TABLE 3. Percent distribution of Virgin Islands farms by acreage: 1964 to 1982. Size of farms (in acres) 1964 1970 1975 1978 1982 Less than 3 0.2 0.4 0.5 0.5 0.6 3 to 9 2.6 1.3 2.1 3.0 2.9 10 to 19 2.5 1.4 1.8 2.8 2.0 20 to 49 3.8 4.0 3.8 4.4 5.0 50 to 99 5.7 5.3 5.7 5.4 5.7 100 to 174 8.0 4.1 6.4 3.8 6.9 175 to 259 5.3 3.0 6.2 7.1 5.4 260 to 499 13.1 12.7 12.3 12.8 11.1 500 to 999 19.6 13.1 7.9 8.8 14.7 1000 or over 39.2 54.7 53.3 51.4 45.7 100.0% 100.0% 100.0% 100.0% 100.0% (39539) (20470) (24703) (24397) (20824) A chi-square test of homogeneity was conducted on the distributions (of the actual number of acreages) to determine if the population remained homogeneous throughout. The large chi-square value produced an associated p less than .0000. One is fairly certain that the distrubtions have changed substantially over time. The computed adjusted residuals, however, suggests that factors other than the abandonment of sugar production in 1966 may have been responsible for the departures from homogeneity in the system. It was also of interest to examine the distribution of farm operators by age group, since with the public financial support for young farmers in recent years, one would normally expect the youthful age groups to reflect these entrants. A 'farm operator' is defined as a "person who operates a farm, either by doing the work himself/herself or by directly supervising the work. The operator may be the owner, a member of the owner's household, a hired manager, or a tenant, renter, or sharecropper .. ." (U.S. Bureau of the Census, 1983, p. A-1). First, however, Table 4 reflects that, since 1969, the average age of farm operators is becoming older, not younger. There does not appear to be any substantial movement of youth into farming, and it is to be observed from the table that the percentage of operators over 55 has increased since 1974. In order to test further the supposition that the age structure of recent years should reflect a change from that of the past, the populations of the last five censuses were tested by a chi-square test of homogeneity to establish if the differences between the observed distributions were due to chance. The computed chi- square and associated probability (p = .293) lend strong evidence that there is no substantive departure from homogeneity of the age structure over time, and that the differences observed are most like- ly due to a chance process. This outcome was indeed surprising, and a possible explanation is explored later in the paper. A final attribute of the farming pattern is the number of farms that have been recorded which produce for home consumption, and those which produce for sale. The last column in Table 1 in- dicates that there is no real constancy in the proportion of sale holdings, but it does appear extraordinary that over the years no more than about two out of three holdings are devoted to pro- duction for sale, or that more than one-third of the designated farm units produce for home consumption only. Thus, the major factors that characterize farming in the Virgin Islands present clear evidence that the overall industry is in a state of decline, both in terms of the total number of acres devoted to productive agriculture, and the number of farm units involved in this production. The following section is therefore given over to a TABLE 4. Percent distribution of Virgin Islands farms by age group: 1964 to,1982. Age group 1964 1970 1975 1978 1982 Less than 25 0.7 0.9 2.1 1.1 2.0 25 to 34 6.1 9.4 6.1 6.3 4.0 35 to 44 19.3 22.6 16.5 19.0 18.2 45 to 54 28.2 20.3 25.4 22.0 22.8 55 to 64 25.0 27.9 27.0 28.1 28.6 65 and over 20.7 18.9 22.9 23.5 24.4 100.0% 100.0% 100.0% 100.0% 100.0% (466) (212) (327) (378) (303) Average age 53.5 51.8 52.4 54.0 55.0 Note. Base data derived respectively from the U.S. Census of Arriculture. Virgin Islands of the United States, U.S. Bureau of the Census. discussion of the Markov chain model used in the projection of the total number, and distribution, of farm units in the years ahead. Projection of Future Size Distributions Basic Elements of the Markov Chain Process The areal organization of functional units through time, and the paths they are likely to follow in future time periods, have often arrested the interest of the geographer, be they units of settlement, industry, or farms (Collins et al., 1974; and Collins, 1975). In a similar vein, agricultural economists share a common interest, as is evident from the works of Judge and Swanson (1961), Dovring (1962), and Krenz (1964). The application of the Markov chain model to spatially distributed time-varying data is contingent on the definition of a set of mutually exclusive states or categories which comprise the total distribution and the area under study. It also assumes that movements of units between states over time can be considered as a stochastic process, i.e., in any given sequence of events, the outcome of each movement depends on chance. The process can be in only one state at a given time and it moves successively from one state to another. And the probability that the process moves from S, to Sj depends only on the state S, that it occupied before the move. For com- plete details on the estimation of the fundamental matrix and related statistics, see Kemeny and Snell (1976, pp. 43-50). The states used in this study are the classifications used by the Bureau of the Census: State Size of farm (acres) S, ................... .............Less than 3 S2 ............... ................. 3 to 9 S3 .............................. l10 to 19 S4 ............................... 20 to 49 Ss ............................. 50 to 99 S6 ........................... 100 to 174 S7 ........................ ...... 175 to 259 Ss ............... .. ........ 260 to 499 S9 ................................ 500 to 999 SIo ........................... 1000 or over Within a given set of states, it is generally possible to estimate the probabilities (p,) of observations moving from one state to another. Such probabilities of movements for a given time period can be summarized in a transition matrix, the elements of which denote the probability of moving from state S, to Sj in the next VOL. XX-PROCEEDINGS of the CARIBBEAN FOOD CROPS SOCIETY 25