Theory of Stoichiometric Intraguild Predation: Algae, Ciliate, and Daphnia.

Consumers respond differently to external nutrient changes than producers, resulting in a mismatch in elemental composition between them and potentially having a significant impact on their interactions. To explore the responses of herbivores and omnivores to changes in elemental composition in producers, we develop a novel stoichiometric model with an intraguild predation structure. The model is validated using experimental data, and the results show that our model can well capture the growth dynamics of these three species. Theoretical and numerical analyses reveal that the model exhibits complex dynamics, including chaotic-like oscillations and multiple types of bifurcations, and undergoes long transients and regime shifts. Under moderate light intensity and phosphate concentration, these three species can coexist. However, when the light intensity is high or the phosphate concentration is low, the energy enrichment paradox occurs, leading to the extinction of ciliate and Daphnia. Furthermore, if phosphate is sufficient, the competitive effect of ciliate and Daphnia on algae will be dominant, leading to competitive exclusion. Notably, when the phosphorus-to-carbon ratio of ciliate is in a suitable range, the energy enrichment paradox can be avoided, thus promoting the coexistence of species. These findings contribute to a deeper understanding of species coexistence and biodiversity.

Oscillations of algal cell quota: Considering two-stage phosphate uptake kinetics.

Elucidating the mechanism of effect of phosphate (PO43-) uptake on the growth of algal cells helps understand the frequent outbreaks of algal blooms caused by eutrophication. In this study, we develop a comprehensive mathematical model that incorporates two stages of PO43- uptake and accounts for transport time delay. The model parameter values are determined by fitting experimental data of Prorocentrum donghaiense and the model is validated using experimental data of Karenia mikimotoi. The numerical results demonstrate that the model successfully captures the general characteristics of algal growth and PO43- uptake under PO43- sufficient conditions. Significantly, the experimental and mathematical findings suggest that the time delay associated with the transfer of PO43- from the surface-adsorbed PO43- (Ps) pool to the intracellular PO43- (Pi) pool may serve as a physiologically plausible mechanism leading to oscillations of algal cell quota. These results have important implications for resource managers, enabling them to predict and deepen their understanding of harmful algal blooms.

Distribution-based maximum likelihood estimation methods are preferred for estimating Salmonella concentration in chicken when contamination data are highly left-censored.

Salmonella is a common chicken-borne pathogen that causes human infections. Data below the detection limit, referred to as left-censored data, are frequently encountered in the detection of pathogens. The approach of handling the censored data was regarded to affect the estimation accuracy of microbial concentration. In this study, a set of Salmonella contamination data was collected from chilled chicken samples using the most probable number (MPN) method, which consisted of 90.42% (217/240) non-detect values. Two simulated datasets with fixed censoring degrees of 73.60% and 90.00% were generated based on the real-sampling Salmonella dataset for comparison. Three methodologies were applied for handling left-censored data: (i) substitution with different alternatives, (ii) the distribution-based maximum likelihood estimation (MLE) method, and (iii) the multiple imputation (MI) method. For each dataset, the negative binomial (NB) distribution-based MLE and zero-modified NB distribution-based MLE were preferable for highly censored data and resulted in the least root mean square error (RMSE). Replacing the censored data with half the limit of quantification was the next best method. The mean concentration of Salmonella monitoring data estimated by the NB-MLE and zero-modified NB-MLE methods was 0.68 MPN/g. This study provided an available statistical method for handling bacterial highly left-censored data.