Directory UMM :Data Elmu:jurnal:A:Agricultural Systems:Vol67.Issue1.2001:

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Logistic modelling to identify and monitor local

land management systems

A. Gobin *, P. Campling, J. Feyen

Institute for Land and Water Management, Katholieke Universiteit Leuven, Vital Decosterstraat 102, 3000 Leuven, Belgium

Received 17 February 2000; received in revised form 20 July 2000; accepted 25 August 2000

Abstract

In the wake of sustainable development, measurable indicators are needed to monitor land resources management. Aerial photograph interpretation, participatory research methods and logistic modelling were combined to establish indicators and to investigate their relationship with local land management systems. Land tenure and customary laws explained the dier-ences in ®eld characteristics at Ikem (southeastern Nigeria). A binary followed by an ordinal logistic model quanti®ed the relationship between ®eld characteristics and local land man-agement. The odds for private land management increased with 102% per 100 m2_{decrease in}

®eld size and with 128% per unit increase in palm tree density. For communal land manage-ment, fallow periods were longer with increasing non-palm tree densities and ®eld sizes; odds increased with 76 and 31%, respectively. Field size, total tree density and palm tree density are important indicators to monitor local land management.# 2001 Elsevier Science Ltd. All rights reserved.

Keywords:Land management; Indicator; Participatory Rural Appraisal; Logistic modelling; Southeastern Nigeria

1. Introduction

Environmental degradation is of great concern in sub-Saharan Africa. Prima facie, loss of sustainability seems linked to rural people's attitude towards land resources. Villagers are often considered to be placing their own short-term survival ahead of long-term land resource sustainability (IFPRI, 1994). In southeastern Nigeria, the

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increased needs of a rising population are regarded as particularly disruptive for the environment since the level of resources per capita declines (Think Tank on Agri-culture, 1993). These negative views are often based on an abstraction of personal observations and judgements but do not necessarily re¯ect the complex reality.

Objective and measurable criteria with potential to compare between areas and monitor changes over time are needed to describe the condition and management of land resources and the pressures exerted upon the land (Young, 1998). International organisations have initiated programmes on developing measurable and policy-relevant environmental indicators (UN, 1995; OECD, 1997) to monitor progress in reaching sustainable development, as de®ned in Agenda 21 (UNCED, 1993). The pressure-state-response approach (Pieri et al., 1995) provides a framework to develop land quality indicators and to place pressure upon land resources, changes in the state of land quality and responses by society to these changes, within the context of policy and natural resource management. However, multiple stakeholders are involved in moulding the desirable goal of sustainable natural resource man-agement and each of them will ®nd dierent indicators relevant to their reasons for monitoring change. Integrating these dierent perspectives, particularly those of local people, into indicators could lead to a better understanding of the processes that cause change (ILEIA, 1996; Abbot and Guijt, 1998). Much of the research has focussed on establishing single indicators with threshold values beyond which sus-tainable land resource management would be at stake.

The objectives of this paper are to elicit local land management systems, to establish indicators that are capable of identifying and hence monitoring local land management, and to investigate the link between the indicators and local land management. Aerial photograph interpretation, participatory research methods and logistic modelling were combined to identify and predict local land management systems on the basis of ®eld plot characteristics. Logistic modelling was used to predict probabilities of local land management systems and to investigate the rela-tionship between the response probability and the explanatory ®eld characteristics. Field characteristics incorporated into the best performing models were regarded as suitable indicators. The models and indicators could be used to monitor local land management and to examine the pressures exerted upon the land.

2. Materials and methods

2.1. Regional setting

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shale dominant inter¯uve, whereas drought-tolerant tree species and tall grasses mainly vegetate the denudated inter¯uve areas.

The 40 km2_{Ikem case study is located at the con¯uence zone of two perennial}

rivers of the River Ebonyi headwater catchment, southeastern Nigeria (Fig. 1). According to the 1991 census, the population density for Ikem averages around 400 persons per square kilometre. Smallholder farmers constitute more than 80% of the population with holdings ranging from 0.5 to 2 ha. The continuously rising popu-lation pressure has turned land into a scarce commodity.

2.2. Participatory Rural Appraisal

Participatory Rural Appraisals (Pretty et al., 1995) were conducted with the aid of trained interpreters/facilitators from outside the village. An introductory meeting and group interview with the village council of elders provided background infor-mation on the history and development at Ikem village. A time line was created to

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present the local history so that the sequence and relative proximity of dierent events could be determined. A checklist of general questions using an open-ended and semi-structured interviewing technique (Mettrick, 1993) provided information on the community's social structure and organisations. The Ikem area was explored with two local village guides to characterise the environment by observation and short interviews. The village and hamlet boundaries, farming areas (including their names), physical features, roads, markets, water supplies and public utilities were outlined on a resource map and related to the 1:50,000 topographic map.

Transect walks (McCracken et al., 1988) were organised and observations made were discussed with villagers met along the transects. A schematic diagram picturing the land characteristics along the transects was produced and re®ned during discus-sions with various interest groups. Individual interviews across the existing social classes and analytical games with social groups provided more insight in household and group land management strategies. For the most common tree species, the local name, use and importance of the tree to the local farming system were recorded, and a branch sample collected. The local tree names were translated into taxonomic names at the Department of Botany, University of Nigeria Nsukka, and the bran-ches with leaves and, where possible, ¯orescences or fruits were crosschecked with the Department's herbarium.

2.3. Selection of strip transects and ®eld plot analysis

Sixty pairs of 1:6000 aerial photographs (1982) from the Ministry of Land Resour-ces were scanned, geo-referenced and related to a 1:50,000 topographic map. Strip transects of 400 m wide and at 600 m intervals were drawn parallel to the direction of the observed gradient in land cover, i.e. perpendicular to the main river (Fig. 1). Field size, number of total trees, mature trees, shrubs and palm trees were recorded for all 388 ®eld plots located within the strip transects. The ®eld plots on the aerial photo-graphs were related to the resource map, the name of the farming area was veri®ed and the present land management was compared to the 1982 management by relating practices in the particular area to events recorded on the time line. The land manage-ment system derived from villagers' accounts was crosschecked with own observa-tions along the transects and aerial photograph interpretaobserva-tions.

The tree crown projection and morphology was used to distinguish between shrub, mature tree and palm tree. Tree density derived from the scanned photo-graphs was also crosschecked with stereoscopic analysis. The photographic thresh-old value for mature trees was set at a crown projection of 5 m in diameter. This threshold value was calculated from the vertical projection of 50 mature tree crowns derived by stretching a tape along the ground in two directions orthogonal to each other and calculating an ellipse cover area.

2.4. Statistics and logistic modelling

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means per local land management system are dierent from each other at the 5% signi®cance level for ®eld size and shrub, total tree, mature tree and palm tree den-sity. Multiple comparison was accomplished through Duncan-Waller multiple range tests at the 5% signi®cance level (SAS, 1990).

The nature of the cell distribution between local land management type and dif-ferent intervals of tree densities and ®eld size were examined using frequency tables and Pearson's, likelihood ratio and Mantel-Haenszelw2_{-tests for large sample sizes,}

or Cochran-Mantel-Haenszel (CMH) statistics for smaller sample sizes. CMH sta-tistics were also used to identify whether the pattern of association was ordinal (i.e. determined by the order of land management).

Both univariate and multivariate logistic models (Hosmer and Lemeshow, 1989) were constructed on two-thirds of the plots, i.e. a subsample of 260 ®eld plots, to de®ne which independent variables are important to identify the type of local land management. The land management types considered in each model were ranked according to decreasing intensity of management. The conditional probability in ak

category model is:

where 14 j< k, Pr is probability, Yis the response variable local land manage-ment,kare categories. The link function is the logit transformation according to:

logitdj e x ln

matrix of intercepts and slope coecients (). The maximum likelihood estimates of

Bj in the logistic regression model are the values that maximise the log-likelihood

function [l(B)], according to:

wherenis the number of observations. The likelihood ratio statistic [=ÿ2 lnl(B)] has an asymptoticw2_{-distribution with}_p _{degrees of freedom under the global null}

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keep individual variables in the model applying aw2_{-criterion of P<0.15. The}

asso-ciation between predicted probabilities and observed responses was examined using percentages of concordant pairs, discordant pairs and the rank correlation index g

to summarise goodness of ®t.

An ordinal logistic modelling strategy was compared to a partially nested dichot-omous strategy. Univariate and multivariate logistic models were validated for all ®ve levels of local land management assuming an ordinal response. The nested dichotomous strategy involved ®rstly modelling private versus communal land management and secondly modelling four dierent levels of communal land man-agement assuming an ordinal response. The response is binary in the case of private (Y=1) versus communal (Y=2) land management, and Eq. (2) can be rewritten as:

logit Pr Y1jx ln PrY1jx

1ÿPrY1jx

B0x01x1. . .6x6 4

Univariate logistic models were ®tted for each of the six variables ®eld size, total tree density, mature tree density, shrub density, palm tree density and non-palm tree density. The variable non-palm tree density was de®ned as the total tree density minus palm tree density. The multivariate solution was ®tted using a stepwise approach. All models were compared on the basis of signi®cant values for the tests described above.

The response was considered ordinal in both cases of distinguishing the four ordi-nal levels (k=4) of communal land management and distinguishing the ®ve ordinal levels (k=5) of local land management. The following cumulative logit was modelled:

models, univariate and multivariate solutions were developed and compared for the ordinal response models.

The exponent of the slope coecients (b) in the logistic models (Eq. (4) and Eq. (5)), the odds ratio (e_{), represents the change in the logit for a change in each}

independent variablex. The Odds for the response 4jare exp[B0₍_x

1ÿx2)] higher at

x=x1than atx=x2and are therefore proportional (Agresti, 1990).

2.5. Validation of the models

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table per model summarising the predicted versus observed responses. Percentages correctly classi®ed, false positive and false negative observations determined the selection of appropriate cut-o values. For binary responses, SAS (1990) provided a bias-adjusted classi®cation table. For multiple responses, the table was constructed on the basis of predicted probabilities. Validation of the ®tted models and respective cut-o values was carried out by classifying the remaining third of all measured plots, i.e. 128 plots, according to the dierent univariate an multivariate models. Field characteristics incorporated into the best performing models were regarded as suitable land management indicators.

3. Results and discussion

3.1. Land tenure at Ikem

Land tenure involves methods of land acquisition and ownership arrangements and strongly in¯uences local land management systems in the Ikem area. Land tenure involves communal, individual (private) and public (state) ownership of land. The customary land tenure system is related to patrilinear inheritance within the family and to the concept of group ownership of rights in land, with every member of the community acquiring inalienable and equal usufructuary rights. The unit of communal landholding is the family, which comprises a man, his wife or wives, children and grandchildren. Family heads grant each family member and children land-use rights for food production. Overall allocation of communal land is decided upon by the village chief, assisted by the community council of elders, for the use and bene®t of his subjects. Communal tenure in Ikem comprised the majority of farmlands and forest lands outside the residential areas as well as communal utilities such as the market.

Individuals obtained land for personal uses from the family heads, the community chief and council of elders on payment of stipulated fees and/or performance of the requisite rites. Land so acquired belonged to the individual and included the home-stead and adjacent homegardens. Land immediately surrounding the settlements remains family or kinship owned. Building a house or hut ensures that the commu-nity regards the land as belonging to the owner. This encourages the owner to plant trees immediately in the close vicinity and carry out other improvements such as fencing. The individual land would be inherited by the owner's descendants as their private property with absolute rights to use it as they wished.

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3.2. Land ownership and trees

The customary law regards tree products from communal lands as collective property. This does not encourage planting them in farming areas and therefore most people plant economically important trees near their homesteads where they can collect the products for their own purposes. Trees planted mostly belong to the humid forest species (Table 1). The economic importance of oil palm (Elaeis gui-neensis) makes it the most widely planted tree on private land. It's uses include palm oil extracted from the nuts, pomade extracted from the kernels, fronds for thatching roofs, termite-resistant wood for construction, fodder for small ruminants and mulch for the homegarden. Each year, a percentage of the palm trees is reserved for tapping the sugary exudate from the stem or cut ¯owers that is left to ferment into palm wine. A density of 40±225 palm trees per ha is common when the trees are grown in association with annual food crops. Oil palm groves and palm-dominated forest, often named oil palm bush (Hopkins, 1979) occur in the vicinity of settlement areas.

In the communal farmlands, plots to be cultivated are cleared except for some of the valuable multipurpose natural trees. Consequently, the majority of useful species is scattered over native farms and scarce patches of forest where the trees can often be overused. Tree use is predominantly con®ned to non-timber products that are essential for food supply on a supplementary or even regular basis, especially during the `hungry period' from the end of the dry season till the ®rst harvests during the

Table 1

Non-wood products from some important tree species at Ikem, southeastern Nigeria

Name (species) Main uses

Humid forest

Icheku(Dialium guineense) Black fruits

Ugba(Pentaclethra macrophylla) Oil bean

Oji(Cola nitida) Kola nut, medicine

Adu(Garcinia kola) Bitter kola, medicine

Ogbonna(Irvingia gabonensis) Bush mango

Uba(Dacryodes edulis) African pear

Eba(Treculia africana) Breadfruit

Udara(Chrysophyllum albidum) Fruit

Iroko(Chlorophora excelsa) Leaves for cooking

Savannah

Ikpakpa(Afzelia africana) Totuso fruit

Abara ugba(Alchornea cordifolia) Preserving food

Abwa(Daniellia oliveri) Goat feed

Okopi(Hymenocardia acida) Leaves

Ede(Parinari polyandra) Medicine

Ugba(Parkia biglobosa) Fruit

Okpeye(Prosopis Africana) Leaves for cooking

Uchakiri(Vitex doniana) Leaves, medicine

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rainy season (Okafor, 1991). Some of the tree products have additional medicinal properties or other uses often rendering them indispensable as sources of cash income (Table 1).

3.3. Local land management systems and ®eld characteristics

The individually owned homegarden comprises multipurpose trees/shrubs and plots with a large range of annual crops and vegetables. The plots or so-called `compound-farms' are often very well protected and fenced to de®ne ownership and prevent animals from entering. Poultry and goats are kept close to the houses and the manure is used on the continuously cropped compound farms. The family/ clan owned `near-®elds' are located close to the settlements. Fewer crops are culti-vated per ®eld in an intensive mixed cropping system associated with oil palm-dominated woodlots. The `compound-and-near ®elds' are customary land use sys-tems that have developed simultaneously with shifting cultivation syssys-tems in the

Fig. 2. Tree density per local land management system as Ikem, southeastern Nigeria. (Duncan-Waller grouping at the 5% signi®cance level is shown as letters in alphabetical order according to the magnitude of the class mean; NC, Near and Compound Fields; CC, Continuous Cultivation; SF, Short Fallow; MF, Medium Fallow; LF, Long Fallow).

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region (Okafor and Fernandes, 1987). The ®eld plots examined had a high average total tree density of 91 trees per ha, of which 32 mature trees and 59 shrubs (Fig. 2). Palm tree densities averaged at 52 trees per ha. As a consequence of the inheritance system, individual or family land is highly fragmented and ®eld sizes averaged at 452 m2_{(Fig. 3).}

The local classi®cation for the communal farmlands or `distant-®elds' is based on fallow period. In general, crop densities and amount of farm inputs decrease and fallow periods increase with distance from the settlement areas. Farmlands located on `good soil' are yearly cropped (continuous cultivation) and have very low tree densities (Fig. 2). The majority of families have a stake in this type of good farmland and ®elds were small (726 m2_{) as a result of fragmentation. Most of the}

tuber crops are produced in the more extensive medium to long term fallow systems. The crop rotation and dominant crops are dependent on the soil type as observed by the farmers (Gobin et al., 1998). Farmers distinguish between farmlands with very long (more than 5 years), medium (between 3 and 5 years) and short (less than 3 years) fallow periods. The generally larger ®elds of the fallow managed ®elds (1840± 3320 m2_{, Fig. 3) were characterised by relatively low mature tree densities (8±11 per}

ha, Fig. 2) as only valuable natural trees were left to grow. Shrub densities in the communal farmlands increased from 1.1 for continuous cultivation, 3.5 for short fallow, 6.1 for medium fallow and 7 shrubs per ha for long fallow managed ®elds. The resulting tree cover pattern re¯ected two peaks regarding the number of trees and shrubs on the ®eld plots (Fig. 2). The number of total trees was highest in the near-and-compound ®elds and a second peak occurred some distance away from the settlement area in the farmlands under long term fallow management.

3.4. Logistic models

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density, 0.315 for the univariate model with shrub density, 0.636 for the univariate model with mature tree density, and 0.581 for the univariate model with total tree density. The maximum likelihood estimates for intercept and slope coecients (Table 2) enabled graphic presentation (Fig. 4) through conversion of the logit to probability according to:

PrY1 e

01x12x2

1e01x12x2 6

Table 2

Analysis of maximum likelihood estimates for binary logistic models predicting private (as opposed to communal) land managementa

Variable S.E.() Wald2 _{P >}2 _{Conditional odds} ratio

95% pro®le likelihood CI

Intercept ÿ84 0.4149 76.0442 0.0001

Total tree density 0.2815 0.0428 43.2462 0.0001 1.325 1.219±1.441

Intercept ÿ3.3556 0.3652 84.4097 0.0001

Mature tree density 1.1832 0.1827 41.9416 0.0001 3.265 2.282±4.670 Intercept ÿ2.3972 0.3083 60.4694 0.0001

Shrub density 0.1749 0.0411 18.1425 0.0001 1.191 1.099±1.291 Intercept ÿ3.7491 0.4398 72.6543 0.0001

Palm tree density 1.5306 0.2239 46.7447 0.0001 4.621 2.980±7.166

Intercept 4.9239 0.89.7 30.5628 0.0001

Field size ÿ0.00813 0.00147 30.5167 0.0001 0.444 0.333±0.592

Intercept 1.1123 0.5178 4.6151 0.0317

Palm tree density 0.8264 0.1428 33.5008 0.0001 2.285 2.727±4.290 Field size ÿ0.0051 0.0010 24.0453 0.0001 0.495 0.347±0.6.8

a _{Odds ratio is e}b_{for tree densities and e}100b_{for ®eld size.}

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wherebyY=1 represents private land management, the intercept and slope coef-®cients and x the covariates (note that x2is zero for the univariate models). The

odds for private land management were positively associated with shrub, total tree, mature tree and palm tree density (conditional odds>1) and negatively associated with ®eld size (conditional odds<1, Table 2), re¯ected in upwards and downwards slopes (Fig. 4), respectively. The predicted odds for private land management were higher per unit increase in tree density: 19% for shrub, 33% for total trees, 227% for mature trees and 362% for palm trees (Table 2). The odds for communal land management are 125% (=1/odds for private) higher per 100 m2_{increase in ®eld size}

(Fig. 4). The adjusted odds for the multivariate model are reduced as compared to the univariate solutions (Table 2). The odds for private land are 2.285 times the odds for communal land per unit increase in palm trees per 0.1 ha and 0.495 times the odds for communal land per 100 m2_{increase in ®eld size.}

The next step in the nested strategy was to construct models for predicting prob-abilities of the four communal land management types (Table 3). The univariate models based on mature and palm tree density were rejected since the likelihood

Table 3

Analysis of maximum likelihood estimates for a multivariate ordinal logistic model predicting dierent levels of communal land management

Variable S.E. () Waldw2 _{P >}_w2 _Conditional odds ratio

Intercept (p1)a 1.1689 0.2788 17.5740 0.0001 Intercept (p1+p2)a 3.1505 0.3493 81.3377 0.0001 Intercept (p1+p2+p3)a 4.9175 0.4392 125.3842 0.0001

Total tree density ÿ0.5710 0.0568 101.2096 0.0001 0.565 0.505±0.631

Shrub density ÿ0.6425 0.0625 105.6157 0.0001 0.526 0.465±0.595

Field size ÿ0.0028 0.00025 121.3091 0.0001 0.756 0.719±0.794

(Total-Palm) density ÿ0.6207 0.0599 107.3489 0.0001 0.538 0.478±0.605

(Total-Palm) density ÿ0.5662 0.0738 58.9298 0.0001 0.568 0.491±0.656 Field size ÿ0.0027 0.0003 81.9435 0.0001 0.764 0.721±0.810

a _{Communal land management systems were ranked prior to modelling: 1 is continuous cultivation, 2} is short-term fallow, 3 is medium-term fallow and 4 is long-term fallow management. Odds ratio is eb_for

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ratio w2_{-test was not signi®cant. The univariate ordinal model based on ®eld size}

(AIC= 347, SC=360.3), followed by the model based on (total-palm) tree den-sity (AIC= 417.7, SC= 431) were better than the models based on total tree denden-sity (AIC=433.3, SC= 446.6) and shrub density (AIC=423.2, SC=436.5). The multi-variate model (AIC=265.6, SC=282.3) shows the best ®t relative to a model with-out covariates (AIC=582.7, SC=592.7). The measure of association is highest for the multivariate model (0.934), followed by the univariate models with covariate ®eld size (0.819), (total-palm) tree density (0.733), shrub density (0.731) and total tree density (0.7). Following Eq. (5) and Eq. (6), the cumulative probability (Fig. 5) was calculated from the maximum likelihood estimates of all (Table 3). The con-ditional odds ratio indicates that an increasing intensity of communal management is predicted with each unit decrease in total tree, (total-palm) tree and shrub density (Table 3, Fig. 5). The odds of a more intensive communal land management are 0.756 times the odds for a less intensive fallow management per 100 m2_{increase in}

observed ®eld size. In the multivariate model, the odds for longer fallow manage-ment are 76% higher per unit increase in (total-palm) tree density and 31% higher per 100 m2_{increase in ®eld size.}

The nested strategy comprising dichotomous models to distinguish private land management followed by ordinal logistic models to predict dierent levels of com-munal land management, was compared to an ordinal logistic modelling strategy to predict all types of land management at once. The univariate model based on total tree density was rejected since the likelihood ratiow2_{-test was not signi®cant.}

Uni-variate models involving the other tree densities failed for the proportional odds test

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or had non-signi®cant values (p>0.05) for some or all maximum likelihood para-meter estimates. Only the univariate ordinal logistic model on the basis of ®eld size was retained (Table 4). Longer fallow practices become 40% more likely per 100 m2

increase in ®eld size. Based on Eq. (5) and Eq. (6) and the parameter estimates (Table 4), the cumulative probabilities were converted to probabilities for each local land management type (Fig. 6), according to:

PrÿYjjxPrYjjx ÿPrYjÿ1jx 7

3.5. Validation of the models

The classi®cation tables for the binary logistic models allowed the speci®cation of cut-o values based on a combination of maximum percentage of correct predic-tions and minimum percentages for false positive and false negative predicpredic-tions

Table 4

Analysis of maximum likelihood estimates for logistic models predicting dierent levels of local land management

Variable b S.E. (b) Waldw2 _{P >}_w2 _Conditional odds ratio

Intercept (p1)a 1.9525 0.2817 48.0388 0.0001 Intercept (p1+p2)a 4.6105 0.4104 126.2357 0.0001 Intercept (p1+p2+p3)a 7.6352 0.6214 150.9947 0.0001 Intercept (p1+p2+p3+p4)a 10.3323 0.7731 178.6035 0.0001

Field size ÿ0.00336 0.000259 169.3686 0.0001 0.714 0.679±0.751

a _{All local land management systems were ranked prior to modelling: 1 is private land management} (near and compound ®elds), 2 is continuous cultivation, 3 is short fallow, 4 is medium fallow and 5 is long fallow management. Odds ratio is eb_{for tree densities and are e}100b_{for ®eld size.}

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Table 5

Bias-adjusted classi®cation table for the best-®tted binary logistic models predicting private land management (see Table 2)a

Pr level Multivariate (Size/Palm) Univariate (Size) Univariate (Palm) Univariate (Mature)

Correct False positive

False negative

0.45 98.1 5.7 1 94.2 18.6 2 94.6 10.4 4.2 90.4 11.4 9.3

0.50 98.5 3.8 1 94.2 17.5 2.5 95 6.7 4.7 89.2 12.5 10.5

0.55 98.5 3.8 1 94.2 16.4 2.9 94.6 6.8 5.1 90.0 3.6 10.8

0.60 98.1 3.9 1.4 95.0 13.2 2.9 94.6 6.8 5.1 89.6 0.0 11.5

0.65 98.1 3.9 1.4 94.2 13.7 3.8 94.6 4.8 5.5 89.6 0.0 11.5

a _{Proposed cut-o values are in italic.}

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Table 6

Classi®cation table for the best ®tted ordinal logistic models predicting communal land management levels (see Table 3) and validationa

Pr level Continuous Cultivation Short Fallow Medium Fallow Long Fallow

Correct False

Validation 83.0 12.0 5.0 60.0 11.0 29.0 68.0 14.0 18.0 78.0 15.0 7.0

(Total-palm) tree density

Validation 73.0 17.0 10.0 62.0 9.0 29.0 74.0 0.0 26.0 79.0 15.0 6.0

Multivariate model (®eld size / (total-palm) tree density)

0.40 98.1 1.9 0.0 91.3 6.7 1.9 72.6 16.8 10.6 81.3 10.6 8.2

Validation 85.0 10.0 5.0 73.0 9.0 18.0 75.0 7.0 18.0 81.0 12.0 7.0

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(Table 5). The cut-o values were set at 0.55 for the univariate logistic model with mature density, 0.50 for palm tree density, 0.6 for ®eld size and 0.55 for the multi-variate model taking both palm tree density and ®eld size into account. Validation of the models using the respective cut-o values showed that 72.7% of the new observations were correctly classi®ed, whereas 6.8% were false positive and 20.5% were false negative using a univariate binary logistic model with mature tree density. The high percentage of false negative cases was due to the low number of mature trees on some near-and-compound ®elds. The univariate model on the basis of ®eld size classi®ed 76.5% of the ®elds as correct, 13.6% as false positive and 9.9% as false negative. False positive cases were all small plots under continuous cultivation, whereas false negative plots were the larger sized near-and-compound ®elds that often occur near newer established settlements. Classi®cation on the basis of the model with palm tree density was correct for 84.1%, false positive for 5.7% and false negative for 10.2% of the validation observations. The multivariate model combining palm tree density and ®eld size provided the best ®t with 86.4% correctly classi®ed, 9.1% for false positive and 17.3% for false negative classi®cations. The false negative classi®cations were small ®elds with a few palm trees that were in a transition stage from communal to private ownership.

Classi®cation tables for the ordinal logistic models were constructed after convert-ing the modelled conditional probabilities to sconvert-ingle probabilities usconvert-ing Eq. (7). Cut-o values were determined for each of the communal land management types based on the same criteria as for the binary models. The cut-o values were set at 0.50±0.55 for the univariate model with ®eld size, 0.45±0.50 for (total-palm) tree density and 0.40±0.65 for the multivariate model incorporating both (total-palm) tree density and ®eld size (Table 6). Validation of the univariate ordinal logistic model with ®eld size resulted in 60±83% correctly classi®ed observations, 11±15% false positive and 5±29% false negative cases (Table 6). The univariate ordinal model on the basis of (total-palm) tree density classi®ed 62±79% of the validation dataset as correct, 0±17% as false positive and 6±29% as false negative (Table 6). Classi®cation on the basis of the multivariate model combining (total-palm) tree density and ®eld size was correct for 73±85%, false positive for 7±12% and false negative for 5±18% of the validation observations (Table 6). False positive cases are all small plots under continuous cul-tivation, whereas false negative plots are the larger sized near-and-compound ®elds that often occur near newer established settlements.

The ordinal univariate logistic model incorporating ®eld size predicted all local levels of management with correct classi®cation of 76.5±95% for the modelled and 71.9±80.5% for the validated ®elds at cut-o probabilities between 0.45 and 0.55 (Table 7). False positive cases accounted for 3.1±7.7% (modelled) and 2.3± 19.5% (validated), and false negative cases for 1.9±15.8% (modelled) and 2.3±22.7% (validated).

3.6. Local land management indicators

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Table 7

Classi®cation table for the ordinal logistic model based on ®eld size (see Table 4) and validationa

Pr level Near and Compound ®elds Continuos Cultivation Short Field Medium Fallow Long Fallow

False negative

0.40 93.1 5.4 1.5 89.6 7.3 3.1 81.9 9.6 8.5 75.0 14.2 10.8 85.8 6.5 7.7

0.45 94.2 4.2 1.5 89.6 5.0 5.4 81.9 8.5 9.6 74.6 13.5 11.9 86.2 6.2 7.7

0.50 95.0 3.1 1.9 88.8 3.8 7.3 83.8 5.8 10.4 75.4 11.5 13.1 85.0 6.2 8.8

0.55 94.6 2.3 3.1 85.4 2.7 11.9 84.6 3.8 11.5 76.5 7.7 15.8 84.6 6.2 9.2

0.60 91.2 1.2 7.7 80.0 0.0 20.0 83.1 2.3 14.6 80.0 0.0 20.0 85.0 5.4 9.6

Validation 78.1 19.5 2.3 71.9 10.2 18.0 71.9 5.5 22.7 80.5 2.3 17.2 80.5 14.8 4.7

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negative cases and the best model performances when using a validation data set. The univariate ordinal model based on ®eld size only, showed a rather high percen-tage of false positive cases for the modelled probability of private land management (Table 7). A nested strategy of estimating the probability of private land manage-ment using the multivariate binary logistic model (Table 2) and subsequently esti-mating the probability for each level of communal land management using the multivariate ordinal logistic model (Table 3), enabled the best classi®cation. The ®tted models and respective cut-o value could then be used to classify future observations in order to monitor changes and transitions to other types of local land management or ownership. The most suitable land management indicators for the area are the independent variables that feed the multivariate models: ®eld size, total tree density and palm tree density.

4. Conclusions

A methodology is presented for establishing land management indicators and investigating the link between the indicators and local land management. Participa-tory research methods helped elicit local land management systems and relate the local terminology to quanti®able ®eld plot characteristics. Land tenure and cus-tomary laws explained the variation in ®eld characteristics between the local land management systems. Logistic models were used to quantify the relationship between ®eld characteristics and local land management systems. Field size, total tree density and palm tree density proved the most successful land management indicators in predicting probabilities of local land management systems.

The proposed indicators and logistic models can support policy-makers in mon-itoring land management changes, investigating transitions to other management types and examining pressures exerted upon the land. The methodological approach can be applied to other areas under similar farming systems. The models will gain further importance if the independent variables for tree densities can be linked to earth observation-derived land cover.

Acknowledgements

Funding for this research was provided by the Belgian Agency for Development Co-operation (BADC) through the Inter-University Project on 'Water Resources Development for domestic use and small scale irrigation in the rural areas of southeastern Nigeria'. Special appreciation is extended to the project sta and farmers of Ikem who contributed to this particular study.

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