I have devised two tests that pit punctuationalism against gradualism. The first is the Test of Adaptive Radiation, which I apply to families of middle Eocene Mammalia and Late Cretaceous Bivalvia. This test shows that species in both of these classes lasted much too long for evolution within them (phyletic evolution) to have produced the new families that arose during brief time intervals. This test would yield similar results for many other taxa. It supports the punctuational model, as does the Test of Living Fossils, which predicts that long, slender clades, having experienced little speciation, should have undergone little evolution. Limited largely to phyletic evolution, this is exactly what happened to them.

Several multivariate morphological studies of numerous fossil lineages have found little or no gradual evolution to have been the norm. One of these included 153 lineage traits and another, 250. Still another produced a rectangular stratophenetic phylogeny, with inferred horizontal speciation events connecting vertical lineages. Taken together these studies provide overwhelming support for the punctuational model.

Many studies have shown that rapid speciation events occur frequently and some are punctuational. Jellyfishes that have appeared recently in saltwater lakes on the Pacific island of Palau are remarkable examples of punctuational speciation, and so is the sudden appearance of the novel sand dollar family Dendrasteridae in the California Miocene.

The punctuational model shows that the value of sexual reproduction must be in producing long-lived adaptive radiations, whereas clones die out quickly.

Let $\gamma _{n}= O (\log ^{-c}n)$ and let $\nu $ be the infinite product measure whose nth marginal is Bernoulli $(1/2+\gamma _{n})$. We show that $c=1/2$ is the threshold, above which $\nu $-almost every point is simply Poisson generic in the sense of Peres and Weiss, and below which this can fail. This provides a range in which $\nu $ is singular with respect to the uniform product measure, but $\nu $-almost every point is simply Poisson generic.

This study investigated associations between socioeconomic status (SES), input quality, and bilingual lexical skills of children raised in Maltese-dominant homes. Children aged 3;04–3;08 (N = 38) and their primary caregivers were categorised as low, medium, or high SES. Children’s lexical skills were assessed through receptive picture name judgement and picture naming, in Maltese and English. Input quality was measured through type counts sampled during caregiver–child play at home. SES influenced children’s English lexical performance, but not Maltese. Aggregated types (Maltese and English) fully mediated SES effects on English picture naming. Maltese types were positively associated with English naming and receptive judgement, suggesting cross-language effects. Further, Maltese and English types had language-specific effects on the respective naming tasks. English type counts, indexing caregiver language mixing, affected Maltese naming negatively. Results support the use of lexically diverse Maltese input in Maltese-dominant homes, complemented by judicious use of English input.

Urban refugees in low- and middle-income countries (LMICs) often face housing insecurity, undermining their ability to achieve self-reliance and well-being. Few studies have evaluated the impact of housing interventions in these contexts. This study offers preliminary evidence on the effectiveness of a 9-month rental assistance program targeting female-headed Venezuelan migrant households in Colombia. Using pre-post data from 517 participants, we assessed changes over time in household-level self-reliance, domains of self-reliance, subjective well-being and perceived agency. We also employed ordinary least squares regression and fixed-effects models to estimate changes in self-reliance and the relationship between self-reliance, psychosocial and housing outcomes. Our analysis found significant improvements in overall self-reliance, well-being and agency after controlling for observed individual and household characteristics. Increases were observed across almost all domains of self-reliance. Fixed-effects models also found that subjective well-being, perceived agency and select housing conditions were positively associated with self-reliance. Rental support appears to promote both material and psychosocial recovery for displaced households by alleviating financial stress and enabling forward-looking behaviors. However, the impact of housing quality dimensions varies, and the sustainability of outcomes remains uncertain. Future evaluations should incorporate longitudinal designs and control groups to inform holistic refugee housing strategies.

Given $\beta>1$, let $T_\beta $ be the $\beta $-transformation on the unit circle $[0,1)$, defined by $T_\beta (x)=\beta x-\lfloor \beta x\rfloor $. For each $t\in [0,1)$, let $K_\beta (t)$ be the survivor set consisting of all $x\in [0,1)$ whose orbit $\{T^n_\beta (x): n\ge 0\}$ never enters the interval $[0,t)$. Kalle et al [Ergod. Th. & Dynam. Sys. 40(9) (2020), 2482–2514] considered the case $\beta \in (1,2]$. They studied the set-valued bifurcation set $\mathscr {E}_\beta :=\{t\in [0,1): K_\beta (t')\ne K_\beta (t)~\text { for all } t'>t\}$ and proved that the Hausdorff dimension function $t\mapsto \dim _H K_\beta (t)$ is a non-increasing Devil’s staircase. In a previous paper [Ergod. Th. & Dynam. Sys. 43(6) (2023), 1785–1828], we determined, for all $\beta \in (1,2]$, the critical value $\tau (\beta ):=\min \{t>0: \eta _\beta (t)=0\}$. The purpose of the present article is to extend these results to all $\beta>1$. In addition to calculating $\tau (\beta )$, we show that: (i) the function $\tau : \beta \mapsto \tau (\beta )$ is left-continuous on $(1,\infty )$ with right-hand limits everywhere, but has countably infinitely many discontinuities; (ii) $\tau $ has no downward jumps; and (iii) there exists an open set $O\subset (1,\infty )$, whose complement $(1,\infty )\setminus O$ has zero Hausdorff dimension, such that $\tau $ is real-analytic, strictly convex, and strictly decreasing on each connected component of O. We also prove several topological properties of the bifurcation set $\mathscr {E}_\beta $. The key to extending the results from $\beta \in (1,2]$ to all $\beta>1$ is an appropriate generalization of the Farey words that are used to parameterize the connected components of the set O. Some of the original proofs from the above-mentioned papers are simplified.

This paper examines the relationship between feminist manifestos and constituent power, focusing on the Chilean feminist movement. Manifestos have long been an influential political tool in shaping political identities and claiming power. However, they are often overlooked in constitutional law. This paper addresses this gap by exploring feminist manifestos, which have been pivotal in denouncing historical exclusion, forming political groups and asserting constituent power. Drawing on the work of Ruth Houghton and Aoife O’Donoghue, the paper investigates how feminist manifestos challenge traditional notions of constituent power. However, it argues that their performative conception of power overlooks the vital role of political representation. The paper argues that political representation is crucial for a fully realised theory of feminist constituent power, as it enables collective action and democratic participation. By looking at the Chilean feminist movement’s involvement in the 2019–2022 constitution-making process, the paper demonstrates how feminist movements, through strategies such as manifestos and strikes, can influence constitutional change, while also highlighting the limitations of excluding political representation from the conversation. Ultimately, the paper asserts that feminist manifestos can reimagine constituent power, but their full potential is limited without a comprehensive understanding of political representation.