How Many Species Have Mass M
Summary (2 min read)
Introduction
- Comparing the predictions of this simplified model with species mass data for the same 4,002 terrestrial mammals from the late Quaternary (Smith et al.
- The authors then show that the model’s predictions, when appropriately parameterized, are also in good agreement with data for 8,617 extant avian species (Dunning 2007).
A Mathematically Solvable Version
- The CE model, however, remains too complex for mathematical analysis, even though it omits many ecological and microevolutionary processes such as interspecific competition, predation, and population dynamics.
- This model can then be used to make inferences about body mass evolution without resorting to laborious simulations.
- For terrestrial mammals, recent empirical studies (Liow et al. 2008) support the assumption that the probability per unit time of a species becoming extinct pe(x) grows weakly with its mass.
- Such a steady state should exist whenever all species within the taxon experience roughly the same set of macroevolutionary selective pressures, that is, under stable macroevolutionary conditions.
- Including now the taxon-specific lower limit xmin on species mass implies the constraint for the steadyf(x ) p 0min state solution and allows us to eliminate one parameter from equation (3).
Mammalian Body Mass Evolution
- The authors find that two alternative methods of choosing b, by numerically matching the modal masses of the model and the empirical data or by matching the expected maximum mass of the model with the observed maximum in the empirical data, produce similar results.
- For simplicity, differences due to sexual dimorphism, geographic variation, and so on were ignored or averaged out.
- The resulting fit (fig. 2A) is in good agreement with the empirical data, except for a slight overestimate of the number of species with mass near 1 kg, an underestimate of the number near 300 kg, and a slight misestimate of the number of very small-bodied species.
- The deviations in the right tail are also seen in the CE model and may be due to, for example, phylogenetically correlated speciation or extinction events in the recent past.
Avian Body Mass Evolution
- Unlike mammals, data on most other taxonomic groups are generally not sufficient to yield accurate estimates of the parameters m and b (but see Novack-Gottshall and Lanier 2008).
- Avian species, however, present an interesting case for study using their model; the distribution of extant avian body masses (fig. 3A) is relatively well characterized (Dunning 2007), and evidence of a minimum species body mass Mmin is reasonable (Pearson 1950).
- Like mammals, this groove passes through thev ≈ 0.5 point , implying that this test cannot rule out them p 0 possibility that Cope’s rule ( ) does not hold for them 1 0 evolution of birds.
- This indicates that for a given diffusion bias m, a significantly larger extinction parameter b is required to produce a comparably realistic mass distribution.
Discussion and Conclusions
- With respect to birds, their analysis leads us to make several concrete predictions about their evolution.
- (2) The body masses ofM r Mmin large avian species ( ), like those for terrestrialM 1 20 g mammals, are constrained mainly by extinction risks that increase progressively with body mass.
- From a more conceptual perspective, the similarity of the results for extant birds and Recent terrestrial mammals suggests that their evolutionary histories, in terms of the processes that govern the variation of species body sizes over evolutionary timescales, are fundamentally the same.
- On the other hand, although the agreement of the simple diffusion-reaction model given in equation (4), when appropriately parameterized, and the observed mass distributions of Recent terrestrial mammals and extant birds is quite good, the model is obviously incomplete in many ways.
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Citations
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287 citations
Cites background from "How Many Species Have Mass M"
...…an increase in size of mammals is limited by the propensity of large species to undergo mass extinctions due to small population sizes, the restriction of resources, and the inability to evade environmental challenges (Kingsolver and Pfennig 2004; Van Valkenburgh et al. 2004; Clauset et al. 2009)....
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171 citations
Cites background from "How Many Species Have Mass M"
...…more realistic by the introduction of size-biased selection and extinction, and anagenetic size change within species between speciation and extinction events (e.g. Stanley 1973; Maurer et al. 1992; Kingsolver and Pfennig 2004; Clauset and Erwin 2008; Mattila and Bokma 2008; Clauset et al. 2009)....
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68 citations
Cites background from "How Many Species Have Mass M"
...…with size-biased selection and extinction, as well as some anagenetic size change within species between speciation and extinction events (e.g. Stanley, 1973; Maurer et al., 1992; McShea, 1994; Kingsolver and Pfennig, 2004; Clauset and Erwin, 2008; Mattila and Bokma, 2008; Clauset et al., 2009)....
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...Body size is therefore thought to evolve multiplicatively, but with size-biased selection and extinction, as well as some anagenetic size change within species between speciation and extinction events (e.g. Stanley, 1973; Maurer et al., 1992; McShea, 1994; Kingsolver and Pfennig, 2004; Clauset and Erwin, 2008; Mattila and Bokma, 2008; Clauset et al., 2009)....
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45 citations
Cites background from "How Many Species Have Mass M"
...Within taxonomic groups, the log right-skewed distribution is the norm within mammals, birds, and insects (Clauset and Erwin 2008; Clauset et al. 2009), but not within marine bivalves (Roy et al. 2002)....
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References
624 citations
"How Many Species Have Mass M" refers background in this paper
...cal limits, perhaps from metabolic (Pearson, 1948, 1950; West et al., 2002) or morphological constraints (Stanley, 1973), and on the upper end by an extinction risk that increases weakly with mass (Liow et al....
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...…their model, the evolution of species mass is bounded on the lower end by hard physiologi- 2 cal limits, perhaps from metabolic (Pearson, 1948, 1950; West et al., 2002) or morphological constraints (Stanley, 1973), and on the upper end by an extinction risk that increases weakly with mass (Liow…...
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598 citations
"How Many Species Have Mass M" refers background in this paper
...A theoretical explanation of this distribution may shed light both on the interaction between ecological and macroevolutionary processes (Stanley, 1975), and on long-term trends in species mass (Alroy,...
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...A theoretical explanation of this distribution may shed light both on the interaction between ecological and macroevolutionary processes (Stanley, 1975), and on long-term trends in species mass (Alroy, ∗This manuscript is a pre-print version that has not undergone final editing....
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582 citations
"How Many Species Have Mass M" refers background or result in this paper
...…mammals, birds, fish and insects, exhibit a canonical form of the species mass distribution (Allen et al., 2006; Koz lowski and Gawelczyk, 2002; Stanley, 1973), in which the typical mass is an intermediate value; for example, in mammals the typical mass is that of the common Pacific Rat…...
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...†Electronic address: aaronc@santafe.edu ‡Electronic address: djs47@physics.ucla.edu §Electronic address: redner@bu.edu 2000a,b), including Cope’s rule, the oft-studied notion that species mass tends to increase within a lineage over evolutionary time (Alroy, 1998; Stanley, 1973)....
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...…of species body mass over evolutionary time assume a cladogenetic diffusion process (Koz lowski and Gawelczyk, 2002; McKinney, 1990; McShea, 1994; Stanley, 1973) where each descendant species’ mass MD is related to its ancestor’s mass MA by a random multiplicative factor λ, i.e., MD = λMA (Fig....
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..., 2002) or morphological constraints (Stanley, 1973), and on the upper end by an extinction risk that increases weakly with mass (Liow et al....
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...This behavior lends some support to the hypothesis that the left tail’s particular shape is caused by strong physiological constraints on body mass evolution near the avian lower limit (Stanley, 1973), which are not included in our model....
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454 citations
"How Many Species Have Mass M" refers background or methods in this paper
...edu 2000a,b), including Cope’s rule, the oft-studied notion that species mass tends to increase within a lineage over evolutionary time (Alroy, 1998; Stanley, 1973)....
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...For the interested reader, details on the preparation of the empirical data are discussed at length by Alroy (1998) and Smith et al. (2003) for mammalian fauna, and by Dunning Jr. (2007) for avian fauna....
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...On the other hand, the most accurate method remains the direct analysis of large amounts of ancestor-descendant data (Alroy, 1998, 2000b; Novack-Gottshall and Lanier, 2008), preferably when derived from as realistic a phylogeny as possible....
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...†Electronic address: aaronc@santafe.edu ‡Electronic address: djs47@physics.ucla.edu §Electronic address: redner@bu.edu 2000a,b), including Cope’s rule, the oft-studied notion that species mass tends to increase within a lineage over evolutionary time (Alroy, 1998; Stanley, 1973)....
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452 citations
"How Many Species Have Mass M" refers background or methods or result in this paper
...For the interested reader, details on the preparation of the empirical data are discussed at length by Alroy (1998) and Smith et al. (2003) for mammalian fauna, and by Dunning Jr. (2007) for avian fauna....
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...We now test the predictions of this simple mathematical model using empirical data for 4002 Recent terrestrial mammals (Smith et al., 2003) and 8617 birds (Dunning Jr....
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...Comparing the predictions of this simplified model with species mass data for the same 4002 terrestrial mammals from the late Quaternary (Smith et al., 2003) (henceforth denoted “Recent” mammals, which includes species that have become extinct during the Holocene), we reproduce Clauset and Erwin’s…...
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...for 4002 Recent terrestrial mammals (Smith et al., 2003) and 8617 extant birds (Dunning Jr....
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...2 (a) The solution of the diffusion-reaction model of species body mass evolution [Equation (4)] with (smoothed) empirical data for 4002 terrestrial mammals from the late Quaternary....
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Q2. What are the future works in "How many species have mass m?" ?
The similarity of these distributions to those of other taxonomic groups suggests that this explanation may be universal, although further empirical work is necessary to substantiate this hypothesis. The authors conclude by noting that the model ’ s good agreement with data suggests that it may be a useful way to establish null expectations in the study of general trends in body mass evolution ( much like diffusion models in population genetics ; Hartl and Clark 2007 ) in the absence of factors such as interspecific competition, population dynamics, geography, predation, and so on.