Invariance in ecological pattern.

Area of Science:

• Ecology
• Theoretical Ecology
• Mathematical Biology

Background:

• Species abundance distributions often follow simple patterns, such as the log series distribution.
• The underlying reasons for this emergent simplicity in complex ecological systems are debated, with explanations including maximum entropy and neutral theory.

Purpose of the Study:

• To propose a unifying framework for understanding ecological patterns based on the concept of invariance.
• To demonstrate how invariance principles can explain the dominance of specific ecological distributions like the log series and lognormal patterns.

Main Methods:

• Applying the concept of invariance, where patterns remain unchanged under specific transformations, to ecological processes.
• Analyzing how invariance in abundance transformations and growth rate symmetries lead to observed ecological patterns.

Main Results:

• The log series distribution emerges when ecological processes affecting abundance are invariant to constant addition or multiplication.
• The lognormal distribution arises when net species growth rates exhibit rotational invariance.

Conclusions:

• Invariance provides a fundamental basis for ecological patterns, unifying existing theories.
• This approach offers simpler derivations for the log series distribution from maximum entropy principles and key results from neutral theory.