Figure 1.
The sampling and differentiation of lineages impacts the potential to resolve clades.
These diagrams depict how patterns of morphological differentiation and sampling of ancestors impact the distribution of potential synapomorphies and thus the intrinsic capability to resolve clades with morphological data. In (a), as there is no morphological change over the duration of the ancestral taxon A, there can be no true synapomorphies which would unite any pair of the sampled taxa (ancestor A or its descendants B and C) to the exclusion of a third. In (b), the taxa with a dashed outline (taxa A and B) have not been sampled and are not included in the supposed cladistic analysis. However, even though A and B are ancestral, the sampled taxa are all descended from the same persistent ancestor and thus no synapomorphy exists to produce an additional nested clade. This causes the node to be intrinsically unresolvable. In (c), under a bifurcating cladogenesis pattern, polytomies are only produced when the ancestor A is sampled, as each morphotaxon can only have two descendants. The fourth example (d) is an example with cryptic cladogenesis and anagenesis, where the formation of several sampled descendants from a cryptic ancestral complex of multiple undifferentiated lineages produces an unresolvable set of relationships. The taxa in (d) labeled A1, A2, A3 and A4 are undifferentiated cryptic lineages, which would be identified as a single morphotaxon ‘A’ for the purposes of taxonomic assessment and phylogenetic analyses.
Figure 2.
Four models of morphological differentiation.
If differentiation occurs instantaneously, there are three possible models of how differentiation may evolve at branching events (cladogenesis). From left to right: (a) under cryptic speciation the two daughter lineages are morphologically identical to their ancestor; (b) with budding cladogenesis, a single daughter lineage is undifferentiated from the ancestor while the other daughter is distinguishable as a separate morphotaxon based on systematic characters; (c) bifurcating cladogenesis produces two daughter lineages which are both recognizably different relative to their ancestor. The fourth pattern of differentiation shown here is repeated events of anagenesis, which is differentiation unassociated with branching. Branching is depicted identically across these figures to contrast the morphological patterns alone and does not reflect discontinuity of populations.
Figure 3.
Under complete sampling, the resolvable proportion of clades is low under all models of differentiation.
The thirteen boxplots in this figure are based on thirteen models of morphological differentiation, listed on the left. Each boxplot represents measurements of the resolvable proportion of clades for 100 simulations performed for each differentiation pattern under complete sampling. Simulations were conditioned to have one hundred sampled taxa on average at a sampling rate of 0.01 per Ltu, under the clade-constant protocol discussed in the methods.
Figure 4.
The resolvable proportion under each differentiation model increases as sampling rate decreases to 0.1 per Ltu, but not evenly across all differentiation models.
As in figure 3, the thirteen boxplots in this figure are based on thirteen models of morphological differentiation, listed on the left. Each boxplot represents measurements of the resolvable proportion of clades for 100 simulations performed for each differentiation pattern under incomplete sampling, with a sampling rate of 0.1 per Ltu. Simulations were conditioned to have one hundred sampled taxa on average at a sampling rate of 0.01 per Ltu, under the clade-constant protocol discussed in the methods.
Figure 5.
At a very low sampling rate (0.01 per Ltu), some but not all models of differentiation predict that almost all clades will be resolvable.
As in figure 3, the thirteen boxplots in this figure are based on thirteen models of morphological differentiation, listed on the left. Each boxplot represents measurements of the resolvable proportion of clades for 100 simulations performed for each differentiation pattern under incomplete sampling, with a sampling rate of 0.01 per Ltu. Simulations were conditioned to have one hundred sampled taxa on average at that sampling rate, under the clade-constant protocol discussed in the methods.
Table 1.
Sampling regimes used in simulations of the fossil record, listed by sampling rate, with equivalent sampling probabilities and completeness.
Figure 6.
Datasets composed only of living morphotaxa are expected to have fewer resolvable clades than datasets from poorly preserved fossil records, under most differentiation models.
As in figure 3, the thirteen boxplots in this figure are based on thirteen models of morphological differentiation, listed on the left. Each boxplot represents measurements of the resolvable proportion of clades for 100 simulations performed for each differentiation pattern, with between 50 and 300 co-extant morphotaxa sampled.
Figure 7.
Clades which that match the fossil record in taxon durations require both high anagenesis and sampling rates to have high intrinsic resolution.
Simulated extinct clades were generated under cryptic cladogenesis with anagenesis, with both varying sampling and anagenesis rates. For each combination of rates, 100 clades were generated, conditioned to have 100 sampled morphotaxa on average. The mean resolvable proportion of clades and the mean proportion of taxa with observed durations at each combination were used to generate two overlaid topographic contours. The shaded region represents the combinations of anagenesis and sampling rates which produce both highly resolvable clades (at least 0.9 intrinsically resolvable) and clades with realistic proportions of taxa with observed durations (at least 0.4 of sampled taxa). Branching and extinction rates were held constant at 0.1 per Ltu.
Figure 8.
At very low sampling rates, none of the differentiation patterns generate realistic frequencies of taxa with observed durations.
The thirteen boxplots in this figure are based on thirteen models of morphological differentiation, listed on the left. Each boxplot represents measurements of the resolvable proportion of clades for 100 simulations performed for each differentiation pattern under incomplete sampling, with a sampling rate of 0.01 per Ltu. Simulations were conditioned to have one hundred sampled taxa on average at that sampling rate.