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Reprinted from: Perspectives on new crops and new uses. 1999. J. Janick (ed.), ASHS Press, Alexandria, VA.

The Dynamic Contribution of New Crops to the Agricultural Economy: Is it Predictable?

Stephan R.P. Halloy* The diversification of agriculture and the development of new crops are closely related. Although diversification is often justified by reference to practical experience, we know little about the theoretical basis for diversification or its causes and effects. Is it theoretically possible to feed the world on a fixed and unchangeable set of species and varieties? Empirical evidence suggests not, but are there fundamental system properties that make this impossible? This paper addresses the following questions: 1. What is the "life cycle" of an economic crop from development to decline? 2. Does "successful" have any objective meaning or threshold in regards to crops? 3. Should we group all crops together or are there distinct functional groups or guilds? Guilds is used as in the ecological literature to signify a group of species having similar ecological (in this case agricultural management) requirements and therefore having similar economic roles. 4. Are there repeatable patterns in the abundance distribution of crops allowing the prediction of future patterns? The actual abundance distribution patterns of crops in New Zealand is tested against three models: the average, the lognormal, and a resource attraction model (RAM). The first two models are top-down (i.e. inferred from the actual distribution pattern). The average distribution over 150 years approximates an exponential function and represents the null model of a return to the mean. The lognormal is one of the distributions which most closely fits many diverse plant and animal communities (Preston 1948, 1962; Sugihara 1980; May 1981). The lognormal is a middle ground approximation between a variety of distributions ranging from the exponential and power functions to the broken stick model (Magurran 1988; Wilson et al. 1998). Here it represents the null model for competing species. The RAM is a bottom-up model (as is the broken-stick), which leads to distributions in the lognormal to power range based on simple rules of competition (i.e. the pattern emerges from rules affecting the bottom level of system integration such as the individual species, Halloy 1998). METHODOLOGY New Zealand was chosen as a valuable case history for crop dynamics as it has a relatively short, but well documented, history of crop introductions and is well known for its development of some high value new crops. In addition, it is physically bounded by the ocean, providing a naturally defined microcosm. All statistics gathered by the Government of New Zealand from 1842 to 1990 on the area covered by cultivated plants were collected and analyzed. Data were pooled by decades. Minimum sample size considered in the statistics has varied from 0.1 to 4 ha (see Halloy 1994 for details). Species were ranked by abundance and frequency distributions were obtained and standardized by area and species. The change in distribution for 1981­90 was tested against predictions based on an average distribution over 150 years, a fitted lognormal and a resource attraction model. The resource attraction model utilized the following conditions: Total resources, 1981: 1,445,858 ha Total resources, 1990: 1,764,922 ha Number of species: 136 Number of sites: 280 + 20 boundary sites Arrangement of species: Random among 280 sites New resources: Rain of resource particles of random size, varying 80% around the mean. Particles refer to a finite quantity or portion of resources, in this case for example a number of hectares.

*The present study was made possible through the support of the New Zealand Institute for Crop & Food Research and the New Zealand Foundation for Research, Science and Technology New Crop program.


Mean resource particle: Minimum species abundance: Number of links: Number of steps: Loss: Distance exponent:

Actual increase 1981­1990/10 years/136 spp. Maximum particle size (i.e. mean +80%) 20 (10 each side) 20 (equivalent to 20 half years) 0.9% of each species at each step 2, fixed. This is the exponent to which the virtual distances between particles is elevated, see Halloy (1998).

GROWING CULTIVATED AREA, DECREASING DIVERSITY During the last 150 years the total cultivated area rises steadily, then slowly levels off (Fig. 1). Sown pastures represent developed areas for which species-specific statistics are unavailable. Species in the remaining areas are divided by the government census into three major functional groups or guilds: field crops, forestry, and orchards. Field crops include annual crops (cereals, pulses, tubers, vegetables), fodder, ornamental, and industrial crops. The number of species (squares) recorded forms a sigmoid curve, which is still rising today although more slowly than in previous decades (Fig. 2). However, a Shannon-Weaver diversity index (triangles) rises steadily to 1951, then falls dramatically. This is largely due to the dominance of a single forestry species, radiata pine (Pinus radiata, Pinaceae) (Halloy 1994). RESULTS Dynamics Crop abundance, as expressed by the proportional area covered, has varied dynamically over the 150 years of record (Fig. 3). Crops arise from nothing, stay around or become abundant for some time then, in turn, disappear, becoming "extinct" at the given scale. The dynamics are reminiscent of other dynamic systems such as the fossil record, where stochastic explanations (Raup 1981) and self-organization (Solé et al. 1997) have been invoked. Stochastic explanations argue that these patterns are the result of random variations in abundance and branching patterns between taxa. Selforganization postulates that such patterns arise from simple rules of interaction multiplied by innumerable individuals in a complex system. In our case, external determinants are also apparent at the level of functional groups: first the dominance of potato and wheat relating to the need to feed the new population; then a prolonged period of dominance of feed crops, to feed the working horse; finally the rise and dominance of longer lived timber crops. Rank Shifting The shading in Table 1 shows the percentage area covered by each crop every decade. Each of the 10 highest ranking species in 1990 covered more than 1% of the cultivated land area. Only four of these (oat, wheat, turnip, barley) were as

1E7 sown grasses 1E6 1E5 1E4 1E3 1E2 1E1 1840 1860 1880 1900 field crops

Area (ha)

forest plantations orchards



1960 1980 2000


Fig. 1. Growth in cultivated area of functional crop groups.

140 120 3

No. cultivated species

100 80


2 60 40 20 0 1840 1 2000 1.5

Fig. 2. The rise and fall of crop diversity (Halloy 1994). 54




Diversity index

important in 1891. Of the next 10, each covering areas of 0.1% or more in 1990, only five covered 0.1% or more in 1891. The average life cycle of a species is 10 years for abundances above 1% of all cultivated areas. The longest lasting species has been barley, persisting for 150 years between 1 and 10%. Only one species (radiata pine), for one decade, surpassed 60% abundance. Only five species have ever surpassed the 20% mark (radiata pine for 4 decades, wheat 6, oats 8, potato 1, maize 1). Abundance Patterns The abundance-rank distribution of New Zealand crops expressed on a log-log scale repeats similar patterns over time (Fig. 4). A choice of a different cut-off point for the minimum cultivated areas could fit the series to a single straight line, that is, there are long segments within each time cut which are straight. Straight lines on a log-log scale represent power distributions, a signature of self-organized criticality (Bak et al. 1988), and are found to be widespread in natural complex systems (Zipf 1949; Bak 1997). However, when considered in their entirety, these curved log-log representations of abundance distribution correspond to the lognormal distribution on a frequency-abundance representation (Fig. 6). Each economic grouping of crops shows an abundance-rank distribution similar to the total but varying in slope (Fig. 5). The more diverse and stable groups (fruit and field crops) show the lesser slopes. The frequency-abundance distribution of crops resembles a lognormal distribution for the 88 "macroeconomic" species (Fig. 6). The 49 minor species on the left are separated by a wide gap. Although only 1990 is illustrated, this pattern was maintained with only slight alterations throughout the 150 years studied. Within the macro-economic species irregularities are partly due to historical contingencies and partly to the fact that the system is composite and made up of several functionally distinct groups, as seen above. If there is a regular trend toward a lognormal it should be possible to predict, within some confidence limits, the development of the abundance distribution over time. The change in abundance distributions between 1981 and 1990 was tested against three predictions: 1) the average of the distributions over 150 years, 2) the lognormal fitted to 1981, and 3) a resource attraction model (RAM). The changes predicted by these three models are compared to the actual changes from 1981 to 1990 in Fig. 7. The resource attraction model approximates the actual change most closely (Chi square of 0.80 as opposed to 1.33 for the lognormal and 3.73 for the average model).

Fig. 3. Abundance dynamics of the 14 highest ranking crops in 1990. Radiata pine, Pinus radiata D. Don, Pinaceae; douglas fir, Pseudotsuga taxifolia Britt., Pinaceae; ponderosa pine, Pinus ponderosa Dougl., Pinaceae; corsican pine, Pinus nigra Arnold, Pinaceae; barley, Hordeum vulgare L., Gramineae; turnips, Brassica rapa L., Brassicaceae; wheat, Triticum aestivum L., Gramineae; brassica, Brassica oleracea L., Brassicaceae; peas, Pisum sativum L., Fabaceae; oats, Avena sativa L., Gramineae; maize, Zea mays L., Gramineae; potato, Solanum tuberosum L., Solanaceae; lucerne, Medicago sativa L., Fabaceae; swedes, Brassica napus L., Brassicaceae.


Table 1. New Zealand cultivated plants ranked by abundance. Shading indicates percent of cultivated area covered by each crop. Numbers indicate the rank order of the cultivated area of each crop for the given year (1= most abundant).



SUMMARY AND CONCLUSION The number of crop species in New Zealand has increased over time and seems to be reaching an asymptote while crop diversity (as measured by diversity indices) has increased then decreased in the last four decades. Crop abundances show dynamic trends similar to other complex systems including the fossil record, with emergence of new crops, a period of economic success, and eventual decline. Effective life spans of crop cultivars in many species are around 5 years (4­10 for wheat, Brennan and Byerlee 1991), equivalent to a depreciation of the present value of crop cultivars by 7% per year (Swanson 1996). The New Zealand data suggests that a similar dynamic is operating at the species level, with species having effective life spans (as important species covering more than 1% of cultivated area) of around 10 years. Out of the 20 major economic species present in New Zealand today, which account for more than 98% of the planted area, 11 have had to be developed from "new" crops within the last 100 years. This includes the largest export earners renowned as examples of new crop development such as radiata pine and kiwifruit, which were practically unknown in 1891. Conversely, of the 20 most important crops in 1891, eight are now minor crops. The turnover of the most abundant species is 3%­33% per decade (Halloy 1994). In New Zealand up to 20 new crops need to be developed to become macro-economic species every decade while one at least is likely to become one of the 20 most important species. Both persistence and dynamics are important economically. The aggregation over time of species which have produced relatively short economic booms (e.g. linen flax, kiwifruit) is as important to a vigorous economy as those rarer species which persist for long periods at lower levels (e.g. barley). Functional economic groups follow similar patterns of abundance distribution as all the species at a range of scales. In every period the abundance distribution shows a grouping of major macro-economic speCultivated area (% of category)


Relative cultivated area (%)

100 spp. timber 21 fruit 41 field crops44 industrial 8 fodder 13 ornamental10










0.01 1









Fig. 4. Abundance-rank distribution of New Zealand crops expressed on a log-log scale for 1871 to 1990.


Fig. 5. Abundance-rank by functional crop groups.



lognormal fit

Absolute difference predicted-actual


average 150 y lognormal 15 RAM

No. of species

30 20 10 0



0.02 0.13 1


64 512



0.02 0.13




Area covered (ha) in octaves

Relative cover (octaves) %

Fig. 6. Frequency-abundance of New Zealand cultivated plants.

Fig. 7. Difference of real changes to predictions.


cies that is very distinct from that of minor species (Fig. 6). This break or boundary suggests an objective threshold which may be used to define "successful" species. The abundance distribution of crops approximates the well known power and lognormal functions. This regularity provides an objective yardstick against which to interpret and analyze the diversity and dynamics of cropping systems. The comparison of actual abundance patterns with fitted lognormal or power distributions provides interesting diagnostic tools which may have potential for measuring properties such as stability, persistence, sustainability, resilience, or susceptibility to disturbance (Frontier 1985; Halloy 1997; Kevan et al. 1997). Projections based on the lognormal distribution and a resource attraction model show that patterns of crop relative abundances may be predictable. The resource attraction model provided a closer fit than a top-down fitted lognormal model. This may be due to the fact that the RAM model is sensitive to actual resource increase, producing a pattern which emerges from simple rules. A dynamic flow of crops has been maintained in the past by accessing new germplasm from abroad. All of our economically important species have been obtained from unsung global reservoirs of biodiversity, and return to them when they fall out of favor. Present large scale extinctions imply that we should not be complacent about the permanence of this essential resource. REFERENCES Bak, P. 1997. How nature works. The science of self-organized criticality. Oxford Univ. Press, Oxford. Bak, P., C. Tang, and K. Wiesenfeld. 1988. Self-organized criticality. Physical Rev. A 38(1):364­374. Brennan, J.P. and D. Byerlee. 1991. The rate of crop varietal replacement on farms, measures and empirical results for wheat. Plant Varieties & Seeds 4:99­106. Frontier, S. 1985. Diversity and structure in aquatic ecosystems. Oceanography and Marine Biology Annu. Rev. 23:253­312. Halloy, S. 1994. Long term trends in the relative abundance of New Zealand agricultural plants. Otago Conference Series 2:125­141. Halloy, S. 1997. Ecosystem disturbance indicators: keystone species and structure of biodiversity. p. 73­81. In: M. Liberman and C. Baied (eds.), Sustainable development of mountain ecosystems: Management of fragile areas in the Andes (in Spanish). UNU and PL-480, La Paz, Bolivia. Halloy, S.R.P. 1998. A theoretical framework for abundance distributions in complex systems. Complexity International 6. Kevan, P.G., C.F. Greco, and S. Belaousoff. 1997. Log-normality of biodiversity and abundance in diagnosis and measuring of ecosystemic health: pesticide stress on pollinators on blueberry heaths. J. Appl. Ecol. 34:1122­1136. Magurran, A.E. 1988. Ecological diversity and its measurement. Princeton Univ. Press, Princeton, NJ. May, R.M. 1981. Patterns in multi-species communities. p. 197­227. In: R.M. May (ed.), Theoretical ecology, principles and applications. 2nd ed. Blackwell Scientific Publications, London. Preston, F.W. 1948. The commonness, and rarity, of species. Ecology 29:254­283. Preston, F.W. 1962. The canonical distribution of commonness and rarity. Ecology 43:185­215, 410­432. Raup, D.M. 1981. Probabilistic models in evolutionary paleobiology. p. 51­58. In: B.J. Skinner (ed.), Paleontology and paleoenvironments. William Kaufmann Inc., Los Altos, CA. Solé, R.V., S.C. Manrubia, M. Benton, and P. Bak. 1997. Self-similarity of extinction statistics in the fossil record. Nature 388:764­767. Sugihara, G. 1980. Minimal community structure: An explanation of species abundance patterns. Am. Naturalist 116: 770­787. Swanson, T. 1996. Global values of biological diversity: the public interest in the conservation of plant genetic resources for agriculture. Plant Genetic Resources Newslett. 105:1­7. Wilson, B.J., H. Gitay, J.B. Steel, and W.M. King. 1998. Relative abundance distributions in plant communities: effects of species richness and of spatial scale. J. Vegetation Sci. 9:213­220. Zipf, G.K. 1949. Human behavior and the principle of least effort: An introduction to human ecology. AddisonWesley, Cambridge, MA.




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