Compensatory Density Dependence Research Articles

Recruitment dynamics of juvenile salmonids: Comparisons among populations and with classic case studies.

Understanding recruitment, the process by which individuals are added to a population or to a fishery, is critical for understanding population dynamics and facilitating sustainable fisheries management. Important variation in recruitment dynamics is observed among populations, wherein some populations exhibit asymptotic productivity and others exhibit overcompensation (i.e., compensatory density-dependence in recruitment). Our ability to understand this interpopulation variability in recruitment patterns is limited by a poor understanding of the underlying mechanisms, such as the complex interactions between density dependence, recruitment, and environment. Furthermore, most studies on recruitment are conducted using an observational design with long time series that are seldom replicated across populations in an experimentally controlled fashion. Without proper replication, extrapolations between populations are tenuous, and the underlying environmental trends are challenging to quantify. To address these issues, we conducted a field experiment manipulating stocking densities of juvenile brook trout Salvelinus fontinalis in three wild populations to show that these neighboring populations-which exhibit divergent patterns of density dependence due to environmental conditions-also have important differences in recruitment dynamics. Testing against four stock-recruitment models (density independent, linear, Beverton-Holt, and Ricker), populations exhibited ~twofold variation in asymptotic productivity, with no overcompensation following a Beverton-Holt model. Although environmental variables (e.g., temperature, pH, depth, substrate) correlated with population differences in recruitment, they did not improve the predictive power in individual populations. Comparing our patterns of recruitment with classic salmonid case studies revealed that despite differences in the shape and parameters of the curves (i.e., Ricker vs. Beverton-Holt), a maximum stocking density of about five YOY fish/m2 emerged. Higher densities resulted in very marginal increases in recruitment (Beverton-Holt) or reduced recruitment due to overcompensation (Ricker).

Effects of early life mass mortality events on fish populations

AbstractMass mortality events are ubiquitous in nature and can be caused by, for example, diseases, extreme weather and human perturbations such as contamination. Despite being prevalent and rising globally, how mass mortality in early life causes population‐level effects such as reduced total population biomass, is not fully explored. In particular for fish, mass mortality affecting early life may be dampened by compensatory density‐dependent processes. However, due to large variations in year‐class strength, potentially caused by density‐independent variability in survival, the impact at the population level may be high in certain years. We quantify population‐level impacts at two levels of mass mortality (50% and 99% additional mortality) during early life across 40 fish species using age‐structured population dynamics models. The findings from these species‐specific models are further supported by an analysis of detailed stock‐specific models for three of the species. We find that population impacts are highly variable between years and species. Short‐lived species that exhibit a low degree of compensatory density dependence and high interannual variation in survival experience the strongest impacts at the population level. These quantitative and general relationships allow predicting the range of potential impacts of mass mortality events on species based on their life history. This is critical considering that the frequency and severity of mass mortality events are increasing worldwide.

Modeling Pesticide Effects on Multiple Threatened and Endangered Cyprinid Fish Species: The Role of Life-History Traits and Ecology

Mechanistic models are invaluable in ecological risk assessment (ERA) because they facilitate extrapolation of organism-level effects to population-level effects while accounting for species life history, ecology, and vulnerability. In this work, we developed a model framework to compare the potential effects of the fungicide chlorothalonil across four listed species of cyprinid fish and explore species-specific traits of importance at the population level. The model is an agent-based model based on the dynamic energy budget theory. Toxicokinetic-toxicodynamic sub-models were used for representing direct effects, whereas indirect effects were described by decreasing food availability. Exposure profiles were constructed based on hydroxychlorothalonil, given the relatively short half-life of parent chlorothalonil. Different exposure magnification factors were required to achieve a comparable population decrease across species. In particular, those species producing fewer eggs and with shorter lifespans appeared to be more vulnerable. Moreover, sequentially adding effect sub-models resulted in different outcomes depending on the interplay of life-history traits and density-dependent compensation effects. We conclude by stressing the importance of using models in ERA to account for species-specific characteristics and ecology, especially when dealing with listed species and in accordance with the necessity of reducing animal testing.

Controlling invasive fish in fluctuating environments: Model analysis of common carp (Cyprinus carpio) in a shallow lake

AbstractClimate change can act to facilitate or inhibit invasions of non‐native species. Here, we address the influence of climate change on control of non‐native common carp (hereafter, carp), a species recognized as one of the “world's worst” invaders across the globe. Control of this species is exceedingly difficult, as it exhibits rapid population growth and compensatory density dependence. In many locations where carp have invaded, however, climate change is altering hydrologic regimes and may influence population demography and efficacy of human control efforts. To further evaluate these processes, we employed a modified version of an age‐based population model (CarpMOD), to investigate how hydrologic variability (change in lake area) influences carp population dynamics and control efforts in Malheur Lake, southeastern Oregon, USA. We explored how changes in lake area influence carp populations under three control scenarios: (1) no carp removal, (2) carp removal during low water years, and (3) carp removal during all years. Lake area fluctuations strongly influenced carp populations and the efficacy of carp control. Modeled carp biomass peaked when the lake transitioned from high‐to‐low levels, and carp biomass declined when lake area transitioned from low‐to‐high. Removing carp during low water periods—when fish were concentrated into a smaller area—reduced carp populations almost as much as removing carp every year. Furthermore, the effectiveness of control efforts increased with the prevalence and severity of low lake conditions (longer durations of very low lake area). These simulations suggest that a drier climate may naturally decrease carp populations and make them easier to control. However, drier conditions may also negatively affect aquatic ecosystems and potentially have a greater impact than non‐native species themselves.

Strong Allee effect and basins of attraction in a discrete‐time zoonotic infectious disease model

AbstractMotivated by the Feline immunodeficiency virus, the virus that causes AIDS in cat populations, we use discrete‐time infectious disease models with demographic strong Allee effect to examine the impact of the fatal susceptible‐infected (SI) infections on two different types of growth functions: Holling type III or modified Beverton–Holt per‐capita growth function (compensatory density dependence), and Ricker per‐capita growth function with mating (overcompensatory density dependence). The occurrence of the strong Allee effect in the disease‐free equation renders the SI population model bistable, where the two coexisting locally asymptotically stable equilibrium points are either the origin (catastrophic extinction state) and the second fixed point (compensatory dynamics) or the origin and an intrinsically generated demographic period population cycle (overcompensatory dynamics). We use the basic reproduction number, , and the spectral radius, , to examine the structures of the coexisting attractors. In particular, we use MATLAB simulations to show that the fatal disease is not only capable of enlarging or shrinking the basin of attraction of the catastrophic extinction state, but it is also capable of fracturing the basins of attraction into several disjoint sets. Thus, making it difficult to specify the asymptotic zoonotic SI disease outcome in terms of all initial infections. The complexity of the basins of attractions appears to increase with an increase in the period of the intrinsically generated demographic population cycles.Recommendations for Resource Managers: Worldwide, disease agents which originate from animals or products of animal origin, such as Ebola virus, COVID‐19, West Nile virus, or malaria are responsible for millions of deaths each year. To help improve control and ultimately eradicate future pandemics in human populations, we use a Feline immunodeficiency virus disease model with the strong Allee effect to understand outbreaks of zoonotic diseases. In general, the strong Allee effect renders a population bistable with a catastrophic extinction state coexisting with a persistence state. We use the basic reproduction number and the spectral radius to obtain conditions for outbreaks of zoonotic diseases and conditions for zoonotic disease extinction. We show that a fatal zoonotic disease is not only capable of enlarging or shrinking the basin of attraction of the catastrophic extinction state, but it is also capable of fracturing the basins of attraction into several disjoint sets. Thus, making it difficult to specify the asymptotic zoonotic disease outcome in terms of all initial infections. The complexity of the basins of attractions appears to increase with an increase in the period of the demographic population cycles.

Lifting the Vendace, Coregonus albula, on the Life Table: Survival, Growth and Reproduction in Different Life-Stages during Very High and Low Abundance Regimes

We analyzed the variability in vendace population parameters in the context of a life table. Parameters related to growth, fecundity and survival were estimated for post-recruitment (age > 1 growing season) life stages of Lake Southern Konnevesi vendace in both very high and low population abundance regimes. Pre-recruitment survival producing population stability was then determined. We found a very strong compensatory density dependence in growth, fecundity and survival: during low abundance, a lifetime reproductive output of a female was almost 20 times that of the abundant regime. To maintain the low abundance regime, pre-recruitment survival must counterbalance it by decreasing to a very low level. Potential drivers of high variability in pre-recruit survival and potential for depensation, Allee effect, are discussed, as well as the implications of the results on fisheries management and risk of extinction due to anthropogenic stressors such as global warming or extensive predator stocking.

Evolutionary management of coral‐reef fisheries using phylogenies to predict density dependence

Harvesting models are based upon the ideology that removing large, old individuals provides space for young, fast-growing counterparts that can maximize (fisheries) yields while maintaining population stability and ecosystem function. Yet, this compensatory density dependent response has rarely been examined in multispecies systems. We combined extensive data sets from coral-reef fisheries across a suite of Pacific islands and provided unique context to the universal assumptions of compensatory density dependence. We reported that size-and-age truncation only existed for 49% of target coral-reef fishes exposed to growing fishing pressure across a suite of Pacific islands. In contrast, most of the remaining species slowly disappeared from landings and reefs with limited change to their size structure (i.e., little to no compensation), often becoming replaced by smaller-bodied sister species. To understand these remarkable and disparate differences, we constructed phylogenies for dominant fish families and discovered that large patristic distances between sister species, or greater phylogenetic isolation, predicted size-and-age truncation. Isolated species appeared to have greater niche dominance or breadth, supported by their faster growth rates compared to species with similar sizes and within similar guilds, and many also have group foraging behavior. In contrast, closely related species may have more restricted, realized niches that led to their disappearance and replacement. We conclude that phylogenetic attributes offered novel guidance to proactively manage multispecies fisheries and improve our understanding of ecological niches and ecosystem stability.

Was historical cisco Coregonus artedi yield consistent with contemporary recruitment and abundance in Lake Superior?

AbstractHistorically, cisco Coregonus artedi Lesueur was the predominant prey fish and target of commercial fisheries throughout Lake Superior, but most spawning stocks collapsed by the mid‐1900s. Stocks partially recovered by the early 1990s, but contemporary abundance is considered to be below historical levels and driven by intermittent recruitment. Stochastic, age‐structured simulation models were used to determine whether historical (pre‐1955) cisco yield in Lake Superior was consistent with contemporary (1992–2015) abundance, life‐history characteristics and recruitment dynamics. When compared to contemporary stocks, the findings suggest historical stocks had: (1) similar recruits per spawner at low spawning stock sizes; (2) lower rates of compensatory density dependence; (3) similar or lower recruitment variation depending on the area and (4) higher median adult and age‐1 density. These findings are consistent with the hypothesis that eutrophication during the historical period supported greater recruitment and adult abundance and that re‐oligotrophication during the contemporary period may be limiting full recovery.

Compensatory and overcompensatory dynamics in prey\u2013predator systems exposed to harvest

Density dependent prey–predator systems under the impact of harvest are considered. The recruitment functions for both the prey and predator belong to the Deriso–Schnute family which allow us to study how the dynamical behaviour of both populations changes when compensatory density dependence turns overcompensatory. Depending on the degree of overcompensation, we show in the case of no harvest that an increase of the fecundity of the prey always acts in a destabilizing fashion. If the degree of overcompensation becomes sufficiently large, such an increase can lead to large amplitude chaotic oscillations of the prey, which actually may drive the predator population to extinction. The impact of harvest also depends on the degree of overcompensatory density dependence. If only the prey is the target population, increased harvest in general seems to stabilize the dynamics. On the other hand, harvesting only the predator may in some cases tend to stabilize dynamics, but there are also parameter regions where this turns out to be a strong destabilizing effect.

Ecological Forecasts Reveal Limitations of Common Model Selection Methods: Predicting Changes in Beaver Colony Densities

Over the past two decades, there have been numerous calls to make ecology a more predictive science through direct empirical assessments of ecological models and predictions. While the widespread use of model selection using information criteria has pushed ecology toward placing a higher emphasis on prediction, few attempts have been made to validate the ability of information criteria to correctly identify the most parsimonious model with the greatest predictive accuracy. Here, we used an ecological forecasting framework to test the ability of information criteria to accurately predict the relative contribution of density dependence and density-independent factors (forage availability, harvest, weather, wolf [Canis lupus] density) on inter-annual fluctuations in beaver (Castor canadensis) colony densities. We modeled changes in colony densities using a discrete-time Gompertz model, and assessed the performance of four models using information criteria values: density-independent models with (1) and without (2) environmental covariates; and density-dependent models with (3) and without (4) environmental covariates. We then evaluated the forecasting accuracy of each model by withholding the final one-third of observations from each population and compared observed vs. predicted densities. Information criteria and our forecasting accuracy metrics both provided strong evidence of compensatory density dependence in the annual dynamics of beaver colony densities. However, despite strong within-sample performance by the most complex model (density-dependent with covariates) as determined using information criteria, hindcasts of colony densities revealed that the much simpler density-dependent model without covariates performed nearly as well predicting out-of-sample colony densities. The hindcast results indicated that the complex model over-fit our data, suggesting that parameters identified by information criteria as important predictor variables are only marginally valuable for predicting landscape-scale beaver colony dynamics. Our study demonstrates the importance of evaluating ecological models and predictions with long-term data and revealed how a known limitation of information criteria (over-fitting of complex models) can affect our interpretation of ecological dynamics. While incorporating knowledge of the factors that influence animal population dynamics can improve population forecasts, we suggest that comparing forecast performance metrics can likewise improve our knowledge of the factors driving population dynamics.

Ecological forecasts reveal limitations of common model selection methods: predicting changes in beaver colony densities.

Over the past two decades, there have been numerous calls to make ecology a more predictive science through direct empirical assessments of ecological models and predictions. While the widespread use of model selection using information criteria has pushed ecology toward placing a higher emphasis on prediction, few attempts have been made to validate the ability of information criteria to correctly identify the most parsimonious model with the greatest predictive accuracy. Here, we used an ecological forecasting framework to test the ability of information criteria to accurately predict the relative contribution of density dependence and density‐independent factors (forage availability, harvest, weather, wolf [Canis lupus] density) on inter‐annual fluctuations in beaver (Castor canadensis) colony densities. We modeled changes in colony densities using a discrete‐time Gompertz model, and assessed the performance of four models using information criteria values: density‐independent models with (1) and without (2) environmental covariates; and density‐dependent models with (3) and without (4) environmental covariates. We then evaluated the forecasting accuracy of each model by withholding the final one‐third of observations from each population and compared observed vs. predicted densities. Information criteria and our forecasting accuracy metrics both provided strong evidence of compensatory density dependence in the annual dynamics of beaver colony densities. However, despite strong within‐sample performance by the most complex model (density‐dependent with covariates) as determined using information criteria, hindcasts of colony densities revealed that the much simpler density‐dependent model without covariates performed nearly as well predicting out‐of‐sample colony densities. The hindcast results indicated that the complex model over‐fit our data, suggesting that parameters identified by information criteria as important predictor variables are only marginally valuable for predicting landscape‐scale beaver colony dynamics. Our study demonstrates the importance of evaluating ecological models and predictions with long‐term data and revealed how a known limitation of information criteria (over‐fitting of complex models) can affect our interpretation of ecological dynamics. While incorporating knowledge of the factors that influence animal population dynamics can improve population forecasts, we suggest that comparing forecast performance metrics can likewise improve our knowledge of the factors driving population dynamics.

Phenological responses in a sycamore-aphid-parasitoid system and consequences for aphid population dynamics: A 20year case study.

Species interactions have a spatiotemporal component driven by environmental cues, which if altered by climate change can drive shifts in community dynamics. There is insufficient understanding of the precise time windows during which inter-annual variation in weather drives phenological shifts and the consequences for mismatches between interacting species and resultant population dynamics-particularly for insects. We use a 20year study on a tri-trophic system: sycamore Acer pseudoplatanus, two associated aphid species Drepanosiphum platanoidis and Periphyllus testudinaceus and their hymenopteran parasitoids. Using a sliding window approach, we assess climatic drivers of phenology in all three trophic levels. We quantify the magnitude of resultant trophic mismatches between aphids and their plant hosts and parasitoids, and then model the impacts of these mismatches, direct weather effects and density dependence on local-scale aphid population dynamics. Warmer temperatures in mid-March to late-April were associated with advanced sycamore budburst, parasitoid attack and (marginally) D. platanoidis emergence. The precise time window during which spring weather advances phenology varies considerably across each species. Crucially, warmer temperatures in late winter delayed the emergence of both aphid species. Seasonal variation in warming rates thus generates marked shifts in the relative timing of spring events across trophic levels and mismatches in the phenology of interacting species. Despite this, we found no evidence that aphid population growth rates were adversely impacted by the magnitude of mismatch with their host plants or parasitoids, or direct impacts of temperature and precipitation. Strong density dependence effects occurred in both aphid species and probably buffered populations, through density-dependent compensation, from adverse impacts of the marked inter-annual climatic variation that occurred during the study period. These findings explain the resilience of aphid populations to climate change and uncover a key mechanism, warmer winter temperatures delaying insect phenology, by which climate change drives asynchronous shifts between interacting species.

Influences of female body condition on recruitment success of walleye (Sander vitreus) in Wisconsin lakes

Stock reproductive potential informs population dynamics and response to harvest. Indices of body condition, like relative weight (Wr), may indicate individual energetic state and provide a mechanistic link between spawning stock traits and recruitment. We tested for relationships among Wr of three female size classes (381–456, 457–557, and ≥558 mm total length), reproductive traits, and age-0 recruitment using data from 92 walleye (Sander vitreus) populations in the Ceded Territory of Wisconsin during 1989–2015 and a lake-specific time series from Escanaba Lake, Wisconsin, during 1958–2014. In Escanaba Lake, Wr was positively related to maturation in small females and was positively related to fecundity and gonadosomatic index in intermediate fish. Among and within populations, Wr demonstrated compensatory density dependence and positive relationships with growing degree-days. Recruitment was positively related to large female Wr variation across lakes and negatively related to small female Wr variation in Escanaba Lake. Improving the condition of large female walleye may promote recruitment, and Wr may serve as an accessible metric of reproductive potential in walleye stock–recruit analyses.

Estimating cross-population variation in juvenile compensation in survival for bull trout (Salvelinus confluentus): a Bayesian hierarchical approach

Juvenile compensation in survival, quantified as compensation ratio (CR), is critical for fish population persistence. At present, no estimate of this key parameter exists for bull trout (Salvelinus confluentus). This species has a conservation listing and is targeted by recreational angling in portions of its range. Obtaining accurate estimates of CR is crucial to aid recovery efforts and develop sustainable fisheries policies. This investigation develops a hierarchical Bayesian meta-analysis to estimate CR and explore the functional form of stock–recruitment for bull trout. Results show bull trout have high scope for density-dependent compensation evidenced by CR estimates generated herein and by previous research. This demonstrates changes in habitat quality and quantity are likely limiting recovery of many populations. However, owing to lack of data, variance is high. Limitations in available data for this analysis are due to the high cost and operational difficulty of sampling, and high uncertainty in CR estimates. This study highlights the importance of collecting additional paired stock–recruitment data to facilitate future investigations and reduce variance in CR estimates for bull trout.

Density‐ and size‐dependent mortality in fish early life stages

AbstractThe importance of survival and growth variations early in life for population dynamics depends on the degrees of compensatory density dependence and size dependence in survival at later life stages. Quantifying density‐ and size‐dependent mortality at different juvenile stages is therefore important to understand and potentially predict the recruitment to the population. We applied a statistical state‐space modelling approach to analyse time series of abundance and mean body size of larval and juvenile fish. The focus was to identify the importance of abundance and body size for growth and survival through successive larval and juvenile age intervals, and to quantify how the dynamics propagate through the early life to influence recruitment. We thus identified both relevant ages and mechanisms (i.e. density dependence and size dependence in survival and growth) linking recruitment variability to early life dynamics. The analysis was conducted on six economically and ecologically important fish populations from cold temperate and sub‐arctic marine ecosystems. Our results underscore the importance of size for survival early in life. The comparative analysis suggests that size‐dependent mortality and density‐dependent growth frequently occur at a transition from pelagic to demersal habitats, which may be linked to competition for suitable habitat. The generality of this hypothesis warrants testing in future research.

Efficacy of largemouth bass stock enhancement in achieving fishery management objectives in Florida

Stock enhancement is a practiced management strategy for sustaining and rebuilding largemouth bass fisheries in Florida and throughout their native and introduced range. However, quantitative assessment comparing efficacy of stocking to traditional management approaches are rare. We adapt an age-structured population model that explicitly represents the size and density-dependent effects on mortality and somatic growth to assess potential outcomes of stocking largemouth bass relative to traditional length-based harvest regulations. We explore two management situations in which stocking might be considered: maintaining high abundance in an exploited population and rebuilding a population that has been depleted. We find that different stocking scenarios comprised of combinations of size, density, and duration at which fish were stocked influence three fishery response metrics: abundance of catchable fish, abundance of trophy-sized fish and relative wild spawner biomass. Stocking larger juveniles can bypass some of the compensatory density dependence and yield a net augmentation of total abundance of catchable largemouth bass, but usually leads to a reduction in the abundance of the wild population and the number of trophy-sized bass. We find enhancements of small (25 mm) fingerlings fail to help maintain or augment wild populations, but could be effective at rebuilding depleted bass populations and may replace the need for effort restriction. Our study suggests stocking is a comparatively powerful tool for achieving high catch rates in largemouth bass fisheries, but may perform poorly at meeting other objectives of largemouth bass management such as production of trophy fish.

Regulation dynamics of exploited and protected populations of Haliotis roei, and their response to a marine heatwave

Abstract Exploited and protected populations of Haliotis roei in Western Australia were significantly perturbed by a marine heatwave of 2010/11. The immediate effects were a decline in large animals and recruitment, followed by a lagged decline in the spawning biomass. The data describing these effects were fitted to models of the population dynamic transitions. Depensatory density dependence in recruitment is offset by compensatory density dependence in during replacement and together they create the population equilibrium points. Equilibrium densities were highly influenced by the environmental perturbation, with observed patterns suggesting a temporary ‘regime shift’ had occurred. The main implication for management is to maximise spawning biomass as recruitment is positively correlated with it with some evidence of an Allee effect at low spawning densities, but no evidence of compensatory density dependence at high densities. Development of forecasting models that utilised pre-recruit densities, adjusted for density-dependent replacement, and incorporated an environmental effect, assisted early-management intervention to stock declines. Such an approach is an alternative to traditional assessments which recommend using biological reference points that assume population regulation occurs in the recruitment transition. This assumption cannot easily explain why the high density unfished stock showed the least resilience to the environmental perturbation.

Weak Effects of Density on Mean Length at Age and Condition of Largemouth Bass at Large Alabama Reservoirs

AbstractWe examined evidence for density‐dependent growth of Largemouth Bass Micropterus salmoides in the recruited life stage (age 2 and older) at eight large (>4,000 ha) Alabama reservoirs from standardized electrofishing survey data. Using mean length at age as a measure of cumulative growth and electrofishing catch rates as the basis for a cumulative index of density, we found weak support for the hypothesis that mean length at age was inversely related to Largemouth Bass density. The mean length at age of age‐5 Largemouth Bass was positively related to the cumulative density index, which is inconsistent with the prediction of an inverse association under compensatory density dependence. Moreover, the strength of the effect was weak, with a 9‐mm increase in mean length at age per 100% increase in the density index. No other age‐classes (ages 2 through 6 were examined) exhibited density‐dependent mean length at age. Similarly, relative weight was unrelated to the density index. Analyses of changes in mean length at age, relative weight, and the density index over time indicate that each of these variables have increased slightly since the mid‐1990s for some age‐classes. Our analysis of Largemouth Bass mean length at age at these reservoirs suggests that strong density‐dependent growth responses are unlikely in the recruited life stage at these large reservoir systems. If this is the case, implementing minimum length limits at these reservoirs is likely to avoid unintended negative consequences for Largemouth Bass growth and size structure.

An alternative reference point in the context of ecosystem-based fisheries management: maximum sustainable dead biomass

Abstract Under the 2013 Reform of the European Union's Common Fisheries Policy (CFP), fisheries management aims to ensure that, within a reasonable time frame, the exploitation of marine biological resources restores and maintains populations of harvested stocks above levels that can produce the maximum sustainable yield (MSY). The CFP also calls for the implementation of an ecosystem-based approach to fisheries management (EBFM). In this paper, we present the concept of maximum sustainable dead biomass (MSDB) and its associated management reference points for fishing mortality and spawning-stock biomass as alternatives to those associated with MSY. The concept of MSDB is illustrated by a dynamic pool production model of a virtual fish stock which takes into account variations in natural mortality (M), fishing mortality (F), and exploitation pattern. Our approach implies a compensatory mechanism whereby survivors may benefit from compensatory density dependence and is implemented through progressive substitution of M with F for varying rates of total mortality (Z). We demonstrate that the reference points for fishing mortality and spawning-stock biomass associated with MSDB are less sensitive to increasing compensation of M with F than those associated with MSY and more sensitive to changes in selection pattern. MSDB-based reference points, which are consistent with maximum stock productivity, are also associated with lower fishing mortality rates and higher stock biomasses than their MSY-based counterparts. Given that selection pattern can be influenced through fishery input measures (e.g. technical gear measures, decisions on areas, and/or times of fishing), whereas variations of M in response to F are not controllable (indeed poorly understood), that the results of many fish stock assessments are imprecise, that maximum stock productivity corresponds to MSDB and that MSY-based reference points may best be considered as limits, we propose that MSDB-based reference points provide a more appropriate basis for management under an EBFM.

Mean and variance of population density and temporal Taylor’s law in stochastic stage-structured density-dependent models of exploited fish populations

How does fishing affect the mean and variance of population density in the presence of environmental fluctuations? Several recent authors have suggested that an increasing ratio of standard deviation to mean (coefficient of variation, or CV) in population density indicates declining population stability. We investigated the relationship between the mean and variance of population density in stochastic, density-dependent, stage-structured fish population models. Our models included either compensatory or overcompensatory density dependence affecting either fertility or juvenile survival. Environmental stochasticity affected either juvenile survival (when density dependence affected fertility) or fertility (when density dependence affected juvenile survival). The mean and variance of population density were compared as fishing mortality changed. In some cases, the relationship between the natural logarithms of mean and variance is linear under some parameters (life history strategy) of some models (the type of density dependence and the timing of density dependence and stochasticity), supporting Taylor’s law. In other cases, the relationship can be non-linear, especially when density dependence is overcompensatory, and depends on the stage observed. For example, the variance of adult density may increase with its mean while the variance of juvenile density of the same population may decline, or vice versa. The sequence in which individuals experience stochasticity and density dependence matters because density dependence can attenuate or magnify the fluctuation. In conclusion, the use of the CV as a proxy for population instability is not appropriate, and the CV of population density has to be interpreted carefully for other purposes.