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The mutation-selection process is the most fundamental mechanism of evolution. In 1935, Ronald Aylmer. Fisher proved his
fundamental theorem of natural selection (FTNS), providing a model in which the rate of change of mean fitness is equal to
the genetic variance of a species. Fisher did exclude transformations in his model but rather trusted that changes would give a
constant supply of fluctuation bringing about the unending increment in mean wellness, in this manner giving an establishment
to neo-Darwinian hypothesis. In this discussion, we fabricate a differential conditions display from Fisher's first standards with
transformations included and demonstrate an overhauled hypothesis demonstrating the rate of progress in mean wellness is
equal to genetic variance plus a mutational effects term, called the fundamental theorem of natural selection with mutations
(FTNSM). The expanded theorem has biological implications significantly different from what Fisher had envisioned; most
critically, mutations with selection do not provide continual upward pressure on fitness. We observe that for small populations,
the model predicts a fitness decline as the deleterious effects of mutation accumulate faster than selection can replenish fitness.
In this talk, we present the new FTNSM model and its relation to Fisher’s original work as well as recent work on mutation
accumulation in small populations. We will show that our model is more complete than other models for understanding
mutation accumulation, and discuss estimation of minimal population sizes for avoiding a near-term mutational meltdown in
William F Basener is an Emeritus Professor in the School of Mathematical Sciences at the Rochester Institute of Technology. He is also founding President of two small software companies and is faculty at the University of Virginia Department of Systems and Information Engineering. His areas of expertise include population modeling, population genetics, topology, data mining, and dynamical systems.