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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

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Whether land acts as a carbon sink or source depends largely on two opposite fluxes: carbon uptake through photosynthesis and carbon release through turnover. Turnover occurs through multiple processes, including but not limited to, leaf senescence, tree mortality, and respiration by plants, microbes, and animals. Each of these processes is sensitive to climate, and ecologists and climatologists have been working to figure out how temperature regulates biological activities and to what extent the carbon cycle responds to global warming. Previous theoretical and experimental studies have yielded conflicting relationships between temperature and carbon turnover, with large variations across ecosystems, climate and time-scale1,2,3,4. Writing in Nature Geoscience, Fan et al.5 find that hydrometeorological factors have an important influence on how the turnover time of land carbon responds to changes in temperature. More

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

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