http://hdl.handle.net/123456789/1385 2026-05-07T21:00:26Z http://hdl.handle.net/123456789/19827 The Orbit Structure of the Product of Four Alternating Groups Acting on the Cartesian Product of Four Sets of Ordered Tuples Moses K. Maraka, Lewis N. Nyaga This paper explores the orbit structure of the direct product of four alternating groups acting on the Cartesian product of four sets of ordered 𝛾-tuples. The associated orbitals and suborbits lengths are determined using combinatorial formulae. Contrary to previous studies involving ordered pairs or fewer group factors, this setting introduces significantly higher combinatorial configurations arising from higher-dimensional tuple structures. This brings rise to a general orbit structure pattern that do not arise in pair-based and fewer group factors cases. The number of orbitals of 𝐴𝑛1 × 𝐴𝑛2 × 𝐴𝑛3 × 𝐴𝑛4 acting on 𝑈1 [𝛾] × 𝑈2 [𝛾] × 𝑈3 [𝛾] × 𝑈4 [𝛾] , (∀ 𝑛 − 𝛾 ≥ 2) is 16 and explicit suborbits lengths formulae are obtained using combinatorial methods. The results extend existing research on ranks and subdegrees while revealing new structural phenomena unique to actions on ordered 𝛾-tuples of direct product of four alternating groups. 2026-04-01T00:00:00Z http://hdl.handle.net/123456789/19826 Seasonal Microbial and Physicochemical Variations in Shared Water Resources Within the Arid and Semi-Arid Southwestern Kenya Landscape Brian Marvis Waswala-Olewe, George Paul Omondi, Romulus Abila, Paul Webala Water scarcity and poor access to potable water are growing concerns in sub-Saharan Africa. This study investigated seasonal variations in microbial contamination and physicochemical properties of surface waterpoints, the primary sources of water in southwestern Kenya, using a cross-sectional environmental surveillance design (May 2024-April 2025). Total coliforms and Escherichia coli isolates were quantified, to assess water safety and ecosystem health using membrane filtration and differential chromogenic agar. Results revealed high microbial contamination in all samples (100% for total coliforms; 62.5% for E. coli), with significantly higher bacterial loads during the wet season. Total coliforms and E. coli averaged 1.13×106 CFUs/mL and 1.34±1.26×105 ; and 2.84×105 CFUs/mL and 9.82±9.78×104 , respectively, for wet and dry seasons respectively. Prevalence of E. coli in sampled sites was statistically significant between seasons (χ2 (1, N=28)=20.57, P<.05). Physicochemical parameters varied seasonally, with the dry season having higher pH, temperature, total dissolved solids and dissolved oxygen, while the wet season had higher conductivity. During the dry season, E. coli and total coliforms were not correlated while in the wet season, a weak but significant correlation existed (r=0.465, P=.003). Microbial parameters showed no significant correlation with physicochemical variables in either season, emphasising distinct seasonal interaction patterns. MANOVA conducted to assess the influence of water bodies, seasons and their interactions on microbial and physiochemical parameters revealed that water quality was significantly influenced by both water body type and season (P<.001). Total coliforms were significantly influenced by season but not water sources. The presence of unsafe microbial loads and poor water quality highlights public health risks and potentially impact on livestock and livelihoods. These microscale findings, advocate for continuous ecological surveillance and public health monitoring on water quality status and community awareness. We recommend promotion of nature-based indigenous solutions for water and ecosystem management amid climate change. 2026-04-01T00:00:00Z http://hdl.handle.net/123456789/19824 Water Quality Parameters Effect on Zooplankton Distribution, Diversity, and Abundance in Water Pans in Semi-Arid Narok Socio-Ecological Landscape, Kenya Dorine Were, Reuben Omondi, Henry Ouma, Paul Angienda, Romulus Abila Water pans in the semi-arid Narok County are essential resources supporting domestic use, livestock production, small-scale irrigation, and aquatic biodiversity. However, these systems face increasing threats from climate variability, population growth, and land-use pressures that alter water quality and ecosystem functioning. Limited empirical data linking specific water-quality stressors such as elevated nitrogen and phosphorus, turbidity, and conductivity to zooplankton populations and ecosystem services hinders effective management in this landscape. This study examined the distribution, diversity, and abundance of zooplankton in relation to water-quality variations and contrasting land-use practices across 20 water pans in the Narok socio-ecological system. Monthly sampling was conducted in February, June, and July 2023, representing the late dry season, early wet season, and postrainy period. Physico-chemical parameters were measured in situ, while nutrients and chlorophyll-a were analyzed using APHA 2017 standard protocols. Chlorophyll-a ranged from 19.08 ± 1.05 µg/L (M118) to 176.61 ± 140.19 µg/L (M396). TN varied from 393.00 ± 30.25 µg/L (M100) to 2,609.43 ± 52.47 µg/L (M392), and TP ranged from 295.43 to 1331.14 µg/L. Zooplankton communities were dominated by Rotifera (48.9%), followed by Copepoda (25.8%), Cladocera (19.9%), and Ostracoda (5%). Taxa richness increased from the dry season (14.21 ± 0.79) to the wet season (16.43 ± 0.67; 4(1), 2026 Original Article p = 0.043), while Shannon-Wiener Index rose from 1.76 to 1.96 and Simpson’s Index reached 10.72. Diversity and richness showed a negative correlation with TN, indicating nutrient enrichment as a major stressor. The dominance of stress-tolerant Rotifers in nutrient-rich pans reflected catchment land-use influences. Conserving these semi-arid water pans through riparian buffer restoration, controlled livestock access, and improved water abstraction is important for sustaining zooplankton biodiversity and ecological integrity. 2026-04-01T00:00:00Z http://hdl.handle.net/123456789/19823 Prioritizing underground roosts for bat conservation in Kenya Millicent J. Bungei, Sospeter Kibiwot, Irene B. Tieleman, Johnstone K. Kimanzi, Bruce D. Patterson, Paul W. Webala Identifying key wildlife resources is vital for lasting conservation efforts. Bats disperse seeds, pollinate plants, consume insects, and support cave-dependent organisms. However, they face significant threats from habitat loss, fragmentation, degradation, mining, cave tourism, cave closures, evictions, and superstitious persecution. Most of Kenya's bat species roost in caves outside the country's 10% of protected areas, where cave conditions and species remain largely unknown. We employed the Scalable Bat Cave Vulnerability Index (BCVI-S) to assess the conservation priorities of bat cave roosts in Kenya, aiming to identify the most vulnerable ones and establish priorities for effective conservation. BCVI-S has two components: (1) Biotic Potential (BP), which evaluates cave's ecological value through bat species richness, abundance, and the presence of threatened and endemic species, and (2) Biotic Vulnerability (BV),which measures human disturbance. Bat assemblages in protected area caves was different than those on unprotected community lands, with Otomops harrisoni contributing to differences between these two groups. Bat species diversity declined near urban areas. Caves with threatened species showed moderate vulnerability, which demonstrates the importance of targeted conservation efforts. Caves in protected areas showed greater Biotic Potential and lower vulnerability scores than those on unprotected community lands. These findings justify the need to incorporate species-level data and indicators of human intrusion in conserving cave-dwelling bats. The BCVI-S is a structured tool for identifying those caves, which are vulnerable, leading to their preservation, planning, empowering local management, and supporting evidence-based policy development. 2026-04-01T00:00:00Z