respectively (Frankino et al. 2005). This demonstrates that appendage size can evolve independent of body size, supporting the idea that the growth and development of the body and body parts can be controlled by mechanisms that can vary independent of each other. An artificial selection study in Manduca sexta demonstrated this same point. Lines were selected for increased or decreased body size. The result was a large body strain and a small body strain (Davidowitz et al. 2005, 2016; Tobler and Nijhout 2010). Interestingly, the large body strain had a shallower wing-body allometry, with wings that were relatively smaller for their body size (Tobler and Nijhout 2010). This too demonstrates that selecting on body size does not result in a matched increase in wing size.
To determine how scaling relationships might evolve, we developed a simple selection model using growth kinetic data of body and wings from Manduca following the approach of Nijhout and Paulsen (1997). Each parameter in Equation (2) was represented by two alleles, one producing a low value and one of high value of either the wing size or body size. Thus eight “genes”, for the eight parameter values, determine the wing-body allometry. Simulations started with a population of 1000 individuals in which all genes had 90% low alleles. Truncating selection for an increased wing-body ratio was done by selecting the top 30% of phenotypes (relative trait size value), calculating the new frequencies of alleles and using those to generate 1000 new diploid virtual individuals by randomly selecting two alleles for each gene from the new frequency distribution (assuming alleles acted additively and there was no linkage among the parameters). Allele frequencies for each generation were then followed along with the change in mean phenotypes (body and wing) and the correlation of each allele with the two phenotypes.
The response to selection for increasing wing-body ratio is depicted in Fig. 8. Panels A and D in Fig. 8 show the change in the mean phenotypes of body and wing, respectively, over the course of 550 cycles of selection. Panels B and E in Fig. 8 show the change in frequency of the large allele (initially at 10%) in the course of this selection. The alleles for body size changed only slightly, but there was a systematic change in the allele frequencies of the genes that control wing size. The frequency of the cc allele changed first and increased in frequency. This was followed by an increase in the frequency of the high allele of the gene for tt, followed by that of the aa allele, and followed much later by the high allele of the gene for bb. This sequence of genetic response to selection on the phenotypes is explained by the fact that not all genes are equally correlated with the phenotypes (Fig. 8C and F). The genes for cc and tt are initially most highly correlated (Fig. 8F) but as their frequencies change so do their correlations: that of cc rises and that of tt declines, resulting in an early rise of the frequency of cc. As gene cc reaches fixation its variation declines as does its correlation with the phenotype, and now the gene for tt becomes the most highly correlated and its frequency begins to change. Only when tt begins to approach fixation does the correlation of aa increase and its frequency now begins to change (Fig. 8D). As gene aa reaches fixation and its variation declines, the gene for bb becomes the only allele correlated with the phenotype, resulting in it increasing towards fixation.
This pattern of genotypic response to selection did not depend on the random recombination of alleles for each of the genes in each generation. It is a property of the system, and depends on the allele frequencies (Nijhout and Paulsen 1997). In our model, there was no functional relationship between the parameters for body and wing growth. In nature their variation is almost certainly correlated to a degree, because both depend on nutrition and temperature, and either of these environmental factors could cause joint variation in final size. Both wing and body also share circulating ecdysone as a growth promoter, and although variation in this hormone could affect growth rates in both structures, it is unlikely that it affects the final sizes of the parts, because they grow and develop at different times (Nijhout and Grunert 2010). In Bicyclus and Drosophila, wing and body size can evolve independently under artificial selection (Frankino et al. 2007; Stillwell et al. 2016). In our selection simulation, there was a slight decrease in body size and a large increase in wing size, so that the wing/body ratio increased approximately 2.5-fold. This change in proportions is of the same magnitude as seen in many exaggerated traits in insects (e.g., Fig. 1). No studies have yet been done on the amount of genetic variation and the pattern of genetic correlations among the parameters for growth of wings and body. Such studies would prove the means to correctly parametrize our selection model and allow for direct comparison to the response to artificial selection on wing-body scaling.
Conclusions
The evolution of novelty can come about by exaggerated change in the size or shape of a pre-existing structure, as has occurred in many insects (Fig. 1). Such novelty involves changes in growth patterns and leads to novel allometric relationship among body parts. Experimental studies have demonstrated that there is genetic variation for allometries and that scaling relationships can evolve under artificial selection. The evolution of allometry must occur through the evolution of the underlying mechanisms that control the growth and sizes of different body parts. Thus to understand the mechanistic basis of the evolution of allometry it is necessary to have an accurate model of growth and a model of how the parameters of growth affect the allometry. Growth of most body parts is sigmoidal, often following Gompertz kinetics. An allometric equation derived from realistic sigmoidal growth patterns of a body and its parts can be used to accurately deduce the non-linear growth kinetics of the two parts. The equation can be used to describe both ontogenetic and static allometry, depending on which of the parameters are fixed and which are used as variables. Not all parameters of the allometry model are equally correlated with the phenotype, and selection on allometry selectively alters those parameters with the highest correlation. The correlations of parameters with the allometry are a systems property that depends on the values of all the parameters in the system, and the amount of variation in each parameter. The non-linear allometry equation can be used as a platform for studying the evolution of complex allometries and the evolution of the underlying growth patterns that give rise to the allometry.
Acknowledgments
We are grateful to Rick Gawne, Jameson Clarke, Emily Laub, and Laura Grunert for many helpful comments during the course of this study and for comments on the manuscript. Supported by grants IOS-0744952, EF-1038593, IOS-1562701, and IOS-1557341 from the National Science Foundation.
References
Author notes
From the symposium “Physical and Genetic Mechanisms for Evolutionary Novelty” presented at the annual meeting of the Society for Integrative and Comparative Biology, January 4–8, 2017 at New Orleans, Louisiana.