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Data

The information used in this study consists of faunal lists compiled by locality. The data on mammalian fossil sites were taken from the FAUNMAP Working Group (1994) compilation (http://www.museum.state.il.us/research/faunmap). This study uses the research database exclusively. Four time periods were chosen to encompass the extent and retreat of the glaciers: preglacial (PG; 40,000 to 20,000 radiocarbon years BP), glacial (G; 20,000 to 10,000 radiocarbon years BP), Holocene (H; 10,000 to 500 radiocarbon years BP), and modern (M; 500 radiocarbon years BP to present). The time periods have a 500‐year margin of error because of uncertainty in dating (FAUNMAP Working Group 1994). Because the relative proportions of ¹²C and ¹⁴C in the earth’s atmosphere have changed over time, the term “radiocarbon years BP” refers to uncalibrated dates before the present. Moreover, the present is defined as 1950. Thus, the date 3000 BP is equivalent to 1050 BC. These time periods were chosen for several reasons. First, dating of localities in the FAUNMAP database older than 40,000 years BP is not reliable (R. Graham, personal communication). Second, mammalian fossil assemblages represent relatively short amounts of time averaging, on the order of hundreds to thousands of years (Graham 1993). By choosing these time periods, I eliminated localities that could not be constrained by this narrow range of time. Because the fossil record does not necessarily preserve all species present in a given locality at a particular moment in time, some degree of time averaging will increase the probability that the species found together at a fossil site give an accurate representation of community composition. Species that may not have been fossilized during one preservation event may be preserved in the next one. On the other hand, too much time averaging may mix species that never interacted. Nonetheless, the chosen time periods allow for the range of sites in each time period to be great enough to calculate distributions and range shifts for the majority of Pleistocene mammals. Because the differences in the length and sampling intensity of different time periods may introduce a bias, two additional intervals were identified (Late Holocene, 5,000 to 0 radiocarbon years BP; late glacial, 15,000 to 10,000 radiocarbon years BP) that were approximately half the length of previously analyzed intervals. It is important to note that because of their time‐averaged nature, the fossil communities in this study are not the same as modern communities. In addition, the correlation between climate change and community dynamics can only be interpreted at the level of the expansion and retreat of the glaciers.

Calculation of Range Shifts

Localities were projected into an Albers equal‐area projection. Mammals occurring in the continental United States during each of the four time periods were identified. The area of each range was calculated as the area (km²) within a polygon enclosing all localities for a given species. The centroid of each range was calculated using a Cartesian coordinate system that accounts for the shape of the earth. All estimates of the area of a species's geographic range are approximations of the true range because of biases in the data used to create the range or because of assumptions made by the estimation techniques. However, geographic ranges of taxonomic groups based on modern data show predictable statistical patterns. For example, range size frequency distributions of modern taxonomic groups typically have a “hollow‐curve” shape, with the majority of species having small ranges (e.g., Anderson 1977; Rapoport 1982; Pagel et al. 1991; Brown 1995). Another such pattern is the relationship between body mass and range area on a log‐log scale, with large‐bodied mammals having larger geographic ranges and small‐to‐medium‐bodied mammals having smaller ranges, on average, and greater variation in geographic range area (Brown 1995). In mammals, one of the best‐known taphonomic biases is related to body size; larger species are more likely to fossilize and be found. This bias, if in operation, would predict a strong, linear relationship between body size and range area because small‐bodied species would only be found in a few sites, whereas large‐bodied species would be found in many sites. This is confounded by the observed pattern among modern mammals of a weak, positive relationship between body size and range area that is best represented by a constraint triangle (Brown 1995). However, if the taphonomic filter of body size systemically biases the data, the relationship between body size and range area should be linear, rather than triangular. Small‐bodied species should have small ranges instead of the great variation in range area observed in modern mammals. This difference should be detectable using correlations. If there is a taphonomic bias due to body size, a correlation coefficient between body size and range area should be strong and positive, whereas, if the relationship is triangular, like that of modern mammals, a correlation coefficient between body size and range area should be weak and positive. The range size frequency distributions and body mass–range area relationships were examined for each time period to determine whether the use of fossil data in the construction of geographic ranges introduced errors or biases not typically found using modern data.

Range shifts were calculated for each of the three time transitions (i.e., preglacial to glacial [PGG], glacial to Holocene [GH], and Holocene to modern [HM]). Range shifts are defined by the change in the median position of the range from one time period to another (distance was calculated using an equidistant projection), the change in range size (as defined by the natural logarithm of the percentage of a convex polygon enclosing site localities from the previous time period), and the direction of the shift (see Lyons 2001, 2003). A species must have a measurable range in adjacent time periods for a range shift to be calculated. Therefore, only species with ranges comprising at least three localities were used in these analyses. The only exceptions were for species that were well sampled (>10 localities) in one time period and poorly sampled (fewer than three localities) in the adjacent time period. In such a case, a species was judged to have shifted its range into or out of the continental United States. In the poorly sampled time period, that species was assigned a range of 1 km² and a position just outside the United States. This assumption was evaluated by conducting the analyses without poorly sampled species.

Community‐Level Patterns of Species Composition

The null model used in this study has been constructed specifically to answer the question, are levels of change in mammalian community composition through time consistent with the predictions of independent range shifts? If species are shifting their ranges independently of one another (individualistically), then a similarity index calculated between a site at time t₁ and that same site at time t₂ (where t₁ is the earlier time period) should not be different from a distribution of similarity indices calculated between a site at t₁ and randomly generated assemblages for time t₂. Typically, random assemblages are created by drawing from a pool of species occurring in a particular region in t₁. However, for the purposes of this study, this creates problems. Theoretically, species will be shifting their range into and out of a region as time progresses. Creating a species pool using the species complement of a region in t₁ does not allow this to happen. Moreover, if species are not moving as much as previous analyses suggest (see FAUNMAP Working Group 1996), this biases actual sites to be much more similar than expected. If species are moving more than previous analyses suggest, actual sites will be more different than expected. In either case, the introduced biases may allow incorrect conclusions to be drawn about changes in community composition through time. To ameliorate this problem, simulated sites were created by randomly sampling from range shifts rather than species pools. As a result, the null model randomizes range shifts among species and in space, making the implicit assumptions that range shifts are distributed independently of species and geographic location and that violation of these assumptions contributes to deviations from the null model. The assumption that species range shifts are independent of geographic location was addressed explicitly by examining the Spearman rank correlation between range shift parameters and the distance of the beginning range centroid from the middle of the continent. The effects of these assumptions will be addressed in “Discussion.”

All three range shift parameters (i.e., distance of centroid shift, direction of centroid shift, and change in range size) were drawn as a unit, and for each time transition, the distribution of range shifts used in the analyses corresponded to the actual range shifts for that transition. Thus, in the simulations, range shifts conform to independence in a mathematical sense. It must be noted that this does not imply that range shifts are random. It simply defines a baseline amount of change expected under individualistic range shifts. By drawing randomly from range shifts to generate communities and comparing them to actual communities, I get a distribution of similarity values that would be expected if the predictions of individualistic range shifts were met for that location. If the actual similarity value for a pair of communities, one older and one younger, falls within that distribution, it is consistent with the predictions of individualistic range shifts and is potentially nonanalogue. Obviously, failure to reject the null model does not mean that the null model is correct, as there are a number of potential null models. However, communities with levels of change through time that are consistent with expectations of change predicted by independent range shifts are defined as nonanalogue in this study. This definition is more specific than that in previous studies that define any amount of community change as nonanalogue (e.g., Graham and Grimm 1990; FAUNMAP Working Group 1996).

The Simulation Model

Range shifts as calculated by Lyons (2003) were randomly sampled with replacement, and artificial distributions of species were created for t₂ by applying these shifts to distributions from t₁. Range shifts were drawn from transition‐specific distributions. For example, the range shifts used in the simulation for the transition from the preglacial to the glacial came entirely from the shifts calculated for that interval (Lyons 2003). For ease in computation, each range was treated as a circle containing the exact area of the range for the species that it represents. Species composition of sites was determined by including a species in the faunal list if its randomly created range covered that site. A similarity index between the site at t₁ and the site in the randomly created t₂ was calculated using the Dice coefficient. The Dice coefficient is calculated as two times the sum of the species shared between two sites divided by the total number of species in both sites (Magurran 1988), or where a is the number of species shared between two communities and n₁ and n₂ are the richnesses of the communities. This process was repeated 10,000 times to create an expected distribution of similarity indices, given independent range shifts (fig. 1). The actual similarity index was compared to this distribution and was considered significant if it fell in the tails of the distribution (i.e., upper or lower 2.5%). Communities were sampled every 2.5° of latitude and 5° of longitude; thus, there were 60 communities sampled. This analysis was conducted separately for each of the three time transitions. Because this analysis focuses on particular geographic locations in space through time, if the sites are more similar than predicted by the null model (i.e., the observed similarity value is located in the right‐hand tail of the null distribution above the 97.5th percentile), then fewer species are substantially shifting their ranges than expected. If the sites are less similar than predicted by the null model (i.e., the observed similarity value is located in the left tail of the null distribution below the 2.5th percentile), then turnover in local communities is even greater than would be expected if species were shifting their ranges independently. Because multiple communities are sampled, the statistical power of the analyses is likely too large. However, the dependent nature of the multiple communities means that traditional correction methods (e.g., Bonferroni correction) are too conservative. Moreover, applying a Bonferroni correction in these analyses means that I raise my Type II error rate to unacceptable levels to avoid Type I errors (e.g., I would have up to seven potential false positives to avoid three potential false negatives using a Bonferroni correction in the preglacial‐to‐glacial comparison). Therefore, the number of significant communities will be reported without a correction. However, the potential for Type I errors makes placing emphasis on the significance levels of individual communities problematic. As a result, I interpret the results in terms of the significance of geographic regions and not individual communities.

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Figure 1: Diagram of the simulation model used in this study. Pentagons within a plane represent species ranges within the United States. Differences in shading of the pentagons indicate different species. A range shift is drawn at random from the observed distribution of range shifts and applied to a pentagon in the observed t₁. This is repeated for all species in t₁ to create the distribution of species ranges represented in the plane labeled random t₂, and a similarity value is calculated between the observed t₁ and the random t₂. This process is repeated 10,000 times to create a distribution of similarity values expected if range shifts are independent. This distribution is compared to the observed similarity value calculated between the observed t₁ and the observed t₂.

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There are problems and biases associated with determining the species compositions of the simulated sites using range information. This method will inflate the number of species in a local site because ranges will be drawn as continuous even though a species never occurs in all localities throughout its range. Rather, a species range more correctly resembles a patchwork of sites and not the continuous distribution normally used to represent it. Therefore, site data will be spatially autocorrelated. Communities close together will contain similar species because their ranges overlap the same sites, not because both species necessarily occur in both sites. However, this bias should not affect the interpretation of the results because this methodology applies the same bias to both the actual and the simulated sites and will inflate the species richness of both. Thus, the effects of spatial autocorrelation are built into the null model.

Sensitivity Analyses

A null model can be a powerful tool for analyzing the natural experiments that make up so much of ecological data. However, many factors can influence community structure, and null models should be carefully designed to answer specific questions. Regardless of the care with which a null model has been designed, if it is systematically biased because of assumptions, then it is dangerously flawed. Because the results of the study presented in this article could be affected by the assumptions made concerning both the null model and the data used, I conducted sensitivity analyses. The effects of each of the assumptions were evaluated by relaxing each assumption in turn, holding everything else constant, and comparing the results to the initial null model analyses. An explanation and justification for each sensitivity analysis conducted is contained in appendix A.

Geographic Range Estimation

The frequency distributions of geographic range size in each time period have the same “hollow‐curve” shape seen in modern taxa (fig. 2). This suggests that the use of fossil data does not introduce systematic biases different from those imposed by modern data. There is a weak, positive correlation between body mass and range area in each time period (PG: , ; G: , ; H: , ; M: , ). In each case, the relationship is triangular rather than linear. This relationship is significant in all but the preglacial, which contains a few extinct large‐bodied species that have small ranges.

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Figure 2: Range size frequency distributions plotted on an arithmetic scale for each time period used in this study

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Independence of Range Shifts from Geographic Location

In each transition, species with range centroids in the center of the continent have larger range shifts than those on the edges (i.e., the distance a centroid shifts has a parabolic relationship with longitude). Spearman rank correlations indicate there is a significant negative relationship between distance a range centroid shifted and the distance of the beginning position of the range centroid from the middle of the continent for each transition (PGG: , ; GH: , ; HM: −0.513, ). There is no relationship between geographic position and change in range size (PGG: , ; GH: , ; HM: , ) or the direction of the centroid shift. Direction was not tested for significance because it was measured on a 360° circle, but visual inspection indicated no relationship. Although the distance a range shifts is not independent of geographic location, the pattern found here should bias the simulations against the results found. As a result, the simulations are conservative with respect to this assumption. This is addressed in more detail below (see “Effects of Model Assumptions”).

Simulations

Overall, the patterns of analogue and nonanalogue communities differed for each time transition, as would be expected with individualistic range shifts. However, substantial areas of the United States contain communities that are more similar than would be expected, given the predictions of individualistic range shifts (fig. 3; table B1). Although the individual species are likely shifting in response to their own cues (i.e., individualistically), the effect on community composition is not straightforward. Areas of both analogue and nonanalogue communities exist. No communities were found to be significantly less similar than expected. Because this analysis is designed to examine changes through time of communities that are fixed in space, these results indicate that a number of species are not shifting their ranges far enough to leave their original community.

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Figure 3: Maps of the United States showing the distribution of analogue and nonanalogue communities for the transition from the preglacial to the glacial (top left), the glacial to the Holocene (top right), the Holocene to the modern (bottom left), and the late glacial to the Late Holocene (bottom right). The actual similarity values for the relationship between a site in the earlier time period and the same site in the later time period for each latitude and longitude combination are reported in table B1. “NA” indicates communities for which no value was calculated (see text for details). Nonsignificant (i.e., ) or nonanalogue communities are represented by light gray squares. Circles represent communities that are more similar than expected. Small light gray circles, ; medium dark gray circles, ; large black circles, .

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Preglacial to glacial. Of the 60 communities sampled, only 26 were significantly more similar than expected (fig. 3; table B1). The significant communities were concentrated in two areas: the midwestern and southeastern portions of the United States (from 37.5°N to 42.5°N and 115°W to 95°W and from 30°N to 35°N and 90°W to 85°W). The nonsignificant communities are concentrated along the border between the United States and Canada and around the Great Lakes. The preglacial‐to‐glacial transition represents 40,000 to 20,000 years BP, a time when the glaciers were advancing. The effect can be seen in the geographic positions of the nonanalogue communities. It would appear from the concentration of nonanalogue communities along the border and the around the Great Lakes that the glaciers are causing an intermingling of two faunas. Species displaced by the glaciers are likely moving south.

Glacial to Holocene. Of the 60 communities sampled, only 26 were significantly more similar than expected (fig. 3; table B1). During this time period, the significant communities were concentrated in the eastern half of the United States, excluding the area around the Great Lakes (from 30°N to 47.5°N and 100°W to 85°W, excluding 40°N to 45°N and 90°W to 80°W). The nonsignificant communities are concentrated in the western half of the United States (from 32.5°N to 47.5°N and 105°W to 120°W) and around the Great Lakes. The glacial‐to‐Holocene transition represents 20,000 to 10,000 years BP, a time when the glaciers were retreating. However, the pattern of nonanalogue communities is more difficult to interpret. The pattern of range shifts indicates that species were not simply tracking the receding glaciers (Lyons 2003). The nonanalogue communities along the border may be due to species that returned north. However, the nonanalogue communities in the western United States were more likely due to changes in moisture gradients.

Holocene to modern. Of the 60 communities sampled, fully 44 were significantly more similar than expected (fig. 3; table B1). The significant communities were concentrated in the center of the United States (from 30°N to 47.5°N and 110°W to 85°W). Although climate change during the Holocene was less dramatic than in the previous intervals, there were still vegetation changes taking place in the early and mid‐Holocene during the Altithermal (Webb 1981, 1992; Overpeck et al. 1992; Williams et al. 2001). However, changes in vegetation are measured on timescales less than the time averaging of mammalian communities. As a result, very few nonanalogue communities are detected in this transition.

Late glacial to Late Holocene. The observed distributions of range shifts for the two transitions were compared by Lyons (2001, 2003) and showed similar patterns regardless of bin length. Of the 60 communities sampled, only 16 were significantly more similar than expected (fig. 3; table B1). The significant communities were concentrated in the southeastern United States (from 30°N to 45°N and 100°W to 85°W). The nonsignificant communities were in the western United States and around the Great Lakes. Although the number of nonanalogue communities is greater for the late glacial–to–Late Holocene transition, the communities that are more similar than expected are concentrated in the same general area. Since the overall pattern in the two time transitions is similar, it would appear that degree of time averaging is similar in both. While there is clearly some effect of bin length, it is unlikely that the use of the longer time periods is greatly affecting the interpretation of geographic patterns.

Sensitivity Analyses

The results of each of the tests are summarized in table 1: while each of the assumptions affected the results quantitatively, the results were generally qualitatively similar to those presented above. Maps showing the majority rule consensus among all the different tests indicate that, overall, the patterns of community composition remained similar for each of the three time transitions (fig. 4). A detailed description of the results of the sensitivity analyses can be found in appendix A.

Table 1: Summary of the results for each of the sensitivity analyses performed in this study

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Figure 4: Maps of the United States showing the agreement between different tests for the transition from the (A) preglacial to the glacial, (B) glacial to the Holocene, and (C) Holocene to modern using a majority rule algorithm. If three of the four tests agreed, the result was indicated on the map. If only two tests agreed, extra weight was given to the results of the similarity indices analyses because they themselves included multiple tests. If all tests were significant but disagreed as to level of significance, a single asterisk is used. However, if all tests indicated the same level of significance, this is indicated by the use of additional asterisks. Nonsignificant or nonanalogue communities ( ) are represented by “ns.” Asterisks represent communities that are more similar than expected. Single asterisk, ; double asterisk, ; triple asterisk, .

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Simulations

Null models have a contentious history in community ecology. They have been both embraced and reviled, depending on the school of thought of a given researcher and the point in the history of ecology at which they were used (Gotelli and Graves 1996). Although a similar debate is occurring today with respect to mid‐domain models (see Colwell et al. 2004 for a review), the most strident debates concerned the application of null models to competition theory in the 1980s. Proponents of null models compared the distribution of species within communities (or some other measure of community structure, such as body size) to randomly generated communities, claiming that differences would show the existence of competition (Connor and Simberloff 1979; Strong et al. 1979). Opponents of null models claimed that null models were biased against detecting biotic interactions or were “too null” (Grant and Abbott 1980; Diamond and Gilpin 1982; Gilpin and Diamond 1984). In a sense, both groups were correct. A null model can be a powerful tool for analyzing the natural experiments that make up so much of ecological data. However, many factors can influence community structure, and null models should be carefully designed to answer specific questions. Moreover, they must be rigorously evaluated with respect to any assumptions necessary to the model.

As a whole, the quantitative empirical estimates of range shifts made by Lyons (2003) are a powerful tool. The overall pattern indicates that the responses of mammalian species to climate change are complex, and while many of the species may be responding individualistically, the effect on community structure is not necessarily a straightforward and complete reorganization of species. Because many species have very slight range shifts, there is some continuity in communities through time. Moreover, this is consistent with the responses of plant communities to climate change. Areas of North America show nonanalogue vegetation combinations, but other areas show combinations that are recognized and named after those seen today (Webb 1981, 1992; Huntley 1990; Overpeck et al. 1992, 2003; Jackson et al. 1997; Jackson and Overpeck 2000; Williams et al. 2001). However, there are differences between the methods used in this study and those used for quantifying vegetation changes. Pollen workers typically calculate the similarity between two regions and use some predetermined value to decide whether the similarity is small enough to be considered nonanalogue. Moreover, analyses involving pollen use difference in abundance as well as species identity. In contrast, the method employed in this analysis of mammals allows each community to have its own threshold of similarity. From a modeling perspective, the individualistic response of species to climate change means that all species responded independently of one another. This response can be modeled mathematically by forcing independence upon range shifts. Drawing randomly from range shifts to simulate communities expected under the predictions of individualistic range shifts allows a statistical definition of nonanalogue mammalian communities.

Effects of Model Assumptions

It must be acknowledged that range shifts are not random, and randomizing them to simulate communities may seem counterintuitive. However, this study attempts to test observed patterns of change against a null model and in so doing, to compare observed levels of change to baseline levels expected under a model of pure individualism. This individualism has two component parts. In the null model, range shifts are distributed independently of geographic position and species identity. However, examination of the raw range shifts indicates that they are not independent of geographic position. In each transition, species with range centroids in the center of the continent have larger range shifts than those on the edges. Indeed, Spearman rank correlations indicate that there are significant negative relationships between the distance a range centroid shifted and the distance of the beginning position of the range centroid from the middle of the continent for each transition. In the simulations, the effect of randomizing from these range shifts is a bias for greater similarity in the midcontinent and lesser similarity on the edges. Simulated range shifts applied to the center of the continent will be smaller, on average, than they truly are, whereas range shifts applied to the edges will be larger, on average, than they truly are. Therefore, this assumption should bias the results so that communities in the midcontinent should be less similar or not significantly different from simulations and communities on the edges should be more similar than expected. In general, this is the opposite of the observed results for each transition (figs. 3, 4). Communities in the midcontinent tend to be more similar than model predictions, and communities on the edges tend to be consistent with model predictions (figs. 3, 4). Therefore, deviations between observed similarity and model predictions are likely due to violation of the assumption that range shifts are independent among species.

As noted above, because I sampled the same points in space through time, the areas of greater‐than‐expected similarity result when more species remain in their home communities than would be expected under a model of pure individualism. However, one aspect of individualism not incorporated into this null model is the expectation that species will also shift their ranges at different rates. Moreover, this model does not address the underlying biotic and abiotic factors that may be ultimately responsible. The next step is to determine the degree to which areas of nonanalogue mammal communities are coincident with areas of nonanalogue vegetation. Areas of nonanalogue vegetation formed under areas of nonanalogue climate (Williams et al. 2001; Overpeck et al. 2003). A similar relationship may be expected between mammals and the plant communities that form their habitat and food preferences. Because detailed analyses of the patterns of mammalian range shifts indicate that species are responding independently of one another (Lyons 2003), it is likely that the greater‐than‐expected similarity found in some regions is due to species responding to common environmental changes and not to one another.

Patterns of community composition differ quantitatively but not qualitatively as different model and data assumptions are relaxed (app. A; table 1; fig. 4). In general, the null model is robust with respect to the assumptions made. The most volatile transition in terms of community composition is the glacial to Holocene. However, reduction of the length of each period (i.e., late glacial to Late Holocene) does not substantially alter geographic patterns of analogue versus nonanalogue communities. Modeling species ranges as circles clearly affects the perceived community composition of coastal regions. However, the potential increase in the overlap of species ranges does not alter patterns of analogue and nonanalogue communities. Moreover, despite the differences in similarity indices, the consensus from the ones examined in this study indicates that the null model is relatively robust with respect to the chosen index. Species with poor sampling in an interval are always problematic in paleontological studies. Here the assumptions made concerning species that shifted their range outside the United States did not affect the general patterns of community composition.

Implications

The results from this study indicate that although species responses are individualistic, likely effects of climate change on local community composition are not straightforward (i.e., not all communities will be nonanalogue). Not all species are equally affected by climate change. Some species will shift their ranges, others will not. Moreover, some species that occur in the same community likely do so because of similarities in their environmental requirements. Even though they respond individualistically, their ranges will continue to intersect through time, and they will likely continue to occur together in a number of localities. Recent analyses using pollen data and climate models indicate that the individualistic responses of species are strongly influenced by the degree to which their niche spaces are represented in the current environment (Jackson and Overpeck 2000). Indeed, areas of nonanalogue vegetation are coincident with areas of nonanalogue climate (Williams et al. 2001; Overpeck et al. 2003). The spatial variation in nonanalogue mammal communities found in this study indicates that similar processes are influencing mammalian dynamics. Analyses combining information about plant and mammal distributions through time are needed to better understand the community dynamics documented in this study.

This study quantitatively examines Pleistocene mammalian community structure. Because the null model was designed to answer a specific question, this quantitative approach is sensitive to areas that are analogue and nonanalogue. Moreover, it provides an objective way to evaluate community structure through time by providing null expectations about the degree to which species range shifts should affect paleocommunities. Finally, this study examines community structure using all mammals, not just those that show dramatic range shifts. Predictions that all fossil mammal communities should be nonanalogue (FAUNMAP Working Group 1996) are not upheld. Whether because of abiotic factors or because of biotic interactions, community composition through time is more complex than previously thought.