Philippa Kaur

The Asiatic cheetah (Acinonyx jubatus venaticus) once roamed throughout the Middle East and central India. Today there remain only an estimated 20 free-ranging individuals in central Iran and 5 in captivity. International economic sanctions against Iran have had devastating effects on its cheetah conservation and management (see go.nature.com/3suohzb; in Farsi). To help overcome these effects, we suggest that Iran work with the Indian government, which is conducting a rewilding programme for cheetahs.
Competing Interests
The authors declare no competing interests. More

This study aimed to compare the extent of contrafreeloading in kea to that in Grey parrots, given that the two species exhibit very different levels of play: specifically, kea exhibit complex and frequent play29,30,35,36, whereas Greys exhibit considerably less play than several parrot species29. We found that, at the group level, although the overall amounts of kea classic contrafreeloading were nonsignificant, as a percentage of behaviour, kea generally contrafreeloaded more than Grey parrots in Experiment 1, whereas the opposite was true for Experiment 2. We compare the various behaviour patterns in detail, and propose explanations for our results below.The most interesting comparisons for Smith et al.’s hypothesis are the results from classic contrafreeloading. In Experiment 1, kea performed this behaviour at non-negligible levels, given the supposed rarity of the behaviour5 (two birds at 50%; the others varying between 39 and 47%). In contrast, although one Grey did classically contrafreeload at a statistically significant level, the other three were at ≤ 36%. These data suggest that the kea may have found the task more engaging than did the Greys. However, given that only two kea chose to pop the lid of an empty cup in control trials significantly above chance, whereas three of the four Greys did so significantly above chance and one at chance, we doubt that the kea found the task inherently rewarding. We note that this comparison between both species must be interpreted cautiously due to differences in methodology: For the Greys, the control trials were performed at the end of the study, by which point they may have learnt to associate lid-popping with reward. However, the data from experimental trials in Smith et al.13 are such that their birds would have been primed in the opposite direction: For example, three of those four birds rarely chose the empty lidded cup when free food was available, nor did they classically or super contrafreeload to any significant extent13; an association-driven explanation is therefore unlikely. In contrast, the kea experienced this control condition at the start of the experiment, allowing them 20 trials to become acquainted with the affordances of both options that would be available throughout the study (lid-popping versus not lid-popping). This opportunity was important for kea, as this species has been previously shown to learn about object properties through extensive object manipulation37. That kea popped lids at or above chance in these first 20 control trials suggested two possibilities: (1) After these 20 trials, the task may have been familiar enough to no longer be of much interest (i.e., no longer novel and worthy of consideration) by the time rewarded trials began (recall nonsignificant downward trends for Harley Quinn and Blofeld). (2) They acquired some interest in popping the lids. This latter case seems more likely, as the lid-popping task still likely provided some added value. Kea engaged in non-negligible levels of classic contrafreeloading, such that the chance to pop a lid and eat could be considered more interesting than simply eating an identical but freely available reward. Furthermore, three kea chose a lidded, empty cup over a free, least-preferred reward at least half the time, again suggesting that the activity held some appeal of its own.In Experiment 2 (which corresponds to classic contrafreeloading), all kea preferred freeloading for the walnut without a shell; two Greys, in contrast, nut contrafreeloaded at a statistically significant extent. This variability in behaviour at both the individual and species levels reveals the significance of a task’s proximate and potentially ultimate values in parrots’ choice to contrafreeload. Interestingly, although species like kea are hypothesized to prefer food items requiring high manipulation38,39, nut-cracking—chosen as an activity to provide direct comparison with the Greys13—is not prevalent in kea diet40, and that activity thus may not have been appropriate as an ethologically relevant one for kea. Greys, in contrast, are known to crack nuts in nature41. Future research could use a more ecologically relevant task for the kea, such as working to access food via digging or scraping32.As with Smith et al.’s Greys13, kea in Experiment 1 performed calculated contrafreeloading to a statistically significant extent. All kea did so on over 83% of trials; for the Greys, three birds were close to 90% but one was at only 67%. Kea consistently selected their preferred food out of the two options provided, suggesting that the lid-popping action did not deter kea from selecting their preferred reward. In related trials, where the lid-status of food paired with an empty cup varied, kea, like some Greys13, preferred lidded food over an empty lidless cup, again showing that lid-popping for food was an acceptable task.When examining situations in which food was discarded after contrafreeloading, we found that this choice in Experiment 1 was most common for Bruce. Notably, Bruce lacks a top mandible, making many of the manipulative behaviours more difficult to execute42. Bruce demonstrated consistent food preferences throughout the experiment, however, indicating that the reason some foods were discarded was, indeed, because they were too difficult for him to manipulate. In Experiment 2, Harley Quinn was the most likely to discard the nut, and did so exclusively in trials in which she chose the walnut without the shell (freeloaded). In these occasions, Harley Quinn was observed choosing the nut by tapping on it or the cup.Like the Greys, the kea failed to super contrafreeload to a statistically significant extent. Furthermore, contrafreeloading trials in which a lid was popped but the food underneath was not consumed occurred most often with the least-preferred food. Given kea’s performance on control trials, the super contrafreeloading results are not surprising. Interestingly, when lid-status of food paired with an empty cup varied, some Greys very rarely—and depending on food desirability—preferred to pop the empty cup’s lid rather than consume the free food; as noted earlier, three of eight kea did so on at least half the trials when the food in the lidless cup was their least preferred option (sultanas). Both kea and Greys thus likely placed the appeal of the task along some “value scale” along with that of the available food rewards, the combination influencing their behaviour when the two variables were presented in various permutations. Notably, even in control trials, where no food was involved, no bird of either species found the task aversive, engaging in the behaviour at least 50% of the time. Future research could investigate how a different, more rewarding task would influence this balance and thus contrafreeloading for both species.One possible alternative explanation for kea’s higher rates of contrafreeloading relative to those of Greys could be their natural tendency to probe and manipulate objects, thus causing them to pry off cup lids rather than manipulate lidless (open) cups. Were this action exploratory in nature, we would have observed significant decreases in behaviour as the experiment progressed, but note that we found no significant changes in any bird. Were they consistently drawn to lids and this behaviour were hard-wired, then we should have observed lid-popping appear significantly above chance across all three types of contrafreeloading. However, as discussed previously, kea did not significantly contrafreeload in the classic condition and actively freeloaded in super contrafreeloading conditions, suggesting that they were not simply interacting with lidded cups preferentially, but rather attending to the contents in the two cups and avoiding the additional manipulation of the lid when it led to a less (or, more often than not, equally) preferred food reward.Another potential explanation for the differences observed between kea and Greys might be found in the theoretical overlap between contrafreeloading and play, and how individuals might view the contrafreeloading action as a type of play. As a seemingly nonfunctional, intrinsically motivating behaviour occurring in low-stress environments, incurring a positive mood, varying between conspecifics, and often incomplete and/or repeated14,15, play shares many proximate-level attributes with contrafreeloading13. Our results demonstrate that kea subjects inhabiting a low-stress, captive environment repeatedly chose to engage in classic contrafreeloading to a non-negligible extent and calculated contrafreeloading to a significant extent, varied in their behaviour between individuals, and at times, left the task incomplete (e.g., left food uneaten). Furthermore, evidence for intrinsic motivation to perform a given task is suggested by the kea’s overall differential behaviour between the two experiments, as well as inter-individual differences.Importantly, this study serves only as a first step into determining whether play manifests as a form of contrafreeloading, but cannot ascertain that this is the only possible explanation for the presence or degree of contrafreeloading in the two species. Several alternative explanatory theories regarding the occurrence of contrafreeloading are enumerated in the discussion of Smith et al. (e.g., work ethic; information gathering; relief from boredom)13, and various other potential explanations (beyond playfulness) may reside at the species-level. Grey parrots (Psittacidae) and kea (Strigopidae) are separated by 50–80 million years of evolution43 and differ in their neurobiology (i.e., the size of the shell region related to vocal and possible cognitive abilities44). Differing ecological evolutionary pressures are also likely relevant: an island-based habitat39, a lack of natural predators30,45, and generalist diets40,46,47 are thought to have shaped the playfulness and cognitive abilities of kea30,40,46,47. Greys, in contrast, evolved predominantly on a continent (i.e., although they can be found on islands such as Principe, the Congo Grey is endemic to central Africa48,49), are subject to considerable predation48,50,51,52, and have a relatively less generalist diet (diverse but almost exclusively vegetarian and in which nuts play a significant role; see review in50). Such disparate evolutionary trajectories may offer other potential explanations for the differences in contrafreeloading observed between the two species, and future research could examine differences at genetic and/or neurological levels.The varying rates of contrafreeloading observed between the species could have also been influenced by other factors. For example, although both parrot groups studied here inhabit enriched environments, are habituated to participating in experimental trials, and have access to food ad libitum, their habitats are markedly different. Notably, the Grey subjects live in “man-made” settings (i.e., Griffin and Athena in a lab; Pepper, Franco, and Lucci in private homes), whereas the kea inhabit a naturalistic zoo enclosure. Physical enrichment, although somewhat different in kind, is unlikely to have differed in quantity, as all birds are provided routine naturalistic foraging, and Lucci lives in a free-flight aviary. More likely is the difference in sociality: Relatively more subjects reside together in the kea group (15) compared to the Greys (two groups of two Greys and one Grey living with two birds of differing species), and thus variables such as social stimulation and flock-based foraging techniques could have contributed to the expression of contrafreeloading (note that subadult male kea are known to obtain food through kleptoparasitism32). In order to elucidate the role of habitat on contrafreeloading, future studies could examine the behaviour of species residing in more comparable captive conditions.Future work should aim not only to apply these same methodologies to a broader range of parrot species, but also objectively quantify frequency and complexity of play across a wide range of parrots to allow a direct correlation between play and contrafreeloading over phylogeny in the parrot order. The apparent link between play behaviour and encephalisation in parrots53 offers another possible avenue for cross-species comparisons on contrafreeloading. Future research could also employ cognitive bias tests to quantify the mood of birds before and following contrafreeloading54, directly manipulate subjects’ participation in play behaviours or other control behaviours and observe whether engaging in play can increase contrafreeloading rates at the individual level, or perform behavioural coding of playfulness and/or arousal before and after contrafreeloading. Future research could incorporate more ecologically relevant contrafreeloading tasks to examine this behaviour at both the individual and species level, and approach the phenomenon by using both genetic and neuroscience techniques.In sum, contrafreeloading is, by its very nature, an enigma whose study presents many difficulties. It varies across the diverse contexts within which it is studied, and given that it is rarely exhibited to a statistically significant extent, analyses that require comparing nonsignificant behaviour patterns across individuals and/or species is a challenging undertaking. Many explanations have been proposed, but contrafreeloading is still poorly understood, and its correlation with play is likely only one of several logical rationales. Nevertheless, our findings suggest that interest in play should not be discounted as a contributing factor. More

Cline and colleagues analysed spatiotemporal datasets covering 5000 km of popular trout rivers from 1983 to 2017, finding that fishing pressure was four times higher in cold-water sections of rivers than adjacent cool-water sections of rivers, with fisher spending in cold-water sections generating US$500,000 km−1 year−1 and cool-water sections generating US$60,000 km−1 year−1. Overall, 17% and 35% of the current cold-water habitats are projected to be warmer than 18 °C (the threshold for trout thermal extremes) by 2040 and 2080, respectively, with some river sections possibly experiencing habitat losses in excess of 80% by 2080. The combined effects of cold-water habitat loss and increased frequency and severity of drought on fishing pressure could result in 64% declines in fishing river sections by 2040 and 76% declines by 2080. The cumulative impacts of these environmental changes in fishing spending across these rivers could put a total of US$103 million year−1 and US$192 million year−1 at risk by 2040 and 2080, respectively. More

Similar non-native and invasive flora, such as the fever tree (pictured) are found in regions previously occupied by the same European empire.Credit: Alamy

In 1860, a British expedition raided the highland forests of South America, looking for a hot commodity: Cinchona seeds. The bark of these ‘fever’ trees produces the anti-malarial compound quinine, and the British Empire sought a stable source of the drug for its soldiers and civil service in India. After cultivation in the United Kingdom, young Cinchona trees were planted across southern India and what is now Sri Lanka.The British quinine scheme failed — instead, a species introduced to Java, now part of Indonesia, by the Dutch Empire later dominated the global market — but Cinchona trees are still common in parts of India.Such botanical legacies of imperial rule are common, finds a study published on 17 October in Nature Ecology & Evolution1. Regions that were once occupied by the same European colonial power — such as India and Sri Lanka — tend to have similar species of non-native and invasive plants. The longer the regions were occupied, the more their populations of invasive species resemble each other, the research found.Alien floraThe link between European colonialism and invasive species is intuitive, and has been noted by other researchers, says Bernd Lenzner, a macro-ecologist at the University of Vienna who led the study. To test the association, his team turned to the Global Naturalized Alien Flora database, which maps the distribution of nearly 14,000 invasive plant species.
The imperial roots of climate science
Across more than 1,100 regions, including 404 islands, the researchers found that regions once occupied by the British Empire had more similarities in their invasive flora than did ‘artificial’ empires that the team assembled from random regions. This was also the case for regions once part of the Dutch Empire (former Spanish and Portuguese colonies had alien-plant compositions similar to those of the artificial empires).Climate and geography play an important part in explaining the overlap in the diversity of invasive species, modelling by Lenzner’s team found, but so does the length of time regions were occupied by an imperial power. Regions that were central to trade, such as southern India for the British Empire and Indonesia for the Dutch Empire, formed clusters with considerable overlap in invasive-plant composition.The analysis did not look at when individual plant species were introduced or why. But anecdotally, many of the plants that were commonly taken to former empires were once of economic value and their populations were probably established on purpose, says Lenzner.Global trade impactsThe study’s conclusions might be “super obvious”, but they have important implications for conservation, says Nussaïbah Raja, a palaeontologist at Friedrich-Alexander University of Erlangen–Nürnberg in Erlangen, Germany. “We should be taking this history into consideration when we think about management of species.” Appreciating the history of introduced plants — as well as their place in today’s ecosystems — could help conservationists to handle future changes in biodiversity, such as those driven by climate change, Raja adds.Global trade is beginning to overwrite the colonial legacy of introduced plants. For example, the analysis showed similarities between invasive plant populations in Fujian, China, and some parts of Australia. Although both places were once connected by the British Empire, more recent global trade might also be partly responsible for the overlap.“We are still seeing these imprints of the colonial-empire legacies from centuries ago,” Lenzner says. “So what we’re doing and the species we’re redistributing today will be visible far into the future.” More

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Our experimental data reveals a scaling law between the mass of a layer along the vertical coordinate, M(z), and the weight that it supports, W(z), namely: (W(z) sim M(z)^a) with (a approx 1.5). To better understand the physical mechanism that yields this scaling law, we derive the force balance equation of a layer of the swarm and solve for W(z). We then equate the analytical expression for W(z) with the experimentally determined scaling law, (W(z) sim M(z)^a), to connect the swarm mass distribution to the exponent a and formulate the expressions for M(z) and W(z) in terms of a. We then consider a dimensional analysis of the strength of each layer of the swarm, S, or the maximum weight that it can support before the grip of the bees on one another breaks. As will be described in detail below, we find that (S sim M^{1.5}), which is close to the experimentally determined (a = 1.53). Deviation from this value increases the fraction of maximum strength exerted by different parts of the swarm.Force balance model of the weight distribution in the swarmWe assume that the swarm is at quasi-equilibrium (the shape does not change although individual bees may move), that all of the bees in each layer contribute equally to supporting the weight of the bees underneath that layer, that the layer thickness is very small, and that the swarm is radially symmetrical about the z-axis. We use a cylindrical coordinate system with a vertical coordinate z, as shown in Fig. 1e, and we consider layers of the swarm along the z-axis of thickness dz. Variables labeled with a tilde, as in (tilde{W}(z)), represent analytically derived expressions; variables without a tilde, as in W(z), represent values determined with power law fits to experimental data.We begin our analysis by applying the force balance principle to each layer of a swarm. As shown by the free body diagram in Fig. 1f, the force with which each layer of bees has to grasp the layer above it is equal to the weight of that layer and all of the layers underneath it: (tilde{F} = tilde{W}(z)). We express (tilde{W}(z)) using the force balance equation (a continuous version of the discrete definition in Eq. (5).):$$begin{aligned} tilde{W}(z) = g int _z^L tilde{M}(z) dz, end{aligned}$$
(8)
where the mass of bees per layer is (tilde{M}(z)), the swarm length is L, and g is the gravitational constant. Inspired by our experimental observation that the mass of the layers near the base is highest and the mass of the layers at the tip of the swarm is lowest in Fig. 3a, we model (tilde{M}(z)) as a monotonically decreasing function of z. To keep the units consistent, we normalize the z coordiante by the length of the swarm:$$begin{aligned} tilde{M}(z) = c left( 1-frac{z}{L}right) ^{tilde{b}}, end{aligned}$$
(9)
where the c factor in this expression ensures that the units of the mass per layer are mass/length, and (tilde{b}) is an unknown exponent. Choosing this function form allows us to easily integrate the expression for (tilde{W}(z)) when we substitute (tilde{M}(z)) into it, set this force balance derivation for (tilde{W}(z)) equal to the experimentally determined expression (W(z) = C M(z)^a), and compare the exponents a and (tilde{b}).To solve the expression for (tilde{W}(z)), we substitute the expression for (tilde{M}(z)), Eq. (9), into Eq. (8) and integrate. We then express (tilde{b}) in terms of the experimentally determined a by equating this expression for (tilde{W}(z)) to the scaling law we observe in our experiments, Eq. (7), (W(z) = C tilde{M}(z)^a). The exponent in the expression for (tilde{M(z)}), Eq. (9), is$$begin{aligned} tilde{b} = frac{1}{a-1}. end{aligned}$$
(10)
The weight supported by each layer is then:$$begin{aligned} tilde{W}(z) = cLg left( 1 – frac{1}{a}right) left( 1-frac{z}{L}right) ^{frac{a}{a-1}}. end{aligned}$$
(11)
Next, we test how well our force balance model predicts the data by comparing the predicted value of (tilde{b}) using the force balance to the value of b calculated using experimental fits. We first separate the expression for the layer mass, Eq. (9) into the product of the layer area, (tilde{A}(z)) and the layer density, (tilde{rho }(z)):$$begin{aligned} tilde{M}(z) sim tilde{A}(z) tilde{rho }(z). end{aligned}$$
(12)
To simplify our analysis, we model (tilde{A}(z)) and (tilde{rho }(z)) with a similar monotonically decreasing function to that in Eq. (9):$$begin{aligned} tilde{A}(z) = c_1 left( 1-frac{z}{L}right) ^{tilde{b}_1}, end{aligned}$$
(13)
and$$begin{aligned} tilde{rho }(z) =c_2 left( 1-frac{z}{L}right) ^{tilde{b}_2} end{aligned}$$
(14)
we can then separately measure the effect of the changes in area and density on the exponent in the mass per layer expression in Eq. (9), (tilde{b} = tilde{b}_1 + tilde{b}_2).We first calculate (tilde{b}) using the expression derived from the force balance, Eq. (10), and our experimental result for a, which yields (tilde{b} = 2 pm 0.47). Second, we calculate b by separately calculating power law fits to the data for A(z) in Fig. 2e according to Eq. (13) and (rho (z)) in Fig. 2d according to Eq. (14), which yields (b_1 = 1.38 pm 0.2) and (b_2 = 0.51 pm 0.09). Thus, (b = b_1 + b_2 = 1.89 pm 0.25). See Supplementary Fig. S5(a–c) for log-log plots of M(z), A(z) and (rho (z)), and Supplementary Fig. S5(d–f) for plots of the resulting b, (b_1), and (b_2).We calculate the deviation of (tilde{b}) from b, (frac{tilde{b} – b}{tilde{b}} = 0.03 pm 0.11), and plot the deviation of b from (tilde{b}) in Supplementary Fig. S5(g) as a comparison for the individual CT scans. The values of b and (tilde{b}) being on the same order of magnitude validates the model and allows us to compare (tilde{W}(z)) to a maximum strength of each layer, which we find with dimensional analysis in the following section.Strength of a swarm layer and individual beesThe strength of the layer, (tilde{S}(z)), or the maximum weight that it could support, can be greater than or equal to (tilde{W}(z)): (tilde{S}(z) ge tilde{W}(z)). If the weight of the bees underneath a layer were to exceed its strength (tilde{S}(z)), the layer would not be able to support the weight of those bees, and the swarm would break apart. We perform a dimensional analysis on the strength of each layer to find the relationship between the mass of a layer and its maximum strength, (tilde{S}(z) sim tilde{M}(z)^{alpha }). Force is proportional to mass, which is proprtional to volume, or a length cubed, so a layer’s strength scales with length cubed, (tilde{S}(z) propto L^3). The mass of each layer, with units of mass/length, is proportional to an area, or a length squared, so (tilde{M}(z)) scales with length squared, (tilde{M}(z) propto L^2). Thus, (alpha) must be 1.5 for (tilde{S}(z) sim tilde{M}(z)^{alpha }) to be dimensionally correct. This is similar to the relationship between weightifting capacity and body weight in Ref.16.Estimating (tilde{W}(z)/tilde{S}(z)) gives a measure of how much of its maximum strength each layer uses to hold up the rest of the swarm:$$begin{aligned} frac{tilde{W}(z)}{tilde{S}(z)} sim left( 1-frac{1}{a}right) left( 1-frac{z}{L}right) ^frac{2a-3}{2a-2} end{aligned}$$
(15)
The average number of bees that a bee in a swarm layer supports, (tilde{F}_{bee}(z)), is equal to the mass of bees supported by a layer divided by the sum of the mass of bees in a layer of bees that has the thickness of the length of a bee, (l approx 1.5), as a continuous version of the discrete equation in Eq. (6):$$begin{aligned} tilde{F}_{bee}(z) =frac{int _z^L tilde{M}(z) dz}{int _z^{z+l} tilde{M}(z) dz}. end{aligned}$$
(16)
After integrating, we get an expression for (tilde{F}_{bee} (z)):$$begin{aligned} tilde{F}_{bee}(z)= frac{left( 1-frac{z}{L}right) ^{frac{a}{a-1}}}{left( 1-frac{z}{L}right) ^{frac{a}{a-1}} – left( 1-frac{z + l}{L}right) ^{frac{a}{a-1}}}. end{aligned}$$
(17)
We use the expression for (frac{tilde{W}(z)}{tilde{S}(z)}), Eq. (15), and (tilde{F}_{bee}(z)), Eq. (17), in the next section to evaluate how the force distribution in the swarm would change for swarms with different values of a.Effect of a on the mass of each layer, the fraction of its maximum stregnth it uses, and the average force per beeWe now consider the effect of varying a on the mass and force distribution inside the swarm. To visualize the effect of a on the distribution of bees, we plot the mass per layer of a 1000-g, 12.5 cm long swarm, (tilde{M}(z)) vs. z/L, with (a = 1.5, 1.01, 1000), and (-0.2) in Fig. 3c and the corresponding average force per bee, (F_{bee}(z)) vs. z/L in Fig. 3d. These values of a are example values for the four possible cases of mass distribution in the swarm. We then evaluate how these values of a affect the fraction of maximum strength each layer uses to support the layers underneath it using Eq. (15).If (a approx alpha), as we found in our experiments, layers with higher mass near the attachment surface support the less massive layers under them, as in the solid black line in Fig. 3c. Correspondingly, Fig. 3d shows (tilde{F}_{bee}(z=0) approx 3) at the top of the swarm, and decreases towards the tip. The strength of each layer and the weight it supports are proportional to one another, (tilde{W}(z)/tilde{S}(z) sim 1/3), meaning that the fraction of maximum strength used by a layer is the same for all z. If (1< a < alpha), the swarm approaches one massive layer of bees, as in the dashed purple line in Fig. 3c. The dimensional analysis results in a very small fraction of the total strength used by this layer, (tilde{W}(z)/tilde{S}(z) rightarrow 0 (1-frac{z}{L})^{-infty }). The force supported by each bee in Fig. 3d shows (tilde{F}_{bee}(z) = 1) for the entire swarm, meaning that each bee only supports its own weight. This configuration would either require packing a large number of bees into one very dense or one very wide layer. A swarm with one very dense layer at the top would compress all of the bees; a swarm with one very wide layer would require a large surface area, which would put the swarm in danger from predators and changes in weather. Thus, despite a potentially lower fraction of strength used by the largest layer of bees, this configuration would put the swarm in danger by requiring a large surface area.For values of (a > alpha), as (a rightarrow infty), all the layers of the swarm have the same mass, as in the dash-dot red line in Fig. 3c. The force per bee in Fig. 3d shows (tilde{F}_{bee}(z=0) approx 8) at the top of the swarm, 2.5 times that of the (a = alpha) configuration. In this configuration, the top layers use a higher percentage of their available strength than the lower layers, (tilde{W}(z)/tilde{S}(z) rightarrow (1-frac{z}{L})). Thus, for large swarms, the bees that support the swarm would be under more strain, and the swarm would be more likely to break under external perturbation.Finally, (a < 0) ((0 le a le 1) results in negative values for (tilde{W}(z))) would suggest that the top layers of the swarm have a lower mass than the bottom layers, as in the dotted orange line in Fig. 3c. This is not a realistic range of values for a, but we include it here as a demonstration of a potential mass distribution with the largest layers being on the bottom of the swarm. This configuration would put even more strain on the layers of bees at the top of the swarm, as smaller layers near the attachment surface have a smaller maximum strength. As (a rightarrow 0) on the (a < 0) side, (tilde{W}(z)/tilde{S}(z) rightarrow infty (1-z/L)^{1.5}), and bees in the top layers use a much greater fraction of their strength than bees in the bottom layers. Accordingly, the mean force per bee in Fig. 3d exceeds the maximum bee grip strength of 35 bee weights, and the swarm could not support itself in this configuration.The swarm configuration with (a approx 1.5) uses the full strength of each layer and puts a lower strain on the bees than most other values of a, and avoids weight distributions that could expose a large number of bees to external danger. More