Related papers: Quantifying extinction probabilities of endangered…
In conservation biology, phylogenetic diversity (PD) provides a way to quantify the impact of the current rapid extinction of species on the evolutionary `Tree of Life'. This approach recognises that extinction not only removes species but…
For many taxa, the current high rates of extinction are likely to result in a significant loss of biodiversity. The evolutionary heritage of biodiversity is frequently quantified by a measure called phylogenetic diversity (PD). We predict…
If predictions for species extinctions hold, then the `tree of life' today may be quite different to that in (say) 100 years. We describe a technique to quantify how much each species is likely to contribute to future biodiversity, as…
Phylogenetic Diversity (PD) is a measure of the overall biodiversity of a set of present-day species (taxa) within a phylogenetic tree. In Maximize Phylogenetic Diversity (MPD) one is asked to find a set of taxa (of bounded size/cost) for…
Planning for the protection of species often involves difficult choices about which species to prioritize, given constrained resources. One way of prioritizing species is to consider their "evolutionary distinctiveness", i.e. their relative…
Phylogenies are commonly used to represent the evolutionary relationships between species, and often these phylogenies are equipped with edge lengths that indicate degrees of evolutionary difference. Given such a phylogeny, a popular…
Survival probability within a certain time horizon T is a common measure of population viability. The choice of T implicitly involves a time preference, similar to economic discounting: Conservation success is evaluated at the time horizon…
Phylogenetic Diversity (PD) is a prominent quantitative measure of the biodiversity of a collection of present-day species (taxa). This measure is based on the evolutionary distance among the species in the collection. Loosely speaking, if…
Phylogenetic diversity is a measure for describing how much of an evolutionary tree is spanned by a subset of species. If one applies this to the (unknown) subset of current species that will still be present at some future time, then this…
Phylogenetic Diversity(PD)is a well-regarded measure of the overall biodiversity of a set of present-day species(taxa)that indicates its ecological significance.In the Maximize Phylogenetic Diversity(Max-PD)problem one is asked to find a…
Under mild non-degeneracy assumptions on branching rates in each generation, we provide a criterion for almost-sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total…
In the NP-hard Optimizing PD with Dependencies (PDD) problem, the input consists of a phylogenetic tree $T$ over a set of taxa $X$, a food-web that describes the prey-predator relationships in $X$, and integers $k$ and $D$. The task is to…
A central goal in ecology is to understand how biodiversity is maintained. Previous theoretical works have employed the rock-paper-scissors (RPS) game as a toy model, demonstrating that population mobility is crucial in determining the…
In the Maximize Phylogenetic Diversity problem, we are given a phylogenetic tree that represents the genetic proximity of species, and we are asked to select a subset of species of maximum phylogenetic diversity to be preserved through…
The fitness of a biological strategy is typically measured by its expected reproductive rate, the first moment of its offspring distribution. However, strategies with high expected rates can also have high probabilities of extinction. A…
For a phylogenetic tree, the phylogenetic diversity of a set A of taxa is the total weight of edges on paths to A. Finding small sets of maximal diversity is crucial for conservation planning, as it indicates where limited resources can be…
We consider the fundamental problem of selecting $k$ out of $n$ random variables in a way that the expected highest or second-highest value is maximized. This question captures several applications where we have uncertainty about the…
Conditions for almost sure extinction are studied in discrete time branching processes with an infinite number of types. It is not assumed that the expected number of children is a bounded function of the parent's type. There might also be…
We use a classical combinatorial inequality to establish a Markov inequality for multivariate binary Markov processes on trees. We then apply this result, alongside with the FKG inequality, to compare the expected loss of biodiversity under…
Network Phylogenetic Diversity (Network-PD) is a measure for the diversity of a set of species based on a rooted phylogenetic network (with branch lengths and inheritance probabilities on the reticulation edges) describing the evolution of…