Table 3 Summary of notations

y

Index for year

p

Index for plant

lsg

Index for the \(g{\textrm{th}}\) genotype in selection population s from inbred line l

f

Index for leaf rank

\([f_{\min }^{y,\,lsg}, f_{\max }^{y,\,lsg}]\)

Largest interval of leaf ranks such that leaves \(f_{\min }^{y,\,lsg}-1\) and \(f_{\max }^{y,\,lsg}\) are observed on at least 10 plants from genotype lsg on year y

\([f_{\min }^0, f_{\max }^0]\)

Common interval to all genotypes and years, equal to \(\bigcap \limits _{y,\,lsg}[f_{\min }^{y,\,lsg}, f_{\max }^{y,\,lsg}]\)

\(F_{ lsg}\)

Overall maximum number of leaves for genotype lsg

\(H_{y,\,lsg,\,p,\,f}\)

Time between sowing and appearance of leaf f on plant p from genotype lsg on year y (in degree-days)

\(Y_{y,\,lsg,\,p,\,f}\)

Time between appearance of leaf \(f-1\) and f on plant p from genotype lsg on year y (in degree-days)

\(\mu _{y,\,lsg,\,f}\)

Mean of \(Y_{y,\,lsg,\,p,\,f}\) i.e. mean interval between appearance of leaf \(f-1\) and f for genotype lsg on year y (in degree-days)

\(\mu _{y,\,lsg}^{C\left(f_{\min }\right)}\)

Mean of \(H_{y,\,lsg,\,p,\,f_{\min }}\) i.e. mean time between sowing and appearance of leaf \(f_{\min }\) for genotype lsg on year y (in degree-days)

\(\sigma _{y,\,lsg,\,f}\)

Standard deviation of \(Y_{y,\,lsg,\,p,\,f}\) (in degree-days)

\(\sigma ^{C(f_{\min })}_{y,\,lsg}\)

Standard deviation of \(H_{y,\,lsg,\,p,\,f_{\min }}\) (in degree-days)

\(X_{y,c}(t)\)

Value of the climatic variable c on day t from year y

\({\overline{\mu }}^{cal}_{y,\,lsg,\,f}\)

Mean calendar time between sowing and appearance of leaf f for genotype lsg on year y (in days)

Plant level phyllochron

Vector \((Y_{y,\,lsg,\,p,\,f})_{f=1, \ldots , F_{lsg}}\) of times between appearance of successive leaves.

Genotype level phyllochron

Vector \((\mu _{y,\,lsg,\,f})_{f=1, \ldots , F_{lsg}}\) of mean times between appearance of successive leaves over the genotype (y, lsg)