with i=1,…n is animal i. exprit is the expression of the probe being studied for animal i at time step t (t∈{0,t ′}), μ 0 is the specific contribution of time step t=0, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\phantom {\dot {i}\!}\tau _{t^{\prime }}$\end{document}τt′ is the effect of time step t ′, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\phantom {\dot {i}\!}\beta ^{t^{\prime }}$\end{document}βt′ is the effect of L/G ratio in this model and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\epsilon _{it} \sim N\left (0, \sigma _{e}^{2}\right)$\end{document}εit∼N0,σe2 is an error term.