Simulation of mackerel (Scomber scombrus) recruitment with an individual-based model and comparison with field data

An individual-based model (IBM) for the simulation of year-to-year survival during the early life-history stages of the north-east Atlantic stock of mackerel (Scomber scombrus) was developed within the EU funded Shelf-Edge Advection, Mortality and Recruitment (SEAMAR) programme. The IBM included transport, growth and survival and was used to track the passive movement of mackerel eggs, larvae and post-larvae and determine their distribution and abundance after approximately 2 months of drift. One of the main outputs from the IBM, namely distributions and numbers of surviving post-larvae, are compared with field data as recruit (age-0/age-1 juveniles) distribution and abundance for the years 1998, 1999 and 2000. The juvenile distributions show more inter-annual and spatial variability than the modelled distributions of survivors; this may be due to the restriction of using the same initial egg distribution for all 3 yr of simulation. The IBM simulations indicate two main recruitment areas for the north-east Atlantic stock of mackerel, these being Porcupine Bank and the south-eastern Bay of Biscay. These areas correspond to areas of high juvenile catches, although the juveniles generally have a more widespread distribution than the model simulations. The best agreement between modelled data and field data for distribution (juveniles and model survivors) is for the year 1998. The juvenile catches in different representative nursery areas are totalled to give a field abundance index (FAI). This index is compared with a model survivor index (MSI) which is calculated from the total of survivors for the whole spawning season. The MSI compares favourably with the FAI for 1998 and 1999 but not for 2000; in this year, juvenile catches dropped sharply compared with the previous years but there was no equivalent drop in modelled survivors.

Environmental selection and resource allocation determine spatial patterns in picophytoplankton cell size

Here we describe a new trait-based model for cellular resource allocation that we use to investigate the relative importance of different drivers for small cell size in phytoplankton. Using the model, we show that increased investment in nonscalable structural components with decreasing cell size leads to a trade-off between cell size, nutrient and light affinity, and growth rate. Within the most extreme nutrient-limited, stratified environments, resource competition theory then predicts a trend toward larger minimum cell size with increasing depth. We demonstrate that this explains observed trends using a marine ecosystem model that represents selection and adaptation of a diverse community defined by traits for cell size and subcellular resource allocation. This framework for linking cellular physiology to environmental selection can be used to investigate the adaptive response of the marine microbial community to environmental conditions and the adaptive value of variations in cellular physiology.

Microbial spatial variability: An example from the Celtic Sea

In July 2004, dominant populations of microbial ultraplankton (<5 μm), in the surface of the Celtic Sea (between UK and Eire), were repeatedly mapped using flow cytometry, at 1.5 km resolution over a region of diameter 100 km. The numerically dominant representatives of all basic functional types were enumerated including one group of phototrophic bacteria (Syn), two groups of phytoplankton (PP, NP), three groups of heterotrophic bacterioplankton (HB) and the regionally dominant group of heterotrophic protists (HP). The distributions of all organisms showed strong spatial variability with little relation to variability in physical fields such as salinity and temperature. Furthermore, there was little agreement between distributions of different organisms. The only linear correlation consistently explaining more than 50% of the variance between any pairing of the organism groups enumerated is between two different groups of HB. Specifically, no linear, or non-linear, relationship is found between any pairings of SYB, PP or HB groups with their protist predators HP. Looking for multiple dependencies, factor analysis reveals three groupings: Syn, PP and low nucleic acid content HB (LNA); high nucleic acid content HB (HNA); HP and NP. Even the manner in which the spatial variability of Syn, PP and HB abundance varies as a function of lengthscale (represented by a semivariogram) differs significantly from that for HP. In summary, although all microbial planktonic groups enumerated are present and numerically dominant throughout the region studied, at face value the relationships between them seem weak. Nevertheless, the behaviour of a simple, illustrative ecological model, with strongly interacting phototrophs and heterotrophs, with stochastic forcing, is shown to be consistent with the observed poor correlations and differences in how spatial variability varies with lengthscale. Thus, our study suggests that a comparison of microbial abundances alone may not discern strong underlying trophic interactions. Specific knowledge of these processes, in particular grazing, will be required to explain the causes of the observed microbial spatial variability and its resulting consequences for the functioning of the ecosystem.

Influence of light in the mixed-layer on the parameters of a three-component model of phytoplankton size class

Phytoplankton size structure is an important indicator of the state of the pelagic ecosystem. Stimulated by the paucity of in situ observations on size structure, and by the sampling advantages of autonomous remote platforms, new efforts are being made to infer the size-structure of the phytoplankton from oceanographic variables that may be measured at high temporal and spatial resolution, such as total chlorophyll concentration. Large-scale analysis of in situ data has revealed coherent relationships between size-fractionated chlorophyll and total chlorophyll that can be quantified using the three-component model of Brewin et al. (2010). However, there are variations surrounding these general relationships. In this paper, we first revise the three-component model using a global dataset of surface phytoplankton pigment measurements. Then, using estimates of the average irradiance in the mixed-layer, we investigate the influence of ambient light on the parameters of the three-component model. We observe significant relationships between model parameters and the average irradiance in the mixed-layer, consistent with ecological knowledge. These relationships are incorporated explicitly into the three-component model to illustrate variations in the relationship between size-structure and total chlorophyll, ensuing from variations in light availability. The new model may be used as a tool to investigate modifications in size-structure in the context of a changing climate.

Spatio-temporal characteristics of Agulhas leakage: a model inter-comparison study

Investigating the variability of Agulhas leakage, the volume transport of water from the Indian Ocean to the South Atlantic Ocean, is highly relevant due to its potential contribution to the Atlantic Meridional Overturning Circulation as well as the global circulation of heat and salt and hence global climate. Quantifying Agulhas leakage is challenging due to the non-linear nature of this process; current observations are insufficient to estimate its variability and ocean models all have biases in this region, even at high resolution . An Eulerian threshold integration method is developed to examine the mechanisms of Agulhas leakage variability in six ocean model simulations of varying resolution. This intercomparison, based on the circulation and thermo- haline structure at the Good Hope line, a transect to the south west of the southern tip of Africa, is used to identify features that are robust regardless of the model used and takes into account the thermohaline biases of each model. When determined by a passive tracer method, 60 % of the magnitude of Agulhas leakage is captured and more than 80 % of its temporal fluctuations, suggesting that the method is appropriate for investigating the variability of Agulhas leakage. In all simulations but one, the major driver of variability is associated with mesoscale features passing through the section. High resolution (<1/10 deg.) hindcast models agree on the temporal (2–4 cycles per year) and spatial (300–500 km) scales of these features corresponding to observed Agulhas Rings. Coarser resolution models (<1/4 deg.) reproduce similar time scale of variability of Agulhas leakage in spite of their difficulties in representing the Agulhas rings properties. A coarser resolution climate model (2 deg.) does not resolve the spatio-temporal mechanism of variability of Agulhas leakage. Hence it is expected to underestimate the contribution of Agulhas Current System to climate variability.

Spatio-temporal characteristics of Agulhas leakage: a model inter-comparison study

Investigating the variability of Agulhas leakage, the volume transport of water from the Indian Ocean to the South Atlantic Ocean, is highly relevant due to its potential contribution to the Atlantic Meridional Overturning Circulation as well as the global circulation of heat and salt and hence global climate. Quantifying Agulhas leakage is challenging due to the non-linear nature of this process; current observations are insufficient to estimate its variability and ocean models all have biases in this region, even at high resolution . An Eulerian threshold integration method is developed to examine the mechanisms of Agulhas leakage variability in six ocean model simulations of varying resolution. This intercomparison, based on the circulation and thermo- haline structure at the Good Hope line, a transect to the south west of the southern tip of Africa, is used to identify features that are robust regardless of the model used and takes into account the thermohaline biases of each model. When determined by a passive tracer method, 60 % of the magnitude of Agulhas leakage is captured and more than 80 % of its temporal fluctuations, suggesting that the method is appropriate for investigating the variability of Agulhas leakage. In all simulations but one, the major driver of variability is associated with mesoscale features passing through the section. High resolution (<1/10 deg.) hindcast models agree on the temporal (2–4 cycles per year) and spatial (300–500 km) scales of these features corresponding to observed Agulhas Rings. Coarser resolution models (<1/4 deg.) reproduce similar time scale of variability of Agulhas leakage in spite of their difficulties in representing the Agulhas rings properties. A coarser resolution climate model (2 deg.) does not resolve the spatio-temporal mechanism of variability of Agulhas leakage. Hence it is expected to underestimate the contribution of Agulhas Current System to climate variability.

Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that “Lévy random walks”—which can produce power law path length distributions—are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent’s goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.

Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that “Lévy random walks”—which can produce power law path length distributions—are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent’s goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.