Paradox of the pesticides
Encyclopedia
The paradox of the pesticides is a paradox
that states that by applying pesticide
to a pest, one may in fact increase its abundance
. This happens when the pesticide upsets natural predator-prey dynamics in the ecosystem.
The paradox can only occur when the target pest has a naturally occurring predator that is equally affected by the pesticide, and therefore presents a case for more specialized pesticide products.
, a set of first-order, non-linear, differential equations that are frequently used to describe predator-prey interactions, can be modified to account for the additions of pesticides into the predator-prey interactions.
The following two equations are the original Lotka-Volterra equation
that describe the rate of change of each respective population as a function of the other organism’s population.
The variables represent the following:
By setting each equation to zero, and thus assuming a stable population, a graph of two lines (isocline
s) can be made to find the equilibrium point, or the point at which both interacting populations are stable.
The isocline
s for the two above equations are:
and 
Accounting for Pesticides
Now, to account for the difference in the population dynamics of the predator and prey that occurs with the addition of pesticides we add the variable of q to represent the per capita rate at which both species are killed by the pesticide. The original Lotka-Volterra equations change as follows:
Solving the isocline
s as we did above we find the following equations to represent the two lines with the intersection that represents the new equilibrium point. The new isocline
s for the populations are:
and 
As one can see from the new isocline
s the new equilibrium will have a higher H value and a lower P value. This means that the number of prey will increase while the number of predator decreases. This means that the prey, which is normally the targeted by the pesticide, is actually being benefited instead of harmed by the pesticide.
, for example, naturally prey upon phytophagous mites, which are common pests in apple orchards. Spraying the orchards kills both mites, but the effect of diminished predation is larger than the pesticide’s, and phytophagous mites increase in abundance.
The effect has also been seen on rice, as documented by the International Rice Research Institute
, which noted significant declines in pest populations when they stopped applying pesticide.
Intraspecific competition
increases with density
. One could expect that a population decrease (due to harvesting, for example) will decrease the population density and reduce intraspecific competition, which would lead to a lower death rate among the prey population.
Studies show furthermore that direct effects on the predator population, through harvesting of the prey, are not necessary to observe the paradox. Harvesting of prey has been shown to trigger a reduction in the predator’s reproduction rate, which lowers the equilibrium predator level. Thus, changes in life history
strategy (patterns of growth, reproduction and survivorship) can also contribute to the paradox.
Seemingly then, the paradox can be accounted for by the indirect effects of harvesting on the native ecological interactions of prey and predator: reduction of intraspecific density effect for the prey, and reduction of the reproductive rate for the predator. The first effect increases the population recovery of the prey, and the second decreases the equilibrium population level for the predator.
(IPM), an ecological approach to pest control that accounts for the interactions between pests and their environment. There is no one way to practice IPM, but some methods include using mechanical trapping devices or increasing the abundance of natural predators.
IPM is also often touted for its environmental and health benefits, as it avoids the use of chemical pesticides.
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...
that states that by applying pesticide
Pesticide
Pesticides are substances or mixture of substances intended for preventing, destroying, repelling or mitigating any pest.A pesticide may be a chemical unicycle, biological agent , antimicrobial, disinfectant or device used against any pest...
to a pest, one may in fact increase its abundance
Abundance
Abundance may refer to:In science and technology:* Abundance , the opposite of scarcities* Abundance , growing food with plentiful resources that will not run out -- sunshine, CO2, and waste or brine water....
. This happens when the pesticide upsets natural predator-prey dynamics in the ecosystem.
The paradox can only occur when the target pest has a naturally occurring predator that is equally affected by the pesticide, and therefore presents a case for more specialized pesticide products.
The Model: Lotka-Volterra equation
To describe the Paradox of the Pesticides mathematically, the Lotka-Volterra equationLotka-Volterra equation
The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order, non-linear, differential equations frequently used to describe the dynamics of biological systems in which two species interact, one a predator and one its prey...
, a set of first-order, non-linear, differential equations that are frequently used to describe predator-prey interactions, can be modified to account for the additions of pesticides into the predator-prey interactions.
The following two equations are the original Lotka-Volterra equation
Lotka-Volterra equation
The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order, non-linear, differential equations frequently used to describe the dynamics of biological systems in which two species interact, one a predator and one its prey...
that describe the rate of change of each respective population as a function of the other organism’s population.
The variables represent the following:
- H- the prey population at a given time
- P- the predator population at a given time
- c- the capture constant
- r- the rate of growth of the prey population
- a- the fraction of prey energy assimilated by the predator & turned into new predators
- m- predator mortality rate
By setting each equation to zero, and thus assuming a stable population, a graph of two lines (isocline
Isocline
thumb|right|300px|Fig. 1: Isoclines , slope field , and some solution curves of y'=xyAn Isocline is a curve through points at which the parent function's slope will always be the same, regardless of initial conditions...
s) can be made to find the equilibrium point, or the point at which both interacting populations are stable.
The isocline
Isocline
thumb|right|300px|Fig. 1: Isoclines , slope field , and some solution curves of y'=xyAn Isocline is a curve through points at which the parent function's slope will always be the same, regardless of initial conditions...
s for the two above equations are:
and Accounting for Pesticides
Now, to account for the difference in the population dynamics of the predator and prey that occurs with the addition of pesticides we add the variable of q to represent the per capita rate at which both species are killed by the pesticide. The original Lotka-Volterra equations change as follows:
Solving the isocline
Isocline
thumb|right|300px|Fig. 1: Isoclines , slope field , and some solution curves of y'=xyAn Isocline is a curve through points at which the parent function's slope will always be the same, regardless of initial conditions...
s as we did above we find the following equations to represent the two lines with the intersection that represents the new equilibrium point. The new isocline
Isocline
thumb|right|300px|Fig. 1: Isoclines , slope field , and some solution curves of y'=xyAn Isocline is a curve through points at which the parent function's slope will always be the same, regardless of initial conditions...
s for the populations are:
and As one can see from the new isocline
Isocline
thumb|right|300px|Fig. 1: Isoclines , slope field , and some solution curves of y'=xyAn Isocline is a curve through points at which the parent function's slope will always be the same, regardless of initial conditions...
s the new equilibrium will have a higher H value and a lower P value. This means that the number of prey will increase while the number of predator decreases. This means that the prey, which is normally the targeted by the pesticide, is actually being benefited instead of harmed by the pesticide.
Empirical Evidence
The paradox has been documented repeatedly throughout the history of pest management. Predatory mitesMITES
MITES, or Minority Introduction to Engineering and Science, is a highly selective six-week summer program for rising high school seniors held at the Massachusetts Institute of Technology. Its purpose is to expose students from minority, or otherwise disadvantaged backgrounds, to the fields of...
, for example, naturally prey upon phytophagous mites, which are common pests in apple orchards. Spraying the orchards kills both mites, but the effect of diminished predation is larger than the pesticide’s, and phytophagous mites increase in abundance.
The effect has also been seen on rice, as documented by the International Rice Research Institute
International Rice Research Institute
The International Rice Research Institute is an international NGO. Its headquarters are in Los Baños, Laguna, Philippines, and it has offices in sixteen countries...
, which noted significant declines in pest populations when they stopped applying pesticide.
Related Phenomena
Recent studies suggest that such a paradox might not be necessarily caused by the reduction of the predator population due to harvesting itself, for example, by a pesticide. The host population is reduced at the moment of harvesting, and simultaneously the intraspecific density effect is weakened. Intraspecific competition accounts for the competition between individuals of a same species. When the population density is high, and resources are consequently relatively scarce, each individual has less access to resources to invest energy in growth, survivorship and reproduction. This causes a decrease in the survival rate, or an increase in mortality.Intraspecific competition
Intraspecific competition
Intraspecific competition is a particular form of competition in which members of the same species vie for the same resource in an ecosystem...
increases with density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
. One could expect that a population decrease (due to harvesting, for example) will decrease the population density and reduce intraspecific competition, which would lead to a lower death rate among the prey population.
Studies show furthermore that direct effects on the predator population, through harvesting of the prey, are not necessary to observe the paradox. Harvesting of prey has been shown to trigger a reduction in the predator’s reproduction rate, which lowers the equilibrium predator level. Thus, changes in life history
Biological life cycle
A life cycle is a period involving all different generations of a species succeeding each other through means of reproduction, whether through asexual reproduction or sexual reproduction...
strategy (patterns of growth, reproduction and survivorship) can also contribute to the paradox.
Seemingly then, the paradox can be accounted for by the indirect effects of harvesting on the native ecological interactions of prey and predator: reduction of intraspecific density effect for the prey, and reduction of the reproductive rate for the predator. The first effect increases the population recovery of the prey, and the second decreases the equilibrium population level for the predator.
Implications
The Paradox of the Pesticides implies the need for more specialized pesticides that are tailored to the target pest. If the pesticide can effectively reduce only the prey population, the predator population will remain largely unaffected except for the change in its food supply. Broad spectrum pesticides are more likely to induce the Paradox and cause an increase in target pest population by killing its predators as well. In certain cases, however, where the predator is closely related to the target pest even narrow spectrum pesticides may be insufficient.Solutions
To deal with the Paradox of the Pesticides, growers may turn to Integrated Pest ManagementIntegrated Pest Management
Integrated pest management is an ecological approach to agricultural pest control that integrates pesticides/herbicides into a management system incorporating a range of practices for economic control of a pest...
(IPM), an ecological approach to pest control that accounts for the interactions between pests and their environment. There is no one way to practice IPM, but some methods include using mechanical trapping devices or increasing the abundance of natural predators.
IPM is also often touted for its environmental and health benefits, as it avoids the use of chemical pesticides.
See also
- Paradox of enrichmentParadox of enrichmentThe paradox of enrichment is a term from population ecology coined by Michael Rosenzweig in 1971. He described an effect in six predator-prey models wherein increasing the food available to the prey caused the predator's population to destabilize...
: Increasing the food available to an ecosystem may introduce instability, and may even lead to extinction.