Field trees are an integral part of the farmed parkland landscape in West Africa and provide multiple benefits to the local environment and livelihoods. While field trees have received increasing interest in the context of strengthening resilience to climate variability and change, the actual extent of farmed parkland and spatial patterns of tree cover are largely unknown. We used the rule-base...

Recent studies have interpreted patterns of remotely sensed tree cover as evidence that forest with intermediate tree cover might be unstable in the tropics, as it will tip into either a closed forest or a more open savanna state. Here we show that across all continents the frequency of wildfires rises sharply as tree cover falls below ~40%. Using a simple empirical model, we hypothesize that t...

As tropical regions are converted to agriculture, conservation of biodiversity will depend not only on the maintenance of protected forest areas, but also on the scope for conservation within the agricultural matrix in which they are embedded. Tree cover typically retained in agricultural landscapes in the neotropics may provide resources and habitats for animals, but little is known about the ...

Theoretically, fire-tree cover feedbacks can maintain savanna and forest as alternative stable states. However, the global extent of fire-driven discontinuities in tree cover is unknown, especially accounting for seasonality and soils. We use tree cover, climate, fire, and soils data sets to show that tree cover is globally discontinuous. Climate influences tree cover globally but, at intermedi...

Using aerial photograph interpretation of circa 2005 imagery, percent tree canopy and impervious surface cover in the conterminous United States are estimated at 34.2% (standard error (SE) = 0.2%) and 2.4% (SE = 0.1%), respectively. Within urban/community areas, percent tree cover (35.1%, SE = 0.4%) is similar to the national value, but percent impervious cover is significantly higher (17.5%, S...

A tree cover of a graph G is defined as a collection of trees such that their union includes all the vertices of G. The cost of a tree cover is the weight of the maximum weight tree in the tree cover. Given a positive integer k, the k-tree cover problem is to compute a minimum cost tree cover which has no more than k trees. Star covers are defined analogously. Additionally, we may also be provi...

Let N = {1, ... ,n} be a finite set of players and K N the complete graph on the node set N w {0}. Assume that the edges of K N have nonnegative weights and associate with each coalition S _~ N of players as cost c(S) the weight of a minimal spanning tree on the node set S u {0}. Using transformation from EXACT COVER BY 3-SETS, we exhibit the tollowing problem to be NP-complete. Given the vecto...

The 2001 National Land Cover Database (NLCD) provides 30-m resolution estimates of percentage tree canopy and percentage impervious cover for the conterminous United States. Previous estimates that compared NLCD tree canopy and impervious cover estimates with photo-interpreted cover estimates within selected counties and places revealed that NLCD underestimates tree and impervious cover. Based ...