Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line

An element of a group is reversible if it is conjugate to its own inverse, and it is strongly reversible if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be expressed as a composite of two involutions. In this paper the reversible maps, the strongly reversible maps, and those maps that can be expressed as a composite of involutions are determined in certain groups of piecewise linear homeomorphisms of the real line

Safeguarding biodiversity and ecosystem services in the Little Karoo, South Africa

Global declines in biodiversity and the widespread degradation of ecosystem services have led to urgent calls to safeguard both. Responses to this urgency include calls to integrate the needs of ecosystem services and biodiversity into the design of conservation interventions. The benefits of such integration are purported to include improvements in the justification and resources available for these interventions. Nevertheless, additional costs and potential trade-offs remain poorly understood in the design of interventions that seek to conserve biodiversity and ecosystem services. We sought to investigate the synergies and trade-offs in safeguarding ecosystem services and biodiversity in South Africa’s Little Karoo. We used data on three ecosystem services—carbon storage, water recharge, and fodder provision—and data on biodiversity to examine several conservation planning scenarios. First, we investigated the amount of each ecosystem service captured incidentally by a conservation plan to meet targets for biodiversity only while minimizing opportunity costs. We then examined the costs of adding targets for ecosystem services into this conservation plan. Finally, we explored trade-offs between biodiversity and ecosystem service targets at a fixed cost. At least 30% of each ecosystem service was captured incidentally when all of biodiversity targets were met. By including data on ecosystem services, we increased the amount of services captured by at least 20% for all three services without additional costs. When biodiversity targets were reduced by 8%, an extra 40% of fodder provision and water recharge were obtained and 58% of carbon could be captured for the same cost. The opportunity cost (in terms of forgone production) of safeguarding 100% of the biodiversity targets was about US$500 million. Our results showed that with a small decrease in biodiversity target achievement, substantial gains for the conservation of ecosystem services can be achieved within our biodiversity priority areas for no extra cost.Centre of Excellence for Invasion Biolog

Short Communications: Small mammal diversity and density on the Bokkeveld escarpment, South Africa – implications for conservation and livestock predation

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Horizon scanning for South African biodiversity: a need for social engagement as well as science

A horizon scan was conducted to identify emerging and intensifying issues for biodiversity conservation in South Africa over the next 5–10 years. South African biodiversity experts submitted 63 issues of which ten were identified as priorities using the Delphi method. These priority issues were then plotted along axes of social agreement and scientific certainty, to ascertain whether issues might be “simple” (amenable to solutions from science alone), “complicated” (socially agreed upon but technically complicated), “complex” (scientifically challenging and significant levels of social disagreement) or “chaotic” (high social disagreement and highly scientifically challenging). Only three of the issues were likely to be resolved by improved science alone, while the remainder require engagement with social, economic and political factors. Fortunately, none of the issues were considered chaotic. Nevertheless, strategic communication, education and engagement with the populace and policy makers were considered vital for addressing emerging issues