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The goal of this study was to examine the fluid flows directly adjacent to propulsor surfaces in order to better understand how metachronal propulsors interact with fluids for thrust production. Based on the direct comparison of the mean contributions of pulling vs. pushing forces throughout the power stroke of replicate individual propulsors (Fig. 4, which are generated by negative vs. positive pressure fields, respectively) we suggest that the propulsors of the animals examined rely predominantly on negative pressure for generating thrust. The assertion that these propulsor level observations to apply to the movement of the whole animal requires the assumptions that, first, the propulsors we quantified are representative of the all the other propulsors contributing to swimming thrust, and second, that the thrust generated for the whole animal is due to accumulated total thrust generated by individual propulsors. Although our data addresses the first of these assumptions by replicating individual propulsors, we cannot document the second assumption that the total thrust represents the sum of all individual propulsor elements. While this second assumption is intuitively appealing, our data is confined to the small spatial and temporal scales around individual propulsor elements. Confirmation that the whole-organism thrust results from of the summation of individual contributions requires experiments at different scales than those used in the current study.
Thrust generated by a propulsor is ultimately determined by the overall pressure gradient across the propulsor. So does it matter whether that gradient is dominated by negative or positive pressure? We believe that this distinction is fundamental for understanding why animal propulsors bend in a surprisingly characteristic and narrow range. Rigid paddle designs are dominated by positive pressure pushing against a fluid, which in turn, generates thrust pushing a body forward. Bending at propulsor margins encourages vortex formation on the lee side of the propulsor (Figs. 2, 3) that differs from rigid propulsors. Counter-rotating vortices formed on the lee side of a bending propulsor accelerate fluid at the intersection of the vortices12,15. The fluid thus accelerated relative to the leading edge of the propulsor is the basis of the pressure gradient across the propulsor surface. In turn, this elevated pressure gradient generates high thrust and is the reason for the dominant contribution of suction thrust to natural bending propulsors. More generally, negative pressure fields are a fundamental feature of vortices which are universally formed around objects moving in fluids (except at the lowest Reynolds numbers). Lift, a different propulsive mode that relies on negative pressure, is a well-known example that illustrates how kinematics and morphology can enhance negative pressure for thrust2. Lift occurs when a foil separates flow traveling over and under the foil surface. With the correct foil shape and kinematics, the separation of flow can generate strong negative pressure fields above the foil leading to an upward pulling thrust on the foil. This lift relies on the negative pressure field and foil shape.
To be clear, the thrust generated by limbs and ctenes in this study is not lift because the forces generated by lift are directed perpendicular to the direction of flow and the forces we describe are oriented in the direction of flow (Fig. 3). However, like lift, we suggest that paddles must move with prescribed kinematics to generate enhanced negative pressure fields. Bending kinematics in particular have been shown to greatly enhance vorticity and along with that, negative pressure11,16,17. Rigid, non-bending paddles generate different hydrodynamic structures than we observed13,14 and do not generate strong negative pressure fields16,17,18,19. Therefore, the kinematics of bending appear to be important for generating strong negative pressure fields around moving propulsors.
Until recently, technical constraints have limited our ability to investigate the scope of the benefits of using negative pressure for thrust. However several numerical studies, and a few experimental studies, have compared rigid to flexible propulsors. These studies have demonstrated that first, bending enhances negative pressure fields, second, bending generates elevated thrust, and third, bending enhances hydrodynamic efficiency12,16,17,20,21,22,23,24. The hydrodynamic patterns around bending propulsors show that negative pressure fields associated with bends generate significantly greater flow velocities than positive pressure fields (Fig. 2e11,12,16,21). This would lead to enhanced momentum transfer and explain the enhanced thrust observed for bending propulsors. The similar bending kinematics between the limbs and ctenes in this study and the swimming and flying animals from Lucas et al.1 suggests that these small paddling swimmers may employ similar hydrodynamic features as flying birds and swimming fish. If these bending patterns are predominately used to generate negative pressure fields for thrust, it follows that there is a need for greater focus on negative pressure around bending propulsors in order to understand the extent of the benefits of animals experience by pulling rather than pushing themselves through fluids.
Despite the vast difference in scale and Reynolds number, the results of this study suggest that the small metachronal paddles of swimming invertebrates may produce some similar effects as flapping wings in birds and insects. For example, there are similarities in the degree of bending and location of bending for the paddles in this study and the spanwise flexibility of birds and insects1. Such spanwise flexibility was found to be beneficial and yielded an increase in thrust coefficient, and a small decrease in power-input requirement, resulting in higher efficiency25.
In addition to the benefits for single propulsors, negative pressure fields can facilitate the movement and coordination of multiple propulsors which have antiplectic metachronal wave kinematics. During an antiplectic metachronal wave, a leading propulsor will begin the power stroke and, after it has initiated its stroke, the propulsor immediately behind it will initiate its own power stroke. This sequential pattern will continue for all the subsequent propulsors in the antiplectic wave. The predominately negative pressure on the leeward of each propulsor can serve to facilitate the kinematics of the adjacent propulsor by reducing the hydrodynamic resistance necessary to initiate and complete its power stroke26. In addition, the negative pressure in the gap between adjacent propulsors can serve as a cue for the adjacent propulsor to initiate its power stroke. It has been suggested that the ctenes of ctenophores require such cues to coordinate the metachronal kinematics26,27,28. At lower Reynolds numbers (Re  More

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Global food demand will rise substantially over the coming decades. Meeting this demand while decreasing the environmental footprint of agriculture is one of largest challenges of the twenty-first century1,2,3. A growing world population and changing diets are projected to double4 meat and dairy consumption between 2000 and 2050. As one of the main feed sources for livestock, grasslands play a key role in meeting this demand. With over 33 million km2, permanent grasslands account for ~ 25% of the world’s land cover. Over two thirds of this area is utilised for agriculture, making it the most dominant land use5. Sustainably increasing grassland productivity is therefore crucial to ensure future global food security6,7.
Phosphorus (P) is an essential nutrient, often limiting plant growth8. P fertilisation is therefore needed to sustain productivity in agricultural systems across the world. Because the world’s P reserves are decreasing, the importance of judicious P use will increase over the coming century. Although estimates of global P reserves vary, the costs of high quality P fertilisers will increase, as will the global demand for these fertilisers9,10,11,12. Differences in climate, geography, agricultural development, and fertilisation practices have led to great global imbalances of P in agricultural land13,14,15,16. In parts of Europe, North America, and China, historical applications of manure and fertilisers have resulted in positive P balances and increased risk of eutrophication of surface waters17. In many other regions, predominantly in tropical areas, farmers struggle to maintain soil P availability to sustain optimal rates of crop production18. Recent predictions suggest that global P inputs in grasslands will have to increase fourfold to support an 80% increase in grass yield projected for 205015, which implies an urgent need to increase use efficiency of P fertiliser sources.
The large diversity in agronomic P status of soils across the world and the projected increase in cost and demand of P fertilisers necessitate a rethink of the use of P resources: are we applying fertilisers at the right rates to the right soils? The success of fertiliser application depends on conditions created by climate and management19,20 and is strongly governed by soil properties such as pH and concentrations of metal oxides and Ca in soil that can impact P availability to plants8,21,22. However, data for these relationships are fragmentary and country- or region-specific, and global assessments are lacking23,24. Here we use a meta-analysis on a global database of 67 studies and 1227 observations with a wide range of soil properties and climatic conditions to assess the general effect of P fertilisation on grassland production across the world. Furthermore, we identify soil-related driving factors that determine the success of fertiliser applications.
Our dataset included data from field grasslands all over the world (Supplementary Fig. 1). Most studies originated from Europe and North America, but due to several studies with many observations from the Australian continent, there were almost as many observations from Oceania. We analysed our dataset using two different metrics: the response ratio (RR) as measure for the relative increase in dry matter yield as a result of P fertilisation, and P agronomic efficiency (PAE) expressing the absolute yield increase per unit of P applied.
Factors controlling the success of phosphorus fertilisation
P fertilisation increased grassland yield by 37% (95% confidence interval: 33 to 40%; Fig. 1; Supplementary Table 3) averaged over all grasslands, soil types, and fertility levels, resulting in a PAE of 32 kg kg−1 (Fig. 2; Supplementary Table 4). In other words, dry matter yields increased by 32 kg per kg of P applied on average. Yield responses to P additions increased with P application rates: rates below 25 kg P ha−1 increased yields by 40% on average, whereas applying over 100 kg P ha−1 increased grass yield by 65%. An exception to this pattern were grasslands fertilised with 25–50 kg P ha−1, which responded to a lesser extent than those in other categories. This is likely an artefact due to a relatively high average soil P status of studies included in this category (Supplementary Fig. 3), which may have led to high yields in the control treatments. The PAE, on the other hand, decreased with P application rates (Supplementary Table 4): yields increased by 53 kg per kg P applied at rates lower than 25 kg P ha−1, but only by 12 kg kg−1 P at rates higher than 100 kg P ha−1. This indicates that finding a balance between P input and yield response is crucial for optimising fertiliser effectivity, as the agronomic efficiency decreases with higher application rates.
Figure 1

Impact of phosphorus (P) fertilisation for the controlling factors crop, P rate, climate, and mean annual temperature expressed as relative yield increase per category. The 95% confidence intervals are represented by the error bars, and the number of studies and observations per category are between parentheses; *,**,***Significant controlling factor effect at an α of 0.05, 0.01 and 0.001, respectively.

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Figure 2

The Phosphorus agronomic efficiency (PAE) for different controlling factors per subgroup. The effect is expressed for crop, climate, and P status (Olsen-equivalent) × P rate (c). Low SPT: ≤ 10 mg P kg−1; high SPT:  > 10 mg P kg−1; low rate: P rate ≤ 50 kg P ha−1; high rate: P rate  > 50 kg P ha−1 The 95% confidence intervals are represented by the error bars, and the number of studies and observations per category are between parentheses; *, **,***Significant controlling factor effect at an α of 0.05, 0.01 and 0.001, respectively.

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Systems that included legumes responded more strongly to P fertilisation than systems without legumes (Fig. 1). On average, P fertiliser increased yield in grass/legume systems by 54%, but only by 25% in grassland systems without legumes. These numbers corresponded with a PAE of 46 kg kg−1 for grass/legume and 22 kg kg−1 for grass-only systems, meaning that P fertilisation was roughly twice as effective in grasslands with legumes than in those without legumes. Legumes like alfalfa and clover are regularly included in grassland mixtures, mainly because they provide extra N inputs to the plant-soil system by establishing a symbiosis with N-fixing microorganisms23. These results likely reflect that legumes generally require more P than grasses, and can acquire it less easily due to thicker roots and shorter root hairs11,25,26.
In our database, more than half (36) of the studies included more than one N treatment. Overall, the N application rate had little effect on the response of grasslands to P fertilisation. There was no significant effect of N rate on the PAE (Supplementary Table 4). Yield responses to P fertiliser at N application rates over 200 kg N ha−1 were slightly but significantly smaller than at lower N rates (Supplementary Table 3). However, if N limitation of the grasslands would have played a prominent role, a general increase in response to P fertiliser with increasing N rate would have been observed. These results suggest that differences in yield responses were mainly driven by a response to P fertilisation rather than to N fertilisation.
Geographical variation in responses
P application increased grassland yields in tropical regions (i.e. latitudes ≤ 35°) significantly more strongly than in temperate grasslands (Fig. 1, Supplementary Table 3). However, because yields of tropical grasslands were relatively low, the PAE of fertiliser application did not differ significantly between the two regions (34 and 31 kg kg−1 for tropical and temperate regions, respectively; Fig. 2, Supplementary Table 4). These results likely reflect that soils in (sub)tropical regions are often highly weathered, nutrient-poor, and have a low P availability due to high abundancy of adsorbents like Al and Fe oxides8. In contrast, decades of manure and fertiliser applications have resulted in a build-up of soil P levels well beyond crop requirements and a corresponding decrease in yield response to P fertiliser application17,27 in many temperate regions (e.g. North America, Europe, and New Zealand). The differences in response of temperate and tropical grasslands are also reflected in the results for mean annual temperature (MAT; Fig. 1, Supplementary Table 3), with grasslands in colder regions (MAT  20 °C reacting the strongest. Higher temperatures may lead to more rapid plant production and to an increase in mineralisation of organic matter. Correlation analysis of the controlling factors showed that MAT and latitude among our studies were strongly correlated (Supplementary Fig. 4; Spearman’s ρ = -0.95).
Yield responses to P fertilisation were significantly smaller in Asia, North America, and Europe (+ 15 to + 29%) than in South America, Oceania, and Africa (+ 58 to + 94%). The PAE ranged from 12 kg kg−1 for studies in Asia to 74 kg kg−1 for studies in Oceania and even 117 kg kg−1 for the one African study included in our dataset (Supplementary Table 4). The continents with grasslands that showed a strong response to P fertilisation roughly coincide with the areas that have relatively low P inputs and outputs, as modelled by Sattari et al.15. Taken together, these results imply that Africa and Oceania with low P inputs responded strongly to P fertilisation whereas grasslands in Europe, North America and Asia with relatively high P inputs over the past decades, showed a weak response to P fertilisation.
Do we apply phosphorus fertilisers to the right soils?
We used various soil parameters as controlling factors (Table 1) to identify what soil properties drive differences in yield response to P fertilisation. One of the most important parameters is the agronomic P status of the soil, which is commonly determined with a soil P test (SPT). Because soil type, climate, and crop response vary considerably across the world, each country and sometimes even region has its own SPT method and classification system28,29. Given this large variety of SPT procedures (and resulting P concentrations) in use, we applied conversion formulas published in peer-reviewed papers to express reported SPT values in our database as ‘Olsen-equivalent’ P values wherever possible (see Supplementary Methods).
Table 1 Controlling factors and categories distinguished in the meta-analysis.
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Grasslands on soils with low SPT values (≤ 5 mg P kg−1) responded strongest to P fertilisation with a yield increase of 110% on average (Fig. 3, Supplementary Table 3). Conversely, P additions to soils with SPT values  > 5 mg P kg−1 increased yields by 7–25%. Although yield response decreased dramatically with increasing SPT values, the responses at relatively high SPT values (10–25 and  > 25 mg P kg−1) were still statistically significant. Critical values (that is, SPT levels for which the yield is 95% of the maximum yield) for grass of 23–25 mg kg−1 Olsen P have been reported previously for English grasslands30, which coincides with the limited yield response for soils in the highest SPT category. A study of 25 Spanish soils also showed an average critical SPT of 24 mg Olsen P kg−1 for ryegrass, although there was a wide spread for individual soils, ranging from 11 to 46 mg kg−131. For a range of Australian grassland species, however, lower critical SPT values (between 9 and 15 mg kg−1) have been determined32. This variety of critical SPT values found in literature illustrates that the effect of P fertilisation is strongly dependent on soil, climate, and even grassland species. Therefore, our results here do not give a hard SPT limit beyond which further P applications are rendered ineffective, but do indicate a strong decrease in effectiveness at higher SPT values.
Figure 3

Effect of different soil characteristics on the impact of phosphorus (P) fertilisation. The effect is expressed for soil P status based on Olsen P-equivalent, soil pH, organic matter content, and clay content. The 95% confidence intervals are represented by the error bars, and the number of studies and observations per category are between parentheses; *, **,***Significant controlling factor effect at an α of 0.05, 0.01 and 0.001, respectively.

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The strong yield response to P fertilisation on soils with low SPT values was not merely the result of a low yield of the control treatments. PAE was also highest (75 kg kg−1) for soils with SPT ≤ 5 mg P kg−1 (Supplementary Table 4) and fertilisation on these soils was 3 to 8 times as effective as on soils with higher SPT values in terms of absolute yield increases. Without correcting for the P application rate, absolute yield responses (average yield of treated plots minus average yield of control plots) to P fertilisation varied substantially (− 2.7 to 11.3 tonnes ha−1; Supplementary Fig. 5). The largest response (on average 2.7 tonnes ha−1 increase) and variation to P fertilisation were found for soils in the lowest SPT category. The yield response decreased with higher SPT (Supplementary Fig. 5). Figure 2 shows that both relatively low (≤ 50 kg P ha−1) and relatively high ( > 50 kg P ha−1) P application rates on soils with a low P status (≤ 10 mg P kg−1 Olsen-equivalent) were more effective than any P fertilisation rate on soils with a relatively high P status ( > 10 mg P kg−1 Olsen-equivalent). The high PAE of large application rates on soils with a low P status (Fig. 2) may be the result of the binding behaviour of P in soil: in soils with a low P status (where relatively more P adsorption occurs), relatively high P inputs are required to raise the level of plant-available P, so grassland on these soils will benefit relatively more from high application rates. Conversely, applying large amounts of P to soils with a relatively high P status ( > 10 mg P kg−1) showed a low PAE.
Yield responses to P applications were highest on grasslands with a soil pH of 5–6 (60% yield increase; Fig. 3) whereas lower and higher pH levels resulted in lower (11–26%) yield responses. We observed the same pattern for PAE, where studies with a pH of 5 to 6 had a 50 kg yield increase per kg of P fertilised, whereas for soils with a pH above 7 this was only 11 kg (Supplementary Table 4). Soil pH is a crucial parameter in determining the availability of P to crops8. In acidic mineral soils, binding of P to Fe and Al (hydr)oxides is often the main factor that governs the level of plant available P. In contrast, in soils with pH values above 7, P is more likely to form poorly soluble Ca-P precipitates, decreasing plant available P. The relative availability of soil P is highest at soil pH levels of 5 to 733,34, which would imply that around this pH fertiliser P application would yield the strongest responses.
We found a positive correlation between the soil organic matter (OM) content and yield response to P fertilisation (Fig. 3). On average, P application increased yield by only 11% on soils with an OM content below 2% (PAE was 7.2 kg kg−1 on average and this effect was not statistically significant). Yield responses were much higher (41–80%) in soils with an OM content of  > 5%. The PAE was 9 times as high in soils with  > 5% OM as in soils with  More

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We estimated the abundance of desert bighorn sheep in a captive facility located within the Chihuahuan Desert of New Mexico (Fig. 1). The area is arid, mountainous, with steep cliffs punctuated by ravines. The entire facility is enclosed by a high fence, preventing desert bighorn sheep ingress or egress. These animals are wild, unconditioned to humans, and used by The New Mexico Game and Fish Department (NMDGF) to establish and bolster other desert bighorn sheep populations within New Mexico16.
NMDGF leads an annual spring census to enumerate desert bighorn sheep numbers within the facility. Methodologically, the census uses a ground crew of spaced individuals walking in a line perpendicular to pen fencing, within the facility (i.e., drive count or census). Each individual keeps track of neighboring individuals to space the line, and to count any desert bighorn sheep breaking past them. Most desert bighorn sheep are herded ahead of the line. Other biologists at high topographical sites use spotting-scopes and binoculars to count and age class the moving sheep. Census counts are classified by animal ages and sex. We consider young sheep any animal ≤ 1.5 years old. Adult rams and ewes consist of males and females aged  > 1.5 years old, respectively. The group “adult” includes all sheep  > 1.5 years old.
We established 11 motion activated camera traps (Bushnell Trophy Cam) at the centers of an 800-m grid with a random geographical start. Cameras were secured to T-posts or existing vegetation when rocky areas thwarted post establishment. Most cameras were oriented north, to minimize sun exposure in the imagery. When vegetation or rock blocked the camera view, the camera orientation was rotated eastward until a clear view was obtained. Camera heights were 0.9–1.2 m with declination perpendicular to the ground. Cameras were checked at 6 month intervals and the retrieved SD cards were never full. Cameras were motion activated and set at the shortest delay possible (10 s; meaning that the camera waits at least 10 s after recording a picture before it will record another). In practice, the fastest trigger speed that cameras recorded imagery was a mean of 14.92 s (N = 6 cameras; SD = 0.94), a value we rounded to 15 s and employed in our analyses. Cameras recorded one image per trigger. We deployed cameras by 15 May 2017 and retrieved cameras no earlier than 30 April 2018. Our analyses period began on 1 October 2017 and ended on 1 May 2018. We employed a 5 month acclimation period to avoid the cameras serving as a novel attractant for desert bighorn sheep, which would violate distance sampling assumptions. Further, we experienced 1 camera failure during this acclimation period, and relocated 2 misplaced cameras. Lastly, some desert bighorn sheep gathered in shady locations near cameras during hot months (June–September) which created extreme variation in the encounter rate. The 1 October 2017–1 May 2018 period lacked all of these issues.
Imagery of desert bighorn sheep were identified and then classified by sex and age class: rams, ewes, young, adults (an adult-sized animal with sex undiscernible), and unknown [undiscernible (e.g. picture of a hoof, or animals blocking a clear view another animal)17]. To quantify distances, an individual stood at each camera and used the printed images of desert bighorn sheep to position another person at the exact locations that an animal was imaged. Distances between individuals were measured with a laser rangefinder and metric tape (Fig. 2; the authors confirm that informed consent was obtained to publish the identifying information/images in an online open-access publication). We supplemented these measurements by recording distances between the camera and several recognizable objects in the images (e.g. rocks, plants), to ensure accurate distance delineations for the imaged sheep.
The sensitivity of a trail camera’s passive infrared sensor (PIR) will decline as radial distance from the camera increases. Other factors, like vegetation and topography, also cause animal detections to decline with distance. This situation makes distance sampling an appealing approach, as its’ foundational premise is that the probability of detecting an animal declines with distance from the observation point15. The technique relies on measured distances between animals and the observation point. Therefore, we used the distance measures of desert bighorn sheep to the respective trail camera imaging them, to estimate sheep abundances using the ‘distance’ package (version 0.9.812) in program R. We analyzed data using a fall period (1 October 2017–31 January 2018) and a spring period (1 March 2018–1 May 2018). Dates for these periods were selected by season while ensuring sufficient sample sizes.
The camera trap operates like a point count sample. The sampling angle for each camera’s field of view was 50°18. Therefore, we multiplied sampling effort by this fraction (50/360) to correctly represent the amount of sampling area.
When analyzing data within a distance sampling approach, obtaining unbiased density estimates relies on correspondence between the sampling period and the period describing when the target species are active and therefore available for detection10,15. In our situation, this means aligning the sampling period of distance measurements with the period of time that desert bighorn sheep were active and able to trigger the trail camera10. In our study, we acquired very few nocturnal images of desert bighorn sheep (Fig. 4). Therefore, we censored study effort and distance data to the period defined by 1 h before sunrise through 2 h after sunset for each month, on a daily basis. Doing so removed  More

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