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As a label for a distinct category of life, “living fossil” is controversial. The term has multiple definitions, and it is unclear whether the label can be genuinely used to delimit biodiversity. Even taking a purely phylogenetic perspective in which a proxy for the living fossil is evolutionary distinctness (ED), an inconsistency arises: Does it refer to “dead-end” lineages doomed to extinction or “panchronic” lineages that survive through multiple epochs? Recent tree-growth model studies indicate that speciation rates must have been unequally distributed among species in the past to produce the shape of the tree of life. Although an uneven distribution of speciation rates may create the possibility for a distinct group of living fossil lineages, such a grouping could only be considered genuine if extinction rates also show a consistent pattern, be it indicative of dead-end or panchronic lineages. To determine whether extinction rates also show an unequal distribution, we developed a tree-growth model in which the probability of speciation and extinction is a function of a tip’s ED. We simulated thousands of trees in which the ED function for a tip is randomly and independently determined for speciation and extinction rates. We find that simulations in which the most evolutionarily distinct tips have lower rates of speciation and extinction produce phylogenetic trees closest in shape to empirical trees. This implies that a distinct set of lineages with reduced rates of diversification, indicative of a panchronic definition, is required to create the shape of the tree of life.