Spatial, temporal and taxonomic scaling of richness in

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Received: 21 July 2017    Revised: 6 April 2018    Accepted: 13 April 2018 DOI: 10.1111/geb.12762

RESE ARCH PAPERS

Spatial, temporal and taxonomic scaling of richness in an eastern African large mammal community Andrew Du1,2,* | Anna K. Behrensmeyer2,3 1 Department of Anthropology, Center for the Advanced Study of Human Paleobiology, The George Washington University, Washington, District of Columbia 2

The Evolution of Terrestrial Ecosystems Program, National Museum of Natural History, Smithsonian Institution, Washington, District of Columbia 3

Department of Paleobiology, National Museum of Natural History, Smithsonian Institution, Washington, District of Columbia

Abstract Aim: Ecological patterns and process change across spatial, temporal and taxonomic scales. This confounds comparisons between modern and fossil communities, which are sampled across very different scales, especially temporal ones. We use a recent bone dataset (i.e., “death assemblages”) from a modern ecosystem to explore spatial, temporal and taxonomic scaling in biodiversity assessments. Our ultimate goal is to create a model based on these scaling relationships to facilitate meaningful compari‐ sons between modern and fossil communities.

Correspondence Andrew Du, Department of Organismal Biology and Anatomy, The University of Chicago, Chicago, IL 60637. Email: [email protected]

Location: Amboseli National Park, southern Kenya.

Present address *Department of Organismal Biology and Anatomy, The University of Chicago, Chicago, IL.

tion methods to investigate how species richness at Amboseli scales as a function of

Funding information National Science Foundation, Grant/ Award number: DGE‐080163; Kenya Wildlife Service; National Museums of Kenya; Smithsonian Institution; National Geographic Society, Grant/Award number: 1508, 4339‐90, 7525‐03 and 8784‐10.

Time period: Mid‐1960 s to present day. Major taxa studied: Large mammals (>1 kg). Methods: We implemented a random placement null model and used model selec‐ time and area [i.e., the species–time–area relationship (STAR) model]. We then ana‐ lysed how the model coefficients change at different taxonomic scales (i.e., genus, family, order). Results: In agreement with previous studies, we find species richness scales posi‐ tively with time and area but with a negative interaction between the two. Rates of richness turnover decrease as taxonomic scale increases. Main conclusions: We hypothesize that decreasing rates of turnover with increasing spatial and/or temporal scale are caused by taking progressively larger samples from a species pool that is changing at a slower rate relative to turnover at the scale of sampling. Because increasing area and time are simply alternative ways of uncovering the species pool, increased time‐averaging of communities results in a more spatially averaged ecological signal. Increasing taxonomic scale causes turnover rates to de‐ crease because of how lower-level taxa are aggregated into coarser, higher-level ones. The STAR model presents a framework for extrapolating and comparing rich‐ ness between small‐scale modern and large‐scale fossil communities, as well as a means to understand the general processes involved with changing scale. KEYWORDS

Kenyan large mammals, palaeoecology, richness, spatiotemporal scaling, species pool, species–time–area relationship, taxonomic scaling, turnover

Global Ecol Biogeogr. 2018;27:1031–1042.

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1 |  I NTRO D U C TI O N

we fit a STAR model to data from the large mammal (>1 kg) skele‐ tal (i.e., “death”) assemblage of Amboseli National Park, southern

Neo and palaeoecological research are complementary and have a

Kenya (see Supporting Information Figure S1 for map). This also

lot to offer each other. For example, many palaeoecological stud‐

served the purpose of using the potential fossil record of a re‐

ies use modern ecological models as an interpretive framework for

cent mammal community to help bridge the gap between neo and

inferring process from fossil patterns (e.g., Patzkowsky & Holland,

palaeoecology. The Amboseli data are ideal for addressing these

2003). Likewise, modern ecologists are beginning to appreciate the

questions because (a) this is a relatively speciose large mammal

historical and large‐scale perspectives that fossil assemblages can

ecosystem with 53 species (from live census data) including 47

offer (e.g., McGill, Hadly, & Maurer, 2005; Rosenzweig, 1998). More

wild herbivores and carnivores and six domestic species (includ‐

recently, researchers have analysed combined neo and palaeoeco‐

ing Homo sapiens) (Behrensmeyer, Western, & Boaz, 1979); (b) the

logical datasets to see if community assembly processes differed in

large spatial extent of the sampled area (area of convex hull = 300

the past compared to the present (Lyons et al., 2016). However, the

km2; Supporting Information Figure S1) enables construction

appropriateness of this cross‐field exchange of ideas and data be‐

of SARs and also encompasses a number of different habitats

tween neo and palaeoecology is contingent upon their comparabil‐

(e.g., woodland, swamp, plains), which are occupied by different

ity across different scales. Unfortunately for the goal of promoting

suites of species (Behrensmeyer et al., 1979; Western, 2007);

more productive neo and palaeoecology dialogues, ecological pat‐

(c) the death assemblage data cover a temporal extent of 40+

tern and process are known to change across spatial, temporal and

years from the mid 1960 s through 2010, providing a time series

taxonomic scales (Levin, 1992; Wiens, 1989). This poses a challenge

and thus STRs. Moreover, Amboseli experienced habitat change

for studying ecological communities that differ by orders of mag‐

during this time period (Western, 2007; Western & Behrensmeyer,

nitude in scale, as is usually required when comparing modern and

2009), which would be expected in many time‐averaged fossil

fossil communities (neo and palaeoecology study comparable spatial

assemblages; (d) previous studies have demonstrated high com‐

scales, but temporal scales are typically 10 –10 and 10 –10 years,

positional fidelity between the living community and the death as‐

respectively).

semblage (Behrensmeyer et al., 1979; Miller et al., 2014; Western

−2

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One way to assess the comparability of ecological phenomena

& Behrensmeyer, 2009); and (e) many of Amboseli’s mammalian

across orders of magnitude of scale is to study scaling relationships

congeners and ancestors are found in eastern African fossil as‐

in ecological patterns. An early example of this approach in ecology

semblages (Bobe, 2011), facilitating direct comparisons with the

is the species–area relationship (SAR), which analyses how species

fossil record.

richness scales with increasing area (Rosenzweig, 1995). Preston

We believe the STAR can be used as an effective tool for en‐

(1960) first proposed that the processes influencing species accu‐

abling comparisons between modern and fossil communities across

mulation across space can be transposed to describe species accu‐

spatiotemporal scales that differ by orders of magnitude. We first

mulation through time. By analogy, he called this relationship the

perform a null model analysis to see whether individuals within spe‐

species–time relationship (STR). Although not as well studied as

cies at Amboseli exhibit clumping and, if so, at what spatiotemporal

the SAR, empirical studies have demonstrated similar functional

scales. We then fit three STAR regression models, which can accom‐

forms between the STR and SAR (Adler & Lauenroth, 2003; Hadly

modate clumping, to the data and use model selection techniques

& Maurer, 2001; Preston, 1960; White et al., 2006). The rate of spe‐

to characterize the functional form of the STAR. We next describe

cies accumulation has been related to the rate of species turnover

how the STAR model coefficients change as a function of taxonomic

(Koleff, Gaston, & Lennon, 2003), and the two concepts are treated

scale to investigate how the latter interacts with space and time to

interchangeably here.

influence richness. This is especially relevant as many palaeoecolog‐

Recently, the SAR and STR were unified into a single interac‐

ical studies are conducted at the genus level or higher (e.g., Bobe,

tion model called the species–time–area relationship (STAR; Adler

2011; Patzkowsky & Holland, 2003). We then estimate scales of

& Lauenroth, 2003; Adler et al., 2005). The area‐by‐time interaction

time–area equivalence (Adler et al., 2005), which are the spatial and

term is consistently negative (Adler & Lauenroth, 2003; Adler et al.,

temporal scales at which the STR and SAR turnover rates are equal,

2005; McGlinn & Palmer, 2009; Raia, Carotenuto, Meloro, Piras, &

so as to understand the relationship between increasing spatial scale

Barbera, 2011) and suggests similar processes underlying commu‐

and increasing temporal scale. Finally, we hypothesize what general

nity assembly across space and time (White, 2007; White, Ernest,

processes might be driving the STAR pattern in order to understand,

Adler, Hurlbert, & Lyons, 2010). A negative interaction term indi‐

from a mechanistic basis, how changing spatiotemporal scales in‐

cates the rate of species accumulation across space decreases as a

fluence our interpretation of ecological dynamics, both in modern

function of time and vice versa.

and ancient communities. While our ultimate goal is to scale up the

The discovery of the STAR has important implications for scal‐

Amboseli STAR model to predict richness in fossil communities, we

ing richness in order to compare neo and palaeoecological studies:

emphasize that our analytical and theoretical framework can also be

one cannot only extrapolate the time span of sampling in modern

used to compare differently scaled communities within modern or

studies but must also take into account sampling area. To this end,

fossil systems.

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2 | M E TH O DS

time, we calculated the geometric mean of species richness, so each unique combination of area and time only had one corresponding richness estimate (Adler & Lauenroth, 2003; Adler et al., 2005). Given

2.1 | Data

the method of iterative aggregation both in time and space, these

Species richness data for the large mammal death assemblages were

data are non‐independent, which violates one of the assumptions of

collected using 103 noncontiguous plots (median size = 0.07 km2; me‐

ordinary least squares regression (Draper & Smith, 1998). However,

dian spacing between neighbouring plots = 0.98 km), which are distrib‐

non‐independence only affects the calculation of parameter stan‐

uted over 300 km2 of the Amboseli Basin, mostly in Amboseli National

dard error estimates and p‐values; the parameter estimates them‐

Park (Supporting Information Figure S1). The plots sampled a total

selves are less efficient but remain unbiased (Draper & Smith, 1998).

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area of 8.27 km and cover the habitats most frequented by the living mammal community. Plots were periodically sampled at the end of the long dry season (August–October) over multiple decades, and the re‐ sulting samples were grouped into time bins (Supporting Information

2.2 | Comparing different models of spatiotemporal turnover

Table S1). The size of each time bin reflects the temporal grain of

We originally followed Adler et al. (2005) and included a random

each time‐averaged death assemblage (median = 6 years; Supporting

placement null model with three other power‐law regression models

Information Table S1), which was estimated using Behrensmeyer’s

in the model selection process. This is not an appropriate compari‐

(1978) weathering stages (Supporting Information Appendix S1). SARs

son, however, because it is unclear how many degrees of freedom

were constructed for each time bin by randomly choosing a plot and

the random placement model has, which in any case are not com‐

then sequentially aggregating these one at a time by nearest distance

parable to the fitted parameters of a regression model. Because

and recording the cumulative area and richness estimates. This pro‐

the random placement model (Adler et al., 2005) ultimately tests

cess was repeated with a new starting plot each time in order to obtain

whether species accumulation is a result of sampling individuals

all possible area combinations along with their respective species rich‐

within species that exhibit no spatial or temporal clumping, we de‐

ness estimates. This entire procedure was repeated using a moving

cided to operationalize this model as a separate null model test. Once

window approach first with a two time bin window (e.g., SARs were

we established that individuals belonging to the same species are

constructed within the first two time bins, then within the second and

spatiotemporally clumped at Amboseli, we moved onto fitting and

third time bin, etc.). Next, a three time bin window was used and so on

assessing the power‐law models, which can accommodate clumping.

until we were left with one replicate that included all time bins. See

For the random placement null model, individuals were shuffled

Supporting Information Appendix S1 for more information on how the

without replacement across time bins and plots (thereby eliminating

Amboseli data were collected and aggregated.

any intraspecific clumping), while preserving the observed number

Time‐averaging refers to information that is combined (“aver‐

of individuals in each time bin/plot combination. The previously de‐

aged”) over time, and palaeoecologists distinguish two categories

scribed spatial and temporal aggregation procedure was then carried

of time‐averaging, “taphonomic” and “analytical” (Behrensmeyer

out, and richness was tallied for each spatiotemporal scale. Such cal‐

& Hook, 1992). Taphonomic time‐averaging is a natural phenome‐

culations were repeated 1,000 times to get 1,000 vectors of random‐

non caused, in this case, by the rate of individual deaths outpacing

ized richness values. For each spatiotemporal scale, the proportion

skeletal destruction rates, so multiple non‐contemporaneous gen‐

of 1,000 null richness values less than or equal to the observed value

erations are deposited in the same death assemblage. This is why

was calculated. This is equivalent to a computed p‐value but cannot

the time bin (i.e., temporal grain) of each death assemblage spans

be strictly interpreted as such due to the sequential aggregation pro‐

multiple years, despite surveys being conducted over periods of days

cedure and the non‐independent nature of these data. Nevertheless,

to weeks (Supporting Information Appendix S1). We do not expect

these numbers are informative indicators of how much and at what

this to bias our results, and in fact it likely leads to a more accurate

spatiotemporal scales the observed richness patterns deviate from

representation of the community because death assemblages rep‐

the shuffled null ones. Because this method produces a large number

resent attritional mortality and continuous sampling over the time

of unique spatial scales, which complicates the graphical presenta‐

period of skeletal accumulation (by virtue of bones remaining on the

tion of results, we decided to combine similar spatial scales and cal‐

landscape after death). Analytical time‐averaging occurs when the

culated the median “p‐value” for those combined scales. If individuals

researcher pools data from different time periods, as is done with

at Amboseli exhibit intraspecific clumping at a particular spatiotem‐

our moving window approach and when STRs are constructed in

poral scale, the corresponding “p‐value” should be low.

general. The effects of taphonomic and analytical time‐averaging are similar, and both are represented in our dataset and analyses. Our methods resulted in a final dataset with area estimates ranging from one to the total number of plots in each time window (range = 0.002–7.2 km2), number of year estimates ranging from one

We then assessed three power‐law models of increasing com‐ plexity describing how species accumulate with area and time (Adler et al., 2005). The three models were fit using ordinary least squares with log10 ‐transformed dependent and independent variables (ob‐ tained following the aggregation procedure described in the previous

time bin to all seven (range = 5–44 years), and their respective spe‐

section). The simplest power‐law model is log10 S = log10 c + z log10 AT

cies richness estimates. For all repeated combinations of area and

, where c is an estimated constant, z is the estimated slope, A is area

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and T is time. This model treats species accumulation as a function

As an example, a ratio of 4 km2/year implies that the rate of tempo‐

of an area × time “volume”, where area and time are assumed to have

ral turnover in an area of 4 km2 is equivalent to the rate of spatial

identical, non‐interactive effects on species richness. The next model

turnover over a 1‐year period. These ratios enable the comparison

is log10 S = log10 c + zlog10 A + wlog10 T, where z is the species richness

of rates of spatial and temporal turnover in a STAR model while ac‐

rate of increase with area, and w is the rate of increase with time.

counting for the interaction term (Adler et al., 2005). They also have

This model stipulates that area and time have independent, non‐in‐

obvious implications for the interpretation of time‐averaged fossil

teractive effects on richness. The final, most complex model is one

assemblages. Knowing the corresponding spatial scale for a time‐av‐

where area and time have independent and interactive effects on

eraged assemblage at which turnover rates are equivalent provides

richness: log10 S = log10 c + z1 log10 A + w1 log10 T + u(log10 A)(log10 T), in

a measure of the relationship between time‐ and spatial‐averaging.

which z1 is the time‐independent rate of richness increase with area

This sheds quantitative light on a long‐standing issue in palaeoecol‐

at unit time (i.e., 1 year), w1 is the area‐independent rate of increase

ogy, that is, how time‐averaging (both taphonomic and analytical)

with time at unit area (i.e., 1 km2) and u is the interaction parameter. This interaction model is best supported in a number of taxonomic

impacts interpretation of species richness measures. All analyses were done in R version 3.3.1 (R Core Team, 2017).

groups (Adler & Lauenroth, 2003; Adler et al., 2005; McGlinn & Palmer, 2009; Raia et al., 2011). To evaluate the fit of each of these three models to the data, we used the Akaike information criterion (AIC). Because of the non‐in‐ dependent nature of the data, however, AIC here only served as an ad hoc way to assess model fit and penalize for complexity (i.e., num‐ ber of parameters; Adler et al., 2005). To estimate AIC for all models, we first calculated residual sum of squares using the observed and expected richness values from each model. We ( then calculated AIC ) RSS + 2K, where assuming a least squares model, where AIC = n ln n n equals the total number of data points, RSS equals the residual sum

3 | R E S U LT S The final analytical dataset includes a total of 3,181 individuals and 34 species. Each plot within a given time bin records a me‐ dian of eight individuals and four species. 97 plots were sampled in more than one time bin, and 53 were sampled in at least four (Supporting Information Figure S3). Time window sizes range from 5 to 44 years (median = 19 years), and area spans 0.002 to 7.175 km2

of squares and K equals the number of estimated model parameters (Burnham & Anderson, 2002, p. 63).

2.3 | Spatiotemporal scaling of richness across taxonomic scales All previously published STAR models were originally fit to species‐ level data (as the “S” in “STAR” stands for species). To see how spa‐ tiotemporal scaling of richness changes as a function of taxonomic scale, we repeated the moving temporal window and spatial aggre‐ gation procedure described above at the genus, family and order level, keeping the STAR acronym for consistency’s sake. We then fit the best‐fit STAR model (previously assessed using AIC) for each taxonomic level. Finally, we compared the estimated model coeffi‐ cients to determine how rates of spatiotemporal turnover vary as a function of taxonomic scale.

2.4 | Calculating scales of time–area equivalence We calculated scales of time–area equivalence for all four taxonomic scales following Adler et al. (2005). Scales of equivalence are defined as the combination of sampled area and time span, where the slopes of the STR and SAR (i.e., turnover rates) are equivalent. Turnover rates here are relative and not dependent on the unit of measure‐ ment. Scales of equivalence are usually presented as ratios, and using the estimated parameters from the interaction STAR model, they are calculated as (Adler et al., 2005): z1 −w1 A = 10 u T

(1)

F I G U R E 1   Null model results showing the spatial and temporal scales at which individuals belonging to the same species are clumped. Null richness values were generated by shuffling individuals across plots and time bins (1,000 iterations), thereby breaking any clumping structure. Clumping is indicated by the proportion of null values that is less than or equal to observed richness at a given spatiotemporal scale. This is similar to a p‐value but cannot be strictly interpreted as such due to the non‐independent nature of these data (see Methods). Because of the large number of unique spatial scales analysed (n = 9,407), we combined similar spatial scales for visual clarity and calculated the median “p‐value” for those aggregated scales. The number of combined scales is indicated by the size of the point. Our aggregating scheme created distinct columns of points, whereas the distinct rows are due to the discrete temporal bins used in the analysis. Darker shaded points represent “significant” clumping. Note the x axis is logged. See also Supporting Information Figure S8

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(median = 2.097 km2). There are 14,768 unique time by area combi‐

which serves to artificially inflate spatial turnover rates (and there‐

nations and respective richness estimates (i.e., there are 14,768 data

fore z1) (Adler & Lauenroth, 2003). Nevertheless, both the z1 and w1

points in all models). Supporting Information Figure S4 shows how

estimates from Amboseli are within the range found in other commu‐

each variable is distributed and how they relate to each other.

nities (Adler & Lauenroth, 2003; Adler et al., 2005; Raia et al., 2011), although z1 and w1 are dependent on the units used to measure time

3.1 | Which STAR model fits best?

and area, respectively, due to the interaction term. The interaction term, u, is negative, a result consistently found in other modern and

The presence of intraspecific clumping of individuals is seen at most,

fossil studies that span many taxonomic groups (Adler & Lauenroth,

but not all, spatiotemporal scales (Figure 1). There is non‐significant

2003; Adler et al., 2005; McGlinn & Palmer, 2009; Raia et al., 2011).

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clumping at small spatial (