Shade canopy density variables in cocoa and coffee agroforestry systems

Abstract

An estimated 3.4 million hectares of cocoa and 9.7 million hectares of coffee are cultivated, globally, under shade trees, i.e. in agroforestry systems. Shade canopies are characterized in terms of tree density (N, trees ha⁻¹), tree basal area (G, m² ha⁻¹) and percent canopy cover (%Cov). N, G and %Cov are named shade canopy density variables (SCDV). The use of these SCDV has two important limitations: (1) different combinations of values of the three SCDV variables generate very different shade tree stands (hence very different shading levels), and (2) Additional factors modify shading under shade canopies with constant SCDV values. This article uses the software ShadeMotion (www.shademotion.net) to show how 24 different, simple, even-sized, mono-layered, Cordia alliodora shade canopies with constant N, G and %Cov display significantly different shade levels and temporal patterns of shading depending on tree stem and crown diameter ratios, tree height, spatial planting configurations (square, random and alleys) and leaf fall patterns. A minimum set of variables capable of providing a more accurate description of the shading characteristics of a cocoa or coffee shade canopy is proposed. Our findings can shed light on the current debate on the pros and cons of the definitions of cocoa agroforestry used by chocolate and certification companies, governments, non-governmental organizations, and donors, especially in West and Central Africa. In this article, emphasis is given to cocoa, but the analysis, results and conclusions are equally applicable to coffee agroforestry systems.

Appendix 1: The mathematical relationships between N, G, %Cov, R, d, and k

With trees of same stem diameter (d), basal area per hectare (G) is obtained by multiplying the sectional stem area of one tree (g, m² tree⁻¹) by the population density represented in number of trees per hectare (N). Symbolically:

${\text{G}} = {\text{g}}*{\text{N}}$

Assuming tree stems are cylindrical, the sectional area can be estimated by the area of a circle of diameter d (in meters i.e. d in cm divided by 100),

$${\text{g }} = \, \left( {{\text{d}}/{1}00} \right)^{{2}} *\left( {\uppi /{4}} \right) \, = \, \left( {\uppi *{\text{d}}^{{2}} } \right)/{4}0000$$

Hence

$${\text{G }} = \, \left( {{\text{N}}*\uppi *{\text{d}}^{{2}} } \right)/{4}0000$$

(1)

Re-arranging Eq. 1

$${\text{N }} = \, \left( {{\text{G}}*{4}0000} \right)/\left( {\uppi *{\text{d}}^{{2}} } \right)$$

(2)

And

$${\text{d }} = \, \left[ {\left( {{\text{G}}*{4}0000} \right)/{\text{N}}*\uppi )} \right]^{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} }$$

(3)

Considering that

$$\begin{aligned} {\text{R }} = & {\text{ k}}/{\text{d}} \\ {\text{K }} = & {\text{ R}}*{\text{d}} \\ {\text{d }} = & {\text{ k}}/{\text{R}} \\ \end{aligned}$$

For a given R

$${\text{G }} = \, \left( {{\text{N}}*{\text{k}}^{{2}} *\uppi } \right)/\left( {{4}0000*{\text{R}}^{{2}} } \right)$$

(4)

$${\text{N }} = \, \left( {{4}0000*{\text{G}}*{\text{R}}^{{2}} } \right)/\left( {\uppi *{\text{k}}^{{2}} } \right)$$

(5)

$${\text{K }} = \, \left[ {\left( {{4}0000*{\text{G}}*{\text{R}}^{{2}} } \right)/\left( {{\text{N}}*\uppi } \right)} \right]^{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} }$$

(6)

Percent canopy cover (%Cov) is obtained by multiplying the opacity-adjusted crown projection area per tree (z) by the number of trees per hectare, divided by 10,000 m² in one hectare and later multiply it by 100 to express the ratio in percent. Assuming that vertical crown projection is circular,

$${\text{z }} = {\text{ k}}^{{2}} *\left( {\uppi /{4}} \right)*{\text{p }} = \, \left( {{\text{R}}*{\text{d}}} \right)^{{2}} *\left( {\uppi /{4}} \right)*{\text{p }} = {\text{ R}}^{{2}} *{\text{d}}^{{2}} *\left( {\uppi /{4}} \right)*{\text{p}}$$

Hence

$$\% {\text{Cov }} = { 1}00*\left( {{\text{N}}*{\text{z}}*{\text{p}}} \right)/{1}0000 \, = \, \left( {{\text{N}}*{\text{R}}^{{2}} *{\text{d}}^{{2}} *{\text{p}}*\uppi } \right)/{4}00$$

(7)

Substituting N by Eq. (1) and rearranging terms,

$$\% {\text{Cov }} = { 1}00*{\text{G}}*{\text{p}}*{\text{R}}^{{2}}$$

(8)

Also

$$\% {\text{Cov }} = \, ({\text{N}}*{\text{p}}*\uppi *{\text{k}}^{{2}} )/{4}00$$

(9)