Figure 1.
In each time step, first an individual dies. Second, parents are selected for reproduction (dotted square). Third, the dead individual is replaced by an offspring. Lastly, we recompute the species number and abundance. We then repeat the cycle. In this case the graph has two species with 5 (red circles) and 4 (blue circles) individuals.
Figure 2.
In an evolutionary graph, individuals occupy the vertices of a graph. In each time step, an individual is selected with a probability proportional to its fitness. In the model without frequency-dependent selection, individuals are selected randomly. In the frequency-dependent selection model, individuals with few connections, and therefore with more rare alleles, have more success at mating and their alleles spread quickly through the population. The process is described by a symmetric genetic similarity matrix , where
denotes the genetic similarity between individual
and
. Dotted links represented by
in the
matrix denote the similarity values
, indicating reproductive incompatibility.
Figure 3.
Radiations, number of species, and diversity (theory).
a, Simulated total number of species (both extant and extinct) as a function of time for the model with (black, also used for b and c) and without frequency-dependent selection (red). , and the minimum genetic similarity value,
, also used for b and c. Time measured in generations. After a transient phase, speciation events occur at a nearly constant rate in the model without frequency-dependent selection. In contrast, the frequency-dependent selection scenario shows a rapid series of fission speciation events followed by a plateau with very low speciation and extinctions events. b, Simulated number of extant species as a function of time for the model with and without frequency-dependent selection. Insets represent the species abundance distribution at stationarity. x and y-axis represent the rank in species abundance from the most common to the most rare and the relative abundance of each species in the community, respectively. Frequency-dependent selection produces more extant species and higher diversity (inset in b). c, Simulated abundance symmetry of the new species after each speciation event. We measured the degree of symmetry in each speciation event as
, where
and
are the size of the smallest new species and the mother species, respectively. Perfect symmetry means that the new species abundance is identical to the mother species abundance; low value means the new species abundance is much smaller than that of the mother species. Thick line represents perfect symmetry.
Figure 4.
Radiations, number of species, and diversity (data).
a, Empirical (black circles) and predicted (red, CI, Methods) species number and speciation events through time for the
cichlid genus [61] in the Lake Barombi Mbo Lake. The best fit is given by the frequency-dependent selection model (
,
and
= 7.8 (
= 9.8 for the model without frequency-dependent selection, see Methods). Inset in a is the relative species abundance at stationarity given by the parameter combination that best describe the data. b, Empirical (black circles) and predicted (red,
CI) species number and speciation events through time for the Darwin's finches [20]. The model without frequency-dependent selection has a slightly lower minimized value than the model with frequency-dependent selection (
,
and
= 15.8 vs.
= 15.9 for the model with frequency-dependent selection). Inset in b is the relative species abundance at stationarity given by the parameter combination that best describe the data. Bottom, Parameter combinations explored for the
genus (left) and the Darwin's finches (right). Coloring indicates the likelihood value associated with different combinations of parameter values, with the region of “best fit” given by the dark blue area (Methods). The surface was plotted as log(
) for better clarity of the isoclines. Note that
applies to a broad range of plausible empirical values of
and
.