Pulse disturbances in age-structured populations: Life history predicts initial impact and recovery time.

Understanding population responses to discrete 'pulsed' environmental disturbances is essential to conservation and adaptive management. Populations of concern can be driven to low levels by disturbance, and understanding interspecific differences in recovery trajectories is necessary for evaluating management options. We analysed single-species models to investigate the demographic and management factors determining the two components of population 'resilience': the magnitude of initial impact on population abundance, and duration of the recovery time. We simulated age-structured populations with density-dependent recruitment, subjected to a pulse disturbance consisting of a period of increased mortality of either the juvenile age class or all age classes, and calculated both impact and return time. For illustration, we used demographic parameters from a suite of 16 fish species. We formulated the model as a renewal equation, allowing us to describe disturbance impacts mathematically as a convolution. We also included nonlinear dynamics, representing populations that recover to a steady state; this is more realistic (in most cases) than prior analyses of resilience in linear models without density-dependence. When the disturbance affected only one or a few young age-classes, longevity was the major life-history determinant of impact and recovery time. Shorter-lived species endured greater impacts when disturbed because each age class is a greater proportion of the population. However, shorter-lived species also had faster recovery times, for the same reason. When disturbance affected adult age-classes, the impact was more immediate and no longer affected by species' longevity, though the effect of longevity on recovery time remained. These results improve our understanding of interspecific differences in resilience and increase our ability to make predictions for adaptive management. Additionally, formulating the problem as a renewal equation and using mathematical convolutions allows us to quantify how disturbances with different time courses (not just an immediate, constant level of disturbance but gradually increasing or decreasing levels of disturbance) would have different effects on population resilience: delayed responses for species in which biomass is concentrated in older age classes, and for disturbances that become progressively more severe.

Entender las respuestas de la población a perturbaciones ambientales, específicamente a pulsadas individuales, es esencial para la conservación y la gestión adaptativa. Las poblaciones de interés pueden reducirse a niveles bajas debido a la perturbación, y es necesario entender las diferencias interespecíficas en las trayectorias de recuperación para evaluar las opciones de gestión. Analizamos modelos para especies individuales para investigar los factores demográficos y de gestión que determinan los dos componentes de la 'resiliencia' de la población: la magnitud del impacto inicial sobre la abundancia de la población y la duración del tiempo de recuperación. Simulamos poblaciones estructuradas por edad con reclutamiento que depende de la densidad, las sometimos a una perturbación pulsada que consiste en un período de mayor mortalidad del grupo etário juvenil o de todos los grupos etários, y calculamos tanto el impacto como el tiempo de retorno. A modo de ilustración, utilizamos parámetros demográficos de un conjunto de 16 especies de peces. Formulamos el modelo como una ecuación de renovación, lo que nos permite describir matemáticamente los impactos de las perturbaciones como una convolución. También incluimos dinámicas no lineales que representan poblaciones que se recuperan hacia un estado estable; esto es más realista (en la mayoría de los casos) que los análisis previos de resiliencia en modelos lineales sin la dependencia de la densidad. Cuando la perturbación ha afectado a uno o a algunos pocos grupos etários jóvenes, la longevidad fue el principal determinante de la historia de vida del impacto y el tiempo de recuperación. Las especies de vida más corta sufrieron mayores impactos cuando fueron perturbadas porque cada grupo etáreo representa una mayor proporción de la población. Sin embargo, las especies con vidas más cortas también tuvieron tiempos de recuperación más rápidos, por la misma razón. Cuando la perturbación afectó a los grupos etários adultos, el impacto fue más inmediato y ya no se vio afectado por la longevidad de las especies, aunque se mantuvo el efecto de la longevidad sobre el tiempo de recuperación. Estos resultados mejoran nuestra comprensión de las diferencias interespecíficas de la resiliencia y aumentan nuestra capacidad para hacer predicciones con fin a la gestión adaptativa. Además, formular el problema como una ecuación de renovación y usar convoluciones matemáticas nos permite cuantificar cómo las perturbaciones con distintos lapsos de tiempo (no solo un nivel de perturbación constante e inmediato, sino niveles de perturbación que aumentan o disminuyen gradualmente) tendrían diferentes efectos sobre la resiliencia de la población: respuestas tardías para especies en las que la biomasa se concentra en grupos etários de mayor edad y para perturbaciones que se vuelven progresivamente más severas.

Setting expected timelines of fished population recovery for the adaptive management of a marine protected area network.

Adaptive management of marine protected areas (MPAs) requires developing methods to evaluate whether monitoring data indicate that they are performing as expected. Modeling the expected responses of targeted species to an MPA network, with a clear timeline for those expectations, can aid in the development of a monitoring program that efficiently evaluates expectations over appropriate time frames. Here, we describe the expected trajectories in abundance and biomass following MPA implementation for populations of 19 nearshore fishery species in California. To capture the process of filling in the age structure truncated by fishing, we used age-structured population models with stochastic larval recruitment to predict responses to MPA implementation. We implemented both demographically open (high larval immigration) and closed (high self-recruitment) populations to model the range of possible trajectories as they depend on recruitment dynamics. From these simulations, we quantified the time scales over which anticipated increases in abundance and biomass inside MPAs would become statistically detectable. Predicted population biomass responses range from little change, for species with low fishing rates, to increasing by a factor of nearly seven, for species with high fishing rates before MPA establishment. Increases in biomass following MPA implementation are usually greater in both magnitude and statistical detectability than increases in abundance. For most species, increases in abundance would not begin to become detectable for at least 10 years after implementation. Overall, these results inform potential indicator metrics (biomass), potential indicator species (those with a high fishing : natural mortality ratio), and time frame (>10 yr) for MPA monitoring assessment as part of the adaptive management process.

Fitting state-space integral projection models to size-structured time series data to estimate unknown parameters.

Integral projection models (IPMs) have a number of advantages over matrix-model approaches for analyzing size-structured population dynamics, because the latter require parameter estimates for each age or stage transition. However, IPMs still require appropriate data. Typically they are parameterized using individual-scale relationships between body size and demographic rates, but these are not always available. We present an alternative approach for estimating demographic parameters from time series of size-structured survey data using a Bayesian state-space IPM (SSIPM). By fitting an IPM in a state-space framework, we estimate unknown parameters and explicitly account for process and measurement error in a dataset to estimate the underlying process model dynamics. We tested our method by fitting SSIPMs to simulated data; the model fit the simulated size distributions well and estimated unknown demographic parameters accurately. We then illustrated our method using nine years of annual surveys of the density and size distribution of two fish species (blue rockfish, Sebastes mystinus, and gopher rockfish, S. carnatus) at seven kelp forest sites in California. The SSIPM produced reasonable fits to the data, and estimated fishing rates for both species that were higher than our Bayesian prior estimates based on coast-wide stock assessment estimates of harvest. That improvement reinforces the value of being able to estimate demographic parameters from local-scale monitoring data. We highlight a number of key decision points in SSIPM development (e.g., open vs. closed demography, number of particles in the state-space filter) so that users can apply the method to their own datasets.

Changing central Pacific El Niños reduce stability of North American salmon survival rates.

Pacific salmon are a dominant component of the northeast Pacific ecosystem. Their status is of concern because salmon abundance is highly variable--including protected stocks, a recently closed fishery, and actively managed fisheries that provide substantial ecosystem services. Variable ocean conditions, such as the Pacific Decadal Oscillation (PDO), have influenced these fisheries, while diminished diversity of freshwater habitats have increased variability via the portfolio effect. We address the question of how recent changes in ocean conditions will affect populations of two salmon species. Since the 1980s, El Niño Southern Oscillation (ENSO) events have been more frequently associated with central tropical Pacific warming (CPW) rather than the canonical eastern Pacific warming ENSO (EPW). CPW is linked to the North Pacific Gyre Oscillation (NPGO), whereas EPW is linked to the PDO, different indicators of northeast Pacific Ocean ecosystem productivity. Here we show that both coho and Chinook salmon survival rates along western North America indicate that the NPGO, rather than the PDO, explains salmon survival since the 1980s. The observed increase in NPGO variance in recent decades was accompanied by an increase in coherence of local survival rates of these two species, increasing salmon variability via the portfolio effect. Such increases in coherence among salmon stocks are usually attributed to controllable freshwater influences such as hatcheries and habitat degradation, but the unknown mechanism underlying the ocean climate effect identified here is not directly subject to management actions.

Shifting Effects of Ocean Conditions on Survival and Breeding Probability of a Long-Lived Seabird.

With a rapidly changing climate, there is an increasing need to predict how species will respond to changes in the physical environment. One approach is to use historic data to estimate the past influence of environmental variation on important demographic parameters and then use these relationships to project the abundance of a population or species under future climate scenarios. However, as novel climate conditions emerge, novel species responses may also appear. In some systems, environmental conditions beyond the range of those observed during the course of most long-term ecological studies are already evident. Yet little attention has been given to how these novel conditions may be influencing previously established environment-species relationships. Here, we model the relationships between ocean conditions and the demography of a long-lived seabird, Brandt's cormorant (Phalacrocorax penicillatusI), in central California and show that these relationships have changed in recent years. Beginning in 2007/2008, the response of Brandt's cormorant, an upper trophic level predator, to ocean conditions shifted, resulting in lower than predicted survival and breeding probability. Survival was generally less variable than breeding probability and was initially best predicted by the basin-scale forcing of the El Niño Southern Oscillation rather than local ocean conditions. The shifting response of Brandt's cormorant to ocean conditions may be just a proximate indication of altered dynamics in the food web and that important forage fish are not responding to the physical ocean environment as expected. These changing relationships have important implications for our ability to project the effects of future climate change for species and communities.

Marine protected area networks in California, USA.

California responded to concerns about overfishing in the 1990s by implementing a network of marine protected areas (MPAs) through two science-based decision-making processes. The first process focused on the Channel Islands, and the second addressed California's entire coastline, pursuant to the state's Marine Life Protection Act (MLPA). We review the interaction between science and policy in both processes, and lessons learned. For the Channel Islands, scientists controversially recommended setting aside 30-50% of coastline to protect marine ecosystems. For the MLPA, MPAs were intended to be ecologically connected in a network, so design guidelines included minimum size and maximum spacing of MPAs (based roughly on fish movement rates), an approach that also implicitly specified a minimum fraction of the coastline to be protected. As MPA science developed during the California processes, spatial population models were constructed to quantify how MPAs were affected by adult fish movement and larval dispersal, i.e., how population persistence within MPA networks depended on fishing outside the MPAs, and how fishery yields could either increase or decrease with MPA implementation, depending on fishery management. These newer quantitative methods added to, but did not supplant, the initial rule-of-thumb guidelines. In the future, similar spatial population models will allow more comprehensive evaluation of the integrated effects of MPAs and conventional fisheries management. By 2011, California had implemented 132 MPAs covering more than 15% of its coastline, and now stands on the threshold of the most challenging step in this effort: monitoring and adaptive management to ensure ecosystem sustainability.

Beyond connectivity: how empirical methods can quantify population persistence to improve marine protected-area design.

Demographic connectivity is a fundamental process influencing the dynamics and persistence of spatially structured populations. Consequently, quantifying connectivity is essential for properly designing networks of protected areas so that they achieve their core ecological objective of maintaining population persistence. Recently, many empirical studies in marine systems have provided essential, and historically challenging to obtain, data on patterns of larval dispersal and export from marine protected areas (MPAs). Here, we review the empirical studies that have directly quantified the origins and destinations of individual larvae and assess those studies' relevance to the theory of population persistence and MPA design objectives. We found that empirical studies often do not measure or present quantities that are relevant to assessing population persistence, even though most studies were motivated or contextualized by MPA applications. Persistence of spatial populations, like nonspatial populations, depends on replacement, whether individuals reproduce enough in their lifetime to replace themselves. In spatial populations, one needs to account for the effect of larval dispersal on future recruitment back to the local population through local retention and other connectivity pathways. The most commonly reported descriptor of larval dispersal was the fraction of recruitment from local origin (self-recruitment). Self-recruitment does not inform persistence-based MPA design because it is a fraction of those arriving, not a fraction of those leaving (local retention), so contains no information on replacement. Some studies presented connectivity matrices, which can inform assessments of persistence with additional knowledge of survival and fecundity after recruitment. Some studies collected data in addition to larval dispersal that could inform assessments of population persistence but which were not presented in that way. We describe how three pieces of empirical information are needed to fully describe population persistence in a network of MPAs: (1) lifetime fecundity, (2) the proportion of larvae that are locally retained (or the full connectivity matrix), and (3) survival rate after recruitment. We conclude by linking theory and data to provide detailed guidance to empiricists and practitioners on field sampling design and data presentation that better informs the MPA objective of population persistence.

A comparison of linear demographic models and fraction of lifetime egg production for assessing sustainability in sharks.

Conventional methods for management of data-rich fisheries maintain sustainable populations by assuring that lifetime reproduction is adequate for individuals to replace themselves and accounting for density-dependent recruitment. Fishing is not allowed to reduce relative lifetime reproduction, the fraction of current egg production relative to unfished egg production (FLEP), below a sustainable level. Because most shark fisheries are data poor, other representations of persistence status have been used, including linear demographic models, which incorporate life-history characteristics in age-structured models with no density dependence. We tested how well measures of sustainability from 3 linear demographic methods (rebound potential, stochastic growth rate, and potential population increase) reflect actual population persistence by comparing values of these measures with FLEP for 26 shark species. We also calculated the value of fishing mortality (F) that would allow all 26 species to maintain an accepted precautionary threshold for sharks of FLEP = 60%, expressing F as a fraction of natural mortality (M). Values of stochastic growth rate and potential population growth did not covary in rank order with FLEP (p = 0.057 and p = 0.077, respectively) and neither was significantly correlated with FLEP. Ordinal ranking of rebound potential positively covaried with FLEP (p = 0.00013), but the relative rankings of some species were substantially out of order. Adopting a sustainable limit of F = 0.16M would maintain all 26 species above the precautionary minimum value of FLEP (60%). We concluded that shark-fishery and conservation policies should rely on calculation of replacement (i.e., FLEP), and that sharks should be fished at a precautionary level that would protect all stocks (i.e., F< 0.16M).

A first estimate of white shark, Carcharodon carcharias, abundance off Central California.

The decline of sharks in the global oceans underscores the need for careful assessment and monitoring of remaining populations. The northeastern Pacific is the home range for a genetically distinct clade of white sharks (Carcharodon carcharias). Little is known about the conservation status of this demographically isolated population, concentrated seasonally at two discrete aggregation sites: Central California (CCA) and Guadalupe Island, Mexico. We used photo-identification of dorsal fins in a sequential Bayesian mark-recapture algorithm to estimate white shark abundance off CCA. We collected 321 photographs identifying 130 unique individuals, and estimated the abundance off CCA to be 219 mature and sub-adult individuals ((130, 275) 95% credible intervals), substantially smaller than populations of other large marine predators. Our methods can be readily expanded to estimate shark population abundance at other locations, and over time, to monitor the status, population trends and protection needs of these globally distributed predators.

Decision analysis for designing marine protected areas for multiple species with uncertain fishery status.

Marine protected areas (MPAs) are growing in popularity as a conservation tool, and there are increasing calls for additional MPAs. Meta-analyses indicate that most MPAs successfully meet the minimal goal of increasing biomass inside the MPA, while some do not, leaving open the important question of what makes MPAs successful. An often-overlooked aspect of this problem is that the success of fishery management outside MPA boundaries (i.e., whether a population is overfished) affects how well MPAs meet both conservation goals (e.g., increased biomass) and economic goals (e.g., minimal negative effects on fishery yield). Using a simple example of a system with homogeneous habitat and periodically spaced MPAs, we show that, as area in MPAs increases, (1) conservation value (biomass) may initially be zero, implying no benefit, then at some point increases monotonically; and (2) fishery yield may be zero, then increases monotonically to a maximum beyond which further increase in MPA area causes yield to decline. Importantly, the points at which these changes in slope occur vary among species and depend on management outside MPAs. Decision makers considering the effects of a potential system of MPAs on multiple species are confronted by a number of such cost-benefit curves, and it is usually impossible to maximize benefits and minimize costs for all species. Moreover, the precise shape of each curve is unknown due to uncertainty regarding the fishery status of each species. Here we describe a decision-analytic approach that incorporates existing information on fishery stock status to present decision makers with the range of likely outcomes of MPA implementation. To summarize results from many species whose overfishing status is uncertain, our decision-analysis approach involves weighted averages over both overfishing uncertainty and species. In an example from an MPA decision process in California, USA, an optimistic projection of future fishery management success led to recommendation of fewer and smaller MPAs than that derived from a more pessimistic projection of future management success. This example illustrates how information on fishery status can be used to project potential outcomes of MPA implementation within a decision analysis framework and highlights the need for better population information.

Frequency responses of age-structured populations: Pacific salmon as an example.

Increasing evidence of the effects of changing climate on physical ocean conditions and long-term changes in fish populations adds to the need to understand the effects of stochastic forcing on marine populations. Cohort resonance is of particular interest because it involves selective sensitivity to specific time scales of environmental variability, including that of mean age of reproduction, and, more importantly, very low frequencies (i.e., trends). We present an age-structured model for two Pacific salmon species with environmental variability in survival rate and in individual growth rate, hence spawning age distribution. We use computed frequency response curves and analysis of the linearized dynamics to obtain two main results. First, the frequency response of the population is affected by the life history stage at which variability affects the population; varying growth rate tends to excite periodic resonance in age structure, while varying survival tends to excite low frequency fluctuation with more effect on total population size. Second, decreasing adult survival strengthens the cohort resonance effect at all frequencies, a finding that addresses the question of how fishing and climate change will interact.

Rotating spatial harvests and fishing effort displacement: a comment on Game et al. (2009).

Game et al. (2009) explored using rapid rotational fishing for increasing herbivore biomass. Their results depend crucially on the assumption that fishing effort that was in closures disappears, rather than shifting elsewhere. If effort shifts, rapid rotation has no effects, but previous age-structured analyses show benefits of longer period rotation that are robust to effort displacement.

Marine reserve networks for species that move within a home range.

Marine reserves are expected to benefit a wide range of species, but most models used to evaluate their effects assume that adults are sedentary, thereby potentially overestimating population persistence. Many nearshore marine organisms move within a home range as adults, and there is a need to understand the effects of this type of movement on reserve performance. We incorporated movement within a home range into a spatially explicit marine reserve model in order to assess the combined effects of adult and larval movement on persistence and yield in a general, strategic framework. We describe how the capacity of a population to persist decreased with increasing home range size in a manner that depended on whether the sedentary case was maintained by self persistence or network persistence. Self persistence declined gradually with increasing home range and larval dispersal distance, while network persistence decreased sharply to 0 above a threshold home range and was less dependent on larval dispersal distance. The maximum home range size protected by a reserve network increased with the fraction of coastline in reserves and decreasing exploitation rates outside reserves. Spillover due to movement within a home range contributed to yield moderately under certain conditions, although yield contributions were generally not as large as those from spillover due to larval dispersal. Our results indicate that, for species exhibiting home range behavior, persistence in a network of marine reserves may be more predictable than previously anticipated from models based solely on larval dispersal, in part due to better knowledge of home range sizes. Including movement within a home range can change persistence results significantly from those assuming that adults are sedentary; hence it is an important consideration in reserve design.

Model-based assessment of persistence in proposed marine protected area designs.

Assessment of marine protected areas (MPAs) requires the ability to quantify the effects of proposed MPA size and placement, habitat distribution, larval dispersal, and fishing on the persistence of protected populations. Here we describe a model-based approach to assessment of the contribution of a network of marine protected areas to the persistence of populations with a sedentary adult phase and a dispersing larval phase. The model integrates the effects of a patchy spatial distribution of habitat, the spatial scale of larval dispersal, and the level of fishing outside of reserves into a calculation of the spatial distribution of equilibrium settlement. We use the amount of coastline predicted to have equilibrium settlement rates that saturate post-settlement habitat as a response variable for the assessment and comparison of MPA network designs. We apply this model to a set of recently proposed MPA networks for the central coast of California, USA. Results show that the area of habitat set aside is a good predictor of the area over which population levels will be high for short-distance dispersers. However, persistence of longer distance dispersers depends critically on the spatial distribution of habitat and reserves, ranging from not persistent anywhere to persistent over a greater area than that set aside in reserves. These results depend on the mechanisms of persistence, with self-replacement supporting short-distance dispersers and network effects supporting long-distance dispersers. Persistence also depends critically on fishery status outside the MPAs, as well as how fishing effort is redistributed after MPA implementation. This assessment method provides important benchmarks, as well as a transparent modeling approach, for improving initial MPA configurations that may result from less-comprehensive rule- or habitat-based methods of designing MPAs.

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.

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.

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.

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.

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.