This interspecies competition leads to a new form of selective pressure. If individuals of one population can exploit a different set of resources or the same resources differently, these organisms can minimize competition with other species and become more reproductively successful compared to individuals that continue to compete directly with other species.
This can lead to a number of outcomes. In one case, one species becomes much better than others at occupying a particular niche, driving the others to extinction. Alternatively, one species may find a way to occupy a new or related niche, and within that particular niche, it can more effectively compete, so that the two species come to occupy distinct niches.
Finally, one of the species may be unable to reproduce successfully in the presence of the other and become at least locally extinct. These scenarios are captured in what is known as the competitive exclusion principle or Gause's Law, which states that two species cannot stably occupy the same ecological niche - over time either one will leave or rather be forced out of the niche, or will evolve to fill a different often subtly niche.
What is sometimes hard to appreciate is how specific a viable ecological niche can be. For example, consider the situation described by the evolutionary biologist Theodosius Dobzhansky :. The reasons why species become extinct is much discussed, particularly the consequences of human activities.
Less often discussed is how environmental changes affect the chances that new species are formed. New species arise when groups of individuals within a species successively become so different that they eventually are recognized as separate species, usually defined as inability to interbreed and produce fertile offspring. Differences can arise in several ways. Groups could become isolated from each other on either side of barriers, for example a mountain range, or they can adapt to different conditions by natural selection.
How often new species form varies dramatically among organism groups and regions. Researchers have, so far, attributed this variation to differences in the strength of the forces that cause the differences. We have demonstrated that speciation and extinction rates inferred from palaeontological and phylogenetic data are expected to differ a priori, even in the absence of any biases, simply because they measure different quantities.
We also showed that a phylogenetic extinction rate of zero does not imply that species are immortal, since it ignores extinction associated with replacement, either through cladogenesis or anagenesis. Fully reconciling the discrepancies between phylogeny and fossil-based estimates of diversification rates therefore requires a better understanding of the contribution of different speciation modes to the evolution and description of species in the fossil record, and how these processes relate to reconstructed phylogenies.
We propose a sixth law of palaeobiology that recognises the effects of different speciation modes on the estimation and interpretation of diversification rates obtained from palaeontological and phylogenetic data.
This law is given by Eqs. Our model illustrates that differences between fossil and phylogenetic estimates of speciation and extinction are expected and ultimately informative about the prevalent mode of speciation. The predictions of the sixth law are supported by the numerical and empirical results presented in this study, and may explain numerous other contrasting findings between phylogenetic and fossil estimates.
Understanding and explicitly modelling the differences between phylogenetic and fossil species concepts should be the basis of future attempts to integrate the two data types. The expected origin time for each set of trees is 32, 52 and time units.
Extant species phylogenies were generated by pruning all extinct taxa from the simulated trees. Stratigraphic range data were generated using the times of origination and extinction of the chronospecies simulated under the BDC speciation model. Incomplete sampling affects many empirical phylogenetic trees and arguably all fossil data sets, erasing a proportion of the speciation and extinction events. To examine the impact of non-uniformly missing data, we excluded entirely extinct ranges only with probability 0.
Note that in these experiments, we did not remove any species from the extant species phylogenies. However, removing species from the extant species phylogenies is expected to have a similar impact on the results, i. Under this model the probability of sampling a given range will be a function of range duration, i.
In the resulting fossil occurrence data sets, the start and end of ranges will be represented by first and last appearances, and thus will underestimate the total range duration. To obtain estimates of the true range durations i.
Temporal variation in diversification rates is also common across clades but is not explicitly accounted for in our model. This resulted in three sets of tree replicates with an expected origin time of 26, 34 and 52 time units.
Second, we generated trees with an episode of high diversification followed by a large increase in extinction equal to speciation in the last interval.
Third, we generated trees under the scenario in which extinction rate in the final interval was much greater than speciation i. Speciation and extinction rates were estimated from completely sampled data sets Supplementary Table 7 , Supplementary Figures 11 , Cryptic lineages are likely to be common in clades with a fragmentary fossil record or when phenotypic changes have low probability of being preserved e.
Note this does not affect the data used to estimate rates from phylogenies. Speciation and extinction rates were estimated from completely sampled data sets Supplementary Table 9 , Supplementary Figures 13 , To establish that our test correctly rejects support for the BDC model when phylogenetic and palaeontological rates are generated under the independent rates model, we simulated data sets of trees and ranges with independent sets of parameters.
One set of trees was used to generate extant phylogenies while the second set was used to generate data sets of ranges. We then analysed sequential pairs of trees and ranges from each independent set using maximum likelihood and tested among the equal, compatible, and incompatible rate models. Anagenesis and bifurcating speciation were not incorporated into these simulations i. Phylogenies of extant species and temporal range data were used to calculate speciation and extinction rates using phylogenetic and palaeontological approaches, respectively.
We constrained the diversification rate to be positive i. We emphasise that this approach does not use any information about the delimitation of chronospecies. In all cases we assumed complete sampling, either of extant or extinct species, unless otherwise specified. The results using data simulated under complete sampling are shown in Supplementary Table 1 and Fig.
Each model describes the distribution of phylogenies and the distribution of stratigraphic ranges with likelihood function:. We determine the model best describing our data by using a likelihood ratio test. We approximate the joint probability. We note that Table 1 main text summarises the empirically determined type-1 errors for our likelihood ratio test in some simulation scenarios, revealing that our approximation in calculating the joint probability Eq.
Model parameters were estimated using maximum likelihood optimisation for combined data sets of phylogenies and stratigraphic ranges. All maximum likelihood optimisations were repeated five times using different initial values to reduce the probability of finding a local optima, and the results with the highest likelihood score were selected. We performed model testing using the likelihood ratio tests described above.
In our tests, we used two thresholds for statistical significance set to 0. Using empirical data available for nine clades, we assessed whether there was significant incongruence between the diversification rates estimated from different data sets and, if so, whether any incongruences could be explained by the BDC model. Fossil data comprise fossil occurrence times for each extinct and extant species with a known fossil record. Phylogenetic data consisted of dated phylogenetic trees of extant taxa.
To incorporate uncertainties associated with the fossil record, in addition to the maximum likelihood inference described above, we analysed the empirical data within a Bayesian framework, using a new implementation of the program PyRate 74 developed for this study.
Since for the empirical phylogenies we do not know the age of the origin and we conditioned the process on the age of the crown, rather than the origin Although the stratigraphic and phylogenetic rates here are assumed to be fully independent parameters as in the incompatible rates model , we used their joint posterior distributions sampled using Markov Chain Monte Carlo MCMC to assess the support for each model.
The estimated times of origination and extinction and the phylogenies of extant taxa were used to test the equal, compatible and incompatible rates models under the maximum likelihood framework described above. The incompatible rates model was preferred if none of the conditions above were met.
We then re-analysed the data sets for which the BDC model was preferred, after constraining the parameter values sampled by the MCMC based on the assumptions of the equal or compatible rates models.
We used the estimated times of origination and extinction for fossil lineages to infer the amount of rate variation from fossil data only.
We used the reversible-jump MCMC algorithm 75 implemented in PyRate to infer the number and temporal placement of rate shifts and to obtain the marginal rates through time 13 , We then computed the ratio between the greatest and the smallest marginal rates independently for speciation and extinction as a measure of the magnitude of rate variation in the data Supplementary Figure In addition, we implemented a BDC skyline model in which speciation and extinction rates may vary across predefined time bins.
This partition scheme was selected to guarantee sufficient statistical power to estimate speciation and extinction rates with both phylogenetic and fossil data. As with the constant rate model, we first ran the analysis under the assumption of independent rates to assess whether the BDC model was supported.
We then ran another analysis on the fern data under the BDC model to estimate compatible phylogenetic and fossil rates and the prevalence of different speciation modes.
Simulated trees were then used to 1 simulate fossil ranges and 2 simulate phylogenies of extant taxa. Prior to analysis the range data were uniformly pruned to match the number of empirical ranges. We generated phylogenies of extant taxa by pruning all extinct tips. Model testing using maximum likelihood was performed as described above.
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