Multiple time–scale dynamics of stage structured populations and derivative–free optimization

The parent-progeny (adult fish–juvenile) relationship is central to understanding the dynamics of fish populations. Management and harvest decisions are based on the assumption of a stock-recruitment function that relates the number of adults to their progeny. Multi-stage population dynamic models provide a modelling framework for understanding this relationship, since they describe the dynamics of fish in several life stages (such as adults, eggs, larvae, and juveniles). Biological processes at various life stages usually evolve at distinct time scales. This thesis contains three papers, which address challenges in modelling and parameter estimation for multiple time-scale dynamics of stage structured populations. A major question is, whether a multi-stage population dynamic model supports the assumption of a stock-recruitment function. In the first paper, we address the parent-progeny relationship admitted by slow-fast systems of differential equations that model the dynamics of a fish population with two stages. We introduce a slow-fast population dynamic model which replicates several well-known stock-recruitment functions. Traditionally, the dynamics of fish populations are described by difference equations. In the second paper, discrete time models for several life stages are formulated. We demonstrate that a multi-stage model may not admit a stock-recruitment function. Sufficient conditions for the validity of two hypotheses about the existence and structure of a parent-progeny function are established. Parameters in population dynamic models can be estimated by minimizing a function of the solution of the ordinary differential equations and available data. Efficient and accurate methods for the solution of differential equations usually evaluate conditional statements. In this case, the objective function may be noisy, instead of continuously differentiable. Furthermore, an algorithm which is used to evaluate the objective function may unexpectedly fail to return a (plausible) value. Then, the optimization problem includes constraints which are only implicitly stated and hidden from the problem formulation. We demonstrate that derivative-free optimization methods find sufficiently accurate solutions for the challenging optimization problems. In the third paper, we compare the performances of several derivative-free methods for a set of optimization problems. We find that a derivative-free trust-region method is most robust to the choice of the initial iterate, but is in general outperformed by direct search methods. Additional numerical simulations in the thesis reveal that direct search methods which approximate a gradient or Hessian find the most accurate solutions. We observe that the optimization problems considered in this thesis are more challenging than a set of noisy benchmark problems. The thesis includes scientific contributions in addition to the results from the three papers

Interactions among species and ecosystems determine their responses to scale-specific fluctuations

Ecosystems are highly connected systems with many interacting components. Understanding the mechanisms creating ecosystem patterns requires an explicit consideration of the scales at which interactions among species and their environments occur. This dissertation focuses on the scale of temporal variability and how temporal variability is incorporated into communities’ dynamics. I first derive an abstract theory that describes the general patterns of variability propagation within communities. Next, I explore the role of species’ interaction strengths on community dynamics across time scales. Finally, I study the impact of human-induced hydrological changes of the Guadalquivir River on the European anchovy fishery in the Gulf of Cadiz.Chapter 1 uses linear response theory to extend the top down and bottom up views of ecology across time scales. Specifically, I study a tri-trophic food chain and how fluctuations in productivity filter up the food chain. I find that variability follows the pattern predicted by top-down equilibrium-based theories at slow time scales. However, at an intermediate time scale, consumers can both decrease and increase the sensitivity of lower trophic levels to variability. For example, perturbations at intermediate frequencies can excite the endogenous cycles of a community leading to resonance. Only at the fastest time scales do top down effects begin to break down as variability becomes dampened at higher trophic levels. This theory provides a robust new framework to interpret food web patterns resulting from resource pulses and other bottom up perturbations. Chapter 2 combines the metabolic theory of ecology and empirical information of consumer-resource interactions to ground the general theory developed in Chapter 1. Body size is not only a significant determinant of vital rates and but also species interaction strengths. This approach allows me to focus on biologically relevant parameter space. I predict that predators can control herbivores and producers\u27 variability at a time scale of days to years. This theory predicts that indirect effects actively shape communities\u27 responses across a wide range of ecologically relevant time scales. Finally, in Chapter 3, I explore the relationship between ecology and society by studying how agricultural water use is connected to the marine anchovy fishery in Spain’s Gulf of Cadiz. Using time series analysis, I explore the correlations between hydrology, the estuarine community, and anchovy recruitment to the Gulf of Cadiz. The Guadalquivir river’s mean annual discharge and seasonality have decreased over the last 90 years due to increasing river regulation and extraction. European anchovies use the river estuary as a nursery. These hydrological changes have reduced anchovy recruitment to the Gulf of Cadiz, connecting terrestrial water use with the marine fishery. I then produce a water allocation theory for terrestrial agriculture and a marine fishery. I predict that even practices that improve water efficiency will not necessarily prevent terrestrial ecosystems from total water consumption. I find that the protection of downriver ecosystem services is only protected when the benefits to marine ecosystems are considered nonsubstitutable with terrestrial ecosystems. The issue of scale – ecological and spatiotemporal – is at the heart of my thesis. My first chapter shows that the percolation of variability is not invariant across time scales. In my second chapter, I predict how body size drives differences in community responses to variability. These theories can provide new insights into how variability impacts communities. Finally, in my last chapter, I explore rivers and migration can create trade-offs between seemingly isolated ecosystems

Modelling abrupt shifts of fish recruitment and growth

Regime shifts in marine ecosystems may result in abrupt changes in fish population dynamics, and not accounting for such shifts could have potentially large and far-reaching consequences for fisheries assessment and management decisions. In this work, I develop a methodology to model abrupt shifts in recruitment and somatic growth, which are two key processes in controlling fish population dynamics. In Chapter 1, I review the impacts of regime shifts on fish populations and find that abrupt shifts in productivity are very common among global fish species. In Chapter 2, I introduce the approach of modelling recruitment and regime shifts. The methodology includes a hidden Markov model for the unobserved environmental regimes, a stock-recruitment (SR) model for the regime-specific SR function, the maximum likelihood approach for evaluating the marginal likelihood, and the corrected Akaike information criterion (AICc) for the model selection. I conduct simulation tests to evaluate the performance of the method and results indicate that our method can objectively identify the unobserved environmental regimes and estimate regime-specific SR model parameters well. In Chapter 3, I extend the hidden Markov approach to model abrupt shifts in fish growth using a von Bertalanffy growth model (VBGM). Simulation results demonstrate that the method can accurately identify abrupt shifts in growth and estimate regime-specific growth parameters well. I apply both the hidden Markov stock-recruit model (HMSM) and the hidden Markov growth model (HMGM) to an Atlantic cod stock on the southern Grand Bank off Newfoundland, Canada. Results indicate that the cod stock has two distinct recruitment regimes and two distinct growth regimes, and our method identify one abrupt shift in recruitment and four abrupt shifts in somatic growth. I consider the methodology proposed in this thesis as a useful tool to model regime-like changes of fish population dynamics. In Chapter 4, I discuss the management implications of abrupt shifts in fish population dynamics and present the current challenges of managing fish stocks under marine ecosystem regime shifts. I consider the conditions under which our method might be useful to better assess and manage fish populations under changing environmental regimes

Climate change impact on high latitude freshwater fish populations

Climate change is one of the greatest threats to animal wildlife in high latitude freshwater ecosystems. Climate warming is rapidly increasing water temperatures in these areas, affecting biological processes of ectotherms such as growth, maturation and reproduction, which in turn trigger population responses. The magnitude of the effects of climate warming will vary depending on the thermal niche and phenotype of species. Climate change will continue to redistribute species, and fish species from warmer temperature guilds will invade and possibly take over areas where cold water fish currently dominate. Hence, it is important to establish the performance of cold vs warmer water species in a warming Arctic. The aim of this thesis is therefore to provide novel insights and predictions on population level implications of climate change for both cold- and cool water fish at high latitudes. The primary focus is on climate effects mediated by direct and indirect individual-level responses to increasing water temperatures, addressed using long-term empirical investigations and modelling in retrospective and prospective studies. In addition, the thesis addresses interactions between climate change and size-selective harvesting, a main pressure on high latitude fish populations, by modelling their cumulative effects to evaluate risks and reveal potential synergistic threats. The thesis documents how both cold- and cool water fish at their northern range edge have increased their somatic growth rates during the last three decades of warming. However, the cool-water adapted vendace and perch displayed a higher increase in juvenile somatic growth with warming compared to cold-water Arctic charr and whitefish, stressing how the thermal niche modulates the magnitude of warming effects. The individual based models developed for this thesis predict a further increase in somatic growth towards year 2100 under warming scenarios (RCP-4.5, -8.5), with cool water fish displaying a greater increase in somatic growth rate than cold water fish. The documented and projected climate driven increase in somatic growth rate mediates changes in survival rates and life history, including a likely increase in juvenile survival, and earlier maturation, the latter being contingent on species’ maturation reaction norm. The demographic implications of these individual effects were investigated via modelling and long-term empirical studies. The population level response to climate warming, mediated by individual effects, was evident in the cool water adapted perch, which experienced a substantial increase in density and importance relative to the cold-water adapted whitefish, which is dominant in the investigated lakes. The population response of this cool water fish was mediated by an increase in juvenile growth rate which resulted in larger size at age and earlier maturation, but also a likely increase in survival through the first critical winter. The modelled populations displayed higher biomass and yield as size at age increased with warming, but this effect was larger in the cool water specie than in the cold water species. In sum, cool water fish will benefit more from climate warming than cold water fish at high latitudes, and where they coexist, cool water fish may become the dominant player in the fish community. The climate driven increase in size at age affects the age-specific exposure to size-selective harvesting, increasing the risk of younger individuals being caught by gillnets. The population level effect of earlier gillnet exposure is an increased age truncation, as illustrated by individual based model outcomes. Also, larger size at age increased the proportion of immature individuals being caught, with the magnitude of the effect being contingent on growth trajectories, their temperature dependence, and orientation of the maturation reaction norm. The increased juvenile mortality and more pronounced age truncation reduce recruitment, increasing the vulnerability of exploited populations to environmental stressors. Fish species with large size, slow growth, and late maturation like Arctic charr were more vulnerable to warming and harvesting than species with a faster life history, like vendace. In conclusion, the stronger positive effects of warming on the performance of cool-water adapted species relative to cold-water salmonids, and the greater vulnerability of the latter when exposed to size-selective harvesting, warn of incipient reorganizations of Arctic fish communities, and invite climate adaptation in the management of high latitude populations

Overexploitation, Recovery, and Warming of the Barents Sea Ecosystem During 1950–2013

The Barents Sea (BS) is a high-latitude shelf ecosystem with important fisheries, high and historically variable harvesting pressure, and ongoing high variability in climatic conditions. To quantify carbon flow pathways and assess if changes in harvesting intensity and climate variability have affected the BS ecosystem, we modeled the ecosystem for the period 1950–2013 using a highly trophically resolved mass-balanced food web model (Ecopath with Ecosim). Ecosim models were fitted to time series of biomasses and catches, and were forced by environmental variables and fisheries mortality. The effects on ecosystem dynamics by the drivers fishing mortality, primary production proxies related to open-water area and capelin-larvae mortality proxy, were evaluated. During the period 1970–1990, the ecosystem was in a phase of overexploitation with low top-predators’ biomasses and some trophic cascade effects and increases in prey stocks. Despite heavy exploitation of some groups, the basic ecosystem structure seems to have been preserved. After 1990, when the harvesting pressure was relaxed, most exploited boreal groups recovered with increased biomass, well-captured by the fitted Ecosim model. These biomass increases were likely driven by an increase in primary production resulting from warming and a decrease in ice-coverage. During the warm period that started about 1995, some unexploited Arctic groups decreased whereas krill and jellyfish groups increased. Only the latter trend was successfully predicted by the Ecosim model. The krill flow pathway was identified as especially important as it supplied both medium and high trophic level compartments, and this pathway became even more important after ca. 2000. The modeling results revealed complex interplay between fishery and variability of lower trophic level groups that differs between the boreal and arctic functional groups and has importance for ecosystem management

Spatiotemporal control of cell cycle acceleration during axolotl spinal cord regeneration

Axolotls are uniquely able to resolve spinal cord injuries, but little is known about the mechanisms underlying spinal cord regeneration. We previously found that tail amputation leads to reactivation of a developmental-like program in spinal cord ependymal cells (Rodrigo Albors et al., 2015), characterized by a high-proliferation zone emerging 4 days post-amputation (Rost et al., 2016). What underlies this spatiotemporal pattern of cell proliferation, however, remained unknown. Here, we use modeling, tightly linked to experimental data, to demonstrate that this regenerative response is consistent with a signal that recruits ependymal cells during ~85 hours after amputation within ~830 μm of the injury. We adapted Fluorescent Ubiquitination-based Cell Cycle Indicator (FUCCI) technology to axolotls (AxFUCCI) to visualize cell cycles in vivo. AxFUCCI axolotls confirmed the predicted appearance time and size of the injury-induced recruitment zone and revealed cell cycle synchrony between ependymal cells. Our modeling and imaging move us closer to understanding bona fide spinal cord regeneration.Fil: Cura Costa, Emanuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Otsuki, Leo. Research Institute Of Molecular Pathology; AustriaFil: Albors, Aida Rodrigo. University Of Dundee; Reino UnidoFil: Tanaka, Elly M.. Research Institute Of Molecular Pathology; AustriaFil: Chara, Osvaldo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin

Spatiotemporal control of cell cycle acceleration during axolotl spinal cord regeneration

Axolotls are uniquely able to resolve spinal cord injuries, but little is known about the mechanisms underlying spinal cord regeneration. We previously found that tail amputation leads to reactivation of a developmental-like program in spinal cord ependymal cells (Rodrigo Albors et al., 2015), characterized by a high-proliferation zone emerging 4 days post-amputation (Rost et al., 2016). What underlies this spatiotemporal pattern of cell proliferation, however, remained unknown. Here, we use modeling, tightly linked to experimental data, to demonstrate that this regenerative response is consistent with a signal that recruits ependymal cells during ~85 hours after amputation within ~830 μm of the injury. We adapted Fluorescent Ubiquitination-based Cell Cycle Indicator (FUCCI) technology to axolotls (AxFUCCI) to visualize cell cycles in vivo. AxFUCCI axolotls confirmed the predicted appearance time and size of the injury-induced recruitment zone and revealed cell cycle synchrony between ependymal cells. Our modeling and imaging move us closer to understanding bona fide spinal cord regeneration

Incorporating the Impacts of Climate Variability on Growth in Fish Population Dynamics Models

Variations in ocean conditions influenced by climate fluctuations may impact fish populations by changing their spatial distribution, physiology, survival, and other ecological features. Somatic growth is a crucial aspect of the biology of fishes and an important contributor to biomass fluctuations. Climate variability also affects somatic growth rates along the fish life span, impacting the fish ecology and the fishery. In this dissertation, I present multiple analyses on how fish somatic growth variability may be incorporated in population dynamics models, a quantitative approach to studying climate's impacts on fish populations. Chapter 1 introduces fish somatic growth variability, population dynamics models and their importance, current strategies to incorporate growth in population dynamics models, and an introduction to the ecology of the Pacific cod in the eastern Bering Sea, fish stock used as a case study in this dissertation. Chapter 2 investigated how projected climate under two emission scenarios (RCP4.5 and RCP8.5) might impact the growth and survival of Pacific cod’s early life stages in the eastern Bering Sea. Specifically, I evaluated the impacts on the following biological variables: (1) hatch success, (2) survival probability, (3) growth, and (4) spatial distribution. I implemented a mechanistic individual-based cod larvae model that quantifies changes and the larval behavioral response to the physical and biological environment. The results indicate that, under the RCP8.5 scenario, the temperature in the larvae habitat will increase by ~ 2 C while pCO2 will triple by 2100 compared to present-day values. These changes will increase hatch success and standard length (mm); however, survival probability will decrease by ~85% and recruitment by 50%. A shallow retention area was detected in the southeast part of the eastern Bering Sea, being this area also the most vulnerable to the future climate. Chapter 3 explored how somatic growth variability impacts the age composition estimation, a critical data input to stock assessment models. I compared the performance of four methods for estimating age compositions of a simulated fish population based on the Pacific cod biology: two methods based on age-length keys (ALK, pooled and annual) and two model-based approaches (generalized additive models-GAM and continuation ratio logits-CRL). CRL was the most robust and precise method followed by annual ALKs, mainly when significant growth variability was present. I applied these methods to survey age subsample data for Pacific cod (Gadus macrocephalus) in the eastern Bering Sea, estimating age compositions that were then incorporated in its stock assessment model. The model that included age compositions estimated by CRL displayed the highest consistency with other data in the model. Chapter 4 used a simulation-estimation framework to expand previous analyses and examine the consequences of spatial and temporal (year- and cohort-specific) variability in somatic growth in stock assessment models. The study included three life history types: small pelagic (e.g., sardine), gadids (e.g., cod), and long-lived (e.g., rockfish). In general, ignoring any variability in somatic growth led to biased and imprecise estimates of stock spawning biomass (SSB) and management quantities. Unequal distribution of fishing mortality across space had large impacts on the performance of estimation models as well. Conversely, accounting for somatic growth variability, either by including an environmental index, estimating annual deviates, or implementing a spatially explicit model, produced unbiased and precise results. Finally, Chapter 5 includes the main conclusions of this dissertation, the pros and cons of population dynamics models, and discusses the limitations of my research and extensions that future investigations could undertake

FLBEIA fisheries management simulation model. Definition of new criteria and guidelines for efficient validation of the model using global sensitivity analysis

229 p.En esta tesis se ha desarrollado el modelo bio-económico de simulación pesquera FLBEIA y se han definido una serie de direcciónes para validarlo y fomentar la validación de los modelos de simulación pesquera. El modelo FLBEIA da respusta a la necesidad de modelos de este tipo identificada en el marco de los análisis de impacto llevado a cabo por la Comisión Europea para anticipar la eficacia de las estrategias de gestión pesquera. La modelización de la incertidumbre ha sido un punto clave en el desarrollo del modelo FLBEIA sigue la aproximación de evaluación de estrategias de gestión que formaliza la incorporación de la incertidumbre en el proceso de toma de decisiones. Al ser los modelos de simulación abtracciones de la realidad, no son capaces de describir el sistema real de manera perfecta y es necesario validarlos para asegurar que representan el sistema modelado de manera idónea. El análisis de sensibilidad global es una de las técnicas cuantitativas más utilizadas en la validación de modelos de simulación. Sin embargo, su uso en modelos pesqueros es escaso. El conjunto de directrices definitivas en esta tesis permite condicionar los modelos pesqueros de manera efectiva y combinar dos de los métodos de análisis de sensibilidad global más utilizados. La combinación de estos métodos permite identificar los factores de entrada que más impactan en los resultados del modelo con un coste computacional aceptable para disponer de un modelo reducido al cual poder aplicar posteriormente el método más costoso. El modelo FLBEIA y las directrices propuestas se han aplicado a la pesquería demersal que opera en la fachada atlántica de la península ibérica