Genomes II: ordered

The previous chapter put genes on the tree as a bag of families, how many copies of each, and nothing more. This chapter gives them structure. A genome becomes one or more chromosomes, each an ordered row of genes, and each gene carries a strand, the direction it reads in. This is the ordered resolution.

Chromosomes split, merge, appear and die

A genome has a karyotype: chromosomes=N chromosomes, each with a topology: "circular" (the default) or "linear", or a per-chromosome list like ["circular", "linear"] for a mixed set. The founding initial_families genes are distributed across the chromosomes in turn. The number of chromosomes can also evolve through different events.

The karyotype itself evolves: four events change the number of chromosomes (Ge10):

• fission (per chromosome). A chromosome splits in two at a uniform cut, both halves keeping its topology; a single-gene chromosome cannot split.
• fusion (per chromosome). Two chromosomes of a genome merge into one. Only two of the same topology: a ring and a molecule with two ends cannot become one molecule, so a circular chromosome never fuses with a linear one, and a genome holding one of each never fuses at all.
• chromosome_origination (per lineage). A de-novo replicon appears: a new chromosome, empty and circular, a plasmid.
• chromosome_loss (per chromosome). A whole chromosome dies, and every gene on it is recorded as a loss. A lineage never loses its last chromosome this way.

The chromosome network

Chromosomes are tracked. A chromosome gets a new id at every event that passes it on or reshapes it: a speciation, a fission, a fusion. Each of those edges is recorded. So the run leaves behind not just the chromosomes at the tips but the genealogy that connects them: the chromosome network. It is the middle of three genealogies that nest, the species tree containing the chromosome network, which contains the gene trees:

species tree  ⊃  chromosome network  ⊃  gene trees

The containment is at each instant: every gene sits on one chromosome, and every chromosome in one lineage. That holds even though a gene's lineage can change chromosome by translocation and species by transfer.

It is a network and not a tree because of one event: fusion joins two chromosome lineages into one, two parents and one child. Fission and speciation are ordinary splits (one parent, two children); initial and origination are roots: the chromosomes the run began with, and the new replicons chromosome_origination creates, kept apart so you can tell which is which. Loss is a leaf. It is a directed graph, and it is written the way graphs are, as an edge list: chromosome_events.tsv on disk, .chromosome_events in Python, one row per event. A run with fissions and fusions gives:

  time   kind          parents -> children
  0.00   initial            -  -> 0          a chromosome the run started with
  0.00   initial            -  -> 1          a chromosome the run started with
  0.75   fission            0  -> 2, 3       a bifurcation
  1.52   fusion          2, 1  -> 4          a reticulation (two parents)
  1.52   fission            4  -> 5, 6
  2.02   fusion          3, 5  -> 7
  2.11   loss               7  -> -          chromosome 7 (and its genes) dies
  2.19   speciation         6  -> 8, 9
  2.49   fission            9  -> 10, 11
  3.27   speciation         8  -> 12, 13
  3.30   fusion        10, 11  -> 14

The rows carry no lineage column; which species holds a chromosome is read off gene_order.tsv, where every chromosome id sits beside its node.

Events act on segments

Once genes have neighbours, a gene-level event acts on a segment, a stretch of consecutive genes, not on one gene. A duplication copies a segment, a loss removes one, a transfer sends one sideways. That produces the signature of real genome evolution: neighbouring genes sharing a history because they were copied, moved or lost together.

How many genes are affected simultaneously by one event? That is its extent. By default, extents are computed from a geometric distribution, but this can be changed to other probability distributions. A bare number is the mean of the draw, so duplication_extent=3 copies about three adjacent genes. The default is a single gene, so every event takes one gene unless you set an extent.

Topology decides where a segment stops. On a circular chromosome a segment that reaches the last gene continues from the first, wrapping position 0, so only the whole chromosome bounds it; on a linear one it stops at the last gene, and a draw that would overrun the end is cut short there.

One consequence of events affecting multiple genes at the same time is that a rate counts starts, not hits. duplication=0.2 with duplication_extent=3 does not mean each gene is duplicated 0.2 times per unit time. A gene is copied whenever any duplication's segment covers it, which happens about three times as often as the starts alone, so roughly 0.2 × 3 = 0.6. If you want genes duplicated at a known rate, divide that rate by the mean extent.

The same reading holds at the nucleotide resolution of Chapter 5, where the extent is in base pairs rather than genes.

Rearrangements: inversion, transposition, translocation

Three more events reshape the order without creating or destroying genes:

• Inversion. Reverse a segment in place, flipping every gene's strand: 2+ 3+ 4+ becomes 4− 3− 2− (Ge9).
• Transposition. Cut a segment out and reinsert it elsewhere on the same chromosome, at a spot drawn uniformly over what is left after the cut.
• Translocation. Move a segment to a different chromosome of the same genome, landing at a random position. A no-op if the genome has only one chromosome.

All three are counted per copy: every gene is a potential start, so a bigger genome rearranges more often; each also takes PerLineage, a fixed budget independent of genome size (Appendix A). A moved segment, transposed or translocated, lands inverted with probability inversion_probability (default 0, so it keeps its orientation).

On the command line

The ordered resolution is --resolution ordered. It adds two sets of flags to the Chapter 3 events, each still a plain number: the chromosome flags, --chromosomes N and --topology taking circular (the default), linear, or a comma-separated list of one per chromosome; and the extent flags, --inversion-extent, --duplication-extent and the rest, each the mean number of genes an event takes. Leave an extent out and every event takes a single gene, which for an inversion means flipping one gene's strand and shuffling nothing:

# chromosomes split and merge along the tree
zombi2 genomes out/ --resolution ordered \
    --origination 0.5 --fission 0.05 --fusion 0.05 --chromosomes 2 --seed 1

# segmental duplications, losses and inversions on three chromosomes
zombi2 genomes out/ --resolution ordered \
    --duplication 0.2 --loss 0.2 --origination 0.5 \
    --inversion 0.3 --chromosomes 3 --seed 1

# segments relocate and move between chromosomes, sometimes inverting
zombi2 genomes out/ --resolution ordered \
    --origination 0.5 --transposition 0.2 --translocation 0.1 \
    --inversion-probability 0.5 --chromosomes 2 --seed 1