Temporal changes in the individual size distribution decouple long-term trends in abundance, biomass, and energy use of North American breeding bird communities

Aim A core objective of contemporary biodiversity science is to understand long-term trends in the structure and function of ecological communities. Different currencies of ecological function – specifically, total abundance, total standing biomass, and total metabolic flux – are naturally linked, but may become decoupled if the underlying size structure of a system changes. Here, we seek to establish how changes in community size composition modulate long-term relationships between different currencies of ecological function for North American birds. Location North America, north of Mexico. Time period 1988-2018. Major taxa studied Breeding birds. Methods We used species’ traits and allometric scaling to estimate individual size measurements and basal metabolic rate for birds observed in the North American Breeding Bird Survey. We compared the long-term trajectories for community-wide standing biomass and energy use to the long-term trends driven by changes in individual abundance alone. Finally, we used dissimilarity metrics to evaluate the link between changes in species and size composition and changes in the relationship between abundance- and size-driven dynamics. Results For a substantial minority of communities, shifts in community size composition have decoupled the long-term dynamics of biomass, energy use, and individual abundance. While trends in abundance were dominated by decreases, trends in biomass were evenly divided between decreases and increases, and trends in energy use featured more increases than expected given changes in abundance alone. Communities with decoupled dynamics showed greater increases in community-wide mean body size than other communities, but did not differ from other communities in overall turnover in species or size composition. Main conclusions Size- and abundance-based currencies of ecological function are linked, but not necessarily equivalent. For North American breeding birds, shifts in species composition favoring larger-bodied species may have partially offset declines in standing biomass driven by losses of individuals over the past 30 years.


Introduction 63
Understanding the interrelated dynamics of size-and abundance-based dimensions of 64 decoupling between the currencies?; 3) To what extent do changes in species composition and 132 community size structure translate into decoupling in the temporal trends of different currencies 133 at the community scale? 134 Methods 135 Code to replicate these analyses is available online on GitHub, and will be archived to Zenodo 136 upon manuscript acceptance. For the purposes of double-blind review, an anonymized copy is 137 available at https://github.com/bbssizeshifts/BBSsims. 138

Bird abundance data 139
We used data from the Breeding Bird Survey (Pardieck et  30-year time period from 1989-2018. We selected these years to provide a temporal window 147 sufficient to detect long-term trends (Cusser et al. 2020), while allowing for a substantial number 148 of routes. To avoid irregularities caused by missing time steps, we restricted the main analysis to 149 routes that had been sampled in at least 27 of 30 years in this window (n = 739) and compared 150 these results to a more strict selection of routes that were sampled in every year (n = 199). 151 Results for this more stringent subset of routes were qualitatively the same as for the more 152 inclusive selection of routes (Appendix S1). We take the route to be the "community" scale (Thibault et al. 2011). We filtered the data to remove taxa that are poorly sampled through the 154 point-count methods used in the Breeding Bird Survey, following Harris et al. (2018). 155

Estimated size data 156
The Breeding Bird Survey dataset contains abundances for all species along each route in each 157 year, but does not include measurements of individual body size. We generated body size 158 estimates for individual birds assuming that intraspecific size distributions are normally 159 distributed around a species' mean body size (following Thibault et al. (2011)). Using records of 160 species' mean and standard deviation of body mass from Dunning (2008) Comparing abundance-and size-based currencies 179 Comparing trends across different currencies is a nontrivial statistical problem. Because different 180 currencies vary widely in their scale of measure (e.g. abundance in the hundreds of individuals; 181 total biomass in the thousands of grams), it is challenging to interpret differences in magnitude of 182 slope across different currencies. Transformation and scaling using common approaches (such as 183 a square-root transformation, or rescaling each currency to a mean of 0 and a standard deviation 184 of 1) destroys information about the degree of variability within each currency that is necessary 185 in order to make comparisons between currencies for the same timeseries. 186 Therefore, rather than attempting to compare slopes across currencies or to transform different 187 currencies to a common scale, we used a simple null model to generate the expected dynamics in 188 biomass and energy use if the individual size distribution had remained constant over time, but 189 allowed abundance to vary consistent with observed dynamics. In effect, we generated the 190 expected dynamics of biomass and energy use if only abundance drove changes in those 191 currencies over time. For each route, we characterized the "observed" timeseries of total biomass 192 and total energy use by simulating size measurements for all individuals observed in each time 193 step and summing across individuals, using the method described above. We then simulated 194 timeseries for "abundance-driven" dynamics of biomass and energy use incorporating observed 195 changes in community-wide abundance over time, but under a scenario of consistent species (and 196 therefore approximate size) composition over time. For each community, we characterized the 197 timeseries-wide probability of an individual drawn at random from the community belonging to 198 a particular species (ܲሺ‫ݏ‬ ሻ ) as each species' mean relative abundance taken across all timesteps: is the abundance of species

Long-term trends 210
For each route, we evaluated the "observed" 30-year trend in biomass (or energy use) and 211 compared this to the trend derived from the "abundance-driven" null model using generalized 212 linear models with a Gamma family and log link (appropriate for strictly-positive response 213 variables such as biomass or total energy use). We fit four model formulas to characterize 1) the 214 trend in biomass (or energy use) over time and 2) whether this trend deviates from the trend 215 expected given only changes in individual abundance. These models correspond to qualitatively 216 different "syndromes" of change: 217 1. biomass ~ year * dynamics or energy use ~ year * dynamics in which "dynamics" refers to 218 being either the "observed" or "abundance-driven" (null model) dynamics. This model fits a 219 slope and intercept for the observed trend in biomass or energy use over time, and a 220 separate slope and intercept for the trend drawn from the abundance-driven, or null model, dynamics. We refer to this model as describing a syndrome of "Decoupled trends" between 222 abundance-driven and observed dynamics. 223 2. biomass ~ year + dynamics or energy use ~ year + dynamics. This model fits a separate 224 intercept, but not slope, for the abundance-driven and observed dynamics. This model was 225 never selected as the best-performing description of community dynamics. 226 3. biomass ~ year or energy use ~ year. This model fits a temporal trend, but does not fit 227 separate trends for the observed and abundance-driven dynamics. We refer to this syndrome 228 as "Coupled trends" between abundance-driven and observed dynamics. characterized the direction of the long-term trend as increasing if this ratio was greater than one, 239 and decreasing if it was less than one.

Relating change in community structure to decoupling between abundance and size-based 241 dynamics 242
We used dissimilarity metrics to explore the extent to which change in community species or 243 size composition caused decoupling between long-term trends in individual abundance and total 244 biomass and energy use. These dissimlilarity metrics are most readily interpretable when making 245 pairwise comparisons (as opposed to repeated comparisons over a timeseries). We therefore 246 made comparisons between the first and last five-year intervals in each timeseries, resulting in a 247 "begin" and "end" comparison separated by a relatively consistent window of time across routes 248 (usually 19-20 years). The use of five-year periods corrects for sampling effects (White 2004), 249 smooths out interannual variability, and, by including a relatively large proportion (1/3) of the 250 total timeseries, partially mitigates the impact of scenarios where the start and end values do not 251 align with the long-term trend. 252 We calculated three metrics to explore how changes in community composition and size 253 structure translate into decoupling between abundance-driven and observed dynamics for 254 biomass and energy use. First, we evaluated the change in average community-wide body size, 255 calculated as the absolute log ratio of mean body size in the last five years relative to the mean 256 body size in the first five years: 257 are the mean body size of all individuals observed in the first and last 5 258 years, respectively. Large changes in average body size are, by definition, expected to translate 259 into decoupling between observed and abundance-driven dynamics.
Second, we calculated measures of turnover in the size structure and in species composition. We 261 calculated turnover in the ISD using a measure inspired by an overlap measure that has 262 previously been applied to species body size distributions in mammalian communities (Read et 263 al. 2018). We characterized each "begin" or "end" ISD as a smooth probability density function 264 by fitting a Gaussian mixture model (with up to 15 Gaussians, fit following Thibault et al. 2011) 265 to the raw distribution of body masses, and extracting the fitted probability density at 1000 266 evaluation points corresponding to body masses encompassing and extending beyond the range 267 of body masses present in this dataset (specifically, from 0 to 15 kilograms; mean body masses 268 in this dataset range from 2.65 grams, for the Calliope hummingbird Selasphorus calliope, to 269 8.45 kg, for the California condor Gymnogyps californianus). We rescaled each density function 270 such that the total probability density summed to 1. To calculate the degree of turnover between 271 two ISDs, we calculated the area of overlap between the two density smooths as: 272 is the probability density from the density smooth for the first ISD at 274 evaluation point ݅ , and is the probability density from the density smooth for the 275 second ISD at that evaluation point. We subtracted this quantity from 1 to obtain a measure of 276 turnover between two ISDs. 277 To evaluate turnover in species composition between the five-year time periods, we calculated 278 Bray-Curtis dissimilarity between the two communities using the R package vegan (Pinheiro et 279 al. 2020). 280 We tested whether routes whose dynamics were best-described by each "syndrome" of change -281 i.e. "Decoupled trends", "Coupled trends", or "No directional change" -differed in 1) the 282 magnitude of change in mean body size; 2) turnover in the ISD over time; or 3) species 283 compositional turnover (Bray-Curtis dissimilarity) over time. For change in mean body size, we 284 fit an ordinary linear model of the form absolute_log_ratio ~ syndrome. We used the absolute 285 log ratio so as to focus on the magnitude, rather than the direction, of change in body size (see 286 also Supp and Ernest (2014) for the use of the absolute log ratio to examine the magnitudes of 287 differences between values). We compared this model to an intercept-only null model of the 288 form abs(log_ratio) ~ 1. Because our metrics for turnover in the ISD and species composition 289 are bounded from 0-1, we analyzed these metrics using binomial generalized linear models of the 290 form ISD_turnover ~ syndrome and Bray_Curtis_dissimilarity ~ syndrome, and again compared 291 these models to intercept-only null models. In instances where the model fit with a term for 292 syndrome outperformed the intercept-only model, we calculated model estimates and contrasts 293 using the R package emmeans (Lenth 2021). 294

295
Of the 739 routes in this analysis, approximately 70% (501/739 for biomass, and 509/739 for 296 energy use) exhibited a significant temporal trend in either abundance or in biomass/energy use 297 that resulted in the route being classified as exhibiting either "Decoupled trends" or "Coupled 298 trends" (Table 1). All results were qualitatively the same using a subset of 199 routes with 299 complete temporal sampling over time (Appendix S1). Trends driven by individual abundance, 300 as reflected by the dynamics of a simple null model, were strongly dominated by declines (67% 301 declines and 33% increases for abundance-driven dynamics in biomass, and 70% decreases and 302 30% increases for abundance-driven dynamics in energy use; Figure 2; Table 2). However, for 303 biomass, the long-term temporal trends were evenly balanced between increases and decreases 304 (49% increasing and 51% decreasing; Figure 2; Table 2). For energy use, there was a greater representation of decreasing trends than for biomass, but still less so than for strictly abundance-306 driven dynamics (65% decreasing and 35% increasing trends; Figure 2; Table 2). 307 These divergent aggregate outcomes in individual abundance, energy use, and especially 308 biomass occurred due to decoupling in the long-term trends for these different currencies. For a 309 substantial minority of routes (20% of all routes for biomass, and 7% of all routes for energy 310 use), long-term dynamics were best-described as a syndrome of "Decoupled trends" (that is, with 311 a different slope for biomass or energy use-driven dynamics than for the "null", individual 312 abundance-driven, trend) (Table 1). When this decoupling occurred, it was dominated by 313 instances in which the slope for individual abundance-driven dynamics was more negative than 314 that for biomass or energy use (Figure 3). 315 Decoupling between the long-term trajectories of individual abundance and energy use or 316 biomass is, by definition, indicative of some degree of change in the ISD over time. Routes 317 whose dynamics for biomass were best-described as syndromes of decoupled trends over time 318 had a higher absolute log ratio of mean mass (i.e. greater magnitude of change, either increasing 319 or decreasing, in mean mass over time) than routes with coupled or no directional trends ( Figure  320 4; Appendix S2 Tables S1-S3). However, there was not a detectable difference in the degree of 321 temporal turnover in the ISD overall (Figure 4; Appendix S2 Table S4), or in species 322 composition (Figure 4; Appendix S2 Table S5), compared between routes that exhibited different 323 syndromes of change. 324

Discussion 325
Abundance, biomass, and energy use are nonequivalent currencies 326 Simultaneously examining multiple currencies of community-level abundance revealed 327 qualitatively different continent-wide patterns in the long-term trends for abundance in terms of individuals, biomass, and energy use. While long-term trends in individual abundance were 329 dominated by decreases, long-term trends in biomass were evenly split between increases and 330 decreases, and trends in energy use were again dominated by declines (Figure 2) these findings reflect turnover in species composition broadly favoring larger-bodied species. A 364 clear next step for this work is to identify the proximate and ultimate drivers of these shifts -for 365 example, by identifying which groups or species are responsible for these trends, how these 366 shifts vary over regions or habitat types, and if and how they are linked to underlying changes in 367 habitat quality or anthropogenic disturbances. An equally important counterpoint to this work 368 will be integrating potential shifts in intraspecific body size, and particularly declines in body 369 size associated with rising temperatures, with the interspecific dynamics documented here 370 (Youngflesh et al. 2022). In principle, declining body size over time could partially offset the 371 interspecific size shifts observed here. Given that interspecific size shifts occur over a 372 dramatically larger range of body sizes than do intraspecific size shifts, we anticipate that, in 373 most instances, the community-wide dynamics would remain qualitatively despite intraspecific 374 size change. While there are not currently robust estimates of intraspecific size changes at the 375 scale of the full Breeding Bird Survey dataset, this is an excellent opportunity for a focused study 376 in a well-documented system to elucidate the net effects of inter and intraspecific size change on 377 community-level properties. Finally, we note that these increases in body size do not generally 378 appear great enough to decouple the long-term trends in energy use from total abundance (Figure  379 3). Energy use scales nonlinearly with body size with an exponent less than 1, which means that 380 community-wide increases in mean body size result in smaller increases in total energy use than 381 in total biomass. 382

Complex relationships between compositional change and community-level properties 383
The decoupling between the long-term trends for biomass, abundance, and energy use 384 demonstrated in many of the communities studied here is symptomatic of a directional shift in 385 the size structure -in these instances, generally favoring larger bodied species. However, 386 examining the community-wide dynamics of turnover in species composition and the overall size 387 structure reveals that the relationship between changes in community structure and changes in 388 the scaling between different currencies of community-wide abundance is considerably more 389 nuanced than simple directional shifts in mean size. Routes that exhibit a statistically detectable 390 decoupling between total biomass and total abundance show large changes in average body size 391 compared to routes for which biomass and abundance either change more nearly in concert with 392 each other or do not show temporal trends (Figure 4; Appendix 2 Tables S1-S3). This aligns 393 naturally with mathematical intuition given the intrinsic relationship between average body size, 394 total abundance, and total biomass. However, these routes are not extraordinary in terms of their 395 overall degree of temporal turnover in either the size structure or in species composition. Rather, the levels of turnover in overall community structure are comparable between routes that show 397 decoupling between abundance and biomass, statistically indistinguishable trends, or no temporal 398 trends in either currency (Figure 4; Appendix 2 Tables S4-S5).  399 For many communities, therefore, there has been appreciable change in the species and size 400 composition that simply does not manifest in a shift in the overall community-wide mean body 401 size or mean metabolic rate sufficient to decouple the dynamics of biomass, abundance, and 402 energy use. These changes may signal changes in functional composition equally important as 403 the ones that manifest in directional shifts in community-wide average body size. For the 404 complex, multimodal size distributions that are the norm for avian communities (Thibault et al. 405 2011), changes in the number and position of modes may be as important as changes in higher-406 level statistical moments such as the overall mean. At present, the field lacks the statistical tools 407 and conceptual frameworks to quantify and interpret these nuanced changes, especially at the 408 macroecological scale of the current study (Thibault et al. 2011, Yen et al. 2017). However, this 409 is an excellent opportunity for more system-specific work, informed by natural history 410 knowledge and process-driven expectation, to characterize more nuanced changes in the size 411 structure of specific communities and identify the underlying drivers of these changes. To 412 facilitate these efforts in the context of the Breeding Bird Survey, we are developing a R package 413 to characterize the individual size distributions for avian communities based on species' 414 identities and/or mean body sizes. 415

Conclusion 416
This analysis demonstrates the current power, and limitations, of a data-driven macroecological 417 perspective on the interrelated dynamics of community size structure and different dimensions of 418 community-wide abundance for terrestrial animal communities. For breeding bird communities across North America, we find that changes in species and size composition produce 420 qualitatively different aggregate patterns in the long-term trends of abundance, biomass, and 421 energy use, highlighting the nuanced relationship between these related, but decidedly 422 nonequivalent, currencies and reflecting widespread changes in community size structure that 423 may signal substantive changes in functional composition. Simultaneously, the complex 424 relationship between turnover in community species and size composition, and the scaling 425 between different currencies of community-level abundance, highlights opportunities for 426 synergies between recent computational and statistical advances, case studies grounded in 427 empiricism and natural history, and future macroecological-scale synthesis to realize the full 428 potential of this conceptual space. 429 Data availability: All data and code supporting this manuscript are available online on GitHub. 535 For the purposes of double-blind review, we have uploaded a copy of these analyses to a 536 temporary GitHub repository at https://github.com/bbssizeshifts/BBSsims. Upon manuscript 537 acceptance, these will be archived in perpetuity on Zenodo. 538 Tables 540 Table 1 31-32% of routes are best described as syndromes of "No directional change" (intercept-only 549 models). For the remaining routes, in most instances, the dynamics of biomass and energy use 550 exhibit a temporal trend, but with no detectable difference in the temporal trends for abundance-551 driven and observed dynamics ("Coupled trends"). However, for a substantial minority of routes 552 (20% overall for biomass, or 30% of routes with a temporal trend; 7% overall for energy use, or 553 10% of routes with a temporal trend), there is a detectable deviation between the trends expected 554 due only to changes in abundance and the observed dynamics ("Decoupled trends"). 555 556 557 The proportion of trends that are increasing (specifically, for which the ratio of the last fitted 560 value to the first fitted value > 1) for abundance-driven and observed dynamics, for routes 561 exhibiting temporal trends ("coupled trends" or "decoupled trends") in total biomass and total 562 energy use (for biomass, n = 501; for energy use, n = 509). Trends that are not increasing are 563 decreasing. 564 Trends in abundance-driven dynamics are dominated by declines (67% of routes for total 565 biomass, and 70% of routes for total energy). Observed dynamics for biomass differ qualitatively 566 from the abundance-driven dynamics. Specifically, observed trends in biomass are evenly 567 divided between increases and decreases (49% increasing). Observed trends in energy use more 568 closely mirror abundance-driven trends (65% declines). 569 decoupled the dynamics of biomass from those that would occur due only to changes in 581 abundance. The slope for abundance-driven dynamics is significantly more negative than for the 582 observed dynamics (interaction term p = 0.0013). B. Underlying changes in the ISD. The 583 individual size distributions for the first 5 years (solid lines) and last 5 years (dashed lines) of the 584 timeseries. The x-axis is body size (as mass in grams; note log scale) and the y-axis is probability 585 density from a Gaussian mixture model fit to a vector of simulated individual masses for all 586 individuals observed in the years in questions, standardized to sum to 1. For the abundance-587 driven (blue) scenario, individuals' species identities (which determine their body size estimates) 588 are re-assigned at random weighted by each species' mean relative abundance throughout the 589 timeseries, resulting in a consistent individual size distribution over time. For the observed (gold) 590 scenario, individuals' body sizes are estimated based actual species abundances at each time 591 step. For this route, species composition has shifted over time and produced different ISDs for 592 the "begin" and "end" time periods. Specifically, the "end" ISD has peaks at larger body sizes 593 (ca. 90g and 500g) not present in the "begin" ISD. This redistribution of density towards larger body sizes results in an overall increase in body size community wide, which partially offsets 595 declines in total biomass from those expected given change in abundance alone. 596