EXPLORING FACTORS INFLUENCING AVERAGE CALL NUMBERS IN OWL NESTLINGS: A GENERALIZED LINEAR MIXED MODEL STRUCTURE WITH LAPLACE APPROXIMATION AND ADAPTIVE GAUSSIAN-HERMITE QUADRATURE METHOD

Abstract

Understanding the factors that influence the begging behavior of owl nestlings (or chicks) is critical for elucidating parent-offspring communication and resource allocation strategies. This study examines the average call numbers of owl nestlings, focusing on the effects of brood size, food treatment, and parental arrival time. Since the data conform to a Poisson distribution, it employs a generalized linear mixed model (GLMM) framework that incorporates both fixed and random effects to account for variability at the individual and nest levels. Laplace approximation and Adaptive Gaussian-Hermite Quadrature (AGHQ) method enhance the precision of parameter estimation. The results demonstrate significant interactions between brood size and food treatment, highlighting the adaptive nature of begging calls in response to parental provisioning strategies. The findings emphasize the importance of advanced statistical methodologies, such as GLMM with Laplace and AGHQ, in studying complex ecological behaviors. This approach provides a robust framework for ongoing research into the dynamics of avian communication and parental investment.

Keywords

• Begging Behavior
• Generalized Linear Mixed Model
• Laplace
• Adaptive Gaussian-Hermite Quadrature

Supporting Institution

The present study was funded by the Dicle University Scientific Research Projects Coordinatorship (DUBAP) through Project FEN.23.029.

Project Number

The present study was funded by the Dicle University Scientific Research Projects Coordinatorship (DUBAP) through Project FEN.23.029.

BAYKUŞ YAVRULARINDA ORTALAMA ÇAĞRI SAYILARINI ETKİLEYEN FAKTÖRLERİN İNCELENMESİ: LAPLACE YAKLAŞIMI VE ADAPTİVE GAUSSİAN-HERMİTE QUADRATURE YÖNTEMİ İLE GENELLEŞTİRİLMİŞ LİNEER KARMA MODEL YAPISI

Abstract

Baykuş yavrularının dilenme davranışını etkileyen faktörlerin anlaşılması, ebeveyn-yavru iletişimi ve kaynak tahsis stratejilerinin aydınlatılması açısından kritik öneme sahiptir. Bu çalışma, kuluçka boyutu, beslenme durumu ve ebeveyn varış zamanı gibi faktörlerin baykuş yavrularının ortalama çağrı sayıları üzerindeki etkilerini incelemektedir. Verilerin Poisson dağılımına uygun olması nedeniyle, bireyler ve yuvalar düzeyindeki değişkenliği dikkate alan sabit ve rastgele etkileri içeren bir genelleştirilmiş lineer karma model (GLMM) çerçevesi kullanılmaktadır. Parametre tahminlerinin doğruluğunu artırmak için Laplace yaklaşımı ve Adaptive Gaussian-Hermite Quadrature (AGHQ) yönteminden faydalanılmaktadır. Sonuçlar, kuluçka boyutu ve beslenme durumu arasında anlamlı etkileşimler olduğunu göstermekte ve dilenme çağrılarının ebeveynin besin sağlama stratejilerine uyum sağladığını vurgulamaktadır. Bulgular, GLMM ile Laplace ve AGHQ gibi ileri düzey istatistiksel metodolojilerin karmaşık ekolojik davranışları incelemedeki önemini ortaya koymaktadır. Bu yaklaşım, kuş iletişimi ve ebeveyn yatırım dinamikleri üzerine devam eden araştırmalar için sağlam bir çerçeve sunmaktadır.

Keywords

• Dilenme Davranışı
• Genelleştirilmiş Lineer Karma Model
• Laplace
• Adaptive Gaussian-Hermite Quadrature

Project Number

The present study was funded by the Dicle University Scientific Research Projects Coordinatorship (DUBAP) through Project FEN.23.029.

References

1. Snedecor, G.W., and Cochran, W.G., Statistical methods, Iowa State University (7th ed., pp. 288)., USA, 1980.
2. Nelder, J.A., and Wedderburn, R.W.M., “Generalized linear models”, Journal of the Royal Statistical Society, Series A: General, 135, 370–384, 1972.
3. McCullagh, P., and Nelder, J.A., Generalized linear models, Chapman and Hall Ltd. (2nd ed.), UK, 1989.
4. Warton, D.I. and Hui, F.K., “The arcsine is asinine: the analysis of proportions in ecology”, Ecology, 92, 3–10, 2011.
5. Breslow, N.E., and Clayton, D.G., “Approximate inference in generalized linear mixed models”, Journal of the American Statistical Association, 88, 9–25, 1993.
6. Ver Hoef, J.M., Blagg, E., Dumelle, M., Dixon, P. M., Zimmerman, D.L., and Conn, P.B., “Marginal inference for hierarchical generalized linear mixed models with patterned covariance matrices using the Laplace approximation”, Environmetrics, e2872, 2024.
7. Rich, J.L., Comparison of generalized linear mixed model estimation methods (Master of science thesis), Montana State University, USA, 2018.
8. Tuerlinckx, F., Rijmen, F., Verbeke, G., and De Boeck, P., “Statistical inference in generalized linear mixed models: a review”, British Journal of Mathematical and Statistical Psychology, 59(2), 225–255, 2006.

9. Naylor, J.C., and Smith, A.F.M., “Application of a method for the efficient computation of posterior distributions”, Journal of the Royal Statistical Society: Series C (Applied Statistics), 31(3), 214-225, 1982.
10. Gbur, E.E., Stroup, W.W., McCarter, K.S., Durham, S., Young, L.J., Christman, M., West, M., and Kramer, M., Analysis of generalized linear mixed models in the agricultural and natural resources sciences, John Wiley and Sons, Inc., New York, 2020.
11. Jiang, J., and Nguyen, T., Linear and generalized linear mixed models and their applications, Springer, Germany, 2007.
12. McCulloch, C., and Searle, S.R., Generalized, linear, and mixed models, John Wiley and Sons, Inc., New York, 2001.
13. Stroup, W.W., Generalized linear mixed models: modern concepts, methods and applications, CRC Press, USA, 2012.
14. Anderson, S.H., “The relative importance of birds and insects as pollinators of the New Zealand flora”, New Zealand Journal of Ecology, 27(2), 83-94, 2003.
15. Roulin, A., and Bersier, L.-F., “Nestling barn owls beg more intensely in the presence of their mother than in the presence of their father”, Animal Behaviour,, 74(4), 1099-1106, 2007.
16. Zuur, A.F., Ieno, E.N., Walker, N.J., Saveliev, A. A., and Smith, G.M., Mixed effects models and extensions in ecology with R, Springer, New York, 2009.
17. Dawber, J., Generalised linear mixed models and its application in R, Summer Research Project. Canterbury University, New Zealand, 2009.
18. Zuur, A.F., Hilbe, J.M., and Ieno, E.N., A beginner’s guide to GLM and GLMM with R: a frequentist and Bayesian perspective for ecologists, Highland Statistics Limited, Newburgh., 2013.
19. Agresti, A., Foundations of linear and generalized linear models. John Wiley and Sons, Inc., New York, 2015.
20. Casella, G., and Berger. R.L., Statistical inference, Duxbury Pacific Grove, CA, 2002.
21. Brooks, M.E., Kristensen, K., van Benthem, K.J., Magnusson, A., Berg, C.W., Nielsen, A., Skaug, H.J., Maechler, M., and Bolker, B.M., “glmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling”, The R Journal, 9(2), 378–400, 2017.
22. Bates, D., Mächler, M., Bolker, B., and Walker, S.,“ Fitting linear mixed-effects models using lme4”, Journal of Statistical Software, 67(1), 1–48, 2015.
23. Pinheiro, J. C., and Bates, D. M., Mixed-effects models in S and S-PLUS, Springer, New York, 2000.
24. Huber, P. J., Ronchetti, E. M., and Field, C., Robust statistics, Wiley, USA, 2004.
25. Akaike, H., “A new look at the statistical model identification”, IEEE Transactions on Automatic Control, 19(6), 716–723, 1974.
26. Schwarz, G., “Estimating the dimension of a model”, Annals of Statistics, 6(2), 461–464, 1978.