We apply the Lagrangian method to study the post-Newtonian evolution of a compact binary system with environmental effects, including a dark matter spike, and obtain the resulting gravitational wave emission. This formalism allows one to incorporate post-Newtonian effects up to any desired known order, as well as any other environmental effect around the binary, as long as their dissipation power or force formulae are known. In particular, in this work, we employ this method to study a black hole–black hole binary system of mass ratio ${10}^5$ by including post-Newtonian effects of order 1PN and 2.5PN, as well as the effect of relativistic dynamical friction. We obtain the modified orbits and the corresponding modified gravitational waveform. Finally, we contrast these modifications against the LISA sensitivity curve in frequency space and show that this observatory can detect the associated signals.

Phaseolus species are cultivated worldwide as a primary food source for human consumption. Common bean (Phaseolus vulgaris L.) and runner bean (Phaseolus coccineus L.) landraces are often cultivated together. The purpose was to document the traditional knowledge held by farmers regarding bean landraces, to describe the diversity through seed morphological descriptors (five quantitative and five qualitative traits), to understand the geographic distribution using Moran’s I statistic, and to analyze the diversity through the Shannon–Wiener Diversity–Equity (H′) index and the Shannon J’ homogeneity index at the community level to better understand the richness of this geographic area. A total of 361 common and runner bean accessions were collected in 10 Andean rural communities of Cotacachi, North Ecuador. We identified 47 landraces, predominantly kept by indigenous female farmers, with limited access to formal education, highlighting the role of this disadvantaged population in agrobiodiversity conservation. The cluster analysis revealed three groups (cophenetic correlation coefficient = 0.6). In the principal component (PC) analysis, 94% of the variation was explained by PC1 and PC2. A positive spatial autocorrelation (Moran’s I: 0.24; z-score: 2.20; p-value: 0.03) was identified, confirming a spatial structure. The Morochos community showed the highest diversity (H′ = 1.55). The information of the diversity and distribution of common and runner bean variability provided in this study is a contribution to further research focused on conservation.