years before Bernoulli’s essay eventuallyappeared in print. Bernoulli’s motivation toadd this formula in the final version(prepared in 1765) was explicitly to showthe superiority of his ‘exact’ approach overthe crude estimate of d’Alembert, accordingto whom the proportion of susceptibleindividuals was “much less than half”.

The reason why Bernoulli’s importantformula has escaped notice for so long maybe its cryptic presentation: one has torecover it by substituting his numericalvalues with their general symbols. Informulating his laudable objectives,however, he is admirably clear: “I simplywish that, in a matter which so closelyconcerns the well-being of mankind, nodecision shall be made without all theknowledge which a little analysis andcalculation can provide.”Klaus Dietz*, J. A. P. Heesterbeek†*Department of Medical Biometry, University ofTübingen, 72070 Tübingen, Germany†Centre for Biometry, PO Box 16, 6700 AAWageningen, The Netherlands1. Bernoulli, D. Mém. Math. Phys. Acad. R. Sci. Paris 1–45 (1766);

English translation by Bradley, L. in Smallpox Inoculation: An

Eighteenth Century Mathematical Controversy (Adult

Education Department, Nottingham, 1971).

2. Anderson, R. M. & May, R. M. Infectious Diseases of Humans —

Dynamics and Control (Oxford University Press, Oxford,

1991).

3. Dietz, K. Stat. Meth. Med. Res. 2, 23–41 (1993).

4. D’Alembert, J. Opuscules Mathématiques, t. II (Paris, David,

1761).

Aquaculture: part of theproblem, not a solutionSir — Aquaculture is claimed to aid theproduction of large quantities of low-costprotein-rich food to help feed the world,and to diminish pressure on oceanfisheries. In our opinion, neither of theseclaims is justified.

First, except in some parts of Asia, themain purpose of aquaculture has been toproduce a luxury product for those whocan afford to pay high prices. Second,Naylor et al.1 analysed the consequences ofaquaculture practices and indicated thatthe growth of global production of farmedfish and shellfish will not relieve pressureon ocean fisheries.

Naylor et al. also indicated thataquaculture can diminish world fisheriesindirectly by habitat modification,collection of wild seedstock, food-webinteraction, nutrient pollution and theintroduction of exotic species. However, inthis last factor the authors referred only topossible hybridization between farmescapees and wild populations of Atlanticsalmon, and to the spreading of pathogens.We believe it is also necessary to considerother consequences of introducing non-indigenous organisms, such as the

elimination of autochthonous species byaltering food webs, competition,hybridization and so on.

For scientists in developing countriessuch as ourselves, this point is of greatimportance. We would like to call to theattention of international organizationssuch as the World Bank, the InternationalDevelopment Bank and the Food andAgriculture Organization (FAO) the needto stop promoting aquaculture as a meansof obtaining income from exports, and toconcentrate on producing food for poorpeople. These organizations should stoppromoting technological packages usingexotic species and instead help thedevelopment of culture technologies fornative species with the potential foraquaculture.

To give some examples: the FAOapproved a technical cooperation projectin Venezuela to genetically improve redtilapia, an unnecessary waste of resourcesthat was a total failure2. The InternationalDevelopment Bank is partially financing aprogramme3 to culture exotic species inPanama, including the scallops Argopectenpurpuratus, the cachamas Colossomamacropomus and Piaractus brachipomus,the channel catfish Ictalurus punctatus, theSergeant or Peacock bass cichlid Cichlaocellaris, the giant prawn Macrobrachiumrosenbergii and the bullfrog Ranacatesbiana.

The World Bank finances severalprogrammes in Latin America (seehttp://www.worldbank.org) introducingspecies such as Litopenaeus vannamei andL. stylirostris into countries where they donot occur naturally. In one Honduranproject, the World Bank claims there is norisk of introducing alien species becausethe shrimps L. vannamei and L. stylirostrisoccur naturally there, in the Gulf ofFonseca. But it does not mention the risk ofintroducing alien species in a Venezuelanproject which also uses L. vannamei,although they are not native to that region.

Aquaculture can make unique contri-butions to world nutrition, thanks to itsextremely high productivity in manysituations and to the fact that aquatic cropsare primarily protein rather than starch.Certain aquatic organisms may be better atconverting primary foods than ruminants,fowl or even pigs. Some, such as filter-feeding fishes and molluscs, feed onmicroscopic plankton that cannot be useddirectly for human food.

However, if the aquaculture industry isgoing to reduce the pressure on wild fishstocks and provide food for the world’sgrowing population, substantial changesmust be made by governments, the privatesector and international funding agencies.They must protect coastal ecosystems;promote research and development of

native species; and encourage farming oflow-trophic-level fish — those low on thefood chain. International technicalfunding agencies can exert great influence in changing practices.Otherwise, as Naylor et al. point out, anexpanded aquaculture industry poses athreat, not only to ocean fisheries, but also to itself.Julio E. Pérez* , Mauro Nirchio†, Juan A. Gomez‡*Instituto Oceanografico, Universidad de Oriente,Cumaná, Venezuela†Escuela de Ciencias Aplicadas del Mar,Universidad de Oriente, Isla de Margarita,Venezuela‡Centro de Ciencias del Mar y Limnológia,Universidad de Panamá, Panamá1. Naylor, R. L. et al. Nature 405, 1017–1024 (2000).

2. Perez, J. E., Gomez, A. & Nirchio, M. Interciencia 24, 321–323

(1999).

3. Programa de Modernización de Servicios Agropecuarios.

Componente Acuicultura (Inter-American Development

Bank, Panamá, 1995). http://www.iadb.org/EXR/doc98/

apr/lcpanaq.htm

Funding would preventwaste of research timeSir — It has become clear over the lastdecade that doing research in Spain is quitea heroic task (see, for example, Nature 407,428 & 941; 2000). Poor funding and lack ofprospects for young researchers are amongthe many obstacles that have precluded therise of Spanish science to the very top.Although an increase in the amount ofmoney devoted to research is an obvious prerequisite, the many problems thatyoung investigators face haven’t beenanalysed in detail.

A numerical comparison with our EUcounterparts (not to mention with theUnited States and Japan) shows the need tocreate positions to absorb many of theexcellently trained postdocs that Spain hassent abroad during the past 15 years. Butnobody is discussing the conditions underwhich these new hirings should take place.The fact is that Spain has no policy ofproviding start-up packages for the newlyhired group leaders. This has unfortunateconsequences, as new researchers sit intheir offices (if they have offices) and beginchasing grants for a period of up to threeyears, losing all continuity with theirresearch projects.

If Spain is to have a core of younginvestigators doing science at its best, thesescientists should be provided not just withpositions but also with funding forresearch. Otherwise, talent is wasted, again.Pedro MartínezDepartment of Anatomy and Cell Biology,University of Bergen, Aarstadveien 19, 5009 Bergen, Norway

correspondence

514 NATURE | VOL 408 | 30 NOVEMBER 2000 | www.nature.com© 2000 Macmillan Magazines Ltd