Smaller species but larger stages: Warming effects on inter‐ and intraspecific community size structure

Abstract Global warming can alter size distributions of animal communities, but the contribution of size shifts within versus between species to such changes remains unknown. In particular, it is unclear if expected body size shrinkage in response to warming, observed at the interspecific level, can be used to infer similar size shifts within species. In this study, we compare warming effects on interspecific (relative species abundance) versus intraspecific (relative stage abundance) size structure of competing consumers by analyzing stage‐structured bioenergetic food web models consisting of one or two consumer species and two resources, parameterized for pelagic plankton. Varying composition and temperature and body size dependencies in these models, we predicted interspecific versus intraspecific size structure across temperature. We found that warming shifted community size structure toward dominance of smaller species, in line with empirical evidence summarized in our review of 136 literature studies. However, this result emerged only given a size–temperature interaction favoring small over large individuals in warm environments. In contrast, the same mechanism caused an intraspecific shift toward dominance of larger (adult) stages, reconciling disparate observations of size responses within and across zooplankton species in the literature. As the empirical evidence for warming‐driven stage shifts is scarce and equivocal, we call for more experimental studies on intraspecific size changes with warming. Understanding the global warming impacts on animal communities requires that we consider and quantify the relative importance of mechanisms concurrently shaping size distributions within and among species.

however, does not go extinct at low temperatures at high values of , and the coexistence region is shifted towards higher temperatures compared to the original model version. In Community II, the qualitative pattern remains the same as in the original model for all values of the background mortality ratethe community shifts with warming from extinction to persistence with juveniles dominating, followed by dominance shift to adults and species extinction, and the alternative stable state region disappears for > 0.1. Interestingly, the juvenile-to-adult dominance shift happens at increasingly lower temperature with increasing , and for > 0.45 the community is dominated by adults at all temperatures.

Effects of varying resource enrichment on the patterns of species' and stages' persistence and dominance across temperature
In this part of the model sensitivity analysis, we explored the effects of resource enrichment on how temperature affects patterns of species' and stages' persistence and the presence of a region with alternative stable states. The resource enrichment level is generally known to strongly influence the patterns of species' persistence and stability across temperature, leading to various dynamic consequences of warming on modeled food webs (Uszko et al. 2017). Here we represent and modify the resource enrichment as the coefficient 0 , which scales the default formula of temperature dependence of the maximum (supply) resource biomass densities, i.e., 0 • ( ) (see Appendix S1: Table S2).
We run a bifurcation analysis, and drew persistence, biomass dominance and alternative stable states boundaries in the temperature-scaling coefficient space × 0 , for community model I (two unstructured consumer species feeding on two resources) and II (one stagestructured consumer species feeding on two resources). Here, we assumed a size-temperature interaction in both the maximum resource density and in the temperature optimum of the maximum consumer ingestion rate , and the diet preference parameter = 0.85. We varied the scaling coefficient 0 , assumed equal for both resources ( and ), between 0 and 3. That is, the result for 0 = 1 is equivalent to the results shown in Fig. 2 (main text) with = 0.85.
We find that the patterns of species and stages persistence, dominance and alternative stable states over temperature are very robust to changes in resource enrichment, both in community models I (Fig. S2A) and II (Fig. S2B). In other words, the temperatures representing species persistence boundaries (solid black lines, Fig. S2) and alternative stable states boundaries (solid red lines, Fig. S2B) are nearly insensitive to changes in the scaling coefficient 0 across most of the considered values. Other than that, the general pattern of species persistence across temperature follows the expected U-shaped pattern (Uszko et al. 2017). That is, consumer species go extinct at both very low and very high temperatures because of too low feeding rates and too high metabolic rates, respectively. Similarly, consumers cannot persist at extremely low resource enrichment values. Interestingly, we found no shift from stable equilibria to limit cycles (Hopf bifurcation) across the considered range of temperature and scaling coefficient 0 . Even though oscillations should, in principle always arise at sufficiently high enrichment when consumers feed with a type II functional response, the actual dynamic behavior depends on several parameters of consumer and resource growth, feeding and mortality (Uszko et al. 2015).

Effects of warming on mean individual consumer body size
Here, we present the results concerning warming effects on mean individual body size in models I (two unstructured consumer species feeding on two resources, Fig. S3A, C) and II (one stagestructured consumer species feeding on two resources, Fig. S3B, D) with (Fig. S3C, D) and without (Fig. S3A, B) a size-temperature interaction in the maximum resource density and in the temperature optimum of the maximum consumer ingestion rate . We do it also for model III (two stage-structured consumer species feeding on two resources (Fig. S5) with a sizetemperature interaction present both in the maximum resource density and in the temperature optimum of the maximum consumer ingestion rate . For models I and II, the diet preference parameter is set to = 0.85, and for model III = 0.75. Even though we assumed fixed body masses of all species and stages in all our models, the mean individual body mass in the community can vary due to changes in relative proportions of species and stages of different body masses.
This exercise clearly shows that mean individual body size changes considerably only when a size-temperature interaction is present. In absence of such an interaction, mean consumer body size stays relatively constant across the entire temperature range studied in both models I and II ( Fig. S3A and B, respectively). Only when a size-temperature interaction is present, mean individual body size in model I either stays constant (when the community is dominated by a single consumer species) or declines (when the two consumers coexist) with warming ( Fig. S3C). In model III, mean individual body size follows a qualitatively similar pattern (Fig. S5A).
When only a single stage-structured consumer is present in the community, the mean size increases with warming due to a shift in intraspecific stage structure towards adult dominance (red and yellow regions, Fig. S3). When the two stage-structured consumers coexist, the shift of dominance towards the smaller consumer species drives the decrease in the mean individual body size, regardless of the simultaneous shift in intraspecific structure in the opposite direction (Fig.   S5A, compare with Fig. 4 in the main text when = 0.75).

Effects of absence vs. presence and nature of a size-temperature interaction on temperature effects on species' and stages' persistence and dominance
Here, we looked into all 12 cases of different combinations of the assumptions of absence vs.
presence of a size-temperature interaction, and of the nature of this interaction. We did this for two main reasons. First, we wanted to see if the 'traditional' assumption of a lack of such an interaction (i.e., size and temperature effects are independent, as in the metabolic theory of ecology )) can reproduce the empirically observed patterns of shifts in species dominance with warming (see Appendix S3). Second, as part of the sensitivity analysis, we wanted to check if the presence of a size-temperature interaction gives similar results depending on how this interaction is implemented in the model. To do this, we run a bifurcation analysis, and drew persistence, biomass dominance and alternative stable states boundaries in the temperature-diet preference space × , for community model I (two unstructured consumer species feeding on two resources) and II (one stage-structured consumer species feeding on two resources).
We implemented the size-temperature interaction in the resources as different temperature sensitivities of resource supply (maximum) density . Following the empirically observed pattern, we assumed that is a declining function of temperature , Uszko et al. 2017, Bernhardt et al. 2018, and that it declines faster for the large than for the small resource. In effect, in absence of consumers, the resource biomass is dominated by the large resource at lower temperatures, and by the small resource at higher temperatures, with the shift occurring around 20 °C (Winder et al. 2009, Daufresne et al. 2009, Yvon-Durocher et al. 2011). In absence of a size-temperature interaction, both resources are dynamically equivalent, and their follows the formula for the small resource . For exact parameter formulations, see Appendix S1: Table S2 and Figure S1A.
We considered two scenarios of the presence of a size-temperature interaction in the consumers. In the first one, as in the main text, we assumed that the temperature optimum of the consumer maximum ingestion rate declines with increasing dry body mass (see Appendix S1: Table S2 and Fig. S1B1). This follows from the observed empirical patterns of declining consumer performance with warming (Angiletta et al. 2004, Lindmark 2020). In the absence of a size-temperature interaction, all species and stages have the same temperature optimum of the maximum ingestion rate at 20 °C (Appendix S1: Fig. S1B2), and only differ in ingestion rates due to their different body masses (that influence independently of temperature). In the second scenario, we assumed that the allometric exponent of the metabolic rate increases with warming following the formula 0.7 + 0.0005 • (Appendix S1: Fig. S1C2), similar to what has been shown in some empirical systems (Ikeda et al. 2001, Lindmark et al. 2018. Consequently, larger consumers suffer from relatively higher metabolic losses at elevated temperatures. In the absence of a size-temperature interaction, all species and stages have an allometric exponent of 0.7, and only differ due to their different body masses (that influence independently of temperature, see Appendix S1: Table S2 and Fig. S1C1). In both scenarios, warming causes lower net biomass production (growth rates) of larger relative to smaller species and stages.
Full results of these complementary analyses are shown in the 12 panels of Fig. S4. We note three major observations. First, with a 'traditional' assumption of body size and temperature independently affecting resource and consumer dynamics, the models fail to reproduce the empirically observed patterns of warming-induced shifts in consumer community size structure.
In fact, in model I (Fig. S4A), warming drives the community in the opposite direction, such that persistence and dominance of the large consumer becomes more likely at elevated temperature, especially when the two consumers do not compete strongly for resources (i.e., at higher diet preference values). In model II (Fig. S4C), the biomass is completely dominated by juveniles across the entire temperature-diet preference space.
Second, the presence of a size-temperature interaction of any type breaks the above pattern. That is, an addition of this interaction in resources or in consumers, or in both, changes the model predictionsit becomes more likely that the small consumer will dominate in community I, and that the adults will dominate in community II (Fig. S4, all panels apart from A and C). Additionally, with presence of any type of a size-temperature interaction, an alternative stable state appears in the temperature-diet preference space in community II (solid red lines, Fig.   S4). In this region, placed at moderate to high values of the diet preference parameter , the dominant stage is determined by initial abundances of juveniles and adults.
Third, the presence of a size-temperature interaction in the temperature optimum of the maximum ingestion rate vs. in the allometric scaling exponent of the metabolic rate leads to similar outcomes, especially in community II where the patterns of alternative stable states and stage dominance are very similar (Fig. S4E-H vs. I-L). However, the two formulations differ in the exact patterns of species persistence and dominance. In case of a size-temperature interaction in the temperature optimum of , we observed a shift towards smaller species regardless of the competitive strength (diet preference ), with weaker competition leading to a wider coexistence region. In the case of a size-temperature interaction in the allometric exponent of , coexistence is only possible at moderate to high diet preference values ( > 0.6), that is when the two consumer species do not compete strongly for resources.

Effects of varying body size ratios of competing consumers on the patterns of species' and stages' persistence and dominance across temperature
Here we explore how varying consumer body sizes ( ; see Appendix S1: Table S2) shape temperature effects on species' and stages' persistence and the presence of alternative stable states. Natural plankton systems typically consist of coexisting consumers spanning a wide body size range (Andersen et al. 2016). As body size controls metabolic and feeding rates (and the scope of their temperature dependence) in our models, altered relative size ratios of competing species/stages can potentially modify the patterns we found. In the original formulation of our model, we consider three different fixed consumer size classes (0.1 and 1 µg dry mass in models I and II, and 0.1, 1 and 10 µg dry mass in model III). Here, we relax this assumption to check the robustness of our results to different body sizes (and body size ratios) of competing consumers.
Specifically, in models I and II we kept the body size of the small consumer ( and , respectively) constant at 0.1 µg, and varied the body size of the large consumer ( and , respectively), rendering body size ratios : and : range from 1 to 100. Note that a decrease in adult-to-juvenile body size ratio in model II may represent a decrease in size at maturation, as predicted by the temperature-size rule. In model III, we considered two alternative assumptions of consumer body sizes: (A) 1, 5 and 10, and (B) 0.001, 0.1 and 10 µg dry mass for the three size categories of , and , and , respectively (see Fig. 1 and Appendix S1: Table S2).
We ran a bifurcation analysis, and drew persistence, biomass dominance and alternative stable states boundaries in the body size ratio-temperature space for Community I (two unstructured consumer species feeding on two resources; Fig. S6A) and II (one stage-structured consumer species feeding on two resources; Fig. S6B), with the diet preference parameter = 0.85. For Community III, we did the same in the temperature-diet preference space × (Fig.   S7). In all models, we assumed a size-temperature interaction in both the maximum resource density and in the temperature optimum of the maximum consumer ingestion rate . As we varied consumer body sizes, we thus also varied the temperature optimum (K) of maximum consumer ingestion rate as = 305.38 • −0.006 , where is the consumer dry body mass (ng). This formula yields the temperature optima of 24, 20 and 16 °C for the three size classes of 0.1, 1 and 10 µg dry body mass as assumed in the original model. Additionally, this formula describes a linearly decreasing temperature optimum with increasing consumer body size on a log-scale, as has been shown for temperature optimum of feeding or growth between (Angilletta et al. 2004) and within (Lindmark et al. 2021) species.
We find that the patterns of species and stage persistence, dominance and alternative stable states are relatively robust to changes in consumer size ratios in Communities I (Fig. S6A), II (Fig. S6B) and III (S2.7 A and B). In all three cases, we observe similar pattern to the one found in the original formulation of the models, that is, increasing temperature causes shifts of persistence and dominance from large to small species, and from small to large stages. In Community I (Fig. S6A), with increasing body size ratio, the coexistence region (between black solid lines, Fig. S6A) shrinks. This is mostly due to the large consumer going extinct at lower temperatures the larger its body size gets. Interestingly, the temperature at which biomass dominance switches from the large to the small consumer (dashed black line, Fig. S6A) stays fairly constant ~25-28 °C at all considered body size ratios. In Community II, the region of temperatures with alternative stable states (i.e. juveniles or adults dominate depending on initial abundances) shrinks with increasing body size ratio (between red solid lines, Fig. S6B). Also in this case, the consumer goes extinct at lower temperatures the larger the adults get (solid black line, Fig. S6B). However, a decreasing adult body size (i.e., size at maturation; below 10 in Fig.   S6B) extends the alternative states region and broadens the consumer persistence range across the temperature axis. Note that when the consumer body size ratio is equal to 1 in Communities I and II, the competing species/stages are dynamically identical and the patterns of their persistence and dominance is driven solely by the size-temperature interaction assumed for the resources (i.e., different temperature sensitivities of their ).
In Community III with smaller relative differences between consumer size classes than in the original model formulation (1, 5 and 10 µg; Fig. S7A), the pattern of species and stages dominance largely resembles the original model (compare to Fig. 4 in the main text). The only substantial difference is that with these alternative body sizes, it is the small consumer biomass that first gets dominated by adults before the same happens in the large consumer (compare the position of orange and yellow dashed lines in Fig. S7A and Fig. 4). When we assumed larger relative differences between consumer size classes than in the original model formulation (0.001, 1 and 10 µg), a diversity of regions of biomass persistence, dominance and bistability opens up in the temperature-diet preference space (Fig. S7B). However, the general pattern remains the same as in the original model (compare with Fig. 4 in the main text)with increasing temperature, the persistence changes from only the large consumer present to consumer coexistence to only the small consumer present, and at the same time the stage biomass dominance changes from juveniles to adults in both consumer species (Fig. S7B). Note that regions of alternative stable states occur mostly at moderate to high temperatures, especially for lower values of the diet preference parameter (i.e., at low levels of intraspecific competition as in Community II; compare Fig. S7B to Fig. 2A in the main text).
We also run the same analysis for all models in which we varied body size ratios while keeping the temperature optima constant (i.e., not as functions of body size) at 24, 20 and 16 °C for the three size classes as in the original model formulation. In this scenario, the patterns of persistence, biomass dominance and alternative stable states were very similar to the original model, and nearly independent from changes in body size ratios. It confirms that body size itself may not be sufficient to produce the expected size shifts with warming as long as it does not modify temperature-dependent processes (in this case, temperature optimum of the maximum ingestion rate; compare with Appendix S2: Fig. S4A and C). Figure S1. Consumer persistence (solid black lines), biomass dominance (dashed black lines) and alternative stable states (solid red lines) boundaries in temperature-background mortality (equal for all consumers within each community, i.e. = or = ) space. A: Two unstructured consumer species feeding on two resources (Community I); B: one stage-structured consumer species feeding on two resources (Community II). In A, on the left hand side of the dashed line, community biomass is dominated by the large consumer , and on the right hand side by the small consumer . In both panels, a size-temperature interaction is present both in the maximum resource density and in the temperature optimum of the maximum consumer ingestion rate , and the diet preference = 0.85. All equilibria are stable.
Temperature ( Figure S2. Consumer persistence (solid black lines), biomass dominance (dashed black lines) and alternative stable states (solid red lines) boundaries in temperature-resource enrichment space. Resource enrichment is represented by the coefficient 0 , which scales the default formula of temperature dependence of the maximum (supply) resource biomass densities (see Appendix S1: Table S2) of both resources ( and ). A: Two unstructured consumer species feeding on two resources (Community I); B: one stage-structured consumer species feeding on two resources (Community II). In A, on the left hand side of the dashed line, community biomass is dominated by the large consumer , and on the right hand side by the small consumer . In both panels, a size-temperature interaction is present both in the maximum resource density and in the temperature optimum of the maximum consumer ingestion rate , and the diet preference = 0.85. All equilibria are stable.

Size-temperature interaction
One stage-structured consumer species (Community II) Two unstructured consumer species (Community I) Figure S3. Equilibrium mean individual dry body mass of consumers along the temperature gradient. Left panels (A, B) show model results with no size-temperature interaction. Right panels (C, D) show model results with a size-temperature interaction present both in the maximum resource density and in the temperature optimum of the maximum consumer ingestion rate . Upper panels (A, C) represent Community I, and lower panels (B, D) represent Community II. Red lines in panel D show an alternative stable state for equilibrium mean individual body mass. In all panels, the diet preference = 0.85.  Figure S4. Consumer persistence (solid black lines), biomass dominance (dashed black lines) and alternative stable states (solid red lines) boundaries in temperature-diet preference space. Shown are results for all combinations of the following assumptions on an interaction between body size and temperature: with a size-temperature interaction in the maximum resource density either absent ( = , panels A, E, I, C, G, K) or present ( ≠ , panels B, F, J, D, H, L), with a size-temperature interaction in the allometric exponent of the metabolic rate either present (panels E-H) or absent (all other panels), and with a size-temperature interaction in the temperature optimum of the maximum consumer ingestion rate either present (panels I-L) or absent (all other panels). All equilibria are stable. For parameter and rate definitions and formulas, see Appendix S1: Table S2 and Figure S1.
Results are shown for Communities I (two unstructured consumer species feeding on two resources, panels A, B, E, F, I, J) and II (one stagestructured consumer species feeding on two resources, panels C, D, G, H, K, L) Two unstructured consumer species feeding on two resources (community I); B: one stage-structured consumer species feeding on two resources (community II). Note that panels J and L are identical with panels A and B of Fig. 2 Figure S5. Equilibrium mean individual dry body mass along the temperature gradient in Community III (two stage-structured consumer species feeding on two resources); a size-temperature interaction present both in the maximum resource density and in the temperature optimum of the maximum consumer ingestion rate , and the diet preference = 0.75. Colored regions indicate the presence of only the large consumer (red), both consumers (coexistence; orange), or only the small consumer (yellow), as in Fig. 4 in the main text. : body mass ratio Figure S6. Consumer persistence (solid black lines), biomass dominance (dashed black line) and alternative stable states (solid red lines) boundaries in body mass ratio-temperature space. A: Two unstructured consumer species feeding on two resources (Community I); B: one stage-structured consumer species feeding on two resources (Community II). In A, below the dashed line community biomass is dominated by the large consumer , and above by the small consumer . In both panels, a size-temperature interaction is present both in the maximum resource density and in the temperature optimum of the maximum consumer ingestion rate described by = 305.38 • −0.006 (see details in Appendix S2), and the diet preference = 0.85. In B, the consumer persistence boundary is marked with a solid black line. All equilibria are stable. Note the logarithmic x-axes.

Extinct
Temperature (°C) Diet preference Figure S7. Consumer persistence, biomass dominance and alternative stable states boundaries in temperature-diet preference space in Community III (two stage-structured consumer species feeding on two resources); a size-temperature interaction present both in the maximum resource density and in the temperature optimum of the maximum consumer ingestion rate described by = 305.38 • −0.006 (see details in Appendix S2). A: Consumer persistence regions (see the legend for color codes) and biomass dominance boundaries (dashed lines of respective colors) in temperature-diet preference space, assuming 1, 5, and 10 µg dry mass for S , and , and , respectively. On the left hand side of the dashed lines, community biomass is dominated by juveniles , and on the right hand side by adults . B: Consumer persistence regions (the small consumer persists in the region to the right hand side of the yellow solid line, and the large consumer persists in the region to the left hand side of the solid orange line), and biomass dominance and alternative stable states boundaries (black dashed lines; dominance patterns described separately for each region) in temperature-diet preference space, assuming 0.001, 0.1, and 10 µg dry mass for S , and , and , respectively. All equilibria are stable.