Readings Seminar
4 Dec 2003
Levins (1969)
LAJ
Levins, Richard. (1969) Some demographic and genetic consequences of environmental heterogeneity for
biological control. Entomological Soc of Amer Bulletin 15(3)1:237-240.
At publication: Committee on Mathematical Biology and Biology Department, University of Chicago
Current: Department of Population and International Health, Harvard School of Public Health
http://www.hsph.harvard.edu/facres/lvns.html
This paper uses metapopulation modeling to assess different strategies of biological pest control by using predators
to affect the extinction rate or migration rate of the pest population. The most effective control can only be achieved
when the strategy considers the biology of the crop and the control organisms as well as the pest.
The graph illustrates a simple relationship between migration, extinction, and N (number of individuals). At very
high N (to the right of the graph), a given change in extinction changes N very little since migration increases
steeply to compensate. As the migration rate levels off in the middle, N changes more with a given change in
extinction, and at the far left, N will reach zero (the population will disappear) if extinction exceeds migration.
Extinction-Based Control:
If extinction varies in time then N will fluctuate. The probability distribution of this fluctuating N will peak at:
Where T=time, m=migration, E=extinction, σE2=variance of extinction. Therefore, the best control will be achieved
when the extinction rate is most variable in time. If the factors affecting extinction vary independently through
space, then local fluctuations will cancel out, and the overall variance will be small. Control will be most effective
if the control organism is uniform in space and variable in time.
Readings Seminar
4 Dec 2003
Levins (1969)
LAJ
Migration-Based Control:
A rough relation of migration and distance is given by:
Where m=migration into a distance plot, m0=migration into an adjacent plot, D=distance to the non-adjacent plot,
and a=constant depending on how migration changes with distance (undefined here). Simply put, this equation
compares the time to reinfestation of a pest from an infested plot to an adjacent non-infested plot to the time to
reinfestation of a more distance plot. Therefore, as D increases, time to reinfestation will increase. In this case, the
most effective control measure would not be uniform in space, but rather would attempt to eliminate specific patches
so as to increase the distance between plots to prevent reinfestation by preventing migration between remaining
infested patches.
Summary of above – strategies are not the same for extinction based and migration based control.
Recommendations for control strategies will be different depending on the approach used and the specific
circumstanced in the region of infestation.
Likewise for local dynamics:
The equation is the same in form as above, with different terms:
Where x=local prey population size, r=intrinsic rate of increase of prey population, k=carrying capacity, p=predation
rate by control organism, σp2=variance of predation rate. As above, extinction will be greatest when the rate of
predation is most variable.
Interesting point – a predator should be chosen such that it is adapted to function best in the conditions at the
beginning of the season. Therefore, it may be best to choose a predator from a location outside the local region. In
other words, if the locally native predators are most active and effective midseason, they will not be most effective
for control (according to this paper). Rather, collect the predator from a climate that most closely resembles the
conditions at the beginning of the growing season of the local region needing control.
Richard Levins is an ex-tropical farmer turned ecologist, biomathematician and philosopher of science whose central
intellectual concern has been the understanding and influencing of processes in complex systems, both abstractly
and as applied to evolutionary ecology, economic development, agriculture and health. He has carried out this
program at the theoretical level by framing the problems of adaptation to the structure of the environment in space
and time, the metapopulation concept for interpreting populations in biogeography, human physiology as a
socialized physiology, and the interpenetration of model building as juggling the partially opposing requirements of
realism, generality and precision.
A major goal is the integration of evolutionary ecology and critical social theory into a broad epidemiology that can
prepare for surprises. Current research examines the variability of health outcomes as an indicator of vulnerability to
multiple non-specific stressors in human communities, interactions among herbivores and their natural enemies in
Readings Seminar
4 Dec 2003
Levins (1969)
LAJ
multispecies systems on citrus trees, and short term (transient) dynamics of model epidemiological and pathological
systems.
His theoretical interests have been applied to problems of community development as part of the Board of Directors
of OXFAM-America and chair of their subcommittee on Latin America and the Caribbean from 1989 to 1995.
Working from a critique of the industrial-commercial pathway of development, he promoted alternative
development pathways that emphasize economic viability with equity, ecological and social sustainability and
empowerment of the dispossessed. As part of the New World Agriculture and Ecology Group, he has helped to
develop modern agroecology, concentrating on the whole-system approaches to gentle pest management. The
"Dialectical Biologist," co-authored with Richard Lewontin, presented the authors' approach to the study of the
philosophy, sociology and history of science.
He studied plant breeding and mathematics at Cornell University, farmed in Puerto Rico and obtained his doctorate
in zoology from Columbia University. He has taught at the University of Puerto Rico and the University of Chicago
before coming to his present position as John Rock Professor of Population Sciences at the Harvard School of Public
Health. Levins is currently on the Advisory Board of the International Society for Ecosystem Health and is a
member of the American Academy of Arts and Sciences. He has received awards as a pioneer of the ecology
movement of Puerto Rico, for his long term contributions to the development of ecological agriculture in Cuba, and
the Edinburgh Science Medal (Scotland) for contributions to science and the broader society. He has received
awards as a pioneer of the ecology movement in Puerto Rico, for long term contributions to the development of
agricultural ecology in Cuba, the Edinburgh Science Medal(Scotland) for contributions to science and the broader
society, the Lukacs 21st Century Award for contributions to statistical and mathematical ecology, and an honarary
doctorate in environmental science from the University of Havana.