The egg production rate is a crucial metric in animal breeding, subject to biological and environmental influences and exhibits characteristics of small sample sizes and non-linearity. Currently, egg production rate prediction research predominantly focuses on single-step point prediction, lacking multistep and interval prediction exploration. To bridge these gaps, this study proposes a recursive, multistep interval prediction method for egg production rates, integrating environmental variables and attention mechanisms. Initially, this study employed three gradient boosting tree models (XGBoost, LightGBM, CatBoost) and the recursive feature elimination (RFE) method to select critical environmental variables and reduce data dimensionality. Subsequently, by scaling the time scale of important environmental variables and utilizing the variational modal decomposition improved by the grey wolf optimization (GWO-VMD) method for time-series decomposition, the volume of important environmental variable data is augmented and its complexity is reduced. Applying the long short-term memory (LSTM) neural network to obtain direct multistep predictions on IMFs, the predicted outcomes are averaged daily to yield the environmental variables for the upcoming two days. Finally, a multistep interval prediction model based on Seq2seq-Attention and Gaussian distribution is proposed in this study, and parameter optimization is carried out using the multi-objective grey wolf optimization algorithm (MOGWO). By inputting the historical egg production rate data and environmental variables into the proposed model, it is possible to achieve multistep point and interval prediction of egg production rates. This method was applied to analyze a dataset of egg production rates of waterfowl. The study demonstrated the feasibility of the recursive multistep prediction approach combined with environmental variables and guides egg production estimation and environmental regulation in animal husbandry.

The accurate and reliable relative humidity (RH) prediction holds immense significance in effectively controlling the breeding cycle health and optimizing egg production performance in intensive poultry farming environments. However, current RH prediction research mainly focuses on short-term point predictions, which cannot meet the demand for accurate RH control in poultry houses in intensive farming. To compensate for this deficiency, a hybrid medium and long-term RH prediction model capable of precise point and interval prediction is proposed in this study. Firstly, the complexity of RH is reduced using a data denoising method that combines complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and permutation entropy. Secondly, important environmental factors are selected from feature correlation and change trends. Thirdly, based on the results of data denoising and feature selection, a BiGRU-Attention model incorporating an attention mechanism is established for medium and long-term RH point prediction. Finally, the Gaussian kernel density estimation (KDE-Gaussian) method is used to fit the point prediction error, and the RH prediction interval at different confidence levels is estimated. This method was applied to analyze the actual collection of waterfowl (Magang geese) environmental datasets from October 2022 to March 2023. The results indicate that the CEEMDAN-FS-BiGRU-Attention model proposed in this study has excellent medium and long-term point prediction performance. In comparison to LSTM, the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) are reduced by 57.7%, 48.2%, and 56.6%, respectively. Furthermore, at different confidence levels, the prediction interval formed by the KDE-Gaussian method is reliable and stable, which meets the need for accurate RH control in intensive farming environments.