Optimal harvesting policy of a prey–predator model with Crowley–Martin-type functional response and stage structure in the predator

In this paper, a three-dimensional dynamical model consisting of a prey, a mature predator, and an immature predator is proposed and analysed. The interaction between prey and mature predator is assumed to be of the Crowley–Martin type, and both the prey and mature predator are harvested according to catch-per-unit-effort (CPUE) hypothesis. Steady state of the system is obtained, stability analysis (local and global both) are discussed to explore the long-time behaviour of the system. The optimal harvesting policy is also discussed with the help of Pontryagin's maximum principle. The harvesting effort is taken as an effective control instrument to preserve prey and predator and to maintain them at an optimal level

Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research

Tradeoffs of managing cod as a sustainable resource in fluctuating environments

Sustainable human exploitation of living marine resources stems from a delicate balance between yield stability and population persistence to achieve socioeconomic and conservation goals. But our imperfect knowledge of how oceanic oscillations regulate temporal variation in an exploited species can obscure the risk of missing management targets. We illustrate how applying a management policy to suppress fluctuations in fishery yield in variable environments (prey density and regional climate) can present unintended outcomes in harvested predators and the sustainability of harvesting. Using Atlantic cod (Gadus morhua, an apex predatory fish) in the Barents Sea as a case study we simulate age-structured population and harvest dynamics through time-varying, density-dependent and density-independent processes with a stochastic, process-based model informed by 27-year monitoring data. In this model, capelin (Mallotus villosus, a pelagic forage fish), a primary prey of cod, fluctuations modulate the strength of density-dependent regulation primarily through cannibalistic pressure on juvenile cod survival; sea temperature fluctuations modulate thermal regulation of cod feeding, growth, maturation, and reproduction. We first explore how capelin and temperature fluctuations filtered through cod intrinsic dynamics modify catch stability and then evaluate how management to suppress short-term variability in catch targets alters overharvest risk. Analyses revealed that suppressing year-to-year catch variability impedes management responses to adjust fishing pressure, which becomes progressively out of sync with variations in cod abundance. This asynchrony becomes amplified in fluctuating environments, magnifying the amplitudes of both fishing pressure and cod abundance and then intensifying the density-dependent regulation of juvenile survival through cannibalism. Although these transient dynamics theoretically give higher average catches, emergent, quasicyclic behaviors of the population would increase long-term yield variability and elevate overharvest risk. Management strategies that overlook the interplay of extrinsic (fishing and environment) and intrinsic (life history and demography) fluctuations thus can inadvertently destabilize fish stocks, thereby jeopardizing the sustainability of harvesting. These policy implications underscore the value of ecosystem approaches to designing management measures to sustainably harvest ecologically connected resources while achieving socioeconomic security.publishedVersio

Modelling Walleye Population and Its Cannibalism Effect

Walleye is a very common recreational fish in Canada with a strong cannibalism tendency, such that walleyes with larger sizes will consume their smaller counterparts when food sources are limited or a surplus of adults is present. Cannibalism may be a factor promoting population oscillation. As fish reach a certain age or biological stage (i.e. biological maturity), the number of fish achieving that stage is known as fish recruitment. The objective of this thesis is to model the walleye population with its recruitment and cannibalism effect. A matrix population model has been introduced to characterize the walleye population into three different groups: newborns, juveniles, and adults. A delay differential equation (DDE) model has also been introduced to characterize walleyes into two groups including juveniles and adults. Local and global stabilities of equilibria have been discussed in both models. Furthermore, numerical simulations are present to visualize the effects of both models

A Stage-structure Leslie-Gower Model with Linear Harvesting and Disease in Predator

The growth dynamics of various species are affected by various aspects. Harvesting interventions and the spread of disease in species are two important aspects that affect population dynamics and it can be studied. In this work, we consider a stage-structure Leslie–Gower model with linear harvesting on the both prey and predator. Additionally, we also consider the infection aspect in the predator population. The population is divided into four subpopulations: immature prey, mature prey, susceptible predator, and infected predator. We analyze the existences and stabilities of feasible equilibrium points. Our results shown that the harvesting in prey and the disease in predator impacts the behavioral of system. The situation in the system is more complex due to disease in the predator population. Some numerical simulations are given to confirm our results

Ontogenetic development underlies population response to mortality [post-print]

Understanding demographic responses to mortality is crucial to predictive ecology. While classic ecological theory posits reductions in population biomass in response to extrinsic mortality, models containing realistic developmental change predict the potential for counterintuitive increase in stage-specific biomass, i.e. biomass overcompensation. Patterns of biomass overcompensation should be predictable based on differences in the relative energetic efficiencies of juvenile maturation and adult reproduction. Specifically, in populations where reproduction is the limiting process, adult-specific mortality should enhance total reproduction and thus juvenile biomass. We tested this prediction by inducing an array of stage-specific harvesting treatments across replicate populations of Daphnia pulex. In accordance with reproductive regulation, the greatest biomass response occurred in the juvenile Daphnia stage and this response occurred most strongly in response to adult mortality. Nevertheless, we failed to detect significant biomass overcompensation and instead report largely compensatory effects. In total, our work demonstrates that knowledge of population structure is necessary to accurately predict population dynamics, but cautions that further research is needed to illuminate the factors generating over-compensatory versus compensatory responses across natural populations

Models for an Ecosystem Approach to Fisheries

This document is one outcome from a workshop held in Gizo in October 2010 attended by 82 representatives from government, NGO's private sector, and communities. The target audience for the document is primarily organizations planning to work with coastal communities of Solomon Islands to implement Community-Based Resource Management (CBRM). It is however also envisaged that the document will serve as a reference for communities to better understand what to expect from their partners and also for donors, to be informed about agreed approaches amongst Solomon Islands stakeholders. This document does not attempt to summarize all the outcomes of the workshop; rather it focuses on the Solomon Islands Coral Triangle Initiative (CTI) National Plan of Action (NPoA): Theme 1: Support and implementation of CBRM and specifically, the scaling up of CBRM in Solomon Islands. Most of the principles given in this document are derived from experiences in coastal communities and ecosystems as, until relatively recently, these have received most attention in Solomon Islands resource management. It is recognized however that the majority of these principles will be applicable to both coastal and terrestrial initiatives. This document synthesizes information provided by stakeholders at the October 2010 workshop and covers some basic principles of engagement and implementation that have been learned over more than twenty years of activities by the stakeholder partners in Solomon Islands. The document updates and expands on a summary of guiding principles for CBRM which was originally prepared by the Solomon Islands Locally Managed Marine Area Network (SILMMA) in 2007

A study of green crab (Carcinus maenas) interactions, cannibalism, and a first approach to model the effects of harvesting on its populations

Green crabs (Carcinus maenas) have been extensively studied because of the negative impacts that they have on the ecosystems that they invade. However, there are still substantial gaps of knowledge about their interactions and population dynamics. As green crabs continue to invade new locations, it is important to gain a deeper understanding of these subject areas in order to prevent or mitigate further introductions or spread. This thesis aims to address these knowledge gaps by focusing on two main topics: (1) green crab predator-prey interactions with smaller conspecifics and a native counterpart, the mud crab (Dyspanopeus sayi), and (2) a first attempt using a model to predict green crab population dynamics and the potential effects of a removal program. First, I analysed long-term observational beach-seine data collected from the southern Gulf of St. Lawrence, and found that there was a negative association between native mud crabs and green crabs in this area. Then I used laboratory experiments to examine their predator-prey interactions and assessed the influence of habitat complexity on the outcome of these interactions. I found that green crab predators consumed almost twice as many mud crabs compared to juvenile green crabs in the two less structured habitats (no substrate or sandy substrate), but predation rates were statistically similar in oyster bed habitat. This study found that mud crab mortality was significantly affected by habitat type, whereas green crab mortality was not. I then focused on green crab cannibalism by adults on juveniles with similar laboratory experiments. In this study, I included habitat types that represented a wider range of structural complexity, and found that cannibalism rates declined with increasing habitat complexity. I also conducted field inclusion experiments that gathered similar results, though the differences were not significant. I identified knowledge gaps and areas of future research by gathering all the available information about green crab life stages. This population information was used to build a relatively simple stage-based population matrix model for green crabs. The outcome of the model estimated that a theoretical green crab population could increase by approximately 43%. The outcome of this model also suggested that even if adult survival is set to zero (representing intensive trapping and effective removal of adults), the population was still able to grow because numbers in the other life stages were abundant enough to feed and maintain the population growth rate. These results suggests that current removal programs that catch mostly adults have little-to-no effect on the population growth rate, indicating that harvesting alone is unlikely to result in a reduction of annual green crab abundance