We calculated maxillary KT from 86 Lake Malawi cichlid species (169 individual fishes) sampled in July 2005 or borrowed from the American Museum of Natural History. Malawi species exhibit a wide spread of KT values (range for individuals, 0.41 – 1.57; Figure 2; [see Additional file 1 for species averages]) comparable to that observed in other fish lineages 3435. The bulk of the specimens had KT values between 0.61 – 0.80 (avg. = 0.77; sd. = 0.16), corresponding to putatively intermediate jaw speeds and force potentials. Planktivores, on average, exhibited higher maxillary KT than other trophic groups [see Additional file 2]. The input (lower jaw, r = 0.473; p < 0.0005) and output (maxilla, r = -0.379; p < 0.0005) links were significantly and antagonistically correlated with KT across the data set (Table 1).

We next asked whether correlations among links and KT were robust to the pattern of Malawi cichlid evolutionary history. It has been known for some time that trait correlations should be corrected for phylogeny because related individuals do not represent independent statistical samples 36. This is a particularly important and difficult problem in the Malawi cichlid assemblage where species are young (e.g., 1000 years, 29) and phylogenetic resolution is limited 3037. Table 1 (above the diagonal) shows evolutionarily independent correlations calculated using the phylogenetic topology shown in Additional file 3, employing an approach described in Hulsey et al. 30. We use a single mitochondrial genealogy because the locus offers more resolution than nuclear genes in this rapidly evolving lineage 3037. The corrected correlations are similar to the uncorrected in all but one case. The lower jaw link, positively associated with KT using uncorrected data, is not associated with KT across the Malawi phylogeny. Further inspection of the data suggests that this is due to lack of power to detect a phylogenetic association (i.e., lack of divergent independent contrasts) as most rock-dwelling mbuna have relatively short lower jaws compared to most non-mbuna taxa.

Given this caveat, our empirical data support results from simulation in other studies 2526: longer lower jaws on average yield higher values of KT while longer maxillae produce the opposite (see also Figure 1). Notably, lower jaw and maxillary links were positively correlated with one another in our data set (corrected r² = 0.44; p < 0.0005; Table 1). Moreover, a simple ratio of LJ/Max lengths was a near perfect predictor of the fully parameterized calculation of KT (Figure 3; r² = 0.94; p < 0.0005). Our data point to an appreciable linear component to variation in this 4-bar linkage system noted for its non-linear evolutionary dynamics 2526.

Comparison of species' trait values (corrected for body size) identified numerous cases of convergence in KT via divergence in link length, or MTOM of form to function 25. The correlations noted above help to explain this observation. For example, both Cynotilapia afra and Pseudotropheus elongatus have KT values of approximately 0.7, but they exhibit distinct morphologies. Cynotilapia afra has relatively long input and output links, while P. elongatus has relatively short elements of each. We reasoned that hybridization between species like these that are MTOM for function might produce F₂ hybrids with extreme KT values, if independent assortment recombines the long lower jaw of C. afra with the short maxilla of P. elongatus (high KT) or the long maxilla of C. afra with the short lower jaw of P. elongatus (low KT). We tested the generality of this prediction using a simple, but realistic genetic model.

Our Mendelian genetic model assumes no evolution and no environmental variance (V_E = 0). We specified that size-standardized lengths of each of the four linkage components (Figure 1) were controlled by 4 independent loci (2 alleles at each locus). Links themselves were modeled to be genetically independent of one another. The effect of each allele was assumed to be equal and additive. Importantly, the assumptions of (i) number of loci per link, (ii) genetic independence of links and (iii) additivity of allelic affects are supported by empirical quantitative genetic data for the cichlid craniofacial skeleton 22. For example, even though the lower jaw and maxilla links are positively (phenotypically) correlated in our data set, this is unlikely to be due to genetic linkage; QTL for the shape of these elements map to distinct chromosomal regions. We used this model to (a) determine if MTOM species would produce hybrids transgressive for function, (b) estimate the percentage of F₂ progeny exhibiting transgression from specific Lake Malawi cichlid intercrosses, and (c) investigate the genetic contribution of each link to the phenomenon of functional transgression.

We assumed that each F₀ parent was homozygous at every locus; since every allele had additive and equal effects, no transgression was produced in the physical lengths of 4-bar links. By contrast, transgression in 4-bar function (KT) was found in 80% of simulated crosses (16/20, Table 2) in which we calculated KT for each and every of 6,561 composite F₂ genotypes. Note that we have employed a modified and conservative definition of transgression, specific to the distribution of KT produced by the model; an individual is 'transgressive' if its KT value lies ± 1 standard deviation (or more) from the mean. The frequency of transgressive individuals, per cross, ranged from 0.1 – 34%, with up to 6% of the KT values lying two (or more) standard deviations beyond the mean for some (e.g., C. afra × P. elongatus; Figure 4).

We used bubble plots to examine the genetic limits to transgression in each of the simulated crosses and the distribution of those limits among the four link lengths (Figure 5). These plots show the frequency of parental (F₀) alleles for each link in F₂ hybrids exhibiting transgressive KT, where hybrid KT is lower (A, C) or higher (B, D) than parental values. For example, in the cross between Cynotilapia afra and Pseudotropheus elongatus, transgressive KT lower than parental values (Figure 5A) is possible with nearly any combination of alleles for the nasal and fixed links. By constrast, transgression is observed in individuals with certain genotypic combinations of lower jaw (more P. elongatus alleles) and maxillary links (more C. afra alleles). Bubble plots for the cross between Protomelas fenestratus and P. ornatus are similar (i.e., negligible influence of nasal and fixed links, importance of lower jaw and maxillary links). These plots can be explained by the starting morphology of the parents (F₀) and the noted relationship (from simulation and our empirical data above) between the input link (lower jaw), output link (maxilla) and KT. Both Pseudotropheus elongatus and Protomelas fenestratus have short maxillae and short lower jaws; Cynotilapia afra and Protomelas ornatus possess long elements of each. Recombination and independent assortment of alleles controlling lower jaw and maxillary links produce functional transgression in KT, according to this model.

Our choice of the 20 crosses to analyze presents a biased estimate of the proportion of crosses that would yield TS. However, because of the computation involved, a full analysis of all possible crosses in our data set is prohibitive. To overcome this, we realized that the simple ratio of lower jaw length to maxilla length is a strong predictor of KT from the fully parameterized calculation (Figure 3). We also realized, from the detailed analysis of the genetic model above, that transgression is usually produced by recombination between loci specifying the lengths of the lower jaw and maxilla. Combining these ideas, we devised a test to ask whether all pairwise crosses between any two of the 86 species in our data set would produce F₂ hybrids transgressive for KT. We generated a matrix encompassing all possible pair-wise combinations of size-adjusted lower jaw and maxilla lengths from all species in the data set. Roughly a third of these combinations (29%) produced transgression in KT value. We next used these data to ask whether the occurrence of transgression in F₂ could be predicted by the degree to which parents (F₀) are MTOM. As a proxy for MTOM, we used a simple metric of KT distance between the parents of any cross. Formally, if MTOM contributes to hybrid transgression in KT, we expect crosses that produce transgressive hybrids to be between parental species with smaller differences in starting KT. This is in fact what we observed (Figure 6; t-test, p < 0.001).

The genomic era has changed the way that evolutionary biologists think about hybridization. Gene flow among recently diverged species (or those evolved through pre-mating barriers) is common rather than the exception 131529. Hybridization may provide an important source of genetic variation in the form of new trait combinations 10 that sometimes help hybrid organisms maneuver across fitness landscapes 14. The phenomenon of TS, wherein hybrids outperform the parents, is a frequent observation in laboratory and natural outcrossings 18.

It has been suggested that strong directional selection and simple genetic architecture should limit TS because they point the phenotypic effects of QTL in the same direction; this would essentially constrain diversification by hybridization 21. Our analysis shows how MTOM promotes TS in function, without transgressive morphology, via recombination and independent assortment. Because multiple morphological solutions exist for any function (i.e., value of KT), MTOM may buffer those constraints, imposed by directional selection, on the extent of mechanical diversity produced by hybridization. As the craniofacial skeleton evolves, functional demands of numerous mechanical systems shape the lengths and linkages of bony elements 28. MTOM of form to function in each of these systems might facilitate, or perhaps even require, the evolution of diversity.

Cichlid specimens were collected during July 2005 from various sites in southern Lake Malawi. Fishes were labeled with a unique identifier and fixed in 10% buffered formalin solution. Upon returning to the U.S., carcasses were transferred to 70% ethanol for storage. Additional specimens were borrowed from the American Museum of Natural History (AMNH) to supplement the collection. Up to three individuals of each species (depending on the number available) were cleared with trypsin and double-stained using alcian-blue (cartilage) and alizarin-red (bone). This method allows clear visualization of the skeletal components while maintaining skull articulations 27. Cleared and stained fish were transferred to glycerin for storage.

We measured the anterior jaw 4-bar linkage model as described 263839. The four physical units of the linkage were quantified on 169 specimens of 86 Lake Malawi cichlid species. Up to three individuals were measured for each species using dial calipers (nearest 0.1 mm) to quantify each link (Figure 1). The four links (lower jaw or input, maxilla or output, nasal or coupler, and fixed or suspensorium) are described in detail, with their respective measurement landmarks, by Hulsey and Wainwright 26. The linkage measurements were used to calculate the kinematic transmission (KT) of each jaw 27. Anterior jaw KT is used as an estimate of the speed of motion transmitted through the 4-bar linkage, and in addition, the measurement of KT simultaneously describes the force transmission (FT) through the 4-bar as the reciprocal of KT 26. The method of KT calculation followed that of Hulsey and Garcia de León 27 and was accomplished using an iterative function in Microsoft Excel^® with a starting angle of 15° and an input angle of 30°.

Correlations were calculated between each of the 4-bar links and KT to examine the relationship therein. Because the structural components of the anterior jaw are highly correlated with body size [26, NFP unpublished] each 4-bar link was corrected for fish standard length (SL) prior to correlation. We used the residuals of linear regression of link length to SL. Felsenstein 36 has shown that correlations may not be statistically independent when compared across taxa with common evolutionary history. Therefore, we calculated phylogenetically independent contrasts following an approach outlined in Hulsey et al. 30. We constructed a phylogeny of 52 Lake Malawi species using sequences from the mitochondrial ND2 gene [see Additional file 1, Additional file 3]. All species were collected from the wild in Lake Malawi from various locations. DNA extractions, PCR parameters, and sequencing followed previously published protocols 30.

The ND2 gene was transformed into its three codon partitions. ModelTest 3.06 40 was used to identify the most likely model of molecular evolution for each codon partition. Standard Bayesian analyses were executed to find the maximum log-likelihood topology using MrBayes 3.0 41. Independent contrast analyses were performed using CAIC 42 in order to assess correlations among the SL-corrected residuals of the four link lengths and among those values and KT. We employed the highest log-likelihood tree from the above Bayesian search to correct for phylogeny [Additional file 3].

Several approaches can be taken to model the generation of novelty in jaw structures and for this project we chose a simple genetic model. Previous studies have examined how 4-bar function changes with different structural configurations, as well as how the 4-bar can evolve based on selection for different KT 25264344. Also, Albertson and Kocher 21 have examined the phenotypic distribution of one interspecific Lake Malawi cross in terms of cranial and jaw morphology. For this paper we wanted a model that would not only describe the distribution of genotypes and phenotypes for specific intercrosses, but also allow the incorporation of empirical data from the Lake Malawi system.

We constructed a simple but realistic individual-based Mendelian genetic model, which incorporated assumptions of no mutation, no selection, and no error. We assumed that the size-standardized (below) length of each of the four anterior jaw links was controlled by 4 independent loci with 2 alleles at each locus, for a total of 8 alleles per link. Links themselves were modeled to be genetically independent of one another. The effect of each allele was assumed to be equal and additive, and therefore each of the four lengths (lower jaw, maxilla, nasal, fixed) for each parental (or F₀) specimen was divided by 8. Note that the assumptions of (i) number of loci per link, (ii) independence of links and (iii) additivity of allelic affects are supported by empirical quantitative genetic data for the cichlid craniofacial skeleton 22. We controlled for differences in body size among species in the model by dividing each parental link length by SL. In this way, the heritable unit of link length can be thought of as the proportion of SL made up by each link. We also ran models using residuals from linear regression of link length on SL as input variables, and this did not change the outcome.

Using this rubric, each allele inherited from a parent would impart 1/8^th of the total length of that link to the offspring. Parents were assumed to be homozygous at all loci. The initial cross among F₀ produced F₁ progeny with identical 4-bar lengths (and KT values) equal to the average of the two parents. A second cross within the F₁ progeny produced all potential parental and recombinant genotypes in the F₂ generation (6,561 possible). Hybrid link lengths were calculated by the summation of all allelic contributions totaled over the four loci per link. Thus, each composite F₂ genotype was assigned a 4-link phenotype, and KT was calculated for all. Some recombinant link lengths did not support a functional jaw linkage in some crosses. This result was taken to represent potentially unfit hybrid individuals within a cross and these individuals were left out of further analyses; this effect has been noted in prior simulation 26. Frequency distributions of F₂ progeny were created (MS Excel^® and SigmaPlot^® 8.0) to compare hybrid KT values to parental KT. Bubble plots were generated (SigmaPlot^® 8.0) to examine the contribution of parental alleles to link length in F₂ exhibiting transgressive KT. A total of 20 interspecific crosses were simulated with this model and F₂ KT values were examined for evidence of transgression. Species were chosen for these 20 iterations (i) if there is a report of hybridization between them in nature, (ii) if laboratory hybrids have been made, or (iii) if we were particularly interested in the cross from inspection of parental morphometrics.

These 20 simulated crosses present a biased look at the possibility of transgressive function in Lake Malawi cichlid hybrids. The calculations are iterative and time consuming. We wanted an unbiased means to ask if a hybrid cross between any two species would produce F₂ with transgressive KT. To accomplish this, we made use of the tight relationship between the fully parameterized model of KT and the simpler ratio of input to output links (Figure 3) and the relationship between input link, output link and KT observed in our data (see Results) and from previous simulation 2526. We generated a 86 × 86 species matrix containing all possible combinations of size-adjusted lower jaw and maxilla lengths from all species in the data set (7,310 combinations). We essentially asked if recombining the maxilla from one species with the lower jaw from the other (and vice versa) would produce hybrid linkages transgressive in KT. We carried out this operation for all pairs of species in the data set.