Connectivity in marine protected areas.
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Biomedical subjects
Louis W Botsford
Publications and source records attributed to Louis W Botsford.
Persistence of spatial populations depends on returning home.
There is a need for better description and heuristic understanding of the sustainability of populations connected over space by a dispersing stage, both for management purposes and to increase our basic knowledge of the dynamics of these populations. We show that persistence of such a population of connected subpopulations depends on whether the sum of the reproductive gains through all possible closed, between-patch reproductive paths through multiple generations, relative to the shortfall in self-persistence in each path, exceeds unity plus extra terms, which only appear if there are four or more patches. These extra terms have the heuristic explanation that they avoid double counting of reproductive paths that arise with four or more patches because there can be nonoverlapping subnetworks. Thus only those patterns of reproduction and connectivity which eventually lead to descendants returning to the patch from which they originate contribute to persistence. This result provides the basis for evaluating connectivity and habitat heterogeneity to understand reserve design, the effects of human fragmentation, the collapse of marine fisheries, and other conservation issues.
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A simple persistence condition for structured populations.
The fundamental question in both basic and applied population biology of whether a species will increase in numbers is often investigated by finding the population growth rate as the largest eigenvalue of a deterministic matrix model. For a population classified only by age, and not stage or size, a simpler biologically interpretable condition can be used, namely whether R0, the mean number of offspring per newborn, is greater than one. However, for the many populations not easily described using only age classes, stage-structured models must be used for which there is currently no quantity like R0. We determine analogous quantities that must be greater than one for persistence of a general structured population model that have a similar useful biological interpretation. Our approach can be used immediately to determine the magnitude of changes and interactions that would either allow population persistence or would ensure control of an undesirable species.
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Estimating the status of nearshore rockfish (Sebastes spp.) populations with length frequency data.
Ecologists often point to excessive truncation of a population's size-structure as a deleterious effect of exploitation, yet the effect of this truncation on population persistence is seldom quantified. While persistence of marine populations requires maintenance of a sufficient level of lifetime reproduction, fishing reduces lifetime reproduction by increasing the total mortality rate, preventing individuals from growing old, large, and highly fecund. We employ a new method of estimating changes in lifetime egg production (LEP) using two samples of the size structure, one in the past and one current, to assess persistence of five species of nearshore rockfish (Sebastes spp.) in California and Oregon, U.S.A. Using length frequency data from catch in the recreational fishery, we estimate that since 1980, four of the five rockfish species considered have experienced declines in LEP to levels that suggest that persistence is impaired. When changes in LEP were estimated for subsets of the data corresponding to neighboring geographical regions, differences in LEP levels were apparent in the neighboring regions, implying that the effects of fishing mortality are not evenly distributed over space. We conclude by discussing the use of this estimation approach to assess the status of other species in data-poor situations.
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Dispersal per recruit: an efficient method for assessing sustainability in marine reserve networks.
Marine reserves are an increasingly important tool for the management of marine ecosystems around the world. However, the effects of proposed marine reserve configurations on sustainability and yield of populations are typically not estimated because of the computational intensity of direct simulation and uncertainty in larval dispersal and density-dependent recruitment. Here we develop a method for efficiently assessing a marine reserve configuration for persistence and yield of a population with sedentary adults and dispersing larvae. The method extends the familiar sustainability criteria of individual replacement for single populations based on eggs-per-recruit (EPR) to spatially distributed populations with sedentary adults, a dispersing larval phase, and limited carrying capacity in the settlement-recruit relationship. We refer to this approach as dispersal-per-recruit (DPR). In some cases, a single DPR calculation, based on the assumption that post-settlement habitat is saturated (i.e., at maximum recruitment), is sufficient to determine population persistence, while in other cases further iterative calculations are required. These additional calculations reach an equilibrium more rapidly than a full simulation of age- or size-structured populations. From the DPR result, fishery yield can be computed from yield-per-recruit (YPR) at each point. We assess the utility of DPR calculations by applying them to single reserves, uniformly distributed systems of reserves, and randomly sized and spaced systems of reserves on a linear coastline. We find that for low levels of EPR in fished areas (e.g., 10% or less of the natural, unfished EPR when post-settlement habitats are saturated by 35% of natural settlement), a single DPR calculation is sufficient to determine persistence of the population. We also show that, in uniform systems of reserves with finite reserve size, maximal fisheries yield occurs when the density of reserves is such that all post-settlement habitat is nearly saturated with settlers. Finally, we demonstrate the application of this approach to a realistic proposed marine reserve configuration.
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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.
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