Department of Integrative Biology and Biodiversity Research (DIBB), University of Natural Resources and Life Sciences (BOKU), Vienna, Austria.
PLoS One. 2021 Apr 26;16(4):e0250515. doi: 10.1371/journal.pone.0250515. eCollection 2021.
This paper explores the ratio of the mass in the inflection point over asymptotic mass for 81 nestlings of blue tits and great tits from an urban parkland in Warsaw, Poland (growth data from literature). We computed the ratios using the Bertalanffy-Pütter model, because this model was more flexible with respect to the ratios than the traditional models. For them, there were a-priori restrictions on the possible range of the ratios. (Further, as the Bertalanffy-Pütter model generalizes the traditional models, its fit to the data was necessarily better.) For six birds there was no inflection point (we set the ratio to 0), for 19 birds the ratio was between 0 and 0.368 (lowest ratio attainable for the Richards model), for 48 birds it was above 0.5 (fixed ratio of logistic growth), and for the remaining eight birds it was in between; the maximal observed ratio was 0.835. With these ratios we were able to detect small variations in avian growth due to slight differences in the environment: Our results indicate that blue tits grew more slowly (had a lower ratio) in the presence of light pollution and modified impervious substrate, a finding that would not have been possible had we used traditional growth curve analysis.
本文探讨了在波兰华沙一个城市公园中 81 只蓝山雀和大山雀雏鸟的拐点质量与渐近质量之比（生长数据来自文献）。我们使用 Bertalanffy-Pütter 模型计算了这些比例，因为与传统模型相比，该模型在比例方面更具灵活性。对于传统模型，比例的可能范围受到先验限制。（此外，由于 Bertalanffy-Pütter 模型推广了传统模型，因此它对数据的拟合必然更好。）对于 6 只鸟，没有拐点（我们将比例设为 0），对于 19 只鸟，比例在 0 到 0.368 之间（Richards 模型可达到的最低比例），对于 48 只鸟，比例大于 0.5（逻辑增长的固定比例），对于其余 8 只鸟，比例在两者之间；观察到的最大比例为 0.835。使用这些比例，我们能够检测到由于环境微小差异而导致的鸟类生长的微小变化：我们的结果表明，在光污染和改良不透水基质的存在下，蓝山雀的生长速度较慢（比例较低），如果我们使用传统的生长曲线分析，就不可能得出这一结论。
