Question

Can Malaria Parasites Control Mosquito Behavior? Are malaria parasites able to control mosquito behavior to their advantage? A study \(^{43}\) investigated this question by taking mosquitos and giving them the opportunity to have their first "blood meal" from a mouse. The mosquitoes were randomized to either eat from a mouse infected with malaria or an uninfected mouse. At several time points after this, mosquitoes were put into a cage with a human and it was recorded whether or not each mosquito approached the human (presumably to bite, although mosquitoes were caught before biting). Once infected, the malaria parasites in the mosquitoes go through two stages: the Oocyst stage in which the mosquito has been infected but is not yet infectious to others and then the Sporozoite stage in which the mosquito is infectious to others. Malaria parasites would benefit if mosquitoes sought risky blood meals (such as biting a human) less often in the Oocyst stage (because mosquitos are often killed while attempting a blood meal) and more often in the Sporozoite stage after becoming infectious (because this is one of the primary ways in which malaria is transmitted). Does exposing mosquitoes to malaria actually impact their behavior in this way? (a) In the Oocyst stage (after eating from mouse but before becoming infectious), 20 out of 113 mosquitoes in the group exposed to malaria approached the human and 36 out of 117 mosquitoes in the group not exposed to malaria approached the human. Calculate the Z-statistic. (b) Calculate the p-value for testing whether this provides evidence that the proportion of mosquitoes in the Oocyst stage approaching the human is lower in the group exposed to malaria. (c) In the Sporozoite stage (after becoming infectious), 37 out of 149 mosquitoes in the group exposed to malaria approached the human and 14 out of 144 mosquitoes in the group not exposed to malaria approached the human. Calculate the z-statistic. (d) Calculate the p-value for testing whether this provides evidence that the proportion of mosquitoes in the Sporozoite stage approaching the human is higher in the group exposed to malaria. (e) Based on your p-values, make conclusions about what you have learned about mosquito behavior, stage of infection, and exposure to malaria or not. (f) Can we conclude that being exposed to malaria (as opposed to not being exposed to malaria) causes these behavior changes in mosquitoes? Why or why not?

Short answer

The Z-statistics and p-values show that there can be a change in the behavior for the group of mosquitoes exposed to malaria in both Oocyst and Sporozoite stages. However, while there is statistical association, it does not imply causation and further study is needed.

Step-by-step solution

Calculating the Z-Statistic (Oocyst stage)

First, calculate the proportion of mosquitoes approaching humans in both Exposure Groups (Malaria and non-Malaria) as \(p_1=20/113\) and \(p_2=36/117\), respectively. Then, calculate the standard error as \(\sqrt{[(p_1*(1-p_1)/113)+(p_2*(1-p_2)/117)]}\). Lastly, compute the Z- statistic as \((p_1-p_2) / standard \ error\)

Calculating the p-value (Oocyst stage)

Use the calculated Z-statistic and a standard normal (Z) table or a software to find the p-value which is the probability that the Z-statistic is lower than the calculated value given that the null hypothesis is true.

Calculating the Z-Statistic (Sporozoite stage)

Using the same methodology as the Oocyst stage, calculate the proportion of mosquitoes approaching humans in both Exposure Groups (Malaria and non-Malaria) as \(p_1=37/149\) and \(p_2=14/144\), respectively. Then, calculate the standard error as \(\sqrt{[(p_1*(1-p_1)/149)+(p_2*(1-p_2)/144)]}\). Lastly, compute the Z- statistic as \((p_1-p_2) / standard \ error\)

Calculating the p-value (Sporozoite stage)

Use the calculated Z-statistic and a standard normal (Z) table or software to find the p-value which is the probability that the Z-statistic is higher than the calculated value given that the null hypothesis is true.

Drawing conclusions from p-values

Use the calculated p-values from Steps 2 and 4 to draw conclusions. If the p-value is less than a predetermined significance level of 0.05, we reject the null hypothesis and conclude that there is statistical evidence showing that the proportion of mosquitoes approaching the human is lower in the Oocyst stage for the group exposed to malaria and higher in the Sporozoite stage for the group exposed to malaria.

Establishing causality or correlation

Causality should not be assumed simply through statistical evidence. Further study is needed to determine whether the exposure to malaria causes these changes in behavior.