Difficulties in summing log-normal distributions for abundance and potential solutions

Area of Science:

• Ecology
• Ecological modeling
• Conservation biology

Background:

• Log-normal distribution is common for animal abundance but has non-intuitive properties.
• Median is often used for uncertain estimates, but summing medians across populations is problematic.
• Naive summation can inflate estimates, impacting conservation decisions.

Approach:

• Reviewed statistical challenges of log-normal distribution in abundance modeling.
• Investigated alternative summation methods for species abundance data.
• Utilized global avian abundance data (Callaghan et al. 2021) as a case study.

Key Points:

• Summing log-normal distributions is complex; median of sums is not sum of medians.
• Naive summation methods can lead to grossly inflated abundance estimates.
• Shifted log-normal distributions provided scale-consistent estimates for global abundance.

Conclusions:

• Estimation methods for abundance significantly impact total estimates and uncertainty.
• Scale-consistent methods are crucial for accurate ecological summaries.
• Careful consideration of statistical methods is vital for conservation implications.