Land use impact on Vitellaria paradoxa C.F. Gaerten. stand structure and distribution patterns: a comparison of Biosphere Reserve of Pendjari in Atacora district in Benin

Abstract

The shea tree, Vitellaria paradoxa, is a socio-economically important tree for the rural population in parts of West Africa. Our study assessed the current status of this native tree species with regard to increasing human pressure in northern Benin. We compared distribution of adult shea trees, seedlings and saplings in farmed lands with protected areas in the Biosphere Reserve of Pendjari (BRP). At our study site near BRP, agricultural activities foster recruitment of shea trees by regularly cropping of vegetation cover. Furthermore, traditional farming practices preserve adult individuals thus permitting regular fruit harvests. Consequently, most of the tallest and largest individuals of shea trees are found in framed lands. In contrast, the highest density of juvenile trees including seedlings (dbh <5 cm) and saplings (dbh 5–10 cm) occurred within BRP. Saplings were negatively affected by farming activities. Furthermore, spatial point pattern analysis revealed differences in the spatial structure of juveniles. Juveniles showed significant aggregations at small scale (<20 m) in BRP as well as significant and positive small-scale associations with adult trees. This contrasts with farmed lands where we did not find such spatial patterns at similar small scale but only a weak aggregation between juveniles and absence of association (attraction) of adults to juveniles. Although our analyses indicate that shea trees are rather well preserved, we conclude that the observed severe reduction of saplings in farmed lands is likely to negatively impact the long-term viability of the tree population. Therefore agroforestry practices must consider the preservation of sapling populations in farming areas for long-term conservation.

Appendix: combining the data from individual mapped replicate plots into mean, weighted O(r), and G(y) functions

For statistical analysis it is common to map several replicate plots of a larger point pattern under identical conditions. In this case the resulting second-order statistics of the individual replicate plots can be combined into average second-order statistics (Diggle 2003). This is of particular interest if the number of points in each replicate plot is relatively low. In this case the simulation envelopes of individual analyses would become wide, but combining the data of several replicate plots into average second-order statistics increases the sample size and thus narrows the confidence limits. Average second-order statistics are also an effective way of summarizing the results of several replicate plots.

When the patterns are strict replicates of an underlying process, the corresponding estimates $\hat{K}_{i} (r)$ of the K-functions from plots i are identically distributed and a reasonable overall estimate can be obtained by simply averaging the individual K-functions (Diggle 2003: Eq. 4.20 at page 52). Using the grid-based estimator of Programita, the resulting estimator of the O-ring statistic is given in the appendix of Riginos et al. (2005).

However, because Ripley’s K-function K(r) is defined as a ratio of expected number of points in circles [= λK(r)] divided by the intensity λ, a better strategy may be to pool separately estimates of λ and λK(r). The resulting average K-function is a weighted average of the individual estimates $\hat{K}_{i} (r)$, where the weight is the number of points in plot i divided by the total number of points in all replicate plots (Diggle 2003: Eq. 8.11, page 123). Note that the resulting average K-function is also an appropriate estimator if the replicates would be differentially thinned versions of a common underlying process (Diggle 2003: p 123).

Using the grid-based estimators of Programita and following the notation in Wiegand and Moloney (2004) (their Eq. 11), the numerical estimator of the bivariate pair-correlation function g ₁₂(r) is calculated as:

$$ \lambda _{2} \ifmmode\expandafter\hat\else\expandafter\^\fi{g}^{w}_{{12}} (r) = \frac{{\frac{1} {{n_{1} }}{\sum\limits_{i = 1}^{n_{1} } {{\mathbf{Points}}_{{\mathbf{2}}} [R^{w}_{{1,i}} (r)]} }}} {{\frac{1} {{n_{1} }}{\sum\limits_{i = 1}^{n_{1} } {{\mathbf{Area}}[R^{w}_{{1,i}} (r)]} }}}, $$

(A1)

where n ₁ is the number of points of pattern 1, R ^w_1,i (r) is the ring with radius r and width w centered in the ith point of pattern 1, Points ₂ [X] counts the points of pattern 2 in a region X, and the operator Area[X] determines the area of the region X.

To integrate the data of N different replicates into a single weighted pair-correlation function, the formula for one replicate (Eq. A1) is extended by calculating, for each spatial scale r, the average weighted number of points of pattern 2 taken over all N replicates and the average weighted area taken over all N replicates:

$$ \lambda _{2} \hat{g}^{w}_{{12}} (r) = \frac{{{\left( {\frac{{n^{1}_{1} }} {N}{\left( {\frac{1} {{n^{1}_{1} }}{\sum\limits_{i^{1} = 1}^{n^{1}_{{_{1} }} } {{\mathbf{Points}}_{{\mathbf{2}}} [R^{w}_{{1,i^{1} }} (r)]} }} \right)} + ... + \frac{{n^{N}_{1} }} {N}{\left( {\frac{1} {{n^{N}_{1} }}{\sum\limits_{i^{N} = 1}^{n^{N}_{{_{1} }} } {{\mathbf{Points}}_{{\mathbf{2}}} [R^{w}_{{1,i^{N} }} (r)]} }} \right)}} \right)}}} {{{\left( {\frac{{n^{1}_{1} }} {N}{\left( {\frac{1} {{n^{1}_{1} }}{\sum\limits_{i^{1} = 1}^{n^{1}_{{_{1} }} } {{\mathbf{Area}}[R^{w}_{{1,i^{1} }} (r)]} }} \right)} + ... + \frac{{n^{N}_{1} }} {N}{\left( {\frac{1} {{n^{N}_{1} }}{\sum\limits_{i^{N}_{{_{1} }} = 1}^{n^{N}_{{_{1} }} } {{\mathbf{Area}}[R^{w}_{{1,i^{N} }} (r)]} }} \right)}} \right)}}}$$

(A2)

where i ^j is the ith point of pattern 1 and replicate j, n ^j₁ is the number of points of pattern 1 and replicate j, and N = ∑_j n ^j₁ is the total number of points of pattern 1 in all replicates. Equation A2 simplifies to:

$$ \lambda _{2} \hat{g}^{w}_{{12}} (r) = \frac{{{\sum\limits_{i^{1} = 1}^{n^{1}_{{_{1} }} } {{\mathbf{Points}}_{{\mathbf{2}}} [R^{w}_{{1,i^{1} }} (r)]} } + ... + {\sum\limits_{i^{N} = 1}^{n^{N}_{{_{1} }} } {{\mathbf{Points}}_{{\mathbf{2}}} [R^{w}_{{1,i^{N} }} (r)]} }}} {{{\sum\limits_{i^{1} = 1}^{n^{1}_{{_{1} }} } {{\mathbf{Area}}[R^{w}_{{1,i^{1} }} (r)]} } + ... + {\sum\limits_{i^{N}_{{_{1} }} = 1}^{n^{N}_{{_{1} }} } {{\mathbf{Area}}[R^{w}_{{1,i^{N} }} (r)]} }}}$$

(A3)

Following the strategy of Diggle (2003) to pool separately estimates of λ ₂ and λ ₂ K ₁₂(r) [and analogously estimates of λ ₂ and λ ₂ g ₁₂(r) for estimating the pair-correlation function] the overall intensity λ ₂ is estimated as λ ₂ = N ₂/A where

$$ N_{2} = {\sum\limits_{j = 1}^N {n^{j}_{{_{2} }} } }, $$

(A4)

is the total number of points of pattern 2 in all N replicates j, and A the total area

$$ A = {\sum\limits_{j = 1}^N {{\mathop A\nolimits^j }} }, $$

(A5)

of all replicates j with area A ^j.

The univariate estimator of g(r) is calculated in a manner analogous to the bivariate functions by setting pattern 1 equal to pattern 2.

Because we did not use edge correction for the distribution function G of nearest neighbor distances we simply summed up the frequency distributions of single replicated and normalized the frequency distribution after combining all replicated to yield the normalized G ₁₂(y) and G(y).

Literature cited in appendix

Diggle PJ (2003) Statistical analysis of point patterns, IInd edn. Arnold, London

Riginos C, Milton SJ, Wiegand T (2005) Context-dependent negative and positive interactions between adult shrubs and seedlings in a semi-arid shrubland. J Vegetation Sci 16:331–340

Wiegand T, Moloney KA (2004) Rings, circles and null-models for point pattern analysis in ecology. Oikos 104:209–229