Best approximation of $(\mathcal{G}_{1},\mathcal{G}_{2})$-random operator inequality in matrix Menger Banach algebras with application of stochastic Mittag-Leffler and $\mathbb{H}$-Fox control functions

We stabilize pseudostochastic $(\mathcal{G}_{1},\mathcal{G}_{2})$ ( G 1 , G 2 ) -random operator inequality using a class of stochastic matrix control functions in matrix Menger Banach algebras. We get an approximation for stochastic $(\mathcal{G}_{1},\mathcal{G}_{2})$ ( G 1 , G 2 ) -random operator inequality by means of both direct and fixed point methods. As an application, we apply both stochastic Mittag-Leffler and $\mathbb{H}$ H -fox control functions to get a better approximation in a random operator inequality.

Testing the decline of the New Holland mouse (Pseudomys novaehollandiae) in Victoria

Many Australian rodent species have become extinct or undergone substantial range contractions since European invasion. Limited and haphazard survey efforts across much of Australia mean we are unsure of many species’ current and former ranges, hampering our ability to identify and remedy causes of decline. The New Holland Mouse (NHM; Pseudomys novaehollandiae) is an endangered rodent species native to south-east Australia that is suspected of undergoing rapid and dramatic range contractions and local extinctions in recent decades. Here, I reassess the species’ distribution across Victoria using extensive survey efforts and, subsequently, provide a summation of potential key threatening processes. In only 40 years, the NHM has been lost from seven of the 12 isolated areas where it once occurred in Victoria. Habitat loss and fragmentation, invasive predators, and potentially disease and genetic inbreeding have likely contributed to the species’ rapid and continuing decline. Conservation priorities include ongoing monitoring and research, cat and fox control, exclusion of rabbit poison-baiting, targeted fire and habitat management, and reintroduction to historically occupied regions where threatening processes have been mitigated.

Success criteria not met, but valuable information gained: monitoring a reintroduction of the tammar wallaby

Context Fauna translocations are a tool for improving the conservation status of threatened species. Reviews of translocations undertaken in Australia and globally have reported that many fail because of predation by exotic predators. The outcome of ~40% of translocations was unknown, often owing to inadequate post-release monitoring. Monitoring methods such as global positioning system data-loggers can provide valuable information on survival, habitat use and sociality, and can be particularly useful for cryptic species. Aims The present study used global positioning system (GPS) data-loggers and VHF radio-transmitters to evaluate the success of a reintroduction of the tammar wallaby and measured survival, short-term home-range, habitat use and proximity between reintroduced individuals (as a proxy for association). Methods Sixty-nine tammar wallabies of captive and wild stock were reintroduced to Kalbarri National Park (KNP) following long-term and broad-scale fox control, with nine receiving GPS data-loggers, and 16 receiving VHF radio-transmitters. Wallabies were intensively monitored for up to 11 months post-release. Mortalities were investigated using DNA identification and field necropsies. Key results In total, 16 of the 25 collared wallabies died within 11–319 days of release. Ten of the sixteen deaths were from predation. Home-range areas were larger than those reported elsewhere. Wallabies utilised long-undisturbed vegetation with a dense canopy cover during crepuscular periods. These areas were likely sought as refuge from predation and thermal extremes. During the main feeding period, a mosaic of recently burnt (i.e. ~1 year) and >10 years since last disturbance was important. Conclusions The reintroduction was not considered successful because two-thirds of the collared wallabies died within 1 year of release and, therefore, the success criteria were not met. Implications Despite long-term fox control in KNP, the majority of collared wallaby deaths were a result of fox predation. This highlights the inherent difficulty of establishing populations of some species in the presence of introduced predators. Additional research could assist in determining appropriate control levels for introduced predators, to help ensure the success of future translocations of this species. Consideration should be given to the prey naivety of source animals, prey-switching by introduced predators, and short-term supplementary feeding to assist population establishment.

Fox control and 1080 baiting conundrums: time to prepare for a CRISPR solution

For many years, managing rock-wallaby colonies (Petrogale lateralis lateralis) in the Western Australian Wheatbelt seemed to be a matter of routinely exposing foxes (Vulpes vulpes) to toxic baits (sodium fluoroacetate, 1080®) laid around their rocky outcrops. Recent research has revealed that 1080 baitings are no longer a viable management option. Baiting is flawed over the long term because it does not erase the wallabies’ pervasive fear of being depredated by foxes, which can still make their menacing presence felt before succumbing to poison bait. Accordingly, a ‘landscape of fear’ exists on all rock-wallaby sites, creating a ‘virtual boundary’ beyond which they fear to forage. Severe overgrazing occurs, ultimately causing population crashes, leaving behind devastated outcrops greatly diminished in carrying capacity. The fallout from this scenario produces a management conundrum. Rock-wallaby populations are unstable in the absence of fox control, and conversely, they are also unstable under long-term fox control. Management is now left with few options, and the future of the colonies remains open. Other conundrums involving bait interference and mesopredator release are described. An alternative to 1080 baiting is clearly needed. Recent developments in gene engineering (CRISPR technology) offer a solution in the foreseeable future.

Short-term tracking of three red foxes in the Simpson Desert reveals large home-range sizes

The red fox (Vulpes vulpes) is probably the most intensively studied introduced predator in Australia, but little is known about its movements in arid areas. Here, we report on the home-range sizes of one male and two female red foxes that were tracked for 2–8 months using collars fitted with ARGOS transmitters in the Simpson Desert, central Australia. Based on the 100% Minimum Convex Polygon method, home-range sizes were 5723 ha, 50 158 ha, and 12 481 ha, respectively. Based on the 95% kernel contour method, home-range sizes were 3930 ha, 26 954 ha, and 12 142 ha, respectively. These home-range sizes are much larger than any recorded previously from elsewhere in Australia, suggesting that red foxes in the Simpson Desert need to roam over extensive areas to find enough resources to meet their energetic needs. Given that predation by red foxes poses a key threat to many small and medium-sized native mammals, we suggest that red fox control operations may need to be undertaken at very large spatial scales to be effective in arid areas.

Population characteristics and management of the long-nosed potoroo (Potorous tridactylus) in high-quality habitat in the Southern Highlands of New South Wales

Since European settlement in Australia the long-nosed potoroo (Potorous tridactylus) has suffered greatly from fox predation and habitat loss, fragmentation and degradation. To better understand the threats it faces we examined the population dynamics of the potoroo at two study sites in the Southern Highlands of New South Wales over five years, using live-trapping. As neither site had experienced inappropriate habitat change for over 25 years, fox predation was considered the major threat to this population. An assessment of fox activity and diet was undertaken at both sites for comparison with potoroo abundance. Potoroos increased at both sites over time, although at one site this increase was only in density and not range. The density increase would not have been detected using camera surveys, a monitoring technique recommended for this species. The relative abundance of foxes fluctuated over the study despite fox control in one of the two sites. Analysis of fox scats at the same sites indicated high levels of predation on potoroos. Future management should aim to provide effective fox control (particularly following any fire due to the associated loss of ground cover) and improved fox monitoring to ensure an accurate understanding of what is happening to the fox population.