Classically, biological reproduction is explained as the building of a new organism from replicated genomic instructions. The corresponding theoretical model is von Neumann's self-reproducing machine, which relies on an invariant universal constructor that can build any machine from instructions. However, the reproductive incompatibility of species and the diversity of developing processes speak against the existence of a universal constructor. Without a universal constructor, the genome as representation of the organism is circularly defined: what the genome represents is specified by the developmental processes represented by the genome.<p>I propose to take invariant reproduction not as a premise, but as an emergent dynamical property.</p><p>Reproduction is seen as the iteration of a transform that maps one generation to the next, a transform shaped by the genome. Invariant reproduction then occurs when a reproductive sequence converges to a fixed point. A reproductive sequence may also diverge, converge to a cycle (multigenerational life cycle), or to one of several fixed points (non-genomic inheritance). When it does converge, it is necessarily to a stable point, implying that development is robust to perturbations. Finally, speciation can be understood as a process by which reproductive transforms become mutually incompatible, that is, the basins of attractions of the fixed points do not overlap any more. In this view, the genome is an inheritable constraint on development, not a representation of the organism. I suggest that this dynamical framework is a more coherent model of biological reproduction than von Neumann's computational framework.</p>

Precise control of odorant concentration is essential for reliable olfactory research, yet existing odorant delivery methods often suffer from solvent interactions and dilution from ambient air, limiting stimulus consistency in olfactory research. We developed an odor sampling bag system using Nalophan plastic to create a closed headspace with air as the carrier medium, eliminating solvent-related variability and ambient air dilution. In two independent experiments, 15 trained panelists each rated the perceived intensity of seven concentrations of benzaldehyde and 2-heptanone using both gas-sampling bags and glass jars. Bags produced higher maximum perceptual intensities (p < 0.001) and greater test-retest reliability than jars (Experiment 1: r = 0.89 vs. 0.81, p < 0.001; Experiment 2: r = 0.86 vs. 0.72, p < 0.001). Notably, the two tested odorants showed different maximum intensities in bags (p < 0.001) but not jars (p = 0.85), suggesting bags better preserve odorant-specific concentration differences. Photoionization detector measurements confirmed stable headspace concentrations over time, comparable to industry-standard Tedlar bags. This cost-effective approach offers improved stimulus control for olfactory psychophysics research. ### Competing Interest Statement Joel D. Mainland serves on the scientific advisory board of Osmo Labs, PBC and receives compensation for these activities. National Institutes of Health, https://ror.org/01cwqze88, F32 DC020380, T32 DC000014, U19 NS112953, R01 DC017757, R01 DC021663

Wittlinger, Wehner and Wolf’s 2006 “stilts and stumps” Science paper revealed how ants pull off extraordinary feats of navigation using a biological odometer, and it inspired Tuthill to consider how…