Extinction, Extirpation, and Exotics: Effects on the Correlation between Traits and Environment at the Continental Level

Abstract

Ecometrics is the study of the relationship between organismal traits and environments. This study used Monte Carlo methods to assess the effects of extinction, extirpation, and exotic species on ecometric correlations at the continental scale. These potentially confounding processes arise from anthropogenic activities, taphonomic biases in fossil assemblages, and selective mass extinctions. Random, independent local extinctions introduced a predictable downward bias in ecometric correlations, which can be corrected by rarefaction if correlations are being estimated from fossil assemblages. Random global extinctions on species have a less predictable effect on ecometric correlations and introduce pronounced effects if more than 25% of the continental fauna is affected; however, global extinctions do not bias the estimation of R2 even though they increase its uncertainty. Selective extinction and introduction of exotic species had little impact on ecometric correlations, though caution is urged in generalizing this result.

Full text

Ann. Zool. Fennici 51: 209–226 ISSN 0003-455X (print), ISSN 1797-2450 (online)
Helsinki 7 April 2014 © Finnish Zoological and Botanical Publishing Board 2014
Extinction, extirpation, and exotics: effects on the
correlation between traits and environment at the
continental level
P. David Polly1 & Sana Sarwar2
1) Departments of Geological Sciences, Biology and Anthropology, Indiana University, 1001 E,
10th Street, Bloomington, IN 47405, USA (*corresponding author’s e-mail: pdpolly@indiana.
edu)
2) St. Bartholomew’s and The Royal London School of Medicine and Dentistry, Turner Street,
London E1 2AD, UK
Received 21 Aug. 2013, nal version received 9 Nov. 2013, accepted 18 Nov. 2013
Polly, P. D. & Sarwar, S. 2014: Extinction, extirpation, and exotics: effects on the correlation
between traits and environment at the continental level. — Ann. Zool. Fennici 51: 209–226.
Ecometrics is the study of the relationship between organismal traits and environments.
This study used Monte Carlo methods to assess the effects of extinction, extirpation,
and exotic species on ecometric correlations at the continental scale. These potentially
confounding processes arise from anthropogenic activities, taphonomic biases in fossil
assemblages, and selective mass extinctions. Random, independent local extinctions
introduced a predictable downward bias in ecometric correlations, which can be cor-
rected by rarefaction if correlations are being estimated from fossil assemblages.
Random global extinctions on species have a less predictable effect on ecometric cor-
relations and introduce pronounced effects if more than 25% of the continental fauna is
affected; however, global extinctions do not bias the estimation of R2 even though they
increase its uncertainty. Selective extinction and introduction of exotic species had little
impact on ecometric correlations, though caution is urged in generalizing this result.
Introduction
Some folks drive the bears out of the wilderness,
Some to see a bear would pay a fee,
Me, I just bear up to my bewildered best
And some folks even seen the bear in me.
(Steven Fromholz 1975)
An ecometric trait is a measureable morpho-
logical feature that interacts with the environ-
ment. In some cases interaction between envi-
ronment and trait is strong enough that the
state of the trait in a species constrains where it
can live and, thus, helps to dene the limits of
its geographic range (Poff 1997, Eronen et al.
2010a, Polly et al. 2011). When shared by many
species, ecometric traits inuence the assembly
of local communities through their joint inu-
ence on the geographic ranges of those species.
Functional traits can therefore inuence species
sorting, favoring species with a particular state
in optimal environments. The average values
of ecometric traits in local communities are,
therefore, expected to be correlated with local
environment (Thompson et al. 2001, Eronen
et al. 2010a, Webb et al. 2010). Body mass in

210 Polly & Sarwar • ANN. ZOOL. FENNICI Vol. 51
mammals (Damuth et al. 1992), body size in
snakes (Head et al. 2009), hypsodonty in ungu-
lates (Eronen et al. 2010b), tooth morphology in
mammals (Evans 2013), limb proportions in car-
nivorans (Polly 2010), stomata counts in leaves
(Beerling et al. 2002), and leaf-shape in plants
(Wolf 1990, Royer et al. 2005) are examples
of ecometric traits where the average value in a
community is strongly enough correlated with an
environmental or climatic parameter the average
trait value can be used to predict environment.
The study of ecometrics is useful for devel-
oping trait-based proxies for studying paleoenvi-
ronments and for understanding the relationship
between biotic and climatic changes (Willis &
MacDonald 2011). A transfer function is estab-
lished using data from the modern world that
relates mean trait value to the environmental
parameter of interest. Paleoenvironmental
parameters can then be estimated from the mean
trait value in fossil assemblages (Kowalski &
Dilcher 2003, Royer et al. 2005, Head et al.
2009, Eronen et al. 2010a, 2010b, 2010c).
Extinction, extirpation (local extinction), or
introduction of species can introduce noise in
ecometric correlations if the cause of the extir-
pation is unrelated to changes in environment.
Ecometric correlations between traits and envi-
ronments arise through a rich historical interac-
tion in deep time between geographic sorting,
adaptive trait evolution, and phylogenetic sorting
involving both extinction and adaptive radiation,
all of which involve tness gradients related to
trait function (Jablonski 2005, Fritz et al. 2013).
Throughout most of geological history, extinction,
extirpation, and immigration were caused primar-
ily by climate, environment, or local community
interactions. In recent history, changes in spe-
cies ranges have been affected by a special kind
of biotic interaction that is unrelated to tness,
namely human extirpation. Human inuences
have included purposeful removal, such as the
extirpation of livestock-preying carnivores (Lalib-
erte & Ripple 2004), large-scale transformation of
dominant vegetation, such the clearing of forests
for agriculture (Tucker & Richards 1983), and
translocation of species from one ecosystem to
another, such as the introduction of mongooses
to control rodent pests (Lowe et al. 2000). The
21st century ranges of animals, especially groups
such as mammalian carnivorans, may therefore
not be in ecometric equilibrium and the inuence
of the functional relationship between ecomet-
ric traits and environments may be masked. For
example, grizzly bears (Ursus arctos), which are
now largely restricted to mountainous forested
environments, ranged across most of the North
American high plains prior to 1850 (Mattson and
Merrill 2002, Servheen 1990); reindeer or caribou
(Rangifer tarandus), which are now restricted to
high latitudes, ranged south into New England
and Wisconsin prior to the mid-1800s (Bergerud
1974); and, prior to 1830 there were sporadic
reports of the jaguar (Panthera onca), which is
now restricted to tropical and subtropical regions,
as far north as Pennsylvania and the Great Lakes
(Ranesque 1832, Daggett & Henning 1974).
Ecometric correlations between the environment
and the average value of a trait across species in
a community could easily be altered by anthro-
pogenic extirpations and introductions, perhaps
in a systematic way that obscures the underlying
ecometric pattern. The effect of human impacts
on ecometric patterns can be minimized by using
pre-disturbance ranges of species instead of their
current ranges, but in many cases human effects
predate historical accounts (Laliberte & Ripple
2004, Willis & Birks 2006, Carrasco et al. 2009).
The expected effect of anthropogenic modica-
tion of species ranges is to lessen the strength of
correlation between traits and environments.
Ecometric correlations can also be lessened
by non-anthropogenic extinctions that are inde-
pendent of environmental changes, such as the
K-Pg asteroid impact, or by non-environmental
barriers that prevent species from dispersing into
regions with which their traits are compatible,
such as when ocean barriers separate areas of
similar habitat (note that convergent evolution
might reproduce ecometric patterns on either
side of such barriers).
Nevertheless, the functional relationship
between ecometric traits and the environment
might still exert an inuence in certain situa-
tions, even in the face of anthropogenic distur-
bance. For example, exotic species introduced
into new environments are unlikely to ourish if
their traits are not compatible with their the local
environment. Species that are extirpated are
likely to have been removed from environments

ANN. ZOOL. FENNICI Vol. 51 • Effect of extinction and extirpation on ecometrics 211
with which their traits were compatible, thus
weakening the ecometric correlation, but they
are unlikely to be pushed into refuges with envi-
ronments that are incompatible with their trait
adaptations, therefore extirpation is unlikely to
introduce false ecometric correlations. Similarly,
species that expand into or retreat from agricul-
turally modied landscapes are likely to do so
on the basis of trait-environment interactions in
the altered landscapes (Poff 1997, Van Kleunen
et al. 2010). Thus, the functional relationship
between trait and environment should hold, even
if ranges and environments are so altered that the
trait is not at ecometric equilibrium.
In this paper, we examined the effects that
random and non-random changes in species
composition have on ecometric patterns using a
dataset of hindlimb traits from North American
carnivorans. Polly (2010) demonstrated in this
group that the gear ratio of the calcaneum, a
bone of the rear ankle, is correlated with loco-
motor posture and habit and that its ecometric
average in faunas sampled at 50 km intervals
was correlated macrovegetation cover and eco-
logical province at continental scale (Fig. 1).
We used an expanded version of those data set
to evaluate the correlation between mean gear
ratio and ve environmental and climatic factors.
We conducted three Monte Carlo experiments to
assess the effects on ecometric correlations of
random local extirpation, random global extinc-
tion, and selective extirpation of large body
sized species. We also evaluated the effect of the
introduction of the small Asian mongoose Her-
Fig. 1. The ecometrics of locomotion in North American carnivorans. (A) Skeleton of a dog, Canis familiaris, show-
ing the location of the femur, metatarsals, and calcaneum, three structures that are indicative of limb mechanics.
(B) Calcaneum in dorsal view, showing measurements of (a) the total length of the calcaneum and (b) the distance
of the sustentacular process from its proximal end, which are used to calculate the ecometric gear ratio used in this
study. (C) Scree plot of the calcaneum gear ratio in the 45 North American carnivorans included in this study. Mean
(dashed line) and standard deviation (grey area) for the entire North American fauna are shown. D. Map of the
mean calcaneum gear ratio in local assemblages sampled at grid points spaced at 50 km intervals.

212 Polly & Sarwar • ANN. ZOOL. FENNICI Vol. 51
pestes javanicus (also known in the literature as
H. auropunctatus), has on ecometric correlations
at the continental scale. This exotic species was
introduced into the Caribbean in the mid-19th
century, where it has become naturalized (Lowe
et al. 2000). Herpestes javanicus is the only car-
nivoran in the Caribbean islands, making it the
sole contributor to the local ecometric averages
there, and the islands have a different climate
and vegetation than most areas of the North
America, thus this species has the potential to
strongly inuence ecometric correlations.
We expected that anthropogenic removal of
species causes greater distortion to ecometric
patterns than does the introduction of exotic spe-
cies because extirpation is unlikely to be related
to a particular ecometric trait (thus producing
local assemblages that are not at “ecometric
equilibrium”), whereas successful introduc-
tion of an exotic species is likely to be related
because it must have traits compatible with its
new habitat in order to ourish (thus reinforcing
“natural” ecometric patterns). Our assessments
are relevant to interpreting ecometric patterns
from modern communities that have undergone
anthropogenic alteration, paleoassemblages that
have been altered by mass extinction, and fossil
assemblages that affected by small sample sizes
or systematic taphonomic biases.
Material and methods
Ecometric traits
The trait we used is the calcaneum “gear ratio”,
which is a single-bone proxy for the proportion
of the out-lever to the in-lever of the hind foot
(Polly 2010). Specically, the gear ratio is the
proportion of the maximum length of the cal-
caneum (measured from the medial tubercle to
cuboid facet) to the position of the sustentacular
facet (measured from the medial tubercle to the
distal margin of the sustentacular process, where
the latter intersects the body of the calcaneum)
(Fig. 1B). This ratio is correlated with the meta-
tarsal/femur ratio, the classic measure of digi-
tigrady and locomotor mechanics in mammals
(Gregory 1912, Garland & Janis 1993). The ratio
ranges from one, which occurs if the sustentacu-
lar process was positioned at the extreme distal
end of the calcaneum (which is not the case in
any living mammal), and increases to innity as
the sustentacular process is positioned more prox-
imally. In practice the ratio ranges from about 1.0
to 1.5 in living carnivorans (Polly 2010). The
proportions of the limb are essentially a mechani-
cal trade-off between power and speed of exten-
sion, with eet-footed, digitigrade cursors having
proportionally short in-levers and strong-limbed
fossorial and arboreal species having propor-
tionally longer ones (Gregory 1912, Hildebrand
1985). The in-lever of the ankle is the calcaneal
process, onto which the gastrocnemius and soleus
muscles insert. In extension, the upper ankle joint
rotates between the tibia and astragalus, the latter
of which ts against the calcaneoastragalar and
sustentacular facets of the calcaneum (Fig. 1B).
The length of the calcaneum relative to the posi-
tion of the sustentacular facet is thus proportional
to the length of the extension in-lever of the foot
relative to the center of rotation of the ankle. Not
only is the gear ratio positively correlated with
both the metatarsal/femur ratio and with degree
of digitigrady, but it is measured on a single,
blocky bone that is commonly preserved in the
fossil record, making the ratio useful for studying
ecometric patterns in the paleontological record
(Polly 2010).
Specimens
Calcaneum gear ratio was measured on 1857
museum specimens belonging to 46 species
of Carnivora (Table 1). All but two terrestrial
North American species are included in these
data, missing only Bassaricyon lasius (Harris’s
Olingo) and Spilogale pygmaea (Pygmy spotted
skunk). These species respectively occur in only
1 and 35 of the 9699 grid points that we used to
sample North America, so their absence has only
a minor effect on the ecometric patterns we mea-
sure. Our data include the measurements studied
by Polly (2010).
Geographic sampling
Carnivoran faunas and environmental data were

ANN. ZOOL. FENNICI Vol. 51 • Effect of extinction and extirpation on ecometrics 213
Table 1. The species included in this study. The mean of skeletal measurements (see Fig. 1) and the mean of the
calcaneal gear ratio are reported for each; n = sample size, D = digitigrade, S = semidigitigrade, P = plantigrade.
Species n n n Posture Mass Calcaneum Sustentacular Gear Gear
(2013) (2010) (2010) (kg) (mm) process (mm) ratio ratio
corr. publ. (2013) (2010)
Herpailurus
yaguarondi 11 1 1 D 5 30.8 23.1 1.33 1.33
Leopardus pardalis 16 4 2 D 12 38.8 28 1.39 1.40
Leopardus tigrinus 2 2 1 D 2.5 25 18.7 1.34 1.34
Leopardus wiedii 2 2 2 D 3.4 27.5 20.8 1.33 1.33
Lynx canadensis 3 3 2 D 12 47.8 35.2 1.36 1.36
Lynx rufus 222 11 4 D 10 42 30.6 1.37 1.41
Puma concolor 14 1 2 D 60 70.8 51.9 1.36 1.41
Panthera onca 14 1 1 D 80 60.6 46.4 1.28 1.31
Herpestes
javanicus 2 2 1 S 0.43 13 10.37 1.25 1.25
Canis latrans 301 2 3 D 13 41.1 32.6 1.26 1.24
Canis lupus 22 2 2 D 45 57.9 46.3 1.25 1.28
Canis rufus 2 2 2 D 24 49.7 39.5 1.26 1.26
Speothos venaticus 6 2 2 D 5.5 25.7 21.9 1.17 1.17
Urocyon cinereo-
argenteus 285 49 2 D 3.5 27.4 21.8 1.26 1.27
Vulpes lagopus 16 7 1 D 3.2 28.3 21.5 1.32 1.33
Vulpes macrotis 4 2 1 D 2 22.5 17.5 1.29 1.29
Vulpes velox 6 2 2 D 2.3 25.3 20.6 1.23 1.23
Vulpes vulpes 37 28 2 D 4.5 32.9 26 1.27 1.26
Ursus americanus 5 4 49 P 100 63.6 55.8 1.14 1.15
Ursus arctos 4 3 4 P 130 88.5 78.8 1.08 1.13
Eira barbara 12 2 1 P 4.5 27 22.2 1.22 1.22
Galictis vittata 7 2 1 P 2.35 17.5 15 1.17 1.11
Gulo gulo 4 4 1 S 12 41.5 34.2 1.21 1.21
Martes americana 3 1 2 P 0.78 18.4 14.7 1.25 1.25
Martes pennanti 3 1 26 P 3 22 17.8 1.24 1.22
Mustela erminea 2 2 5 S 0.2 6.1 5.3 1.15 1.15
Mustela frenata 239 26 1 S 0.1 8.1 6.7 1.21 1.20
Mustela nigripes 2 2 22 S 0.8 13 11.3 1.15 1.15
Mustela nivalis 2 2 2 S 0.1 3.6 3 1.22 1.22
Neovison vison 23 22 2 S 1.2 12.3 10.6 1.17 1.17
Taxidea taxus 8 3 1 P 8 29.3 23.8 1.23 1.25
Lontra canadensis 3 2 1 S 8.5 27.4 21.9 1.25 1.30
Lontra longicaudis 2 2 2 S 9 23 18.9 1.22 1.22
Conepatus
leuconotus 7 2 2 S 2 21.6 18.4 1.18 1.18
Conepatus
semistriatus 10 2 3 S 1.2 19.8 17 1.16 1.16
Mephitis macroura 2 1 1 P 1 16.9 13.2 1.28 1.28
Mephitis mephitis 5 2 11 P 1.7 20.4 16.8 1.22 1.22
Spilogale gracilis 5 5 1 P 0.5 11.7 9.5 1.23 1.23
Spilogale putorius 5 3 1 P 0.78 12.1 9.9 1.22 1.22
Bassaricyon gabbii 10 2 42 P 1.07 17.9 14.3 1.25 1.25
Bassariscus astutus 13 2 1 S 0.9 16.2 13.2 1.22 1.27
Bassariscus
sumichrasti 2 2 1 S 0.53 19.5 14.7 1.33 1.33
Nasua narica 5 5 1 P 4 28.9 23.4 1.23 1.23
Potos avus 4 3 2 P 2.2 23.3 19.8 1.18 1.18
Procyon
cancrivorus 4 4 5 S 8 37.8 31.4 1.21 1.21
Procyon lotor 503 42 3 S 7 28.7 23.4 1.22 1.24

214 Polly & Sarwar • ANN. ZOOL. FENNICI Vol. 51
sampled using a grid of points spaced evenly at
50 km intervals (Polly 2010). We used equally
spaced points because the commonly used lati-
tude and longitude grids are denser toward the
poles and thus disproportionally weight high
latitudes (Polly 2010, Polly & Eronen 2011). At
this spatial resolution, there are 9699 grid points
on the continent of North America; one or more
carnivoran species occur at 8438 of them (8509
if the points where Herpestes javanicus occurs
are included). A database of the 50 km points
with their associated environmental data is avail-
able from the rst author on request.
Ecometric means of local faunas
The ecometric mean of each 50 km grid point
was calculated by averaging the gear ratio for
all species whose geographic ranges intersect
with it (Fig. 2A). Range data for North American
carnivorans were taken from the Digital Dis-
tribution Maps of the Mammals of the Western
Hemisphere, 3.0 (http://www.natureserve.org/
getData/mammalMaps.jsp) assembled by Bruce
Patterson, Wes Sechrest, Marcelo Tognelli,
Gerardo Ceballos for The Nature Conservancy
Migratory Bird Program (Conservation Inter-
national CABS, World Wildlife Fund US, and
Environment Canada WILDSPACE) (Patterson
et al. 2003). The digital range maps were com-
piled from published scientic sources, nota-
bly including Hall (1981) and Wilson and Ruff
(1999), a complete list of which is packaged with
the data. These geographic data include both
historical ranges, as far as they are known, and
areas where species have since been extirpated,
making them maximal historical ranges. The
ranges of some species, such as the wolf (Canis
lupus), were probably even more extensive in
Fig. 2. The experiments performed in this paper. (A) Ecometric maps are created by sampling the species that
occur at each 50 km grid point and averaging their calcaneum gear ratios. The ecometric map at the upper right is
colored according to the mean of the species in the corresponding cell. (B) Experiment 1, in which species were
dropped idependently at each grid point and the ecometric pattern recalculated. (C) Experiment 2, in which random
sets of species were dropped from all grid points in which they occur and the ecometric pattern recalculated (the
red species was randomly dropped in this example). (D) Experiment 3, in which species were dropped as in Experi-
ment 2, but where the probability of being dropped was weighted by body mass (the smaller species were dropped
in this cartoon).

ANN. ZOOL. FENNICI Vol. 51 • Effect of extinction and extirpation on ecometrics 215
pre-Columbian times than these maps indicate
(Laliberte & Ripple 2004).
Environmental data
Correlation between the ecometric means and
environmental factors was assessed by resam-
pling four environmental data sets using the
same 50 km grid point scheme and calculat-
ing coefcients of determination from the data
points (see below for discussion about the effects
of spatial autocorrelation).
Elevation data were resampled from the Ter-
rainBase data set (Hastings & Dunbar 1998).
TerrainBase contains elevation and ocean depth
data in meters from mean sea level at 5-minute
grid resolution. An elevation was assigned to
each 50 km grid point from the value of the near-
est neighbor point in the TerrainBase data.
Annual mean air temperature and precipi-
tation were resampled from Willmott and Leg-
ate’s (1988) database. This spatial data set was
derived directly from original weather station
observations (24 941 for temperature and 26 858
for precipitation) an interpolated by Willmott
and Legate to a 0.5° ¥ 0.5° grid using Shepard’s
distance-weighting method. We resampled their
data using our 50 km grid points using the value
of each of our point to its nearest-neighbor in
Willmott and Legate’s data.
Macrovegetation data were resampled from
Matthews’ Global Distribution of Vegetation
(Matthews 1983, 1984). These data report domi-
nant vegetation cover at one degree resolution,
categorized using the UNESCO forest classica-
tion system which divides vegetation cover into
31 categories, such as tropical evergreen rainfor-
est, cold-deciduous forest with evergreens, xero-
morphic scrubland, or desert. The Matthews data
classies vegetation prior to human modication
as far as possible. We assigned vegetation data to
our 50 km grid points using each point’s nearest-
neighbor in the vegetation data set.
Ecoregion categories were resampled from
Bailey (1998, 2004). These ecoregions are
macroscale climatic areas dened primarily
by seasonal interactions between temperature
and precipitation and secondarily by dominant
vegetation type. The regions are hierarchically
arranged into Domains (four in North America),
Divisions (28 in North America), and Provinces
(59 in North America). For example, the eastern
Kansas prairies belong to the humid temperate
domain, the prairie division, and the forest-
steppes and prairies division, whereas the east-
central Texas prairies just to the south of the ones
in Kansas belong to the humid temperate domain
and the prairie division, but to the prairies and
savannas province. Bailey’s system, especially
its larger hierarchical categories, is derived from
Köppen (1931) and Dice (1943). We assigned an
ecoregion to each of our 50 km grid points by
intersecting the points with the ecoregion GIS
layer available from the USDA Forest Service.
Ecometric correlations
For each of the ve environmental factors, the
coefcient of determination (R2) was calculated
to describe the proportion of the variance in
mean calcaneum gear ratio associated with each
factor. For elevation, annual precipitation, and
mean annual temperature, all of which are con-
tinuous variables, R2 was calculated simply by
squaring the product-moment correlation (R).
For macrovegetation and ecoregion, which are
categorical variables, the variance in calca-
neum gear ratio was partitioned into the sum-of-
squares explained by the categories (SSmodel) and
residual sum-of-squares (SSresidual) using analysis
of variance (ANOVA), from which R2 was cal-
culated as:
R2 = SSmodel/(SSmodel + SSresidual) (1)
Condence intervals were calculated for R2
using a bootstrap procedure (Manly 2007). To
do this, geographic points were resampled 100
times with replacement and R2 was recalculated.
The 2.5 and 97.5 percentile values of the result-
ing distribution were used as to estimate 95%
condence intervals.
Spatial autocorrelation
Spatial autocorrelation is a potential source of
spurious correlation between geographically dis-

216 Polly & Sarwar • ANN. ZOOL. FENNICI Vol. 51
tributed variables caused by the fact that points
near one another tend to have similar values
(Moran 1950, Cliff & Ord 1970, Clifford et al.
1989, Lennon 2000). We did not make any spe-
cial effort to correct for autocorrelation, because
it did not affect the interpretations we drew. Nev-
ertheless, the reader should be aware that spatial
autocorrelation may inate ecometric correla-
tion coefcients more with some environmental
factors than others. For example, the ecological
province variable, which is a categorical clas-
sication of geographically contiguous regions
with similar climate and vegetation, has a lower
spatial resolution than temperature, precipita-
tion, elevation, or vegetation. The lower spatial
resolution of the ecoregion data set will tend to
inate its correlation with the ecometric data
relative to the other environmental data sets. In
contrast, the temperature, precipitation, and ele-
vation data have precisely the same spatial reso-
lution, so any difference in correlation between
them and the ecometric data is real, regardless
of the effects of spatial autocorrelation. Because
our focus is the effect of species sampling rather
than the absolute values of the correlation coef-
cients and because the correlation between traits
and environment is itself a spatial correlation, we
did not adjust our data for these autocorrelation
effects because of the risk of removing the very
effect we were trying to study.
Effects of within-species sampling
In addition to exploring how the gain or loss of
species affects ecometric correlations, we also
assessed how within-species sampling affects
the ecometric values of individual species and,
consequently, the correlations between the eco-
metric means of local communities and environ-
mental factors. Differences between the ecomet-
ric pattern in the original data set (n = 276 indi-
viduals representing 45 native terrestrial North
American carnivorans and one exotic, Herpestes
javanicus; (Polly 2010) and our expanded data
(n = 1857 individuals representing the same
46 species) were assessed by comparing the
changes in species mean and the local communi-
ties means at each of the 50 km grid points. First,
the Pearson product-moment correlation (R) was
calculated between the original and new mean
point values. Second, anomalies between the two
data sets were calculated by subtracting the new
point values from the original ones and map-
ping the residuals. The anomaly map was visu-
ally inspected for patterns that would indicate a
biased change in the geographic distribution of
the mean gear ratio. Note that sample sizes were
misreported in Polly (2010) because of a miss-
sorted data column, as discussed below.
Randomization and rarefaction
experiments
We conducted three experiments in which we
simulated the effects of extinction on ecometric
patterns by dropping species and recalculating
the ecometric correlations. In the rst exper-
iment, we randomly dropped species at each
grid point independently of which species were
dropped at other points (Fig. 2B). This experi-
ment simulated localized extinctions randomly
distributed across the continent and mimicked
the effects of either incomplete point sampling of
modern faunas and randomly distributed tapho-
nomic biases among fossils sites. In the second
experiment, we randomly dropped species from
all points at which they occur (Fig. 2C). This
experiment simulated the effects of complete, but
random extinction of species. In the third exper-
iment, we dropped species from all points where
they occur with a probability that was a function
of their body mass (Fig. 2D). This experiment
simulated the effect of selective extinction, such
as occurred in the Late Pleistocene mass extinc-
tions (Koch & Barnosky 2006) and is occurring
today in a possibly localized fashion with large
carnivores (Berger 1999, Laliberte & Ripple
2004), and of non-randomly distributed tapho-
nomic biases in the fossil record (e.g., selective
preservation of large or small body size taxa).
For these experiments, we used a modied
form of rarefaction analysis (Sanders 1968, Sim-
berloff 1972, Raup 1975), which is a type of
statistical power analysis, to study the effect of
species loss on ecometric correlation. For each
experiment, we dropped species from the analy-
sis, recalculated mean calcaneum gear ratio for
each grid point, and recalculated the correlation

ANN. ZOOL. FENNICI Vol. 51 • Effect of extinction and extirpation on ecometrics 217
between gear ratio and the ve environmental
variables. In all three experiments, we started by
dropping one species and recalculating, continu-
ing one by one until there were only three species
left. In the rst two experiments, the species that
were dropped at each step were chosen com-
pletely randomly, whereas in the third experiment
the species were chosen randomly but with the
choice weighted by the natural logarithm of their
body mass (as reported in Table 1) so that the
likelihood of a species being dropped was pro-
portional to ln(body mass). Specically, the prob-
ability of selecting a species was weighted by –1
¥ ln(body mass) + 5, which produces a linear,
positive weighting scale in which small body
sizes are more likely to be included in the sample
than large ones. Each step in the rarefaction was
repeated 25 times to estimate the variance due to
which particular species were dropped.
Results and discussion
Comparison of original and expanded
data sets
Despite a nearly sevenfold increase in the number
of individuals in our data set as compared with
that in Polly (2010), neither the ecometric means
of individual species nor the ecometric means of
local faunas changed appreciably. Of the 32 spe-
cies whose sample size (n) was larger in the 2013
data set, there was no change in the mean gear
ratio of 14 and there was a maximum change of
0.06 in Galictis vittata (which included a change
in a now-corrected mismeasurement in the origi-
nal data) (Table 1). This result indicates that dif-
ferences in calcaneum gear ratio between species
are large enough that within-species means can
be sufciently estimated from relatively small
numbers of individuals.
Note that sample sizes were misreported
in Polly (2010). The sample size column of
appendix 13.1 of that paper, which was added
after review, was sorted alphabetically by spe-
cies whereas the rest of the table was sorted by
family. This mistake is evident in the discrep-
ancy between the n reported in appendix 13.1
and table 13.3 of the 2010 paper. The sorting
mistake had no impact on the other data or sta-
tistics reported by Polly (2010). We report the
correct n for the 2010 data here (Table 1).
The expanded sample also had no appreciable
impact on the ecometric correlations (Table 2). R2
values were not signicantly different between
the data sets for any of the ve environmental
variables (as judged by the 95% condence inter-
vals). Furthermore, the correlation between data
sets was very high (R = 0.975) when the mean
values at each of the 50 km grid points were
compared. The average change in mean gear
ratio at corresponding grid points was 0.002, as
compared with the range of 0.142 between grid
points within the data set. To determine whether
the changes, however small, were geographically
biased anomalies were calculated by subtract-
ing the new data set from the original. Increases
in gear ratio tended to be scattered through the
mountainous west and in the far north (driven by
Panthera onca, Canis lupus, and Vulpes lagopus)
and decreases tended to be in the northern Mid-
west and Great Plains (driven by Vulpes vulpes
and Lynx rufus) (Fig. 3). However, the anomalies
were small, the maximum being 0.05 and the
minimum –0.01 (out of the total range of 0.142
between points). Thus, the large increase in the
Table 2. Comparison of R
2 of mean calcaneum gear ratio and ve environmental variables from three data sets.
Original data Expanded data Expanded Data
(without H. javanicus) (with H. javanicus) (without H. javanicus)
R
2 95% CI R
2 95% CI R
2 95% CI
Elevation 0.07 0.06–0.07 0.06 0.056–0.073 0.07 0.056–0.080
Annual precipitation 0.01 0.01–0.02 0.03 0.022–0.036 0.02 0.016–0.033
Mean annual temperature 0.48 0.46–0.49 0.50 0.479–0.509 0.49 0.476–0.510
Vegetation 0.49 0.47–0.51 0.50 0.484–0.514 0.50 0.470–0.518
Ecological province 0.70 0.69–0.72 0.69 0.676–0.707 0.69 0.666–0.710

218 Polly & Sarwar • ANN. ZOOL. FENNICI Vol. 51
number of individuals used to estimate the eco-
metric pattern did very little to change it.
Strength of ecometric correlations
Visual inspection of the relationship between
gear ratio and the ve environmental variables
helps understand the relative strengths of cor-
relation and the effects of different patterns of
extinction, as discussed below. The scatter plots
in Fig. 4 show the striking distinction between
the variables with strong and weak relationships
to gear ratio: neither elevation nor annual precip-
itation have a relationship, but mean annual tem-
perature, vegetation, and ecological province do,
regardless of effects of spatial autocorrelation.
Experiment 1: random, independent
local extinction
When the loss of species is independent at each
grid point, the ecometric correlations decline
steadily and predictably toward zero as more
species are removed (Fig. 5A–J). In this experi-
ment, species were selected randomly for extinc-
tion at each 50 km grid point from the list of
all North American carnivorans and dropped
from the calculation of the mean gear ratio at
that point if they occurred there. The effect of
extinction at one grid point was independent
of the effects at others, modeling a situation in
which the extirpation (or taphonomic recovery)
of species differs locally from one point to the
next. One can think of this model of extinction as
randomly moving each data point in Fig. 4 inde-
pendently, with the change proportional to the
number of species used in the calculation. When
most of the species are included in the analysis,
the change at each data point is small and the
basic pattern of correlation is preserved despite
the noise introduced by local changes in species
composition; however, when only a few species
are included, the change at each data point is
large and the basic correlation is lost.
Our results demonstrate that even when 50%
of the species are lost in this fashion, the R2
values for temperature, vegetation, and ecologi-
cal province are substantially higher than for
elevation and precipitation. This suggests that
local taphonomy, local extirpation, or local errors
in records of whether a species is present will not
affect ecometric studies so long as the effects at
each geographic point in the analysis are inde-
pendent of one another. This pattern of preserva-
tion is likely to be the case in the fossil record,
where each site has its own preservational idio-
syncrasies (e.g., one site may be a carnivore den
that selectively preserves medium size species,
another may be a oodplain deposit that selec-
tively preserves large species, and another may
be an owl accumulation that selectively preserves
small species); however, this pattern is unlikely
in modern mammal faunas where extirpations
and introductions tend to occur at regional scales.
Experiment 2: random global extinction
When the loss of species was global, the effect
was quite different (Fig. 5K–T). In Experiment
2, species were randomly selected for extinc-
tion once from the North American faunal list
and then excluded from the calculation of the
ecometric mean at every grid point at which
they occur. This experiment thus models global
extinction of species.
Fig. 3. Map showing anomalies in the mean gear
ratio of carnivoran faunas between the 2010 data set
and the current expanded one. Warm colors show
where gear ratio increased, cold colors show where it
decreased. The scale is comparable to that of Fig. 1D.

ANN. ZOOL. FENNICI Vol. 51 • Effect of extinction and extirpation on ecometrics 219
Fig. 4. Relationships between mean calcaneum gear
ratio and ve environmental variables based on the
entire 2013 data set (with Herpestes). Each point
shows the values at one of the 50 km grid points. Note
that vegetation (D) and ecological province (E) are cat-
egorical variables that have been sorted by the mean
gear ratio value of each category to better illustrate the
strength of the relationship. Category labels are given
in Appendices 1 and 2. The sorting does not inuence
R
2.
The effects of global extinction were far less
predictable than local, independent extinctions.
For variables whose real ecometric correlation
is high (temperature, vegetation, and ecologi-
cal province), the R2 value could be higher or
lower as a result of extinction, though more often
lower. Nevertheless, even with only a few spe-
cies remaining in the analysis, the expectation of
R2 remained high (i.e., the average R2 when 40
species are extinct is similar to R2 with no extinc-
tion). The reason for the unpredictable behavior
is that each extinction affects a large and variable
number of the data points, proportional to the
size of the species’ geographic range (which are
listed in Appendix 3). Loss of a species with a
large geographic range and with a gear ratio that
is either especially low or especially high will
affect the mean of many of the local assemblages.
If some regions are systematically affected, for
example, by the loss of an arctic species, the
resulting shift could increase or decrease the eco-
metric correlation. For example, the jaguar, Pan-
thera onca, a species with a high gear ratio, has a
large distribution in the warmer southern part of
the continent. Mean annual temperature is posi-
tively correlated with mean gear ratio (Fig. 4B).
Loss of P. onca will tend to decrease the mean
gear ratio at many of the geographic points where
mean annual temperature is high, which will
cause a decrease in the ecometric correlation.
Conversely, the loss of the arctic fox, Vulpes
lagopus, which is also comparatively digitigrade,
would decrease the mean gear ratio at many of the
coldest points, and thus increase in the ecometric
correlation. Interestingly, the R2 for temperature,
a continuous variable, was often near 0.0 after
ten or more species were extinct, whereas the R2
for vegetation and ecological province, which are
categorical variables, seldom dropped below 0.4.
For variables whose real correlation is low, the

220 Polly & Sarwar • ANN. ZOOL. FENNICI Vol. 51
Fig. 5. Results of the three Monte Carlo experiments shown as rarefaction graphs (elevation, annual precipitation,
mean annual temperature, macro-vegetation cover, and ecological region). The x-axis shows how many of the
species were included in the calculation and the y-axis shows the proportion of variance of the mean gear ratio is
explained by that variable (R
2). (A–E) Experiment 1 without Herpestes javanicus (independent extinction at each
grid point). (F–J) Experiment 1 with H. javanicus (independent extinction at each grid point). (K–O) Experiment 2
without H. javanicus (random species-wide extinction). (P–T) Experiment 2 with H. javanicus (random species-wide
extinction). (U–Y) Experiment 3 without H. javanicus (species-wide extinction weighted by body mass). (Z–DD)
Experiment 3 with H. javanicus (species-wide extinction weighted by body mass).

ANN. ZOOL. FENNICI Vol. 51 • Effect of extinction and extirpation on ecometrics 221
effect of extinction often raised the R2 value, but
never much higher than 0.2.
Global extinction of species thus could have
a profound effect on measuring ecometric pat-
terns. Nevertheless, variables with a high and
low ecometric R2s will only be conated when
more than a quarter of the species are lost (i.e.,
10 out of 45), and with categorical variables only
after about three quarters are lost. Logically, the
extirpation of species from large regions, such as
has been the case with large carnivorans such as
grizzlies, wolves, jaguars, and mountain lions,
is likely to have a similar effect as the global
extinctions modeled here. This suggests that if
large regional extirpations affect more than a
quarter of the fauna, ecometric patterns may be
confounded.
Experiment 3: non-random global
extinction
When the global loss of species was not random
but related to body size, the effect on ecometric
correlations was essentially the same as if the
extinctions were random (Fig. 5U–DD). This
result is interesting because it more realisti-
cally models real carnivoran extirpations, which
have preferentially involved large predators, and
the Late Pleistocene extinctions than the other
experiments. The reason that body size ltering
has no effect is because the correlation between
gear ratio and body mass is complex. Many large
carnivorans, such as canids and felids, tend to be
digitigrade and have a high gear ratio, but at the
same time the largest species (bears) are strongly
plantigrade and have low gear ratios. Thus a bias
in extinction by body size affects both extremes
of the gear ratio and has very little effect on the
overall pattern. If selection probability had been
weighted by a factor with a stronger correlation
to gear ratio, the outcome of this experiment
might have been quite different.
The effect of exotic introductions
Herpestes javanicus is the only established
exotic carnivoran in North America. To address
whether its presence biases ecometric correla-
tions, we conducted all our analysis with and
without it. Its potential for biasing is strong
because it is the only carnivoran to occur on
many Caribbean islands, whose climatic and
vegetation conditions are outliers for North
America, and as a singleton taxon in these areas,
it is the sole contributor to the ecometric mean
in most of the areas where it was introduced.
Nevertheless, its effect on ecometric correla-
tions (Table 2) or the Monte Carlo experiments
(Fig. 5) was minimal. For none of the ve envi-
ronmental variables did its inclusion cause the
R2 value to change by more than 0.01, hardly
enough to have an appreciable affect and cer-
tainly not enough to make a strong correlation
appear weak or vice versa.
There are three main reasons why H. javani-
cus does not have a strong impact on ecometric
correlations. First, it is only one among 45 other
species contributing to the ecometric patterns.
The gain or loss of a single species is unlikely to
change the relationship between mean locomo-
tor morphology and environment in the North
American carnivoran meta-community. Second,
its geographic distribution includes only 73 of
the 8509 grid points in North America (Appen-
dix 3). Each grid point contributes equally to the
correlation, and so the effect of H. javanicus is
minimized even if its effect on the mean at those
points is strong. Third, and most important for
generalizing these results, the gear ratio value of
H. javanicus (1.25) is typical of the areas where
it has become naturalized: regions where mean
annual temperature is warm, where vegetation
consists of tropical and subtropical formations,
and in tropical and subtropical maritime prov-
inces (cf. Fig. 4). Thus, even if it formed a greater
proportion of the carnivoran fauna and was dis-
tributed more widely, it would be compatible
with the ecometric results derived from other spe-
cies. Note that while an introduced species may
not have an effect on ecometric patterns, it may
well have an effect on local ecosystems.
Conclusions
We found that the effects of extinction, extirpa-
tion, and range changes have a minimal effect on
ecometric correlations when they affect no more

222 Polly & Sarwar • ANN. ZOOL. FENNICI Vol. 51
than a quarter of the species. At a continental
scale, correlations between calcaneum gear ratio,
an index that represents one aspect of average
locomotor specialization within a local commu-
nity, are either very strong (as with mean annual
temperature, vegetation cover, or ecological
province) or very weak (as with elevation and
annual precipitation). The gain or loss of even
more than a quarter of species does not alter the
ecometric correlations enough to prevent weakly
and strongly correlated environmental variables
from being distinguished, even though extinc-
tions alter the correlations.
The effects of independent local extinctions
are different from global extinctions. Indepen-
dent local extinctions always cause a decline in
ecometric correlations and the amount of decline
has a strong curvilinear relation to the propor-
tion of the species that are affected. Despite
the downward bias in correlation, up to three
quarters of species can be dropped from the
analysis with this mode of extinction without
danger of misidentifying variables with high or
low ecometric correlation. This result indicates
that ecometric correlations can safely be esti-
mated from fossil assemblages in most cases,
because taphonomic and other preservational
biases are usually independent from site to site.
Even when only a small proportion of the total
fauna is represented in the assemblages, our
results suggest that the overall ecometric pattern
will be recoverable. Indeed, the tight relationship
between the number of species and the expected
drop in R2 suggests that the real correlation can
be estimated from fossil data using rarefaction
methods.
The effects of global extinction and large-
scale extirpation have a stronger effect on eco-
metric correlations. The loss of species with
large geographic ranges, which are typical in
mammals, potentially affects geographic points
across a large proportion of the continent. If
that species is a signicant contributor to local
ecometric means and if its range is correlated
with one or the other extreme of the environmen-
tal variable, its loss could drive the measured
correlation up or down, depending on the cir-
cumstances. Thus, the effects of global extinc-
tions have a less predictable effect on ecometric
patterns than local extinctions. However, with
global extinctions the statistical expectation of
R2 does not change as species are lost. This
means that loss of species increases the uncer-
tainty with which R2 is known, but it does not
bias it in any particular direction, unlike local
extinction, which biases R2 downward.
We found that selective extinction where the
probability of losing a species is proportional to
its body size has the same effect on ecometric
correlations as does purely random extinction,
at least in regard to calcaneum gear ratio. This
result would likely be different if the ecometric
trait in question had a more direct relationship to
body size (metabolic rate or diet, for example).
Finally, the introduction of exotic species, at
least in small numbers, has only minor effects
on ecometric correlations. Impact of exotics is
minimized when they form a small proportion
of the total continental fauna and when they
have invaded only small parts of a continent.
Exotics succeed in establishing themselves only
when their traits are compatible with their new
environments, which means that their impact on
ecometric correlations is also minimized because
they are expected to be congruent with the pre-
established pattern. The success of the exotics
may, of course, have profound effects on local
ecosystem functions even when they do not
affect ecometric correlations.
Acknowledgements
This paper is dedicated to Mikael Fortelius, friend and
mentor. He, arguably more than anyone else, developed
the ecometric insights that underpin the work in this paper
through his work on regional patterns in hypsodonty. His
tireless efforts at communicating ideas and bringing people
together have made a signicant impact on the elds of
vertebrate paleontology and climate change biology. Ernie
Lundelius inspired this paper by asking what happens when
bears are driven out of the wilderness. He pointed out to us
that in the 19th century bears, the most plantigrade of carniv-
orans, were extirpated from the Texas hill country and asked
how this affected the correlation between digitigrady and
environment in North America. We would like to thank Dean
Adams, Jessica Blois, Allison Bormet, Jussi Eronen, Jason
Head, Christine Janis, Michelle Lawing, Ernie Lundelius,
Pasquale Raia, and an anonymous reviewer for discussions
that improved this paper. We thank Jussi Eronen, Jukka
Jernvall, Anu Kaakinen, Pirkko Ukkonen, and Suvi Viranta
for organizing this volume and improving our manuscript.
Allison Bormet and Michelle Lawing collected some of the

ANN. ZOOL. FENNICI Vol. 51 • Effect of extinction and extirpation on ecometrics 223
data we analyzed. We thank Janet Braun (Oklahoma Museum
of Natural History), Robert Fisher (Smithsonian Institu-
tion), Olavi Grönwall (Naturhistoriska riksmuseet, Sweden),
Benjamin Hess (North Carolina State Museum of Natural
Sciences), Randall Irmis (Utah Museum of Natural History),
Ernie Lundelius (University of Texas, Austin), Lee Lyman
(University of Missouri, Columbia), Lyn Murray (University
of Texas, Austin), Francisco Pastor Vázquez (Universidad de
Valladolid), Cindy Ramotnik (University of New Mexico,
Museum of Southwestern Biology), Ron Richards (Indiana
Stat Museum), Matthew Rowe (William Adams Zooarchae-
ology Collection, Indiana University), Laura Scheiber (Wil-
liam Adams Zooarchaeology Collection, Indiana Univer-
sity), Norm Slade (University of Kansas), William Stanley
(Field Museum of Natural History), Jeff Stephenson (Denver
Museum of Nature and Science), Phil Myers (Museum of
Zoology, University of Michigan, Ann Arbor), and Eileen
Westwig (Department of Mammalogy, American Museum
of Natural History) for access to specimens and data in
their care. This work was supported by a grant from the US
National Science Foundation (EAR-0843935) and is a con-
tribution to the Integrative Climate Change Biology (iCCB)
program of the International Union of Biological Sciences.
References
Bailey, R. G. 1998: Ecoregions of North America. — US
Department of Agriculture, Forest Service.
Bailey, R. G. 2004: Identifying ecoregion boundaries. —
Environmental Management 34: 14–26.
Beerling, D., Lomax, B., Royer, D., Upchurch, G. & Kump,
L. 2002: An atmospheric pCO2 reconstruction across the
Cretaceous-Tertiary boundary from leaf megafossils. —
Proceedings of the National Academy of Sciences of the
United States of America 99: 7836–7840.
Berger, J. 1999: Anthropogenic extinction of top carnivores
and interspecic animal behaviour: implications of the
rapid decoupling of a web involving wolves, bears,
moose and ravens. — Proceedings of the Royal Society
B 266: 2261–2267.
Bergerud, A. T. 1974: Decline of caribou in North America
following settlement. — Journal of Wildlife Manage-
ment 38: 757–770.
Carrasco, M. A., Barnosky, A. D. & Graham, R. W. 2009:
Quantifying the extent of North American mammal
extinction relative to the pre-anthropogenic baseline. —
PLoS ONE 4(12): e8331, 10.1371/journal.pone.0008331.
Cliff, A. & Ord, J. 1970: Spatial autocorrelation: a review of
existing and new measures with applications. — Eco-
nomic Geography 46: 269–292.
Clifford, P., Richardson, S. & Hémon, D. 1989: Assessing
the signicance of the correlation between two spatial
processes. — Biometrics 45: 123–134.
Daggett, P. M. & Henning, D. R. 1974. The Jaguar in North
America. — American Antiquity 39: 465–469.
Damuth, J. D., Jablonski, D., Harris, R. M., Potts, R., Stucky,
R. K., Sues, H. D. & Weishampel, D. B. 1992: Tax-
on-free characterization of animal communities. — In:
Beherensmeyer, A. K., Damuth, J. D., diMichele, W. A.,
Potts, R., Sues, H. D. & Wing, S. L. (eds.), Terrestrial
ecosystems through time: evolutionary paleoecology of
terrestrial plants and animals: 183–203. University of
Chicago Press, Chicago.
Dice, L. 1943. The biotic provinces of North America. —
University of Michigan Press, Ann Arbor.
Evans, A. R. 2013: Shape descriptors as ecometrics in dental
ecology. — Hystrix 24: 133–140.
Eronen, J. T., Polly, P. D., Fred, M., Damuth, J., Frank, D.
C., Mossbrugger, V., Scheidegger, C., Stenseth, N. C.
& Fortelius, M. 2010a. Ecometrics: the traits that bind
the past and present together. — Integrative Zoology 5:
88–101.
Eronen, J. T., Puolamäki, K., Liu, L., Lintulaakso, K.,
Damuth, J., Janis, C. & Fortelius, M. 2010b: Pre-
cipitation and large herbivorous mammals I: estimates
from present-day communities. — Evolutionary Ecology
Research 12: 217–233.
Eronen, J. T., Puolamäki, K., Liu, L., Lintulaakso, K.,
Damuth, J., Janis, C. & Fortelius, M. 2010c: Precipita-
tion and large herbivorous mammals II: applications
to fossil data. — Evolutionary Ecology Research 12:
235–248.
Fritz, S. A., Schnitzler, J., Eronen, J. T., Hof, C., Böhning-
Gaese, K. & Graham, C. H. 2013: Diversity in time and
space: wanted dead and alive. — Trends in Ecology and
Evolution 28: 509–516.
Garland, T. & Janis, C. 1993: Does metatarsal/femur ratio
predict maximal running speed in cursorial mammals?
— Journal of Zoology 229: 133–151.
Gregory, W. 1912: Notes on the principles of quadrupedal
locomotion and on the mechanism of the limbs in hoofed
animals. — Annals of the New York Academy of Sciences
22: 287–294.
Hall, E. 1981: The mammals of North America, vols. 1 & 2.
— John Wiley, New York.
Hastings, D. & Dunbar, P. 1998: Development and assess-
ment of the Global Land One-km Base Elevation digital
elevation model (GLOBE). — IAPRS 32(4): 218–221.
Head, J. J., Bloch, J. I., Hastings, A. K., Bourque, J. R.,
Cadena, E. A., Herrera, F. A., Polly, P. D. & Jaramillo,
C. A. 2009: Giant boid snake from the Palaeocene neo-
tropics reveals hotter past equatorial temperatures. —
Nature 457: 715–718.
Hildebrand, M. 1985: Walking and running. — In: Hil-
debrand, M., Bramble, D. M., Liem, K. F. & Wake, D.
B. (eds.), Functional vertebrate morphology: 38–57.
Belknap Press, Cambridge, Massachussetts.
Jablonski, D. 2005: Evolutionary innovations in the fossil
record: the intersection of ecology, development, and
macroevolution. — Journal of Experimental Zoology
(Mol. Dev. Evol.) 304B: 504–519.
Koch, P. & Barnosky, A. 2006: Late Quaternary extinctions:
state of the debate. — Annual Review of Ecology and
Systematics 37: 215–250.
Köppen, W. 1931: Grundriss der klimakunde. — W. de
Gruyter & Co., Berlin.
Kowalski, E. & Dilcher, D. 2003: Warmer paleotempera-
tures for terrestrial ecosystems. — Proceedings of the

224 Polly & Sarwar • ANN. ZOOL. FENNICI Vol. 51
National Academy of Sciences of the United States of
America 100: 167–170.
Laliberte, A. & Ripple, W. 2004: Range contractions of
North American carnivores and ungulates. — Bioscience
54: 123–138.
Lennon, J. 2000: Red-shifts and red herrings in geographical
ecology. — Ecography 23: 101–113.
Lowe, S., Browne, M., Boudjelas, S. & De Poorter, M. 2000:
One hundred of the world’s worst invasive alien species
a selection from the global invasive species database.
— Invasive Species Specialist Group (ISSG), World
Conservation Union (IUCN): Aukland, New Zealand.
Manly, B. F. J. 2007: Randomization, bootstrap, and Monte
Carlo methods in biology. — Chapman & Hall/CRC
Press, Boca Raton, Florida.
Matthews, E. 1983: Global vegetation and land use: new
high-resolution data bases for climate studies. — Journal
of Climatology and Applied Meteorology 22: 474–487.
Matthews, E. 1984: Prescription of land-surface boundary
conditions in GISS GCM II: A simple method based on
ne-resolution data bases. — NASA Technical Memo-
randum 86096: 1–20.
Mattson, D. J. & Merrill, T. 2002: Extirpations of grizzly
bears in the contiguous United States, 1850–2000. —
Conservation Biology 16: 1123–1136.
Moran, P. 1950: Notes on continuous stochastic phenomena.
— Biometrika 37: 17–23.
Patterson, B., Ceballos, G., Sechrest, W., Tognelli, M.,
Brooks, T., Luna, L., Ortega, P., Salazar, I. & Young,
B. 2003: Digital distribution maps of the mammals
of the western hemisphere. — CD-ROM compiled by
NatureServe.
Poff, N. L. 1997: Landscape lters and species traits: towards
mechanistic understanding and prediction in stream
ecology. — Journal of the North American Benthologi-
cal Society 16: 391–409.
Polly, P. D. 2010: Tiptoeing through the trophics: geographic
variation in carnivoran locomotor ecomorphology in
relation to environment. — In: Goswami, A. & Friscia,
A. (eds.), Carnivoran evolution: new views on phylogeny,
form, and function: 347–410. Cambridge Studies in Mor-
phology and Molecules, New Paradigms in Evolutionary
Biology, Cambridge University Press, Cambridge.
Polly, P. D. & Eronen, J. T. 2011: Mammal associations in
the Pleistocene of Britain: implications of ecological
niche modelling and a method for reconstrucing palae-
oclimate. — In: Ashton, N., Lewis, S. G. & Stringer,
C. (eds.), The ancient human occupation of Britain:
279–304. Elsevier, Amsterdam.
Polly, P. D., Eronen, J. T., Fred, M., Dietl, G. P., Mosbrugger,
V., Scheidegger, C., Frank, D. C., Damuth, J., Stenseth,
N. C. & Fortelius, M. 2011: History matters: ecometrics
and integrative climate change biology. — Proceedings
of the Royal Society B 278: 1121–1130.
Ranesque, C. S. 1832: On the large wandering tygers or jag-
uars of the United States. — Atlantic Journal 1: 18–19.
Raup, D. 1975: Taxonomic diversity estimation using rar-
efaction. — Paleobiology 1: 333–342.
Royer, D. L., Wilf, P., Janesko, D. A., Kowalski, E. A. &
Dilcher, D. L. 2005: Correlations of climate and plant
ecology to leaf size and shape: potential proxies for
the fossil record. — American Journal of Botany 92:
1141–1151.
Sanders, H. 1968: Benthic marine diversity: a comparative
study. — American Naturalist 102: 243–282.
Servheen, C. 1990: The status and conservation of bears of
the world. — International Conference on Bear Resarch
and Management Monograph 2: 1–32.
Simberloff, D. 1972: Properties of the rarefaction diversity
measurement. — American Naturalist 106: 414–418.
Thompson, J. N., Reichman, O. J., Morin, P. J., Polis, G.
A., Power, M. E., Sterner, R. W., Couch, C. A., Gough,
L., Holt, R., Hooper, D. U., Keesing, F., Lovell, C. R.,
Milne, B. T., Molles, M. C., Roberts, D. W. & Strauss, S.
Y. 2001: Frontiers of ecology. — Bioscience 51: 15–24.
Tucker, R. & Richards, J. 1983: Global deforestation and the
nineteenth-century world economy. — Duke University
Press, Raleigh, North Carolina.
Van Kleunen, M., Ewald, W. & Fischer, M. 2010: A meta-
analysis of trait differences between invasive and non-
invasive plant species. — Ecology Letters 13: 235–245.
Webb, C. T., Hoeting, J. A., Ames, G. M., Pyne, M. I. & Poff,
N. L. 2010: A structured and dynamic framework to
advance traits-based theory and prediction in ecology. —
Ecology Letters 13: 267–283.
Willis, K. J. & Birks, H. J. B. 2006: What is natural? The
need for a long-term perspective in biodiversity conser-
vation. — Science 314: 1261–1265.
Willis, K. J. & MacDonald, G. M. 2011: Long-term ecologi-
cal records and their relevance to climate change predic-
tions for a warmer world. — Annual Review of Ecology,
Evolution, and Systematics 42: 267–287.
Willmott, K. M. & Legates, D. R. 1988: Global air tem-
perature and precipitation: regridded monthly and annual
climatologies (version 2.01). — Center for Climatic
Research, University of Delaware, Newark, Delaware.
Wilson, D. & Ruff, S. 1999: The Smithsonian book of North
American mammals. — Smithsonian Institution Press:
Washington, DC.
Wolf, J. 1990: Palaeobotanical evidence for a marked tem-
perature increase following the Cretaceous/Tertiary
boundary. — Nature 343: 153–156

ANN. ZOOL. FENNICI Vol. 51 • Effect of extinction and extirpation on ecometrics 225
Appendix 1. Labels for vegetation types shown in Fig. 4D.
28 tropical/subtropical drought-deciduous
woodland
27 tropical/subtropical evergreen needle-leaved
forest
26 xeromorphic forest/woodland
25 xeromorphic shrubland/dwarf shrubland
24 tropical evergreen rainforest
23 trop/subtropical evergreen seasonal
broad-leaved forest
22 drought-deciduous shrubland/thicket
21 evergreen broadleaved sclerophyllous
woodland
20 tropical/subtropical drought-deciduous forest
19 evergreen broadleaved sclerophyllous forest
18 evergreen broadleaved shrubland/thick
17 tall/medium/short grassland
16 evergreen needleleaved or microphyllous
shrubland/thicket
15 tall/medium/short grassland
14 meadow
13 medium grassland
12 tall/medium/short grassland
11 cold-deciduous forest
10 desert
9 cold-deciduous forest
8 tall grassland
7 evergreen needleleaved woodland
6 temperate/subpolar evergreen needle-leaved
forest
5 ice
4 cold-deciduous woodland
3 arctic/alpine tundra
2 forb formations
1 cold-deciduous subalpine/subpolar
shrubland/dwarf shrub
Appendix 2. Labels for ecological provinces showing in Fig. 4E.
32 Mixed forest–coniferous forest–alpine meadow
31 Steppes and shrubs
30 Steppes
29 Dry steppes
28 Deciduous or mixed forest–coniferous
forest–meadow
27 Polar desert
26 Broadleaf forest–meadow
25 Forest-steppe–coniferous forest–meadow–tundra
24 Mixed forest–meadow
23 Steppe–open woodland–coniferous forest–alpine
meadow
22 Mixed forests
21 Broadleaved forests, continental
20 Glacial ice
19 Mixed forest–coniferous forest–tundra, medium
18 Mixed deciduous-coniferous forests
17 Steppe–coniferous forest
16 Forest-steppes and prairies
15 Mixed forest–coniferous forest–tundra, high
14 Broadleaved forests, oceanic
13 Ice and stoney deserts
12 taiga (boreal forests)
11 Arctic tundras
10 Forest-tundras and open woodlands
9 Tundra–polar desert
8 Taiga–tundra, high
7 Tundras
6 Tundra–meadow
5 Open woodland–tundra
4 Taiga–tundra, medium
3 Forest–meadow, high
2 Forest–meadow, medium
1 Oceanic meadow–heath
60 Oceanic semideserts
59 Desert or semidesert–open woodland or
shrub–desert or steppe
58 Shrub or woodland–steppe–meadow
57 Forest–steppe
56 Open woodlands, shrubs, and savannas
55 Deserts on sand
54 Semi-evergreen forests
53 Semidesert–shrub–open woodland–steppe or
alpine meadow
52 Open woodland–deciduous forest–coniferous
forest–steppe or meadow
51 Mediterranean hardleaved evergreen forests,
open woodlands and shrub
50 Deciduous forests
49 Semi-evergreen and evergreen forests
48 Evergreen forest–meadow or paramos
47 Semideserts and deserts
46 Mediterranean woodland or shrub–mixed or
coniferous forest–steppe or meadow
45 Evergreen forests
44 Coniferous open woodland and semideserts
43 Steppe or semidesert–mixed forest–alpine
meadow or steppe
42 Semidesert–open woodland–coniferous
forest–alpine meadow
41 Prairies and savannas
40 Semideserts
39 Dry steppe
38 Shortgrass steppes
37 Steppe–coniferous forest–tundra
36 Coniferous-broadleaved semi-evergreen forests
35 Lower Mississippi Riverine Forest Province
34 Redwood forests
33 Broadleaved-coniferous evergreen forests

226 Polly & Sarwar • ANN. ZOOL. FENNICI Vol. 51
Appendix 3. Geographic range size of North American
carnivorans expressed in number of 50 km grid points
at which they occur and in square kilometers.
Number of Area (km2) Taxon
grid points
6800 17 000 000 Canis latrans
6399 15 997 500 Vulpes vulpes
5282 13 205 000 Mustela erminea
5258 13 145 000 Neovison vison
4893 12 232 500 Mephitis mephitis
4728 11 820 000 Lontra canadensis
4649 11 622 500 Procyon lotor
4400 11 000 000 Mustela nivalis
4358 10 895 000 Mustela frenata
4023 10 057 500 Canis lupus
3861 9 652 500 Lynx rufus
3828 9 570 000 Ursus americanus
3397 8 492 500 Urocyon cinereoargenteus
3290 8 225 000 Lynx canadensis
3185 7 962 500 Gulo gulo
3044 7 610 000 Taxidea taxus
3033 7 582 500 Martes americana
2943 7 357 500 Puma concolor
2084 5 210 000 Ursus arctos
1917 4 792 500 Vulpes lagopus
1556 3 890 000 Bassariscus astutus
1531 3 827 500 Spilogale gracilis
1383 3 457 500 Martes pennanti
1175 2 937 500 Spilogale putorius
1001 2 502 500 Mustela nigripes
919 2 297 500 Nasua narica
889 2 222 500 Panthera onca
792 1 980 000 Canis rufus
716 1 790 000 Mephitis macroura
709 1 772 500 Vulpes macrotis
675 1 687 500 Leopardus pardalis
516 1 290 000 Eira barbara
498 1 245 000 Lontra longicaudis
470 1 175 000 Leopardus wiedii
465 1 162 500 Herpailurus yaguarondi
397 992 500 Potos avus
296 740 000 Galictis vittata
266 665 000 Vulpes velox
245 612 500 Bassariscus sumichrasti
193 482 500 Conepatus semistriatus
89 222 500 Conepatus leuconotus
73 182 500 Herpestes javanicus
30 75 000 Bassaricyon gabbii
30 75 000 Procyon cancrivorus
2 5 000 Speothos venaticus
2 5 000 Leopardus tigrinus
8509 21 272 500 North America
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