Using network properties to predict disease dynamics on human contact networks.

Recent studies have increasingly turned to graph theory to model more realistic contact structures that characterize disease spread. Because of the computational demands of these methods, many researchers have sought to use measures of network structure to modify analytically tractable differential equation models. Several of these studies have focused on the degree distribution of the contact network as the basis for their modifications. We show that although degree distribution is sufficient to predict disease behaviour on very sparse or very dense human contact networks, for intermediate density networks we must include information on clustering and path length to accurately predict disease behaviour. Using these three metrics, we were able to explain more than 98 per cent of the variation in endemic disease levels in our stochastic simulations.

When logic fails ecology.

Ecology plays an important role in society, informing policy and management decisions across a variety of issues. As such, regularities in processes would indicate higher levels of predictive outcomes and would reduce the amount of research required for specific issues that policy makers need addressed. Scientific laws are considered the pinnacle of success and usefulness in addressing regularities or universal truths. Ecology studies complex interactions of individuals with unique behaviors, making the identification of laws problematic. Two equations, Malthusian growth and the logistic equation, continue to receive attention and are frequently cited as exemplar laws in ecology. However, an understanding of scientific laws shows that neither are good candidates for law status. In this paper, I will discuss why ecology is not well structured for scientific laws, as they are currently understood. Finally, I will consider alternative proposals for the role of laws in ecology and alternate forms of laws that may be applicable.

The effects of dispersal patterns on marine reserves: does the tail wag the dog?

The concept of marine reserves as a method of improving management of fisheries is gaining momentum. While the list of benefits from reserves is frequently promoted, precise formulations of theory to support reserve design are not fully developed. To determine the size of reserves and the distances between reserves an understanding of the requirements for persistence of local populations is required. Unfortunately, conditions for persistence are poorly characterized, as are the larval dispersal patterns on which persistence depends. With the current paucity of information regarding meroplanktonic larval transport processes, understanding the robustness of theoretical results to larval dispersal is of key importance. From this formulation a broad range of dispersal patterns are analyzed. Larval dispersal is represented by a probability distribution that defines the fraction of successful settlers from an arbitrary location, the origin of the distribution, to any other location along the coast. While the effects of specific dispersal patterns have been investigated for invasion processes, critical habitat size and persistence issues have generally been addressed with only one or two dispersal types. To that end, we formulate models based on integrodifference equations that are spatially continuous and temporally discrete. We consider a range of dispersal distributions from leptokurtic to platykurtic. The effect of different dispersal patterns is considered for a single isolated reserve of varying size receiving no external larvae, as well as multiple reserves with varying degrees of connectivity. While different patterns result in quantitative differences in persistence, qualitatively similar effects across all patterns are seen in both single- and multiple reserve models. Persistence in an isolated reserve requires a size that is approximately twice the mean dispersal distance and regardless of the dispersal pattern the population in a patch is not persistent if the reserve size is reduced to just the mean dispersal distance. With an idealized coastline structure consisting of an infinite line of equally spaced reserves separated by regions of coastline in which reproduction is nil, the relative settlement as a function of the fraction of coastline and size of reserve is qualitatively very similar over a broad range of dispersal patterns. The upper limit for the minimum fraction of coastline held in reserve is about 40%. As the fraction of coastline is reduced, the minimum size of reserve becomes no more than 1.25 times the mean dispersal distance.