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1. Maternal effect senescence and caloric restriction interact to affect fitness through changes in life history timing

   https://doi.org/10.1111/1365-2656.14220  

   Hernández, Christina M; van_Daalen, Silke F; Liguori, Alyssa; Neubert, Michael G; Caswell, Hal; Gribble, Kristin E (January 2025, Journal of Animal Ecology)

   Abstract Environmental factors and individual attributes, and their interactions, impact survival, growth and reproduction of an individual throughout its life. In the clonal rotiferBrachionus, low food conditions delay reproduction and extend lifespan. This species also exhibits maternal effect senescence; the offspring of older mothers have lower survival and reproductive output. In this paper, we explored the population consequences of the individual‐level interaction of maternal age and low food availability.We built matrix population models for both ad libitum and low food treatments, in which individuals are classified both by their age and maternal age. Low food conditions reduced population growth rate () and shifted the population structure to older maternal ages, but did not detectably impact individual lifetime reproductive output.We analysed hypothetical scenarios in which reduced fertility or survival led to approximately stationary populations that maintained the shape of the difference in demographic rates between the ad libitum and low food treatments. When fertility was reduced, the populations were more evenly distributed across ages and maternal ages, while the lower‐survival models showed an increased concentration of individuals in the youngest ages and maternal ages.Using life table response experiment analyses, we compared populations grown under ad libitum and low food conditions in scenarios representing laboratory conditions, reduced fertility and reduced survival. In the laboratory scenario, the reduction in population growth rate under low food conditions is primarily due to decreased fertility in early life. In the lower‐fertility scenario, contributions from differences in fertility and survival are more similar, and show trade‐offs across both ages and maternal ages. In the lower‐survival scenario, the contributions from decreased fertility in early life again dominate the difference in .These results demonstrate that processes that potentially benefit individuals (e.g. lifespan extension) may actually reduce fitness and population growth because of links with other demographic changes (e.g. delayed reproduction). Because the interactions of maternal age and low food availability depend on the population structure, the fitness consequences of an environmental change can only be fully understood through analysis that takes into account the entire life cycle. 

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2. Hausdorff Dimension of Caloric Measure

   https://doi.org/10.1353/ajm.2025.a954648  

   Badger, Matthew; Genschaw, Alyssa (April 2025, American Journal of Mathematics)

   abstract: We examine caloric measures $$\omega$$ on general domains in $$\RR^{n+1}=\RR^n\times\RR$$ (space $$\times$$ time) from the perspective of geometric measure theory. On one hand, we give a direct proof of a consequence of a theorem of Taylor and Watson (1985) that the lower parabolic Hausdorff dimension of $$\omega$$ is at least $$n$$ and $$\omega\ll\Haus^n$$. On the other hand, we prove that the upper parabolic Hausdorff dimension of $$\omega$$ is at most $$n+2-\beta_n$$, where $$\beta_n>0$$ depends only on $$n$$. Analogous bounds for harmonic measures were first shown by Nevanlinna (1934) and Bourgain (1987). Heuristically, we show that the \emph{density} of obstacles in a cube needed to make it unlikely that a Brownian motion started outside of the cube exits a domain near the center of the cube must be chosen according to the ambient dimension. In the course of the proof, we give a caloric measure analogue of Bourgain's alternative: for any constants $$0<\epsilon\ll_n \delta<1/2$ and closed set $$E\subset\RR^{n+1}$$, either (i) $$E\cap Q$$ has relatively large caloric measure in $$Q\setminus E$$ for every pole in $$F$$ or (ii) $$E\cap Q_*$$ has relatively small $$\rho$$-dimensional parabolic Hausdorff content for every $$n<\rho\leq n+2$$, where $$Q$$ is a cube, $$F$$ is a subcube of $$Q$$ aligned at the center of the top time-face, and $$Q_*$$ is a subcube of $$Q$$ that is close to, but separated backwards-in-time from $$F$$: \begin{gather*} Q=(-1/2,1/2)^n\times (-1,0),\quad F=[-1/2+\delta,1/2-\delta]^n\times[-\epsilon^2,0),\\[2pt] \text{and }Q_*=[-1/2+\delta,1/2-\delta]^n\times[-3\epsilon^2,-2\epsilon^2]. \end{gather*} Further, we supply a version of the strong Markov property for caloric measures. 

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3. Optimal bounds for ancient caloric functions

   https://doi.org/10.1215/00127094-2021-0015  

   Colding, Tobias Holck; Minicozzi II, William P. (December 2021, Duke Mathematical Journal)
4. BMO Solvability and Absolute Continuity of Caloric Measure

   https://doi.org/10.1007/s11118-020-09833-9  

   Genschaw, Alyssa; Hofmann, Steve (March 2021, Potential Analysis)

   null (Ed.)
5. A Weak Reverse Hölder Inequality for Caloric Measure

   https://doi.org/10.1007/s12220-019-00212-4  

   Genschaw, Alyssa; Hofmann, Steve (April 2020, The Journal of Geometric Analysis)