Philippa Kaur

It is well known that parrots are excellent vocal learners; here we quantified that ability across a wide variety of species, using human mimicry as a proxy for vocal learning of natural repertoires. Results confirm that parrot vocal mimicry varies substantially both within and among species22. Parrot age, social interactions, and sex do not appear to be universal drivers of vocal learning ability within the order Psittaciformes, but all of these factors may have effects within individual species.Vocal learning variation by speciesWithin species, mimicry sound repertoires are extremely variable bird to bird; for example, our data indicate that a grey parrot may mimic anywhere from 0 to 600 different human words. Many other species showed smaller repertoires but similar variability. It is not entirely clear whether this range of variation would be present in natural sounds within wild parrot populations, but research has demonstrated intraspecific repertoire size variation in multiple species of parrots30,31.The vast majority of parrots presented a pattern in which their repertoire size was largest for words, intermediate for phrases (composed of the reported words), and smallest for non-linguistic sounds (Fig. 2). In the wild, parrots mimic the most socially relevant vocalizations, and presumably do so in captivity as well15. Thus, the spoken word and phrase interactions with their human “flock” likely reflect the most socially relevant cues. The interesting exceptions to this pattern were Fischer’s lovebirds, cockatiels, and Senegal parrots who all used more sounds than phrases. Cockatiels are well-known in the pet world to be excellent whistlers, and thus it was satisfying to see that our data support that informal information. We suspect that deviations from the typical patterns may represent acoustic learning preferences, templates, or limitations32.Although individual variation was substantial, we nevertheless saw strong evidence that overall vocal learning abilities differed by species. Pacific parrotlets and sun parakeets showed very limited human mimicry, while grey parrots, Amazona parrots, cockatoos, and macaws were generally very accomplished mimics. The patterns that we documented appeas to reflect natural vocal repertoire variation across species. The documented calls of wild parrots generally range from 5 to 15 calls25,33,34,35,36. Several species, however, present additional complexity: yellow-naped parrots (Amazona auropalliata), palm cockatoos (Probosciger aterrimus), and grey parrots all have natural repertoires of more than 25 discrete elements, with additional elements given in duets13,27,37 Members of these three groups, grey parrots, Amazona parrots and cockatoos also had relatively large repertoires in our study. In several of these species (particularly grey parrots) our measure of mimicked “words” (60) was higher than estimates of natural call “elements” (39) in the literature27. This discrepancy suggests that parrots are capable of learning vocalizations with more than 25 elements and, simultaneously, might reflect a sampling bias wherein survey-takers are more likely to report on individuals with high mimicry ability.Parrot species varied in their tendency to improvise new combinations of elements, although most species did rearrange words to some degree. Research shows that parrot vocalization length and structure carry signal content, so there may be selective pressures favoring this ability24,33. If so, then our data suggest that those pressures are strongest in some cockatoos and weakest in sun parakeets and green-cheeked parakeets. In general, species with larger repertoires also showed more vocal flexibility (Fig. 2, Appendix 6). Additionally, wild birds typically use particular vocalizations in set contexts, so the ability to do so is likely to be adaptive24. Previous studies of captive parrots have demonstrated contextual use of mimicked words, both in tutored lab settings and in home-raised birds28,38. In our sample, contextual use of learned sounds was supported across 89% of individuals and most species. Survey-taker responses on this topic are necessarily subjective, so we emphasize that this rate of contextual use should be interpreted as a general estimate. Nevertheless, the data indicated that parrots frequently associated mimicked human sounds with appropriate human contexts. This finding is particularly revealing because the relevant human contexts are, by their nature, outside the range of typical wild parrot experiences. Contextual vocalization use must, therefore, rely on extremely flexible vocal learning mechanisms.Vocal learning variation by ageOn average, birds aged with high confidence were younger than those aged with low or medium confidence. This pattern might indicate that people tend to overestimate the age of captive birds of uncertain age. This pattern might also reflect the facts that older birds are more likely to be wild-caught and that younger birds are more likely to have good hatch-date documentation. In either case, there are few ramifications of inaccurate age estimates relating to vocal behavior because our data gave no evidence that adult vocal mimicry repertoires varied with age. Our analyses of grey parrots confirmed that repertoires expanded through the juvenile phase, but did not show reliable expansion among adults. Studies of wild birds indicate that parrots can learn vocalizations throughout life; such open-ended learning is limited to a subset of vocal learning species, and can generate different outcomes as animals age15. In some species, animals can add new vocal features over the course of a lifetime, leading to repertoire expansion39,40. In other species, animals may replace parts of their repertoire with newly-learned vocalizations, leading to stable vocal production repertoire sizes across age groups39,41. Our data suggest that parrots fit the second pattern; although they are open-ended vocal learners, their adult repertoires change more by element replacement, than by expansion. This does not necessarily imply that vocalizations are “forgotten” through time, but merely that some sounds are no longer used as conditions change42. Many parrot vocalizations function in social coordination with flock-mates22. The fission–fusion nature of parrot flocks creates changing social conditions for each individual over its lifetime43. A vocal replacement model for repertoire learning would allow individuals to adjust their vocal signatures to match new social situations and stop producing vocalizations that are no longer socially relevant11,44.Vocal learning variation by sexOur analyses of the full data set confirmed the generally held understanding that males and females in most species of parrots have similar vocal learning abilities15. We did, however see sex differences in some species that merit future study. First, we found a substantial overrepresentation of males in our sample. This could be interpreted several ways; (1) there are legitimately more males in the parrot pet trade, (2) pet owners are giving us accurate data but are more likely to give us data on males or (3) some bias exists in which pet owners assume their talking parrots are males, rather than females. Possibilities 1 and 2 seem unlikely because after we eliminated all parrots sexed with low confidence, we were left with a nearly 1:1 ratio of males:females in the subset of parrots that were sexed with high confidence. That trend suggests that the male bias in our data comes (at least in part) from a human tendency to label their pet parrots as male when the sex is not clear. Among songbirds, there is a strong tendency to assume that singing birds are male, and a similar bias may hold true for parrots45. It is unclear whether parrots in this study were mislabeled as male because they vocalize or, more simply, because that is the default human tendency for any animal.Although we conclude that some of the male bias in our data is human error, we also saw patterns that suggest real sex differences in vocal learning some species. For example, Pacific parrotlets are a dimorphic species, and all of our sampled birds were sexed by plumage46. Thus, we expect sexing in this species to be fairly accurate. Our data set included 10 males and no females, a bias unlikely to result purely from sampling error. We saw a similar trend in cockatiels for which there was a large overabundance of males in the data set, even among the 17 birds sexed with high confidence. Humans may be more likely to report on parrots that are good mimics. Therefore, the results likely reflect a real-world tendency for male cockatiels to mimic more human sounds than females. Figure 3 suggests that the same might be true for galahs, sulphur-crested cockatoos, rose-ringed parakeets, Senegal parrots, and budgerigars. Existing research supports the idea that sex differences in vocal behavior are important in several of these species. Among galahs, male and female calls evoke different responses47, and patterns of call adjustment vary by sex among budgerigars20. We also note that several of these species (Pacific parrotlets, rose-ringed parakeets, budgerigars, and cockatiels; Appendix 2b) show sex-based differences in both plumage and vocal learning, raising questions about whether those traits co-evolve.In addition to sex-based differences in the tendency to mimic humans, several well-sampled species showed evidence of sex-based differences in repertoire sizes. Particularly interesting are the blue-and-yellow macaws, in which repertoire size was significantly male-biased. We had more females (15) than males (9) in the data set, but males used on average 3–4 times as many mimicry sounds, phrases and words as females did. Galahs and budgerigars showed a similar male-bias in repertoire sizes, matching the trend of males being overrepresented in our data set for those two species. Prior research on galahs and budgerigars has found that males can be more vocal and more flexible with their vocalizations; perhaps these abilities translate to learning more call types20,47. A similar, but weaker, male mimicry increase occurred in rose-ringed parakeets. In only one species, yellow-headed parrots, did females show a significantly larger mimicry repertoire than males in any category (Appendix 5). Interestingly, the tendency to mimic humans (measured as sampling in the data set) and repertoire sizes did not always show the same patterns. Among sulphur-crested cockatoos, cockatiels, and Senegal parrots, males were more likely to show human mimicry, but their repertoires were not larger than the repertoires of females. This suggests that in some species, females may be less likely to mimic vocalizations, but when they do so they have just as large a vocabulary as males.The reported sex differences in parrot vocal mimicry repertoires are intriguing, but also are tentative conclusions. In many species, including our best sampled species, grey parrots, we saw no evidence of sex-differences in repertoire size. The sex-biases that we did document lose statistical significance after controlling for the many comparisons that we conducted. Nevertheless, we expect that some of our data represent true biological differences, especially because studies of wild birds have shown similar trends47,48. Thus, we offer our data as a starting point for additional research. Taken together, the analyses by sex provide interesting points of comparison to other vocal learning animals. Our combined analyses suggest that sex differences in vocal learning are vastly smaller and less common among parrots than they are among oscine passerines and hummingbirds45,49,50. Sex-based patterns of vocal learning in parrots appear more similar to those of vocal learning mammals than to those of other vocal learning birds51. Overall, parrots and songbirds present excellent comparative study systems for all aspects of sex differences in song learning, from the mechanistic to the functional17,51.Vocal learning variation by social contextMany parrot vocalizations function in social organization for individuals within flocks, and the ability to learn from conspecifics is essential to parrot familial and social integration12,15,52. Although our study specifically examined vocal learning of human sounds, we thought it possible that the presence of other parrots would increase mimicry rates if parrots learned human vocalizations from their parrot companions. Anecdotal stories of parrots teaching words to other parrots abound53, and studies of grey parrot cognition show that vocal modeling by multiple tutors can lead to better learning of human words54. Most existing results, however, are based on human tutoring, with controlled studies of parrot-parrot word transmission lacking. Here we tested whether social interactions with other parrots correlated with more vocal learning of human sounds. Our data gave no evidence that parrot-parrot social interactions drive human vocal mimicry. This was true across the full sample (controlling for species identity), and for our best sampled species, grey parrots. Although companion parrots are known to learn from conspecifics, that learning does not appear to shape repertoire sizes53. Open questions remain about whether signal complexity, repertoire size, or aspects of vocal learning covary with social complexity at a larger scale among parrots55. Follow up studies should address these questions using phylogenetically-controlled methods56. More

Global statistics on declining biodiversity can give the impression that every population of every species is in a downward spiral. In fact, many populations are stable or growing, while a small number of species faces truly existential challenges. These photos capture some specific crises. They are images of threats unfolding, of desperate attempts at species defence and of the beautiful living world that is at stake.
The 15th United Nations Biodiversity Conference, COP15, opens in Montreal, Canada, on 7 December. At the meeting, delegates will attempt to agree on goals for stabilizing species’ declines by 2030 and reverse them by mid-century. The current draft framework agreement promises nothing less than a “transformation in society’s relationship with biodiversity”.
Help for the kelp. Tasmania’s forests of giant kelp (Macrocystis pyrifera) are dying as climate change shifts ocean currents, bringing warm water to the east coast of the temperate Australian island. The kelp forests host an entire ecosystem, including abalone and crayfish — both economically important species and part of local food culture. Now, researchers at the Institute for Marine and Antarctic Studies in Hobart are breeding kelp plants that can tolerate warmer conditions, and replanting them along the coast — a trial for what they hope will become a landscape-scale restoration. More

Study area descriptionYangtze River Basin is situated in central China (Fig. 1). Its geographical coordinates are between 30° 48′ 30″–31° 02′ 30″ N and 112° 48′ 45″–113° 03′ 45″ E. Taizishan is located in the transition zone between the north and south of China, with an altitude of 403–467.4 m. It belongs to the subtropical monsoon humid climate zone and has obvious karst landforms. The farm area is 7576 hectares, the forest coverage rate is 82.0%, and the vegetation is mainly Masson pine, fir, and various broad-leaved tree species. Increased forest coverage reduces sediment production30. The soil is mainly viscous yellow–brown soil and loess parent material. Rain is concentrated in summer, with an average annual rainfall of 1094.6 mm and an average annual temperature of 16.4 °C. Rainfall-related flood risk increased in the Yangtze River Delta in recent years31.The study was based in a Pinus massoniana forest in the Taizishan forest farm of Hubei Province. The Pinus massoniana (Masson pine) is a common species distributed in Central China.Figure 1Geographic location of the study area. Maps were generated using ArcGIS 10.8 for Desktop (http://www.esri.com/software/arcgis/arcgis-for-desktop).Full size imageExperiment designWe chose the Pinus massoniana forest with 47a in the study area as the research object. In the typical Pinus massoniana forest, the separate layers of litter (semi-decomposed and non-decomposed layers) were collected from several 1 m × 1 m quadrat and placed in grid bags. The litter of the semi-decomposed layer have no complete outline, and the color was brown. As the litter leaves of the completely decomposed layer are powdery and are combined with the soil layer, this layer is difficult to collect. Before testing, it was necessary to clean the soil off the pine needles and then allow the litter to dry naturally. The characteristics of the semi-decomposed and non-decomposed litter layers are shown in Table 1. The soil samples need to be dried and screened by 10 mm. When filling the soil trough, every 0.1 m of soil thickness was one layer, for a total of four layers (0.4 m). The characteristics by soil particle sizes are different (Fig. 2). The soil samples were dried naturally, crushed, and then sieved. The soil trough (2 m long, 0.5 m wide and 0.5 m deep) was filled to have a bulk density of 1.53 g·m−3. In this process, an appropriate amount of water was sprinkled on the surface of each soil layer to achieve a soil moisture content consistent with the surrounding, undisturbed, or natural, state. The simulation experiment was conducted in the Jiufeng rainfall laboratory at Beijing Forestry University, China. We used a rainfall simulation system (QYJY-503T, Qingyuan Measurement Technology, Xi’an, China) used a rotary downward spray nozzle. The system is able to simulate a wide range of rainfall intensities (10 to 300 mm h−1) using various water pressure and nozzle sizes controlled by a computer system.Table 1 Characteristics of the non-decomposed and semi-decomposed layers of Pinus massoniana litter.Full size tableFigure 2Soil particle composition of study area soil layers.Full size imageAccording to the results of the field forest investigation, the litter was covered with the experimental treatments shown in Table 2. The treatments mass coverage of non-decomposed litter layer was named as follows: N1 denoted litter mass coverage 0 g·m−2, N2 was ‘the non-decomposed litter mass coverage 100 g·m−2’, N3 was ‘the non-decomposed litter mass coverage 200 g·m−2’, and N4 was ‘the non-decomposed litter mass coverage 400 g·m−2’, N5 was ‘the semi-decomposed litter mass coverage 100 g·m−2’, N6 was ‘the non-decomposed litter mass coverage 100 g·m−2 and the semi-decomposed litter mass coverage 100 g·m−2’, N7 was ‘the non-decomposed litter mass coverage 200 g·m−2 and the semi-decomposed litter mass coverage 100 g·m−2’. N2, N3 and N4 were the undissolved state of litter layer, and N4 (non-decomposed state, ND), N7 (initial stage of litter decomposition, ID), N6 (middle stage of litter decomposition, MD) and N5 (final stage of litter decomposition, FD) respectively represent different stages of litter decomposition.Table 2 The experimental design of this study.Full size tableAccording to the rainfall in the Taizishan area of Hubei Province, erosive rainfall and extreme rainstorms were selected as the research conditions. Summer rainfall events occur mainly in the summer in this area, and a rainfall intensity of 60 mm·h−1 was the most common erosive rainfall intensity. Under extreme weather conditions, the rainfall intensity can reach up to 120 mm·h−1. Our experiments were conducted with 60 and 120 mm·h−1 rain intensities with a rainfall that lasted 1 h. According to the field investigation data of forest land, this area is a low mountain and hilly area with a slope mostly between 5° and 10°. Therefore, 5° and 10° were selected for the slope treatments in this study. The combination of slope and rainfall intensity was named as follows: T1 denoted ‘Slope 5° and rainfall intensity 60 mm·h−1’, T2 was ‘Slope 10° and rainfall intensity 60 mm·h−1’, T3 was ‘Slope 5° and rainfall intensity 120 mm·h−1’, and T4 was ‘Slope 10° and rainfall intensity 120 mm·h−1’. With two rainfall intensities, two slopes, seven litter coverage gradient and two repetitions combined, this study had a total of 56 rainfall events.Experimental procedureBefore the test, the soil samples were wetted for 10 h and then drained for 2 h to eliminate the effect of the initial soil moisture on the soil detachment measurement. When the simulated rainfall started, all the runoff and sediment produced from plot were collected every 5 min in the first 10 min, and then collected once every 10 min during the subsequent 50 min. At the same time, runoff velocity, depth and temperature were measured and vernier calliper (accuracy 0.02 mm) respectively.The overland flow velocity was measured using dying method (KMnO4 solution)32. After judging the flow pattern, we confirmed the correction coefficient K value (in laminar flow state, K = 0.67; transition flow state, K = 0.70; turbulent flow state, K = 0.8). The average velocity of overland flow was obtained by multiplying the correction coefficient K and the instantaneous velocity. Runoff depth was measured using vernier calliper (accuracy 0.02 mm). Runoff temperature was measured using thermometer. When the rainfall experiment finished, the collected runoff samples were measured volumetric cylinder and then settled for at least 12 h. The clear water was decanted, and the samples were put into an oven to dry for 24 h under 105 °C. The sediment sample was dried and weighed with an electronic scale.Calculation of hydrodynamic parametersOverland flow has the characteristics of a thin water layer, large fluctuations of the underlying surface, and unstable flow velocity. At present, most scholars use open-channel flow theory to study overland flow33,34. In open-channel flow theory, the Reynold’s number (Re), Froude constant (Fr), flow index (m), resistance coefficient (f), and soil separation rate (({D}_{r})) are the basic parameters of overland flow dynamics, through Reynold’s number (Re), Froude constant (Fr), flow index (m) can distinguish flow patterns. Re is calculated as:$$Re=Rcdot V/nu ,$$where Re is the Reynolds number of the water flow, which is dimensionless, and can be used to judge the flow state of overland flow. When Re ≤ 500, the flow pattern is laminar; when 500   5000, the flow pattern is turbulent. R is the hydraulic radius (m), which is generally replaced by flow depth as measured by a vernier calliper (accuracy 0.02 mm). (V) is the average velocity (m·s−1); (nu) is the kinematic viscosity coefficient (m2·s−1), and the calculation formula is (nu) = 0.01775·10−4·(1 + 0.0337 t + 0.00021 t2), where t is the test overland flow temperature35.Fr is the Froude constant, which is the ratio of the inertial force to gravity and can be used to distinguish overland flow as rapid flow, slow flow, or critical flow. When Fr  1, the fluid is rapid flow.Fr is calculated as:$$Fr=V/sqrt{gcdot R},$$where (Fr) is the Froude constant of the water flow, which is dimensionless; (V) is the average velocity (m·s−1); g is the acceleration of gravity and has a constant value of 9.8 m·s−2; R is a hydraulic radius (m), and is generally replaced by flow depth as measured by a vernier calliper (accuracy 0.02 mm).Regression fitting is made for runoff depth (h) and single width flow (Q). The runoff depth equation for slope is as follows:$$h=k{q}^{m},$$where q is the single width flow (L·m−1·s−1); h is the depth of water on the slope (m); and m is the flow index, which reflects the turbulent characteristics of the flow state. The larger m is, the more energy the flow consumes in the work of resistance. The comprehensive index (k) reflects the characteristics of the underlying surface and the water viscosity of the slope flow. The larger k is, the stronger the surface material of the slope works on the flow.The resistance of overland flow reflects the inhibition effect of different underlying surface conditions on the velocity of overland flow. The Darcy–Weisbach formula is widely used in research because of its two advantages: applicability and dimensionlessness under laminar and turbulent flow conditions36,37.The resistance coefficient (f) is calculated as follows:$$f=8cdot gcdot Rcdot J/{V}^{2},$$where the resistance coefficient f has no dimension; g is the acceleration of gravity and is always 9.8 m·s−2; R is a hydraulic radius (m), generally replaced by flow depth measured by a vernier calliper (accuracy 0.02 mm); (V) is the average velocity (m·s−1); and J is the hydraulic gradient, which can be converted by the gradient in a uniform flow state and is generally replaced by the sine value of the gradient.Shear stress ((tau)) is the main driving force that affects the stripping of soil particles from the surface soil38. Shear stress is calculated as:$$tau =rcdot gcdot Rcdot J,$$where (tau) is the shear force of runoff (Pa); and r is the density of water and sediment concentration flow (kg·m−3). This study used a muddy water mass and volume ratio in the unseparated state to calculate the density of water and sediment concentration flow.Flow power (W) is the runoff power per unit area of water and refers to the power consumed by the weight of water acting on the riverbed surface to transport runoff and sediment. W is calculated as:$$W=tau cdot V,$$where W is the flow power (N·m−1·s−1); and (tau) is the shear force of runoff (Pa).Soil separation rate (({D}_{r})) refers to the quality of soil in which soil particles are separated from the soil per unit time. The calculation formula is as follows:$${D}_{r}={W}_{d}-{W}_{w}/tcdot A,$$where ({D}_{r}) is the rate of soil separation (kg·m−2·s−1); ({W}_{w}) is the dry weight of soil before the test; ({W}_{d}) is the dry weight of soil after the test, measured by the drying method (kg); t is the scouring time (s); and A is the surface area of the soil sample (m2). More

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Many eukaryotes display intraspecific genome size (GS) variation due to varying amounts of non-coding DNA1,2,3,4,5. Such GS variation can be mediated by additional genomic elements, which are physically represented either by extra (B-)chromosomes or by large heterozygous insertions into the regular chromosomes. On a DNA sequence level, non-coding DNA can be classified as highly repetitive, e.g. interspersedly repeated transposable elements or tandemly repeated satellite DNA, or as the result of previous duplications of the genome followed by pseudogenization6. The long-term gain and loss of such non-coding DNA sequences is thought to be governed by largely neutral evolutionary processes, and their excessive accumulation in some genomes can be explained by genetic drift7,8, even though selection might also sometimes play a role9,10.Non-coding DNA can affect organisms in different ways. A large number of studies document correlations between genome size and organismic traits such as cell size11,12, body size13,14, or developmental rates15, sometimes even at the within-population level13. Under some circumstances, differential amounts of non-coding DNA might even affect fitness16. Furthermore, DNA can have coding-independent effects that operate at lower levels, such as intragenomic selection. For example, (additional) genomic elements might increase their own fitness by increasing their transmission rates to offspring by meiotic drive, sometimes at the expense of their host’s fitness17,18,19. Meiotic drive in this classical sense occurs during the chromosome segregation during the meiotic divisions, even though later stages during gametogenesis can also be affected20. Recognizing and disentangling such effects is important for a better understanding of the evolution of eukaryotic genomes, in particular, the evolutionary causes of the large intraspecific genome size variation.Here we study meiotic transmission patterns of additional genomic elements in the monogonont rotifer Brachionus aplanchnoidis. Individuals of this species can differ by up to almost two-fold in genome size, which is mediated by several Megabase-sized independently segregating genomic elements (ISEs) consisting mainly of tandemly repeated satellite DNA21. The genomic data are consistent with a mixture of both B-chromosomes and large insertions to normal chromosomes21,22. Individual rotifers and their clonal offspring can be characterized by the number and size of their ISEs and their composition stays constant through hundreds of asexual (mitotic) generations22. Occasionally, monogonont rotifers engage in sexual reproduction (Fig. 1), producing sexual females, whose oocytes undergo classical meiosis with two polar bodies formed23. Unfertilized haploid eggs develop mitotically into males, and sperm production does not involve any meiotic maturation divisions24. By analyzing the genome size distributions of haploid males produced by different mother clones, it has been shown that ISEs segregate in a manner suggesting that they do not pair with each other, nor with any other part of the genome22. For instance, a clone containing three ISEs will produce males (and gametes) that might contain either zero, one, two, or three ISEs, corresponding to four different GS classes of the males in this clone. The frequencies of these different GS classes roughly approximated those expected by random segregation. However, previous studies in B. asplanchnoidis did not resolve different steps during meiotic transmission, so they were not designed to detect meiotic drive or subsequent changes in meiotic transmission, and they also did not test whether there were subtle deviations from completely independent segregation.Figure 1Schematics of rotifer life cycle. Monogonont rotifers are cyclical parthenogens, capable of both ameiotic parthenogenesis and sexual reproduction. The production of sexual females is triggered by quorum sensing chemicals, released by the animals themselves at high population density. In contrast to parthenogenetic females, sexual females produce oocytes by meiosis, and give rise to either haploid males or diploid resting eggs, depending on whether they get fertilized by a male24.Full size imageIn the present study, we test for meiotic transmission biases of ISEs. If meiotic transmission would be completely unbiased, the frequencies of haploid oocytes, or males, with different numbers of ISEs should be identical to those expected by random segregation. For example, a mother with two ISEs should produce males with zero, one, or two ISEs (hence, three male GS classes), which have relative frequencies of 0.25, 0.5, and 0.25, respectively. However, if ISEs avoid segregating into polar bodies due to meiotic drive17,20,25, one would expect to see an increase in the relative frequency of male GS classes with two ISEs, compared to those with no ISE . By contrast, if ISEs are preferentially sequestered into polar bodies due to meiotic drag 7,26, the GS class with two ISEs should be underrepresented. Our experimental approach for detecting meiotic transmission biases relies on measuring (by flow-cytometry) the observed relative frequencies of each male GS class and comparing these to their relative frequencies expected under unbiased transmission (Fig. 2). To allow for clear comparisons, the main output variable in these analyses is the observed/expected ratio (O/E-ratio), i.e., the observed frequency divided by the expected relative frequency for each GS class. If there were no transmission biases, O/E-ratios across all GS classes should equal one. In contrast, O/E-ratios larger than one indicate overrepresentation of a certain GS class, and if O/E ratios increase or decrease with genome size, this indicates drive or drag at a meiotic or postmeiotic stage (Fig. 2d,h).Figure 2Principle of inferring meiotic transmission patterns from the genome size distributions of haploid rotifer males. The first four panels (a–d) show a rotifer clone with one ISE (i.e., two corresponding male GS classes). The last four panels (e–h) show a clone with four ISEs (i.e., five corresponding male GS classes). a, e Example of flow cytometry data. b, f Conceptual model of ISE meiotic segregation. c, g Theoretically predicted GS distributions of males (relative to the female GS) under meiotic drive, meiotic drag, or in the absence of meiotic drive. d, h Theoretically predicted O/E ratios (observed vs. expected frequencies of different male GS classes) under drive, drag, or on absence of drive. O/E values of  > 1 indicate over-representation of a GS class (relative to the frequency expected from unbiased transmission).Full size imageWe implemented these ideas in a mathematical model that contains the two parameters, transmission bias and cosegregation bias. Values for transmission bias may range from − 1 to 1 in our model. For instance, a value of 0.1 denotes a 10% increase in probability that an ISE segregates towards the egg pole (this is equivalent to a transmission rate of 0.55 for this ISE, i.e. mild meiotic drive). Concerning the second parameter, cosegregation bias, a positive value means that pairs of ISEs have an increased probability of being sequestered towards the same pole (irrespective of whether this is the egg pole or polar body pole), while a negative bias favors migration towards opposite poles. Please note that a cosegregation bias value of − 1 (i.e., 100% probability that ISEs migrate towards opposite poles) resembles the default segregation pattern of regular chromosomes. By estimating the transmission bias and cosegregation bias parameter for each rotifer clone, we tried to infer and compare general meiotic transmission patterns across clones, even if they contained different numbers and types of ISEs.Transmission biases may not only arise during meiosis, as described above but also during later stages of male embryonic development. For instance, they might be caused by differences in the survival of embryos, or due to differences in the fitness of hatched males containing different numbers of ISEs. To address these potential sources of variation, we compared the transmission biases in relatively young, synchronized male eggs, older eggs accumulating in growing cultures, and hatched males. Finally, to address the question of whether a high number of ISEs affects male embryonic survival in general, we estimated and compared hatching rates of (haploid) male eggs and (diploid) female eggs in 19 rotifer clones of different genome sizes (which is highly correlated with the number and size of ISEs in the genome22).Our results suggested that the ISEs in B. asplanchnoidis exhibit diverse meiotic segregation patterns: In some rotifer clones, transmission bias was positive, while the ISEs of other clones showed negative transmission bias (indicative of drag). Furthermore, we obtained evidence for a negative cosegregation bias in some clones, i.e., pairs of ISEs showed an increased probability to segregate towards opposite poles. Overall, these transmission patterns seemed to be determined early in the haploid life cycle, probably at or shortly after meiosis, since early and late stages of male embryonic development showed very similar GS distributions. Finally, we found that very large genome size (i.e., a large numbers of ISEs) was associated with reduced male embryonic survival. More

Study sites and study designThe study was performed in the frame of a dog ecology research project, with details on the study locations published elsewhere15,42,43. For the current study, five study sites located in Indonesia and Guatemala were included. Site selection was carried out by each country’s research team, taking into consideration rural and urban settings, as well as differing expected number of dogs present at each location. The Indonesian study sites were semi-urban Habi and rural Pogon, in the Sikka regency, at the eastern area of Flores Island (Supplementary Fig. 6). In Guatemala, the study sites were Poptún (urban setting), Sabaneta and La Romana (both rural settings), located in the Guatemalan department of Péten, in the northern part of the country (Supplementary Fig. 7). Data were collected during May to June 2018 in Guatemala and from July to September 2018 in Indonesia.In each location, a 1 km2 area was predefined using Google Earth within which the study took place. The 1 km2 area was chosen because of the research goals of another part of the project, investigating the contact network of the dogs15. Within these areas, the teams visited all dog-owning households. In each household, the study was presented to an adult of the family, who was then asked if they owned a dog and if they were willing to participate in the study. After the dog owner’s oral or written consent was granted, a questionnaire was answered, and the dogs collared. The handling of the dogs was performed by a trained veterinarian or a trained veterinary paramedic of the team.The questionnaire data was collected through interviews with the dog owners. Multiple dogs per household could be included as multiple entries in the questionnaire. The detailed questionnaire contains information on the household location, dog demographics (age, sex, reproductive status) and management (dog’s purpose, origin, confinement, vaccination status, feeding and human-mediated transportation within and outside the pre-determined area).All dogs of a household fulfilling the inclusion criteria were equipped with a geo-referenced contact sensor (GCS) developed by Bonsai Systems (https://www.bonsai-systems.com), containing a GPS module and an Ultra-High-Frequency (UHF) sensor for contact data recording43,44. GCS devices report a 5-m maximum accuracy, a run-time of up to 10 years, can store up to 4 million data points and carry a lithium-polymer-battery (LiPo). For this study, only GPS data were analysed. The GCS were set to record each dog’s geographical position at one-minute intervals. Dogs remained collared for 3 to 5 days with the duration of the data collection being limited by the device’s battery capacity, as batteries were not re-charged or changed during the study. Throughout the time of recording, date, hour, GPS coordinates and signal quality (HDOP) raw data were collected by the GPS module and amassed into the workable databases.Exclusion criteria were dogs of less than four months of age (since they were not big enough to carry a collar), sick dogs and pregnant bitches (to avoid any risk of stress-induced miscarriages). Reasons for non-participation of eligible dogs included dog owner’s absence, dog’s absence, inability to catch the dog, and refusal of participation by the dog owner. In addition, dogs foreseen for slaughtering within the following four days were excluded in Indonesia to ensure data collection for at least four to five days. All dogs included in this study were constantly free roaming or at least part-time (day only, night only and for some hours a day). Human and/or animal ethical approval were obtained depending on the country-specific regulations. All the procedures were carried out in accordance with relevant guidelines. Ethical clearance was granted in Guatemala by the UVG’s International Animal Care and Use Committee [Protocol No. I-2018(3)] and the Community Development Councils of the two rural sites, which included Maya Q’eqchi’ communities45. In Indonesia, the study was approved by the Animal Ethics Commission of the Faculty of Veterinary Medicine, Nusa Cendana University (Protocol KEH/FKH/NPEH/2019/009). In addition, dogs that participated in the study were vaccinated against rabies and/or dewormed to acknowledge the owners for their participation in the study.Data cleaningData were stored in an application developed by Bonsai Systems compatible with Apple operating system (iOS iPhone Operating Systems), downloaded as individual csv file for each unit, and further analysed in R (version 3.6.1)46.The GPS data were cleaned based on three automatised criteria. First, the speed was calculated between any two consecutive GPS fixes, and fixes with speed of  > 20 km/h were excluded, given the implausibility of a dog running at such speed over a one-minute timespan47. It is noteworthy that car travel causes speeds over 20 km/h. However, as we were interested in analysing the dog’s behaviour outside of car transports, removing these fixes was in line with our objectives. Second, the Horizontal Dilution of Precision (HDOP), which is a measure of accuracy48 and automatically recorded by the devices for each GPS fix, was used to exclude fixes with low precision. According to Lewis et al.49, GPS fixes with HDOP higher than five were excluded, which deleted 1.3% of data in Habi, 2.2% in Pogon, 3.3% in Poptún, 1.8% in La Romana and 2.1% in Sabaneta. Third, the angles built by three consecutive fixes were calculated for each dog. When studying animals’ trajectories as their measure of movement, acute inner angles are often connected to error GPS fixes50. The fixes having the 2.5% smallest angles were excluded, to target those fixes with highest risks of being errors, while balancing against the loss of GPS fixes due to the cleaning process. With the exclusion of the smallest angles, 2.6% of data were deleted in Habi, 3% in Pogon, 2.9% in Poptún, 2.6% in La Romana and 2.7% in Sabaneta. After the automatised cleaning was concluded, 18 obvious error GPS fixes (unachievable or inexplicable locations by dogs) still prevailed in the Habi dataset and were manually removed.Habitat resource identification and calculation of terrain slopeTo analyse habitat selection of the collared FRDD, resources were delimited by a 100% Minimum Convex Polygon (MCP) including all cleaned GPS fixes per study site, using QGIS51 (Fig. 1).Figure 1GPS fixes plotted over a Google satellite imagery layer with its respective outlined computed Minimum Convex Polygon (MCP) delimitating the habitat available for the study population in: (a) Habi; (b) Pogon; (c) Poptún; (d) La Romana and (e) Sabaneta. Source QGIS (version 3.4 Madeira, http://qgis.org), map data: Google Satellite.Full size imageResources were defined by taking into consideration the following criteria: resources are (i) likely to impact upon movement patterns of dogs, (ii) identifiable by landscape satellite topography, and (iii) chosen considering information on relevant gathering places for FRDD observed by the field teams. Three resources were disclosed in all study sites: buildings, roads and vegetation coverage. All habitat relevant resources were manually identified within the available area (MCP) in QGIS using satellite imagery. All building-like structures were identified using vector polygons and summed under the layer “buildings”. Roads were identified and manually traced using vector lines in all sites, except in Poptún where the roads were automatically traced using an OpenStreetMap road layer of the area (https://www.openstreetmap.org/export). A buffer vector polygon was generated to encompass the full potential width of the roads, with a 5 m width in Habi and Poptún (semi-urban and urban site) and a 2 m width in Pogon, La Romana and Sabaneta (rural sites). In Habi, a “beach” layer was defined by generating a five-meter buffer from the shoreline in both directions using a vector polygon. The layer “sea” was defined as the vector polygon resulting from the difference between the MCP sea outer limit and the beach buffer polygon. Vegetation coverage was distinct between study sites with sparse vegetation and bushes present in all sites except Pogon, and dense forest-like vegetation present in La Romana and Pogon. These two types of vegetation were defined as “low” and “high vegetation”, respectively. In Habi and La Romana, “low” and “high vegetation”, respectively, were manually identified using vector polygons and summarised under the respective layers. Finally, open field in Habi, high vegetation in Pogon and low vegetation in Poptún, La Romana and Sabaneta were the last vector layers to be established since they represented the difference between all other polygon vector layers and the MCP total area. After all resource vector polygons had been created, an encompassing vector layer was generated by merging all resource polygon vectors for final resource classification (Fig. 2). As part of the resource classification in Habi, the airport terminal and runaway as well as waterways enclosed in the MCP area were identified but excluded from the analysis.Figure 2(a) Habi, (b) Pogon, (c) Poptún, (d) La Romana and (e) Sabaneta Habitat classification vector layers. The different habitat resources, identifiable by colour, were merged to create the comprehensive Habitat classification vector. In the Indonesian sites (a, b) and Guatemalan sites (c–e) buildings are coloured red, vegetation low in Habi, Poptún, La Romana and Sabaneta is coloured light green, vegetation high in Pogon and La Romana dark green, roads black, beach yellow, sea dark blue, airport grey, waterways light blue and open field light orange. The airport area (gray) and waterways (light blue) in Habi were not classified as separate habitat layers and were excluded from further analysis. Source QGIS (version 3.4 Madeira, http://qgis.org), map data: Google Satellite.Full size imageAfter the construction of the habitat resource layers, all GPS fixes were assigned to the respective resource they were located, using the QGIS join attributes by location algorithm. Fixes located exactly on the MCP border in Indonesia were not classified automatically and had to be manually classified to the respective resource.In non-flat topographies (all locations expect Habi) we tested the hypothesis of whether the steepness would influence the dogs’ movement patterns. The degrees of slope were calculated using a 30-m raster-cell resolution (STRM 1-Arc Second Global, downloaded from the United States Geological Survey (USGS) Earth Explorer, https://earthexplorer.usgs.gov/). The slope was assigned by the QGIS join attributes by location algorithm to each GPS fix.Statistical analysisTo quantify habitat selection in each study site, we compared resources used by the dogs with the resources available, according to Freitas et al.52. Adapting the methodology applied by O’Neill et al.18, the observed number of GPS fixes for each dog was used to generate an equivalent number of locations that were randomly distributed within the MCP area using the Random points in layer bound vector tool from QGIS. For example, if dog “D300” had 100 recorded GPS fixes, 100 random points were generated within the MCP of the respective study site and assigned to “D300”. Random points were then assigned to the respective resources and slope of that location, as previously done with the observed GPS fixes. Using this approach, the habitat resources used by each dog could be compared to the available resources in the respective study site, using a regression model.Observation independence is a fundamental presupposition of any regression model. However, the spatial nature of the point-referenced data permits perception of spatial dependence. In our dataset, spatial autocorrelation was proven for all study sites using the Moran’s I test. Therefore, we applied a spatial regression model, which takes into consideration spatial autocorrelation while exploring the effects of the study variables. A mixed effects logistic regression model accounting for spatial autocorrelation was created to quantify the effect of variables on used (i.e. observed GPS fix) versus available (i.e. randomly generated GPS fixes) resources, using the fitme function in the spaMM package in R53,54. The model’s binary outcome variable was defined as either observed (1) or random (0) GPS fix, i.e. the dog being present or absent from a position. The explanatory variable was the resource classification with “buildings”, “roads”, “low vegetation”, “beach”, “sea” and “open field” as levels in Habi; “buildings”, “roads” and “high vegetation” in Pogon; “buildings”, “roads”, “low vegetation” in Poptún and Sabaneta; and “buildings”, “roads”, and “high” and “low vegetation” in La Romana. Different habitat resources were used interchangeably as reference level. In all study sites except Habi, the slope was included as an additional explanatory variable. As observations were not evenly distributed in time, with less observations recorded towards the end of the study, a variable ”hour” was added as an additional continuous fixed effect.Each observed GPS fix was assigned to the hour of its record, with the earliest timestamp registered in each study site being assigned the hour zero. The randomly generated points were randomly assigned to an hour within the determined time continuum of the observed GPS fixes. As our focus was investigating habitat selection at a population-level, we assumed there was no within-dog autocorrelation (space/time) and each dog was independent and exhibited no group behaviour38. Still, to partially account for spatial autocorrelation of each dog’s household, the random effects included in models were defined as each dog’s household geographical location recorded during fieldwork by a GPS device. The restricted maximum likelihood (REML) through Laplace approximations, which can be applied to models with non-Gaussian random effects55, and the Matérn correlation function were used to fit the spatial models with the Matérn family dispersion parameter ν, indicator of strength of decay in the spatial effect, was set at 0.554. More

Buisson, E., Archibald, S., Fidelis, A. & Suding, K. N. Ancient grasslands guide ambitious goals in grassland restoration. Science 377, 594–598. https://doi.org/10.1126/science.abo4605 (2022).Article 
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Study areaFigure 2 shows the location of the study area on a map of China generated by ArcGIS software. This study’s field experiments were carried out in the Shuanghe Town agricultural comprehensive water-saving demonstration area (40°42′ N; 107°24′ E), which is located in the middle reaches of the Hetao Irrigation Area of Inner Mongolia. The duration of the experimental process ranged from April in 2018 to October in 2020. The experimental area was characterized by a mid-temperate semi-arid continental climate. The average annual precipitation was determined to be 138 mm and the average evaporation was approximately 2332 mm. The majority of the rainfall was concentrated during summer and autumn seasons, and the accumulation of salt in the surface soil was considered to be serious in the spring and winter months. The average rainfall during maize growth period was 75.3 mm. The 0 to 40 cm soil layers in the experimental area were categorized as silty loam soil, with an average bulk density ranging from 1.42 to 1.53 g cm−3. A maize straw layer with a thickness of 5 cm was buried at a depth of 40 cm, and then the land was leveled. Also, in addition to autumn watering and spring irrigation procedures, water from the Yellow River was used three times for irrigation during the entire growth period of the maize crops. The adopted irrigation method belonged to border irrigation. Urea (46% N) were used as the fertilizer types.Figure 2The location of the study area.Full size imageField trials design and data collectionWe carried out experiment 1 from 2018 to 2019, and the data obtained were used for model training and to determine the hyper-parameters. The experimental design is shown in Table 1. The PNN model trained from the data obtained in experiment 1 predicted the optimal range of irrigation amount and nitrogen application rate (N rate) for each growth period of maize. In these ranges, the soil organic matter and total nitrogen could be kept above 20 g/kg and 1.6 g/kg, respectively, the soil salt content was less than 2 g/kg, and the pH value was between 6.5 and 7.5. In order to verify the accuracy and feasibility of the range of irrigation and nitrogen application simulated by PNN, the field experiment 2 was set in 2020 based on the range simulated by PNN and to evaluate the fitting degree between measured and simulated values of soil indicators under the same amount of irrigation and nitrogen application. The experimental design is shown in Table 2.Table 1 Experimental 1 design scheme.Full size tableTable 2 Experimental 2 design scheme.Full size tableThe experimental design were repeated for three times. The plot area of each treatment measuring 8 × 9 = 72 m2. The surrounding area was separated using 1.2 m buried polyethylene plastic film, and 30 cm was left at the top to prevent fertilizer and water from flowing into each other. The field management process was consistent with that used by the local farmers. The film width of maize was 1.1 m, with each film covering two rows. The plant spacing was approximately 45 cm, and the row spacing was 35 cm. In addition, the planting density of the maize was 60,000 plants/hm2.During the entire growth period of the maize crops, soil samples were collected from the 0 to 20 cm, 20 to 40 cm, 40 to 60 cm, 60 to 80 cm, and 80 to 100 cm soil layers using a soil drill and a three-point method was adopted. The soil samples were stored at 4 °C for the determination of total nitrogen, organic matter, total salt content, and pH values. The total nitrogen, organic matter, total salt content, and pH were determined using a KDN-AA double tube azotometer, MWD-2 microwave universal digestion device, TU1810PC ultraviolet–visible spectrophotometer, and a TU18950 double beam ultraviolet–visible spectrophotometer, respectively.Soil parameters measured include organic matter (SOM), total nitrogen (TN), Salt and pH. The data set includes pre-irrigation and post-irrigation reports from 2018 to 2020. Statistical parameters regarding the soil data are shown in Table 3.Table 3 Various meteorological variables and their descriptive statistics.Full size tableThe dataset obtained in Experiment 1 in 2018 to 2019 was 2490 rows in size, the 80/20 principle was used to data into training, and testing sets were required for ML modeling; 80% of data were employed for model training, while the remaining 20% were used for testing. Specifically, the data corresponding to the treatments with the nitrogen application rate (N rate) of 75 kg/hm2 (N3) in all the treatments (W1N3, W2N3, W3N3) were used as the test set, and the data of the other treatments were used as the training set. The training set was used to initiate ML parameter training. Subsequently, The test set was employed to assess the model. The dataset size in 2020 was 1080 rows, which was used to verify ML modeling.Figure 3 shows the changes of soil indexes over time for each treatment in the field test (take the 0–40 cm soil in the main distribution area of maize roots as an example). There are differences under the influence of different irrigation amounts. When irrigation is 90 mm, soil SOM is 13.25% and 7.00% higher than 60 mm and 120 mm, and soil TN is 4.59% and 6.50% higher than 60 mm and 120 mm, respectively. The soil Salt was 23.30% lower than 60 mm, and the pH was 4.16% and 4.36% lower than that of 60 mm and 120 mm, respectively. It can be seen that irrigation of 90 mm is more favorable for increasing soil SOM and TN contents and reducing soil salinity and alkalinity. Soil SOM and TN contents were the highest at n 75 kg/hm2, which were 4.38% and 8.34% higher than those at N = 93.3 kg/hm2, respectively. Soil Salt was the lowest at N = 60 kg/hm2, which was 3.02% lower than those at N = 75 kg/hm2, with a small gap with other levels. In conclusion, nitrogen application of 75 kg/hm2 was beneficial to increase soil organic matter and nitrogen content, and nitrogen application of 60 kg/hm2 was beneficial to controlling soil salt content.Figure 3Changes in soil organic matter, total nitrogen, salinity, and pH under different treatments over time (a case study of 2019).Full size imageMachine learning (ML) models used for irrigation and nitrogen application strategiesFive ML frames were used to estimate the irrigation and N rate. These models are preference Neural Network (PNN), Support Vector Regression (SVR), Linear Regression (LR), Logistic Regression (LOR), and traditional BP Neural Networks (BPNN). Among them, the prediction effects of linear, Poly, and rbf kernel functions are respectively tried in SVR framework. The torch framework was used to train and test machine learning models in Python.Development of preference neural networkModel frameworkThe preference neural network (PNN) which was proposed for the first time in this study was a typical deep learning model. PNN can be regarded as an approximate natural function in order to describe the complete dependence of the soil fertility indexes, including the effects of soil total nitrogen, organic matter, total salt content, and pH values on irrigation and nitrogen applications. More specifically, PNN has the ability to optimize the function by constructing the mapping y = f (x, θ) and learning parameter θ.First, the input end of PNN model was defined as matrix X ∈ ℝn×d (in which n is the sample size, n = 2490; and d is the dimension of each input vector, d = 6), where {xi} i=1, …, n ∈ X represents the vectorized set of total nitrogen, organic matter, salt content, and pH used for measuring the soil fertility, as well as the nitrogen application and irrigation durations (expressed by days after sowing). At the same time, the output end of the model was defined as the matrix Y ∈ ℝn×2, which represented the levels of the irrigation and nitrogen fertilizer applications. The goal of the proposed PNN model was to learn the fixed mapping Y′ = f (X; θ) ⇒Y through the given input matrix X, where θ is the well optimized learnable parameters which can be obtained via PNN training. Meanwhile, the predicted value Y′ will infinitely approach the measured value Y. The structure and the algorithm of this study’s PNN model is shown in Fig. 4 and Table. 4.Figure 4Schematic diagram for the PNN structural connections. In the figure, it can be seen that when each input vector passed through each layer of the PNN, it is first multiplied by the Hadamard product of the weight matrix and preference value matrix for the purpose of obtaining a weight matrix with preference properties. After the matrix was activated by the Relu Function, Batch Normalization Module Methods and the Dropout Module were used for random suspension and normalization processing, and the input of the next layer was obtained.Full size imageTable 4 Algorithm of Preference neural network.Full size tableLayer-by-layer affine transformationA good definition of the affine transformation of the information flow between layers is considered to be the key to neural network model training. Generally speaking, the learnable parameter θ of each layer of a model includes the weight parameter w and the preference parameter b. The hidden representation hl of the l-th layer in PNN is defined as follows:$${h}_{l}({h}_{l-1};{W}_{l},{b}_{l})={h}_{l-1}^{mathrm{T}}{W}_{l}+{b}_{l}$$
(1)

where Wl and bl represent the learnable weight and bias variables of the l layer, respectively, and hl-1 is the hidden representation of the upper layer. Therefore, when l = 1, then h0 = X.In the present study, using the hierarchical update rules, a given input data stream was allowed to pass through each hidden layer with intermediate operations, and then finally reached the output end.Preference structureThe correlation between different production behavior factors (e.g., irrigation levels) and different natural factors (e.g., soil organic matter) differs in agricultural production. However, the traditional fully connected neural network has the characteristic that nodes of one layer are fully connected with all nodes of subsequent layers, resulting in the neurons between production behavior factors and natural factors with very weak correlation still all being connected. Conversely, connections between neurons corresponding to factors with solid correlations are not strengthened.Therefore, in this study the preference value module was specially developed. By first calculating the correlation and significance between different production behavior factors (irrigation amount, N rate) and different soil fertility factors (organic matter, total nitrogen, total salt and pH), the preference value between the above two types of variables was calculated, and the preference matrix was constructed. Then the Hadamard product of the weight matrix and preference matrix was used to realize the artificial intervention and guidance to the neural network’s learning process.In order to reduce the adverse impact of non-normality of data on correlation analysis as much as possible, this study rank-based inverse normal (RIN) transformations (i.e., conversion to rank score) methods were used to normally process the data28. The RIN transformation function used here is as follows:$$f(x)={Phi }^{-1}left(frac{{x}_{r}-frac{1}{2}}{n}right)$$
(2)

where Φ–1 is the inverse normal cumulative distribution function, and n is the sample size.The normal cumulative distribution function is represented as follows: for discrete variables, the sum of probabilities of all values less than or equal to a, and its formula is as shown below:$${F}_{X}(a)=P(Xle a)$$
(3)
The RIN normalized conversion values meet the requirements of normal distribution, Pearson correlation analysis and t-test can be directly performed, and the formula used was as follows:$$r(X,Y)=frac{mathrm{Cov}(X,Y)}{sqrt{left(mathrm{Var}left[Xright]mathrm{Var}left[mathrm{Y}right]right)}}$$
(4)

where r (X, Y) is the Pearson Correlation Coefficient, Var [X] is the variance of X, and Var [Y] is the variance of Y, Cov (X, Y) is the covariance of X and Y, which represents the overall error of the two variables. The t-test is performed on the normalized data after rank-based inverse normal (RIN) transformation method, and the formula is as follows:$$t=sqrt{frac{n-2}{1-{r}^{2}}}$$
(5)

where n is the number of samples, and r represents the Pearson Correlation Coefficient. Preference value is the concentrated embodiment of correlation and significance between variables, and the calculation formula is as follows:$${PV}_{ij}=frac{r({X}_{i},{Y}_{j})}{{P}_{ij}+e}$$
(6)

where PVij represents the preference values between the variables Xi and Yj, Xi represents the ith production behavior factor (e.g., irrigation amount), and Yj represents the jth soil fertility factor (e.g., soil organic matter content), ({P}_{ij}) is obtained by looking up the table based on the t, and e is a constant, taking 0.001 in order to prevent the denominator of the formula from being 0.In order to make the preference values of the various indicators in the same order of magnitude more stable, the preference values were normalized:$${PV}_{normal}=pm frac{left|{PV}_{i}-{PV}_{avg}right|}{sqrt{frac{sum_{i=1}^{N}{({PV}_{i}-{PV}_{avg})}^{2}}{N-1}}}$$
(7)

where N represents the number of variables related to the experimental treatments, PVi -PVavg takes the absolute value, while the positive or negative values of the PVnormal were determined by the positive or negative values of the correlation r.The PNN integrated the preference matrixes into the neural network structures by identifying the Hadamard products of the learnable weights between the preference matrixes and the input and output data. By referring to Eq. (1) in the hierarchical affine transformation, the preference constraint of PNN could be expressed as follows:$${h}_{l}({h}_{l-1};{W}_{l},{b}_{l})={h}_{l-1}^{T}{W}_{l}odot P+{b}_{l}$$
(8)

where P is the preference matrix calculated by Eq. (8), and ⊙ represents the Hadamard product of the corresponding elements of the matrix. The structure of preference neural network and preference value are shown in Figs. 5 and 6.Figure 5Schematic diagram of the preference connection structures of the preference neural networks. The depth of the network detailed in the figure only illustrates the preference connection structure (for a better demonstration), and does not indicate the depth of the PNN used in the experiment.Full size imageFigure 6PVnormal between production behavior factors and natural factors. Since soil depth, days, irrigation amount and N rate were all artificially set variables, and there was no objective correlation in the data set. Therefore, the preference values among these variables were default e = 0.001.Full size imageHyper-parameters of PNNWe conducted experiments on the datasets with varying the hyper-parameters (such as the number of PNN layers and hidden layers, the number of nodes in each layer, learning rate, dropout rate and batch size) to understand that how the Hyper-parameters impact on the performance of PNN.We select the activation function and learning rate by referring to the neural network structure commonly used in similar fields (1 hidden layer and 64 hidden nodes)29,30. It is found that ReLU has better performance than other activation functions (sigmoid, tanh). The performance is best when the learning rate is around 0.005. It is generally believed that neural networks with more hidden layers are able, with the same number of resources, to address more complex problems31, but excessively increasing network depth will easily lead to overfitting32. Since there is no direct method to select the optimal number of hidden layers and nodes33, this study first calculated the structure of one hidden layer and 64 nodes in each layer, and found that the combined effect was poor (R2 of irrigation and nitrogen application were 0.3971 and 0.4124, respectively). Therefore, the trial-and-error method is adopted. The number of hidden layers starts from 1 and is incremented by 1 to test the maximum number of 10 hidden layers. The number of nodes in each layer were tested with a maximum number of 100 hidden neurons, starting with 5 and increasing by 5.We found that when the number of hidden layers of PNN exceeds 6, and the number of nodes in each layer exceeds 65, the performance will drop significantly. The reason behind this phenomenon could be the current dataset size is insufficient for larger scale of the PNN model. In the consideration of that the size of new dataset we can obtain very year is similar to the current dataset size, we believe that current hyper-paramter settings of PNN is in a reasonable condition.After that, the number of layers was fixed as 6, and the number of nodes in each layer were tested 10 times with 60 as the starting point and 1 as the increment, we found that when the number of nodes was 64, the improvement of the fit degree was no longer noticeable. On this basis, we changed different activation functions and learning rate again, and found that PNN still has the best performance when the activation function is ReLU and the learning rate is 0.005. Then, different batch sizes and dropout rates were tried. The two parameters had weaker effects on the performance than the other parameters, and the performance was optimal at 256 and 0.1, respectively.The hyper-parameters include:

1.

number of PNN layers;

2.

number of hidden layers;

3.

types of activation function;

4.

percentage of dropout;

5.

learning rate;

6.

loss function;

7.

optimizer;

8.

batch size;

9.

number of epochs;

10.

number of workers.

The ideal PNN structure for the study comprises these layers:

1.

number of PNN layers is 8;

2.

number of hidden layers is 6;

3.

Fully connected layers with 64 nodes and ReLU activation function

4.

dropout with 0.1.

5.

the learning rate is 0.005;

6.

loss function is Huber Loss Methods (HLM);

7.

optimizer: ADAM;

8.

epochs is 500;

9.

the batch size is 256;

10.

number of workers is 6.

Hyper-parameters of other modelsLR algorithms and LOR do not have hyper-parameters that need to be adjusted. A part of the hyper-parameters of the SVR model was determined by referring to Guan Xiaoyan’s research34, and a part of the hyper-parameters of the BPNN model was determined by referring to Gu Jian’s research27. RMLP takes the same hyperparameters as PNN. The hyperparameters of SVR and BPNN models are shown in Table 5.Table 5 Hyper-parameters of other model.Full size tableModel performance evaluationThe proposed PNN model was trained and validated using the field measured data from 2020 and the performance achievements of PNN were evaluated by the root mean square errors, mean square errors, and mean absolute errors as follows:$$RMSE=sqrt{frac{{sum }_{i=1}^{n}{({y}_{ipre}-{y}_{imea})}^{2}}{n}}$$
(9)
$${R}^{2}=1-frac{{sum }_{i=1}^{n}{({y}_{ipre}-{y}_{imea})}^{2}}{{sum }_{i=1}^{n}{({y}_{ipre}-{y}_{iavg})}^{2}}$$
(10)
$$MAE=frac{{sum }_{i=1}^{n}left|{y}_{ipre}-{y}_{iavg}right|}{n}$$
(11)
Model multidimensional fertility targetsThe soil fertility grade classification of soil organic matter, soil total nitrogen content and salt content in this study was based on the soil fertility grade classification results by the Agriculture and Animal Husbandry Bureau of Bayannur City, along with the local standard Technical Specifications for the Assessment and Rating Criteria of Cultivated Land Quality (DB 15/T 1086, 2016), as the shown in Tables 6 and 7.Table 6 Soil organic matter and Soil total nitrogen degrees.Full size tableTable 7 Grading of the salinization degrees.Full size tableIn the evaluation system of soil fertility referencing the Technical Specifications for Assessment and Rating Criteria of Cultivated Land Quality (DB 15/T 1086, 2016), the pH was divided into four grades according to the membership degrees of the land productivity evaluations, as detailed in Table 8.Table 8 pH grading degrees of the cultivated land.Full size tableBased on the classification standard of soil fertility obtained by the Bureau of Agriculture and Animal Husbandry of Bayannur City, when the farmland soil is at the high fertility level, the soil organic matter and total nitrogen content should be more than 20 g/kg and 1.6 g/kg, respectively. Soil salt content was less than 2 g/kg. Meanwhile, the pH value is kept between 6.5 and 7.5. More