The identifcation and separation of intrinsic variability from age-related phenomena has been the subject of a growing body of literature, supporting renewed interest in traditional analytic methodologies including use of the  von Foerster equation  for predicting population growth and cell age distributions. Here we discuss how some of the most popular implementations of this machinery assume a strong condition on the ergodicity of the cell cycle duration ensemble and that two common definitions for the term , ergodicity, while identical in an ensemble with a fixed number of individuals , are in fact unique constraints when the ensemble is growing. We further explore the impact on growthrate of generational correlations between cell cycle durations  . Finally, we explore the growthrate gain - the phenomenon that noise in the cell cycle duration leads to an improved bulk growthrate - in this context. We highlight that, fundamentally, this effect is due to asymmetric division.
Many single-cell observables are highly heterogeneous. A part of this heterogeneity stems from age-related phenomena : the fact that there is a nonuniform distribution of cells with different ages. This has led to a renewed interest in analytic methodologies including use of the " von Foerster equation " for predicting population growth and cell age distributions. Here we discuss how some of the most popular implementations of this machinery assume a strong condition on the ergodicity of the cell cycle duration ensemble . We show that one common definition for the term ergodicity, "a single individual observed over many generations recapitulates the behavior of the entire ensemble" is implied by the other, "the probability of observing any state is conserved across time and over all individuals" in an ensemble with a fixed number of individuals but that this is not true when the ensemble is growing. We further explore the impact of generational correlations between cell cycle durations on the population growth rate . Finally, we explore the "growth rate gain" - the phenomenon that variations in the cell cycle duration lead to an improved population-level growth rate - in this context. We highlight that, fundamentally, this effect is due to asymmetric division.
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The identifcation and separation of intrinsic variability
Many single-cell observables are highly heterogeneous. A part of this heterogeneity stems
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has been the subject of a growing body of literature, supporting
: the fact that there is a nonuniform distribution of cells with different ages. This has led to a
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traditional
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"
A
"
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and that two common definitions
. We show that one common definition
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, ergodicity, while identical
ergodicity, "a single individual observed over many generations recapitulates the behavior of the entire ensemble" is implied by the other, "the probability of observing any state is conserved across time and over all individuals"
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, are in fact unique constraints
but that this is not true
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on growthrate
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on the population growth rate
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growthrate gain
"growth rate gain"
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noise
variations
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leads
lead
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bulk growthrate
population-level growth rate