Oh, I didn’t mean for you to define the period explicitly as a fixed interval period. I assume this can vary by catastrophe. Like maybe population declines over 5 years with massive crop failures. Or, an engineered pathogen causes massive population decline in a few months.
I just wasn’t sure what exactly you meant. Another intepretation would be that P_f is the total post-catastrophe population, summing over all future generations, and I just wanted to check that you meant the population at a given time, not aggregating over time.
Oh, I didn’t mean for you to define the period explicitly as a fixed interval period. I assume this can vary by catastrophe. Like maybe population declines over 5 years with massive crop failures. Or, an engineered pathogen causes massive population decline in a few months.
Hi @MichaelStJules, I am tagging you because I have updated the following sentence. If there is a period longer than 1 year over which population decreases, the power laws describing the ratio between the initial and final population of each of the years following the 1st could have different tail indices, with lower tail indices for years in which there is a larger population loss. I do not think the duration of the period is too relevant for my overall point. For short and long catastrophes, I expect the PDF of the ratio between the initial and final population to decay faster than the benefits of saving a life, such that the expected value density of the cost-effectiveness decreases with the severity of the catastrophe (at least for my assumption that the cost to save a life does not depend on the severity of the catastrophe).
I just wasn’t sure what exactly you meant. Another intepretation would be that P_f is the total post-catastrophe population, summing over all future generations, and I just wanted to check that you meant the population at a given time, not aggregating over time.
I see! Yes, both Pi and Pf are population sizes at a given point in time.
Oh, I didn’t mean for you to define the period explicitly as a fixed interval period. I assume this can vary by catastrophe. Like maybe population declines over 5 years with massive crop failures. Or, an engineered pathogen causes massive population decline in a few months.
I just wasn’t sure what exactly you meant. Another intepretation would be that P_f is the total post-catastrophe population, summing over all future generations, and I just wanted to check that you meant the population at a given time, not aggregating over time.
Hi @MichaelStJules, I am tagging you because I have updated the following sentence. If there is a period longer than 1 year over which population decreases, the power laws describing the ratio between the initial and final population of each of the years following the 1st could have different tail indices, with lower tail indices for years in which there is a larger population loss. I do not think the duration of the period is too relevant for my overall point. For short and long catastrophes, I expect the PDF of the ratio between the initial and final population to decay faster than the benefits of saving a life, such that the expected value density of the cost-effectiveness decreases with the severity of the catastrophe (at least for my assumption that the cost to save a life does not depend on the severity of the catastrophe).
I see! Yes, both Pi and Pf are population sizes at a given point in time.