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although extinction would appear to be an obvious
endpoint for a species, what if a species evolves into
something else or splits into two?
Aze et al. [6] recently proposed dated, fossil-based
phylogenies of 339 morphospecies and 210 evolutionary species for Cenozoic macroperforate planktonic
foraminifera, whose diversity peaked at 62 and 43
species, respectively. Here, we use these phylogenies
and our continuous-time diversification model [7] to
show how four palaeontological species concepts can
generate very different macroevolutionary dynamics.
We begin by outlining the four concepts.
Biol. Lett. (2012) 8, 139–142
doi:10.1098/rsbl.2011.0699
Published online 7 September 2011
Palaeontology
The meaning of
birth and death
(in macroevolutionary
birth –death models)
Thomas H. G. Ezard1,2,*, Paul N. Pearson3,
Tracy Aze3 and Andy Purvis1
2. THE CONCEPTS
In classical Linnean taxonomy, the members of a
‘species’ are recognized because they share diagnostic
characters with a designated type specimen; practical
application in the fossil record often results in the delimitation of morphospecies [8]. Consider, for example,
a well-known fossil species such as Homo erectus. Fossils are assigned to this species—to the exclusion of
all others—if they share characters with the type specimen. As fossil discoveries accumulate, a stratigraphic
range for the species is built up. Thus, a temporal duration can be achieved without reliable knowledge of
speciation and extinction. A taxonomist may split (by
naming new forms) or lump (by synonymy), but the
resulting units will still be morphospecies.
In a perfectly complete fossil record (figure 1a), a
morphospecies originates with the first specimen to display its diagnostic characters and terminates with the
death of the last such specimen. If populations evolve
continuously, these diagnostic characters may be polymorphic as morphospecies intergrade for extended
periods (shaded rectangles in figure 1b). The appearance or disappearance of morphospecies through such
intergradation is termed pseudospeciation and pseudoextinction, to emphasize that there is no change in
the number of evolving lineages [8,9] and that extinction can occur through anagenesis. Morphospecies
can persist through a ‘budding’ speciation and therefore
be paraphyletic. Figure 1b illustrates how this fossil
record might be split into five morphospecies: b persists
through two speciation events; g2 arises through pseudospeciation and terminates through pseudoextinction.
What we term Hennigian morphospecies (by analogy
with [10]) are similar except that they are not permitted
to persist through speciation: the ancestor is presumed
to bifurcate into two daughter species and immediately
go extinct. However, one of the daughter species will—
at least initially—not be diagnosably distinct from
its ancestor except by stratigraphic position and assumed phylogeny [10]. Figure 1c shows how the five
morphospecies yield nine Hennigian morphospecies.
Two further concepts collapse intergrading morphospecies into a single species. Evolutionary species
[11] originate at cladogenesis and terminate with
extinction of the lineage. The timing of cladogenesis is
conservatively inferred to have been when contemporaneous populations no longer intergrade (dotted lines in
figure 1); it therefore postdates origination of the
descendant morphospecies. The recognition of evolutionary species requires that, when speciation occurs,
one of the two species be identified as a continuation
of the ancestral species on account of greater similarity
1
Division of Biology, Silwood Park Campus, Imperial College London,
Ascot, Berkshire SL5 7PY, UK
Department of Mathematics, University of Surrey, Guildford,
Surrey GU2 7XH, UK
3
School of Earth and Ocean Sciences, Cardiff University,
Cardiff CF10 3YE, UK
*Author for correspondence ([email protected]).
2
Birth–death models are central to much macroevolutionary theory. The fundamental parameters
of these models concern durations. Different
species concepts realize different species durations because they represent different ideas of
what birth (speciation) and death (extinction)
mean. Here, we use Cenozoic macroperforate
planktonic foraminifera as a case study to ask:
what are the dynamical consequences of changing
the definition of birth and death? We show strong
evidence for biotic constraints on diversification
using evolutionary species, but less with morphospecies. Discussing reasons for this discrepancy,
we emphasize that clarity of species concept
leads to clarity of meaning when interpreting
macroevolutionary birth–death models.
Keywords: birth; death; extinction; speciation;
species concept
1. INTRODUCTION
Birth–death models originated in population biology to
address the demise of eminent Victorian families [1].
The models’ substantial use in macroevolution applies
the same principles to speciation and extinction [2,3],
and they are increasingly being used to investigate the
importance of particular traits for diversification [4],
the constraints imposed by diversity-dependence [5]
and many other questions. Regardless of the particulars of
each model, the basic idea remains consistent: the time
between events on a phylogenetic tree provides data
from which macroevolutionary inferences are made.
We need to know what we mean by births and deaths
in this context, since flipping among species concepts
alters their definition. For example, what is meant by
the birth of a species? The answer may seem obvious
at first, yet is anything but. All species trace their ancestry to the origin of life. Hence the birth of a species
must be recognized either by the acquisition of some
species-defining characteristic or by evolutionary divergence among populations (cladogenesis). Similarly,
Electronic supplementary material is available at http://dx.doi.org/
10.1098/rsbl.2011.0699 or via http://rsbl.royalsocietypublishing.org.
One contribution of 12 to a Special Feature on ‘Models in palaeontology’.
Received 8 July 2011
Accepted 12 August 2011
139
This journal is q 2011 The Royal Society
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140 T. H. G. Ezard et al.
(a)
The meaning of birth and death
a
(b)
g3
b
a
(c)
g3
g2
a
g
b
b
g1
(d)
g1
a
γ
(e)
β
g2
Figure 1. A schematic of (a) morphospace occupation, (b) morphospecies, (c) Hennigian morphospecies, (d ) evolutionary
species and (e) evolutionary Hennigian species. Vertical lines represent species. The grey rectangles in (b) represent intergradation of sister species; dotted lines across all panels denote the end of intergradation.
to the ancestral condition. Figure 1d shows how the five
morphospecies collapse to three evolutionary species.
Hennigian evolutionary species (termed Hennigian
species in [10]) also start at cladogenesis but terminate
in either extinction or another cladogenetic event: ancestral species do not persist through speciation. Figure 1e
shows how the three evolutionary species of figure 1d
translate to five Hennigian evolutionary species.
As a result of these definitions, the average durations
differ markedly among species concepts (electronic supplementary material, figure S1): evolutionary species
11.89 Myr (95% parametric CI 10.13–13.95); Hennigian evolutionary species 5.39 Myr (4.84–6.00);
morphospecies 8.33 Myr (7.43–9.34); Hennigian morphospecies 3.90 Myr (3.60–4.21). What impact do
these different durations have on macroevolutionary
dynamics?
3. THE MODEL
We used parametric survival analysis with censoring [12]
to obtain extinction and speciation functions for all
macroperforate planktonic foraminifer species that
originated during the Cenozoic [6]. Survival analysis
generates ‘hazards’, which here are instantaneous rates
of speciation or extinction. We modelled time to extinction and speciation as Weibull random variables, which
tests for changes in hazard as species age [12]. Constant
extinction (i.e. Van Valen’s law [13]) is a special case
where the time between events is a Poisson process.
We flipped among species concepts by applying different
censoring rules. Censoring is typically used when an
individual survives to the end of an experiment: an individual’s ‘undeath’ is valuable information on the risk of
death and therefore species’ duration (electronic supplementary material, figure S2).
Species’ duration was regressed against overall diversity (ln-transformed), palaeoclimate (the deep-sea
oxygen isotype ratio [14] as a single proxy), depth habitat
(open tropical/subtropical ocean mixed layer; open ocean
thermocline; and open ocean sub-thermocline) and morphological types (presence/absence of keels, spines and
symbionts). The minimum adequate model for each concept was obtained using the corrected Akaike Information
Criterion [15] from combinations of main effects and
two-way interactions (for more details, see [7]).
Once the speciation and extinction functions had
been obtained independently, we united them in the
multivariate Euler– Lotka equation [16] to provide a
Biol. Lett. (2012)
continuous-time estimate of per capita growth r for an
ecologically structured clade [7]. The ecological structure results from significant differences in speciation or
extinction hazards among morphological types (see the
electronic supplementary material). Since a species of
one type can produce descendants of another, we
used the matrix of observed, type-specific speciation
probabilities to relate all potential ancestors [7]. In
this ‘multi-type’ scenario, r is the dominant eigenvalue
of the system [16].
Analysis was performed in R [17] using the ‘deSolve’
package [18].
4. RESULTS
Species with persistent ancestry show increasing extinction hazard with age, unlike Hennigian concepts
(figure 2). While the species most likely to speciate are
the youngest under all four concepts, the conceptspecific hazards show marked variation (figure 2a–d:
compare the heights of the speciation curves at, say,
10 Myr). These differences in speciation and extinction
hazards generate very different estimates of r (figure 2e):
evolutionary species strongly indicate constraints on
diversification, but estimated limits to morphospecies
diversity were much higher than those observed (the
inferred ‘carrying capacities’ were slightly over 100 morphospecies and nearly 4000 Hennigian morphospecies).
All parameters and model comparisons are given in the
electronic supplementary material; the importance of
species’ ecology for macroevolution was strongly evident
for all concepts (electronic supplementary material,
tables S1–S3).
5. DISCUSSION
Changing the meaning of birth and death by changing
the species concept has substantial dynamical consequences for macroevolutionary inference (figure 2)
because each species concept generates a different
distribution of species’ durations (electronic supplementary material, figure S1), provoking alternative
analytical interpretations.
The species most likely to speciate are the youngest
for all four concepts (figure 2a–d), which is consistent
with the ‘early-burst’ pattern of early, rapid diversification followed by diversity-dependent slowdowns [5].
The estimates of nonlinearity in extinction hazards
have overlapping confidence intervals (electronic
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The meaning of birth and death T. H. G. Ezard et al.
Hennigian
(a)
persistent ancestry
(b)
(e)
0.30
0.20
0.10
0.03
(d)
evolutionary species
(c) 0.70
0.20
0.10
0.03
0
10
20
30
duration (Myr)
40
0
10
20
30
duration (Myr)
40
0.25
0.20
clade growth
morphospecies
hazard
0.70
hazard
141
0.15
0.10
0.05
0.00
−0.05
10
20
50
70
no. species
Figure 2. Extinction (dashed lines) and speciation (solid lines) hazards for statistically distinct ecological groups in the mean
environment, which generated very different estimates of clade growth for the four concepts (e). (a –d) Red, spinose; green,
keeled; blue, symbionts; grey, spinose and symbionts; black, remainder. (e) Black squares, evolutionary species; grey circles,
morphospecies; filled (squares or circles), persistent ancestry; open (squares or circles), Hennigian. Only significantly different
groups are shown, hence the different number of hazards for speciation and extinction within and among concepts. Hazards
among groups are parallel at the mean climate, but will not be elsewhere because of significant interactions between group
and environment (see the electronic supplementary material). ‘Durations’ for speciation hazards are ‘time from speciation’.
supplementary material, tables S1 and S2) for evolutionary species and morphospecies, suggesting that
increased extinction risk with age is not strongly related
to anagenesis as might be expected under a Red Queen
scenario [13]. Death comes more quickly when species are not permitted to persist through speciation;
Hennigian morphospecies are particularly prone to generating macroevolutionary dynamics with high turnover
rates or punctuated bursts of diversification. Hennigian
concepts complicate interpretation because it is hard
to disentangle speciation and extinction from the
additional births and deaths: there are clear differences
in extinction hazards with and without persistent ancestry (figure 2a versus 2b and figure 2c versus 2d). By
treating speciation and extinction independently, we
obtain different distributions (e.g. times to extinction),
different hazards (e.g. each speciation generates two
Hennigian species but one evolutionary species) and
therefore different estimates of clade growth with and
without persistent ancestry, even though the number
of species is the same.
The constraint of diversity-dependence is lower for
morphospecies than for evolutionary species because
morphospecies’ numbers can fluctuate owing to anagenesis, i.e. pseudoextinction and pseudospeciation. If
morphological change is continual, analyses of morphospecies are biased towards finding that extinction hazard
increases with species’ age [19], which is a pattern we
detect (figure 2b). If we suppose a changing climate
provokes—at least sometimes—anagenesis, then the
significant interaction between climate and diversity
for all morphospecies’ hazards suggests a less-tightly
constrained biotic limit to morphospecies diversity
Biol. Lett. (2012)
than to the numbers of evolutionary species (electronic
supplementary material, table S3). We are therefore
even less likely to detect a fixed limit on biodiversity
using morphospecies than with evolutionary species
(evidence for a variable limit in evolutionary species’
diversity is presented in [7]). With evolutionary species, fluctuations owing to anagenesis are not visible,
as they occur within the same lineage.
Although higher taxa (e.g. genera) can represent evolutionarily significant units [20], fossil records that are
complete enough to support species-level analyses are
particularly valuable for studying macroevolutionary
dynamics. Our delimitations of the species concepts
assume known phylogenetic relationships [6] and that
contemporaneous species can be distinguished morphologically (Darling & Wade [21] review cryptic and nearcryptic diversity in this clade). Because our models are
deterministic, they are expected to slightly overestimate
growth rates of assemblages exposed to a changing
environment [22], but can nevertheless recover key
features of evolutionary history [7]. Species-level completeness highlights the choice among species concepts
because different meanings of birth and death lead to
different interpretations of the same evolutionary history.
We thank Albert Phillimore, Lynsey McInnes and three
anonymous reviewers for valuable comments that improved
our work and NERC for funding (NE/E015956/1 to A.P.
and P.N.P.).
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