Evolution__3rd_Edition

592 PART 5 / Macroevolution
Time (Myr BP)
(a)
Hyracotherium
Mesohippus
Merychippus
Equus
Nanniippus
60 50 40 30 20 10
0
0
Million years ago
(b)
0
5
Equus complicatus Equus scotti
Equus simplicidens
Dinohippus mexicanus
Onohippidium galushai
Hypohippus sp. Dinohippus leidyanus
10
15
20
Megahippus mattewi Pliohippus permix
Megahippus mckennai
(Pseudohipparion)
Protohippus simus (Hipparions)
Merychippus isonesis
Archaeohippus Anchitherium
“Merychippus” primus Merychippus insignis
blackbergi clarencei
Merychippus gunteri
Parahippus leonensis
25
30
35
40
45
50
55
Parahippus tyleri
Miohippus quartus
Mesohippus barbouri
Mesohippus bairdii
Epihippus uintensis Epihippus gracilis
Orohippus pumulis
Hyracotherium tapirinum Hyracotherium vaccassiense
Hyracotherium angustidens
Figure 21.1
(a) Modern horses are descended from a group containing
a number of lineages that have increased in average body size
through the past 50 million years. The inset shows the smallest
known species of Hyracotherium, H. sandrae (from the early
Eocene of Wyoming) silhouetted against a cat for size
comparison. (100 lb ≈ 45 kg.)(b) The phylogenetic relations
of fossil and modern horse species. (c) First molar tooth in
500
400
300
200
100
Body mass (kg)
(d)
(c)
Species pair
Equus simplicidens-Equus complicatus
Parahippus leonensis-Merychippus primus
Parahippus leonensis-Protohippus simus
Miohippus quartis-Anchitherium clarencei
Mesohippus bairdii-Mesohippus barbouri
Equus simplicidens-Equus scotti
Dinohippus mexicanus-Equus simplicidens
Dinohippus leidyanus-Dinohippus mexicanus
Dinohippus leidyanus-Onohippidium galushai
Merychippus isonesis-Pliohippus permix
Megahippus mckennai-Megahippus matthewi
Anchitherium clarencei-Megahippus mckennai
Anchitherium clarencei-Hypohippus large sp.
Parahippus leonensis-Merychippus insignis
Parahippus leonensis-Merychippus isonesis
Parahippus leonensis-Merychippus gunteri
Parahippus tyleri-Parahippus leonensis
Miohippus quartus-Archaeohippus blackbergi
Miohippus quartus-Parahippus tyleri
Mesohippus bairdii-Miohippus quartus
Epihippus gracilis-Mesohippus bairdii
Orohippus pumulis-Epihippus uitensis
Orohippus pumulis-Epihippus gracilis
Hyracotherium vaccassiense-Oronippus pumulis
Hyrocotherium angustidens-Hyracotherium vaccassiense
Hyracotherium angustidens-Hyracotherium tapirinium
Mean species pair evolutionary rate*
M1APL(1)
M1PRTL(3)
However, the use of natural logarithms can be puzzling for people who think
intuitively about changes in terms of percentages rather than logarithms. For them, a
change of 10% is meaningful, a change of 0.1 natural logarithmic units less so.
Fortunately, natural logarithms behave much like percentage changes for short time
intervals. Suppose, for instance, a lineage is evolving at 1 darwin. For times up to about
1,000 years, the percent change will be approximately constant per year for all 1,000
years. That is, after 1,000 years the lineage will have changed by close on 0.1%, and by
about one-thousandth of that amount (that is, 0.0001%) every year up to then. For
2 cm
0.8 in
M1TRNW(2)
M1MSTHT(4)
M1APL(1)
M1TRNW(2)
M1PRTL(3)
M1MSTHT(4)
∆t
(Myr) (d) (d) (d) (d)
2.0 0.000 –0.014 0.115 0.054
3.0 –0.009 –0.026 –0.012 0.154
6.0 0.051 0.034 0.073 0.247
7.0 0.065 0.057 0.049 0.046
1.0 0.157 0.146 0.136 0.050
2.0 0.040 0.005 0.162 0.097
2.0 0.064 0.081 0.088 0.142
2.0 –0.004 –0.026 0.074 –0.054
2.0 0.033 0.027 0.030 –0.074
2.5 0.072 0.101 0.185 0.180
2.0 0.036 0.022 0.064 0.219
4.0 0.083 0.096 0.094 0.109
8.0 0.062 0.072 0.077 0.077
3.0 0.053 0.011 0.038 0.228
3.0 0.030 0.014 0.028 0.339
2.0 –0.023 –0.107 –0.116 0.172
2.0 –0.062 –0.039 –0.179 0.088
7.0 –0.017 –0.018 –0.029 –0.021
5.0 0.067 0.052 0.066 0.091
6.0 0.022 0.018 0.012 0.022
14.0 0.023 0.037 0.032 0.036
4.5 0.047 0.052 0.042 –0.007
4.5 0.026 –0.010 0.006 0.020
2.5 0.011 0.029 0.012 0.068
3.0 0.010 0.026 –0.020 0.000
3.0 0.101 0.106 0.091 0.096
Equus simplicidens-Equus complicatus
0.045 0.047 0.0690 0.104
crown and side view, showing four aspects that were
measured. (d) Evolutionary rates for the four measures,
in 26 inferred ancestor–descendant species pairs,
expressed in darwins (d). It is not important to study
the numbers in detail! They are meant only to illustrate
the results that come out of a study of evolutionary rates.
Redrawn, by permission of the publisher, from
MacFadden (1992).
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