Tandem Duplicate Genes in Maize Are Abundant and Date to Two Distinct Periods of Time

Tandem duplicate genes are proximally duplicated and as such occur in similar genomic neighborhoods. Using the maize B73 and PH207 de novo genome assemblies, we identified thousands of tandem gene duplicates that account for ∼10% of the annotated genes. These tandem duplicates have a bimodal distribution of ages, which coincide with ancient allopolyploidization and more recent domestication. Tandem duplicates are smaller on average and have a higher probability of containing LTR elements than other genes, suggesting origins in nonhomologous recombination. Within relatively recent tandem duplicate genes, ∼26% appear to be undergoing degeneration or divergence in function from the ancestral copy. Our results show that tandem duplicates are abundant in maize, arose in bursts throughout maize evolutionary history under multiple potential mechanisms, and may provide a substrate for novel phenotypic variation.

maize tandem duplicate genome evolution copy number variation transposable element Gene duplications provide a mechanism through which functional novelty may arise. Many protein-coding genes in eukaryotes are part of large families of genes with related function and are consistent with origins in gene duplication (Rubin 2000). The pattern of duplicate gene distribution across the genome can have important consequences for the evolutionary fate of duplicate genes. For example, genes that are duplicated in tandem (proximal in the genome) are in the same genomic neighborhoods and potentially have shared regulatory elements, and thus may diverge differently than dispersed duplicates. The initial impact of gene duplication on phenotypes likely occurs via gene dosage effects. In many cases, the sudden change of gene product concentration has deleterious effects on the physiology of the organism and will be selected against (Innan and Kondrashov 2010). In some cases, however, the increased gene expression may be beneficial, and there will be selection to maintain the duplication (e.g., tandem duplications conferring soybean cyst nematode resistance at Rhg1 (Cook et al. 2012)). Tandem duplicates can segregate within a species due to either spontaneous birth of a duplicate within an individual in the species or loss of a progenitor duplicate copy in some individuals within the species. Either of these fates can lead to phenotypic variation within the species.
Over evolutionary time, the fate of tandem duplicate genes is less straightforward than simply either retention or purging. Mutations in the regulatory regions or mutations in the coding sequence, may cause the duplicates to be expressed in different tissues or may engender nonredundant functional roles (Flagel and Wendel 2009). These random mutations that accumulate among duplicate copies of a gene may slowly erode their functions. One general outcome of this process is called subfunctionalization, where each copy is retained, but each may perform a subset of the functions of the ancestral copy (Force et al., 1999). Several models such as the "duplication-degeneration-complementation" model or the "escape from adaptive conflict" model have been used to describe these scenarios as possible subfunctionalization outcomes for tandem duplicates (Innan and Kondrashov 2010).
Many studies of tandem duplicates have focused on specific gene families, such as resistance gene clusters and ribosomal gene clusters (Hill et al. 1977;Anderson and Roth 1981;Leister 2004). In addition, a number of classical tandem duplicates have been identified in mapping studies, owing to a large phenotypic impact. For example, the R locus in maize was determined to be tandem duplicated genes by crossing and observation of recombination frequency (Dooner and Kermicle 1971). Other examples of classical tandem duplicates that have been discovered in maize and contribute to phenotypic variation include the White Cap locus (Tan et al. 2017), the anthocyaninless1 locus (Laughnan 1952), and the P locus (Athma and Peterson 1991) which all influence grain color, the MATE1 locus that contributes to aluminum tolerance (Maron et al. 2013), and the Tunicate1 locus that results in the characteristic phenotype of pod corn in which the glum covers the kernel (Han et al. 2012;Wingen et al. 2012).
Identification of tandem duplicates through phenotypic analysis can bias the understanding of genome-wide rates, evolutionary impacts, and potential phenotypic impacts of tandem duplicates within the genome. In contrast, "bottom-up" approaches can identify duplicates in a way that does not condition on the duplicate visibly altering a phenotype. On a genome-wide basis, tandem duplicates may be identified from sequence similarity in long reads (Dong et al. 2016), optical maps (Mak et al. 2016), or by orthologous searches of all genes within an assembled reference genome (Cannon et al. 2004). Alternatively, de novo assemblies of multiple individuals within a same species would provide an ideal setting for high-resolution identification and analysis of variance for tandem duplicates within a species. There are few plant species with multiple de novo genome assemblies, and as such, genome-wide studies of tandem duplicate gene variation across multiple individuals within a species have been limited to date in plants.
While a number of tandem duplicates have been deeply characterized for their phenotypic effect and there are descriptive studies on tandem duplicate identification in plant species, there still remain a number of important questions surrounding the role of tandem gene duplication in genome evolution. Here we use the genomic resources available in maize including multiple annotated whole genome de novo assemblies to determine the rate of tandem gene duplication on a genome-wide scale and the extent to which these tandem duplicates are shared among individuals within the species. A number of previous studies have shown pervasive copy number variation within maize (Springer et al. 2009;Chia et al. 2012), but the nature of the methods used in these studies resulted in ambiguity as to if these copy number variants resulting from tandem duplication or duplicate copies dispersed throughout the genome.
Additionally, we seek to test the following hypothesis regarding tandem duplicates on a genome-wide scale. We hypothesize that tandem duplicates will arise largely during periods of genome instability, for example following the allopolyploid event in the history of the maize lineage (Cannon et al. 2004). We hypothesize that tandem duplicates will have unique genomic features relative to genes that do not have tandem duplicates, such as gene size and exon number. The nature of these unique features can provide some mechanistic insights into the origin of tandem duplicates. Finally, we hypothesize that tandem duplicates will show different substitution rates relative to other maize genes based on the relaxed purifying selection that can lead to subfunctionalization and neofunctionalization.

Tandem Duplicate Identification
Putative tandem duplicate clusters were identified by comparing the B73 version 4 (Jiao et al. 2017) and PH207 version 1 (Hirsch et al. 2016) maize genome assemblies each to the Sorghum bicolor v3.1 genome assembly (DOE-JGI, http://phytozome.jgi.doe.gov/) with SynMap v2 (Lyons et al. 2008) as described in (Brohammer et al. 2018). Up to 15 intervening genes were allowed between potential tandem duplicates. To remove any false positive assignments from SynMap and identify any false negative assignments, the longest transcripts from adjacent maize genes were translated to amino acids, aligned (10 interactions of refinement) with Clustal-omega (Sievers et al. 2011), and back-translated to nucleotides. Pairwise similarity was calculated with the "compute" program from the "analysis" package (Thornton 2003). The alignment similarity was downweighted for the proportion of alignment gaps by calculating the similarity in aligned regions multiplied by the proportion of the total alignment that was not gapped. Pairwise similarity was down-weighted to account for the pairwise similarity metrics being undefined in gapped regions; two genes may have high similarity in a short conserved region, but un-alignable sequence for most of their other sequence. A distribution of adjusted pairwise similarities for adjacent genes in the B73 and PH207 assemblies is shown in Figure S1. Adjacent genes with at least 0.3 adjusted pairwise similarity and genes within SynMap tandem duplicate clusters with at least 0.3 adjusted pairwise similarity were retained for analysis.

Tandem Duplicate Gene Cassette Identification
We defined tandem duplicate cassette as a group of at least two interleaved tandem duplicate clusters. Tandem duplicate cassettes were identified by comparing annotated gene coordinates among individual tandem duplicate clusters. A schematic of the procedure for identifying cassette duplications is shown in Figure S2. Genes within each tandem duplicate cluster were sorted from lowest coordinate to highest coordinate. Tandem duplicate clusters on the same chromosome were sorted by the start coordinate of the first gene. Tandem duplicate clusters that overlapped each other were identified. Clusters that were fully nested within another cluster were not considered as cassettes. Tandem duplicate clusters that were interleaved within each other were retained as putative cassette duplications ( Figure S2).

General Linear Model Analysis of Factors Explaining
Tandem Duplicate Gene Density A general linear model was fit to explain variation in tandem duplicate gene density using various genomic characteristics with the R version 3.4.1 computing environment (Team 2017). The model regressed tandem duplicate gene density against all annotated gene density, RNA transposable element density, DNA transposable element density, and subgenome assignment: where g is gene density, r is RNA TE density, d is DNA TE density, and s is subgenome assignment. Assessment of model fit was done by examining the variance explained and the deviance for each explanatory variable. Significance of a variable in the model was tested with analysis of variance (ANOVA) of nested models.
All density calculations were performed in 1Mb windows across the genome. Density was defined as the proportion of bases in each window that are within a feature of a given type. Gene and transposable element annotations were obtained from Gramene (ftp://ftp.gramene.org/pub/ gramene/release-57/gff3/zea_mays/repeat_annotation/B73v4.TE.filtered. gff3.gz). Subgenome assignments were from previously reported syntenic block assignments (Brohammer et al. 2018). Windows were classified into "maize1," "maize2," or "nonsyntenic" based on majority assignment. Because annotated gene density is correlated with subgenome assignment (Schnable et al. 2012), we tested models with and without an interaction between subgenome and gene density. Models with an interaction between subgenome and gene density did not significantly improve model fit (ANOVA of nested models, P . 0.2).

Duplication Date Estimation
The dates of tandem duplications were estimated with BEAST version 2.4.7 (Bouckaert et al. 2014). Amino acid alignments of the subgenome homeologues, tandem duplicates, and putative Sorghum ancestral genes that were previously determined (Brohammer et al. 2018) were generated with Clustal-omega version 1.2.1 (Sievers et al. 2011). The alignments were back-translated to nucleotides. Each gene alignment was analyzed with BEAST with the following parameters: a GTR+Gamma nucleotide substitution model, estimated transition probabilities and equilibrium base frequencies, a random local clock to allow for branchspecific rate variation, and a monophyletic divergence between the maize subgenomes with a prior of N(11.9, 1) on the divergence date (Swigonová et al. 2004). The MCMC was run for 10,000,000 steps.
Resulting trees from the BEAST analysis were parsed to obtain the time to most recent common ancestor (TMRCA) between tandem duplicate genes. Homologous genes between B73 and PH207 that share a duplication state were counted as a single duplication event. Gene duplications likely do not follow the infinite sites mutational model (Kimura 1969;Ohno 1970), and identity by state does not necessarily imply identity by descent. This analysis assumed that tandem duplicates are evolving along truly separate trajectories, and that gene conversion among tandem duplicates is negligible.

Relative Rates Calculations
Relative rates of sequence evolution of maize tandem duplicates were compared with other grass genes by performing Clade model C (CMC) tests (Weadick and Chang 2012) in PAML v4.9e (Yang 2007) on tandem duplicates in orthologous gene groups. CMC tests compare dN/dS ratios among a subset of the branches in a gene tree ("foreground") to the dN/dS ratios on the rest of the tree ("background"). Similar to the BEAST analysis described in the previous section, CMC tests assume that the genes in the tree are independent and non-recombining.
To build alignments and gene trees for each tandem duplicate cluster, orthologous gene groups were identified among publicly available grass genomes from Phytozome V12 and Ensembl Plants V34 using OrthoFinder v1.14 (Emms and Kelly 2015). The species, sources, and versions of the genomes used as OrthoFinder input are shown in Table S1. OrthoFinder was run with the "dendroblast" ortholog search method, and default parameters for MCL clustering. Amino acid sequences from B73 and PH207 were kept in separate files to allow them to be compared to each other as well as to other grasses. Only orthologous gene groups between 10 and 75 genes were retained for analysis because larger orthologous groups are likely to be gene families that have already diverged in function, and smaller groups do not have enough branches to test relative rates. A distribution of orthologous gene group sizes is shown in Figure S3. Orthologous gene groups that contained between 10 and 75 genes, contained maize tandem duplicates, and contained complete tandem duplicate clusters (i.e., tandem duplicate clusters that were not split among multiple orthologous groups) were retained for downstream analysis.
Within each of the orthologous groups that passed the above filtering criteria, the amino acid sequences were aligned with clustal-omega and then back-translated to nucleotides using the CDS sequences provided with the genome assemblies. Alignments were filtered to contain only sites with at most 50% gaps (at least eight species) across all sequences, because gaps greatly increase computation time and are not informative for calculating substitution rates. While it is possible that we are excluding a set of rapidly evolving sites with this filter, models of evolution under selective constraint do not yet incorporate insertion and deletion events, and alignments are likely to be misleading in these regions. Maximum likelihood trees were estimated from the filtered alignments with RAxML, using the default rapid hill-climbing search algorithm and a GTR+Gamma nucleotide substitution model.
Four models were fit to the filtered alignments and trees with the 'codeml' program in PAML ( Figure S4). We tested whether certain foreground branches of the tree exhibited significantly divergent evolutionary rates relative to the remainder of the tree. Model 1 marks all genes as evolving at the same rate (null model) (Weadick and Chang 2012). Model 2 marks maize genes (including tandem duplicates) and common ancestors of maize genes as foreground and other grass genes as background. Model 3 marks maize tandem duplicates and common ancestors of maize tandem duplicates as different from all other genes. Model 4 distinguishes maize tandem duplicates and common ancestors of maize tandem duplicates from maize genes ( Figure S4). The bestfitting model for each orthologous group was identified via a likelihood ratio test against the null model. In orthologous groups where maize genes were evolving at a different rate than tandem duplicate genes (models 3 and 4), omega was compared between tandem and nontandem maize genes to determine relative constraint. If omega in tandem duplicates was higher than non-tandem duplicates, the tandem duplicate was classified as under weaker constraint, and if it was lower than the non-tandem duplicate it was classified as under stronger constraint. If omega was larger than 10 no test was done as dS was considered too small to test.
We also applied the Hudson-Kreitman-Aguadé (HKA test; Hudson et al. 1987) to test whether tandem duplicates are evolving at different rates from non-tandem duplicates, as implemented in the MLHKA program (Wright and Charlesworth 2004). High-quality SNP calls from 62 diverse inbred lines (Brohammer et al., 2018) were used for diversity data. The number of nucleotide differences between the B73 v4 genome assembly and the Sorghum bicolor v. 3.1 genome assembly was used for divergence data. Diversity and divergence values were treated on a gene-by-gene basis. The list of annotated genes was randomly shuffled and separated into 100-gene windows. For each window, we fit two models: one model treated the tandem duplicates as having a different substitution rate than non-tandem duplicates, and the other model treated all genes as having the same substitution rate. Each window was run with 200,000 MCMC steps. Significance was assessed by likelihood ratio tests (LRT) for each window, with the number of tandem duplicate genes as the degrees of freedom for the chi-squared distribution for the LRT test statistic. If the absolute value of the log(likelihood) was higher for the model with tandems under selection, the window was considered to not have enough power to test the relative rates hypothesis.

Data Availability
All supplementary files are available at FigShare. Scripts to perform tandem duplicate identification, sequence alignment and backtranslation, orthologous gene group identification, and relative rates comparisons are available at https://github.com/TomJKono/ Maize_Tandem_Evolution. Sequence alignments will be made available through the corresponding author upon request. Supplemental material available at Figshare: https://doi.org/10.25387/g3.6062972.

RESULTS
Tandem duplicate gene clusters are prevalent in maize genomes To identify tandem duplicate gene clusters (i.e., proximally duplicated groups of genes) we utilized the B73 de novo genome assembly generated with single-molecule technology (Jiao et al. 2017) and the PH207 de novo short-read genome assembly (Hirsch et al. 2016). The singlemolecule technology used for the B73 genome assembly provides a high confidence assembly for evaluating tandem duplicate clusters. The PH207 genome assembly was generated with permissive parameters to avoid collapsing tandem duplicate gene clusters (Hirsch et al. 2016). However, by the nature of a short read assembly, the PH207 de novo assembly will likely have an underrepresentation of the total tandem duplicate clusters.
Putative tandem duplicates were identified and curated based on a weighted similarity metric that allowed for some interspersed genes. In total, 1,758 tandem duplicate clusters were identified in B73 and 1,467 tandem duplicate clusters were identified in PH207 (Table 1 and Table  S2). The total number of annotated genes in tandem duplicate clusters was 4,448 (11.3% of the total genes) in B73, and 3,788 (9.3% of the total genes) in PH207. As expected, the number of tandem duplicate clusters and the number of genes within tandem duplicate clusters was slightly lower in PH207. The B73 abundances are likely a more accurate representation of the number of tandem duplicate genes within the maize genome.
Similar numbers of shared and private tandem duplicates are observed within species Having access to multiple de novo genome assemblies within maize allowed us to determine the consistency of tandem duplicate gene cluster characteristics within the species. A similar distribution was observed between B73 and PH207 for the number of genes per cluster, and the majority of tandem duplicate genes clusters contained only two genes ( Figure 1A). Within clusters, most genes were directly adjacent with no intervening genes in both B73 and PH207 ( Figure S5), even though intervening genes were permitted during tandem duplicate identification. Intervening genes were permitted to account for mechanisms that would not cause a duplicate to be directly adjacent but in the same genomic neighborhood, to allow for instances in which a gene is inserted after the duplicate event, and for possible misassembly and misannotation of genes. Only 17% of the duplicate gene clusters that were identified had an interval of greater than two intervening genes between members of the cluster. To determine if specific tandem duplicates were shared between the assemblies, we used homology information that linked the B73 and PH207 gene models (Brohammer et al. 2018). Only 50.3% of the B73 tandem duplicate gene clusters and 60% of the PH207 tandem duplicate clusters were shared between the two genomes ( Figure 1B).
Another way that individuals can differ with regards to tandem duplicates is the number of duplicate copies within a shared tandem duplicate cluster. To evaluate differences in tandem duplicate copy number between the two genotypes, we compared the 885 tandem duplicate clusters that were shared between the B73 and PH207 genome assembly. Tandem duplicate genes shared between B73 and PH207 exhibited similar cluster sizes as shown by strong heat along the diagonal in Figure 1C. That is, when homologous genes were part of tandem clusters in B73 and PH207, these clusters often contained similar numbers of genes. However, there was variation in tandem duplicate cluster size with a difference of up to 16 more copies in one of the genotypes compared to the other ( Figure 1C).
Cassette tandem duplication events are rare and often private Tandem gene duplication events can occur as a single gene duplication event or in sets of genes that duplicated as a tandem cluster (i.e., Gene A-1 Gene B-1 followed by Gene A-2 and Gene B-2, see Figure S2). Cassette tandem duplicate gene clusters likely arise from a single event in which a set of genes is duplicated simultaneously. However, it is possible for tandem duplicate cassettes to be generated from multiple duplication events. Candidate tandem duplicate cassettes were identified from interlaced tandem duplicate gene clusters ( Figure S2). Cassette duplications were rare in both of the inbred lines with only 58 and 60 cassette duplications in B73 and PH207, respectively ( Figure 1D). A higher frequency of private cassette tandem duplicates was observed relative to non-cassette tandem duplicates ( Figures 1B and 1D). Only 14 cassettes were shared across genotypes, which equates to approximately one-quarter of the tandem duplicate cluster cassettes in either genome. There was variation for the composition of the cassette between the two genotypes for 10 of the 14 shared cassettes. These differences may be the result of multiple duplication events in one genotype that did not occur in the other, but they are more likely the product of differential loss of a common complete duplication event.
Tandem duplicate clusters are dispersed throughout the genome and correlate with gene density Tandem duplicate genes were identified relatively homogenously throughout the genomes of B73 and PH207 (Figure 2 and Figure S6). A lower density of tandem duplicates was observed around the centromere where the density of genes is generally lower (Schnable et al. 2009). To test what variables most explained the distribution of tandem duplicates in the genome, a general linear model was fit with density of tandem duplicates per 1 Mb window regressed against gene density, RNA TE density, DNA TE density, and subgenome assignment within each window. With regards to subgenome, maize is a paleopolyploid that has returned to a diploid state. Two subgenomes remain in the diploid from the most recent allopolyploid event and have been previously characterized based on the number of retained co-orthologous genes to other grass species including Sorghum and rice (Schnable et al. 2011;Brohammer et al. 2018). A number of differences are present between the subgenomes such as expression level (Schnable et al. 2011).
As expected, gene density explained the most variance in tandem duplicate density per window (t-test of regression coefficient, P , 0.001), and only 1% more variance was explained by a model containing all of these factors than a model with only gene density. When comparing the proportion of bases within a window in the genome vs. the proportion of genic bases in tandem duplicates we do not see any significant relationship (R=-0.037; P = 0.092). This indicates that the high proportion of variation explained by gene density is a product of the fact that there are more genes in these regions to be potentially duplicated rather than there being a mechanistic impact of having higher gene density on creating more or less than expected numbers of tandem duplicates relative to the number of genes in a window. When testing the effects of transposable elements, both class 1 and class 2 transposable element density were significant at the P , 0.05 threshold, and higher transposable element density was associated with higher tandem duplicate density. Maize subgenome 2 had lower tandem duplicate density than subgenome 1 (P , 0.001). On average, 49.5% of tandem duplicate clusters were in subgenome 1 (37.7% genome-wide), 21.6% were in subgenome 2 (24.0% genome-wide), and 28.9% were in non-syntenic regions (38.3% genome-wide) of the genome. This is consistent with the results of the general linear model where subgenome 1 has proportionally more tandem duplicates relative to the number of genes in the subgenome (Table 1).

Extant tandem duplicates date to two distinct periods
Phylogenetic analyses were used to estimate the date of origin of tandem duplicates. For each tandem duplicate cluster, all maize B73 and PH207 homeologs (i.e., subgenome 1 and subgenome 2 copies) and the corresponding Sorghum gene for each of the tandem duplicate clusters were included. Phylogenetic trees were calibrated based on the estimated divergence time of maize and Sorghum at approximately 12 million years ago (Swigonová et al. 2004). Our hypothesis was that tandem duplicate gene clusters that were shared between B73 and PH207 would be older than those that are unique to either one of the genomes. We see examples of tandem duplicates that were shared and date near the divergence time of maize and Sorghum at approximately 11.7 million years ago ( Figure 3A). Additionally, we observe private tandem duplicates that were estimated to have arisen relatively recently ( Figure 3B).
Across all the tandem duplicate gene clusters a bimodal age distribution was observed, with most tandem duplicates either dating to approximately the time of maize and Sorghum divergence or dating quite recently in evolutionary time ( Figure 3C). Consistent with our hypothesis, tandem duplicate gene clusters that were shared between the two genomes were mostly inferred to be ancient for both subgenome 1 and subgenome 2 gene clusters. Private syntenic duplicates had both ancient and recent inferred ages. Of the 1,044 private clusters, 628 had an estimated date in the ancient peak and likely represent a gene loss event in one genotype and not the other. A comparable number of non-syntenic tandem duplicate gene clusters arose during both of the bimodal age peaks, similar to what was observed for private syntenic tandem duplicate gene clusters.
One explanation for the large proportion of inferred recent duplications is the action of gene conversion. Gene conversion would cause tandem duplicate genes to have higher sequence similarity than nonrecombining duplicates of the same age, and thus would bias estimates toward recent events. Gene conversion is often associated with increased GC content due to GC-biased gene conversion (Pessia et al. 2012). Indeed, tandem duplicate genes showed a higher GC content on average than the GC content that was observed for all maize genes whether in the syntenic or non-syntenic portion of the genome ( Figure 4A). If GC biased gene conversion were contributing to the recent date estimates of tandem duplicates (less than 2 million years ago), we would expected recent tandem duplicates to have higher GC content than ancient tandem duplicates. However, the opposite was observed. Tandem duplicates that were inferred to be ancient had consistently higher GC content, and those that were inferred to be recent exhibited a high proportion of low GC content genes ( Figure 4B). Thus, GC-biased gene conversion was likely not artificially deflating age estimates between duplicates to a substantial degree. However, this is based on using GC content as a proxy for biased gene conversion, and we are not estimating the rate of gene conversion among tandem duplicates. Tandem duplicated genes are shorter and more likely to contain LTR transposable elements One possible mechanism through which tandem duplicates could arise is through transposable elements. Some TIR elements are enriched for local movement and could contribute to tandem duplication of entire genes that are captured and moved locally. In contrast, LTR elements do not typically move locally, but may also generate tandem duplicates. The mechanism of LTR movement is expected to generate single-exon tandem duplicate genes upon local transposition. In both B73 and PH207, a higher proportion of single exon genes in tandem duplicate gene clusters than was observed genome-wide in non-tandem duplicates ( Figure 5A, 5B). Instances in which a tandem duplicate cluster comprised a gene with multiple exons and its tandem duplicate contained only a single exon would further support the mechanism that the gene was duplicated through an RNA intermediate. Of the clusters that had a single exon gene (24% of total clusters), only one-third in B73 and twothirds in PH207 also had a gene with multiple exons. However, 835 (B73) and 815 (PH207) clusters had multiple exons in both genes in the tandem duplicate gene cluster. These results indicate that while some tandem duplicate genes may have arisen through an RNA intermediate, this was not the predominant mechanism.
Another explanation for having a higher than expected proportion of single exon genes in tandem duplicate gene clusters is that these genes were generally shorter and therefore easier to duplicate. For both single exon genes as well as genes with multiple exons in both B73 and PH207, genes that were in tandem duplicate gene clusters were shorter than the genome-wide distribution of gene sizes for single and multi exon gene models based on full gene model length ( Figure 5C).
In addition to physically copying genes, transposable elements can also contribute to generating tandem duplicate gene clusters by providing microhomology for nonhomologous recombination. We investigated the relative proximity of tandem duplicate gene clusters to LTR, LINE, SINE, and TIR elements and found no difference in distance to nearest transposable element for tandem duplicate genes vs. the genome-wide distribution of non-tandem duplicate genes ( Figure  S7). However, there was a substantial enrichment of LTRs inserted into tandem duplicate genes (20.0% of tandem duplicates contained LTRs vs. 8.2% of non-tandem duplicates) and a de-enrichment of tandem duplicate genes that were captured (the entire genic sequence being nested within an element) by LTRs relative to the rate in non-tandem duplicates (2.6% of tandem duplicates vs. 4.6% of non-tandem duplicates; Table 2).
Recent tandem duplicates evolve at different rates than other maize genes We were interested in examining the relative substitution rates of recent tandem duplicates to infer potential evolutionary trajectories of newly arisen tandem duplications. Substitution rates of recent tandem duplicate genes present in syntenic regions were compared to non-tandem duplicate maize genes and grass orthologs with clade models in PAML (Yang 2007;Weadick and Chang 2012). Only duplications that were private to a subgenome and private to either B73 or PH207 were analyzed, as a proxy for recent gene duplication events. A total of 120 grass orthologous groups with maize tandem duplicates met our filtering criteria (see Methods). Four competing models were tested that included testing 1) evolutionary rates of grass genes equal maize genes and equal tandem duplicate genes, 2) evolutionary rates of grass genes do not equal maize genes but equal tandem duplicate genes, 3) evolutionary rates of grass genes equal maize genes but do not equal tandem duplicate genes, and 4) evolutionary rates of grass genes do not equal maize genes and do not equal tandem duplicate genes ( Figure S4). The majority (74.2%) of the tandem duplications did not show evidence of evolving at a different rate from their grass orthologs (models 1 and 2). Of the 31 (25.8%) tandem duplicate clusters that have evolved at a different rate than the remainder of the tree (models 3 and 4), 10 tandem duplicates showed lower dN/dS than the remainder of the tree, seven showed higher dN/dS than non tandem duplicates, and 14 did not have enough dS to compare substitution rates ( Figure S4). To validate these results we also applied the Hudson-Kreitman-Aguade (HKA) test, which tests for independence of nucleotide diversity from divergence from the outgroup. The majority of genes (94%) did not have sufficient power to test for selection. Of those that could be tested, approximately 13% of tandem duplicates showed evidence of evolving at a different rate than non-tandem duplicates. From the HKA test there are less tandem duplicates showing evidence of evolving at a different rate than non-tandem duplicates. However, only a small portion of tandem duplicates could be tested. Additionally, the HKA test makes a number of assumptions about demographic history that are violated for tandem duplicates. It should also be noted that both of these tests are tests of coding sequences and do not assay the noncoding sequences which could alter gene functionality. Additionally, specific gene conversion events could potentially alter dN and/or dS which could impact omega estimates in the PAML analysis.

DISCUSSION
Tandem duplicate gene studies in plants have primarily focused on single loci and questions about evolutionary mechanism and functional impacts on a genome-wide scale have been limited by available genomic resources. Maize offers a unique opportunity to address questions regarding tandem duplicate origin and evolution given its large, highly repetitive genome and the availability of multiple high quality and wellannotated de novo genome assemblies. Using these resources, we showed that tandem duplicate gene clusters are prevalent in maize, and there is variation within maize lines for tandem duplicate content in the genome. While tandem duplicate clusters are dispersed in genome space, standing variation in tandem duplicates date to two distinct times. A variety of features in the genome were evaluated for association with tandem duplicates, and gene density was the most informative factor for explaining variation in tandem duplicate location across the genome. Tandem duplicate genes are shorter than non-tandem duplicate genes and are more likely to contain LTR transposable elements, which may speak to their origin. For a subset of the tandem duplicates that could be tested, approximately one-quarter were evolving at different rates than other maize genes. These duplicates, along with others that are likely evolving in regulatory control, have potential to generate new functional variation.
While tandem duplicate gene clusters are abundant and generally dispersed throughout the genome at a density similar to the genomewide gene density, we observed some bias in the location of tandem duplicate gene clusters. Specifically, maize subgenome 2 has proportionally fewer tandem duplicates than either subgenome 1 or nonsyntenic regions, accounting for their relative gene densities. There are several explanations for this. One is that duplications may not arise in maize subgenome 2 as readily as other genomic regions. This is unlikely, however, because the patterns of transposable elements and recombination dynamics of subgenome 2 are similar to subgenome 1 (Schnable et al. 2011). Additionally, subgenome 2 is under weaker purifying selection than subgenome 1 (Schnable et al. 2011), meaning that gene duplications should be more prevalent in subgenome 2 but this was not observed. Another explanation is that genes in subgenome 2 "degenerate" more rapidly than in subgenome 1, and that genes that are truly tandem duplicates are too divergent at the sequence level at this point in time to be identified as duplicates by our methods. It has also been shown that subgenome 2 has a higher ongoing deletion rate than subgenome 1 (Schnable et al. 2011), and as such may have proportionally fewer tandems due to a faster rate of deletion from subgenome 2.
While dispersed throughout the genome, the estimated ages of standing tandem duplicates is not dispersed throughout evolutionary time. In fact, tandem duplicates have a bimodal distribution of estimated ages ( Figure 3C). The older peak in the estimated age distribution coincides with the divergence of maize from Sorghum (Swigonová et al. 2004). This is not unexpected, because the genomic instability and rearrangements caused by an allopolyploidy event can result in many tandem duplicates (Blanc and Wolfe 2004). The more recent peak coincides with the expansion of maize as an agricultural plant (Wang et al. 2017). The demographic effects and linked selection associated with domestication of maize (Wright et al. 2005) would have multiple effects that affect tandem duplicates: both genetic hitchhiking near "domestication loci" and reduction in the efficacy of purifying selection may increase the frequency of gene duplications in the genome.
There are two processes that can potentially contribute to the observed pattern of bimodally-distributed tandem duplicate dates. One is that the allopolyploid event that occurred near the divergence time of the maize progenitor from the Sorghum bicolor progenitor led to an increased rate of tandem duplication. Genome instability through Figure 3 Date estimates of maize tandem duplications. A) Example of a BEAST tree that dated a tandem duplicate gene cluster as an ancient duplication. B) Example of a BEAST tree that dated a tandem duplicate gene cluster as a relatively recent duplication. In both trees red shows the consensus topology and alternate shading color indicates alternate topologies. The trees in A and B are calibrated based on an approximate divergence date for maize and Sorghum of 12 million years ago. C) Distribution of estimated syntenic and nonsyntenic duplication ages. Estimates dates are based on substitution rates relative to the outgroup Sorghum for each tandem duplicate gene based on branch length determined from the BEAST trees. The black triangle shows the estimated divergence date of maize and Sorghum. Shared tandem duplicate clusters are contained in both B73 and PH207 and private are only duplicated in one of the two genomes.
increased probability of meiotic errors has been documented during both genome duplication events and polyploidization events (reviewed by Hollister (2015)). However, duplicated genes also exhibit a propensity for loss or functional divergence, processes which erode evidence of recent duplication. These mechanisms are not independent. It is possible that both of these processes are acting in maize to contribute to the standing variation of tandem duplicates. However, a detailed study of many independent maize genome assemblies in a population with known genetic structure would be required to assess the relative contributions of these two mechanisms.
In addition to determining when in evolutionary history tandem duplicates arose, we also tried to determine their mechanistic origin. Our results suggest that tandem duplicates have a close association with transposable elements. This is evident at both the genomic distribution level (Figure 2), and direct comparison of gene model annotations and transposable element annotations, where there is an enrichment of LTRs that are nested within tandem duplicates relative to non-tandem duplicates ( Table 2). This suggests that tandem duplicates may arise through a mechanism that preferentially operates on highly repetitive sequence such as transposable elements, such as unequal crossing over (Smith 1976). Errors in meiotic chromosome pairing are often the result of repetitive elements like tandemly arrayed genes (Yandeau-Nelson et al. 2006), and may contribute to the substantial level of gene copy number variants observed in maize (Springer et al. 2009;Swanson-Wagner et al. 2010). Tandem duplicates may also be generated via transcription-mediated mechanisms associated with RNA transposable elements. We observed a higher proportion of single exon genes in tandem duplicate gene clusters relative to non-duplicated genes. A strong signature of an RNA-intermediate in a tandem duplication would be if one gene within the tandem duplicate contained multiple exons and the other gene within the tandem duplicate contained only a single exon that is the product of a spliced mature Figure 5 Size distribution of tandem duplicate gene clusters. A) Number of exons in B73 tandem duplicates relative to all other genes genome-wide. B) Number of exons in PH207 tandem duplicates relative to all other genes genome-wide. C) Gene length distribution for single-exon genes and multi-exon genes in B73 and PH207. Figure 4 GC content of tandem duplicate gene clusters. A) GC content of genome wide genes (gray), syntenic tandem duplicates (blue), and non-syntenic tandem duplicates (black). B) GC content of ancient ($ 10MYA, purple solid) and recent (# 2MYA, purple dotted) tandem duplications. Distributions contain both B73 and PH207 tandem duplicate gene clusters. mRNA. We did not see this pattern in many of tandem duplicate gene clusters. Tandem duplicate genes, whether single exon or multi exon, however, were generally shorter than non-tandem duplicates. This points to an explanation that single exon genes, which are generally shorter, are easier to copy intact through mechanisms such as nonhomologous recombination (Smith 1976), rather than a RNA intermediate.
In this study, we constrained our analyses to annotated genes. However, tandem duplication can affect regulatory elements or gene fragments (Rogers et al. 2017). Duplication of functional elements that are not full-length protein coding genes likely has an impact on phenotypic variation, and therefore, evolution of genome structure. Our work presents a special case of tandem duplications, in which entire genes are duplicated. However, we show that even this special case of tandem duplication can affect thousands of genes genome-wide and has the potential for functional outcomes.

ACKNOWLEDGMENTS
This work was supported by the National Science Foundation [IOS-1546727] to CNH and SEM. ABB was supported by a DuPont Pioneer Bill Kuhn Honorary Fellowship and a MnDRIVE Global Food Ventures fellowship. The authors acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the research results reported within this paper http://www.msi.umn.edu.

LITERATURE CITED
n Table 2 Counts of tandem duplicate genes and non tandem duplicate genes that contain a transposable element insertion or are nested within a transposable element in the B73 genome