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... Minimum prey size of pelagic predators, in contrast, changed little as small, readily accessible prey were consumed by all predator sizes to presumably help meet the metabolic demand of active foraging in pelagic habitats (Griffiths 2020). The ready accessibility of small prey reflects the greater abundance (Ursin 1973;Hartvig et al. 2011;Tsai et al. 2016) and easier catchability (e.g., lower handling time) of small organisms relative to larger organisms (Woodward and Warren 2007). ...
... However, unequal availability across body sizes (i.e., size-structured prey communities), due to the greater abundance of smaller organisms, cause predators to consume more small prey than otherwise dictated by preference. This unequal-abundance bias in PPMR was addressed by Ursin (1973) who simulated equal availability by using biomass instead of count to calculate a weighted mean prey body size. The simulation has been widely used to estimate the PPMR (Horbowy 1982;Dekker 1983;Bundgaard and Sparholt 1992;Lewy and Vinther 2004;Andersen 2019). ...
... We used Ursin's PPMR and Tsai et al.'s Proxy to test our hypotheses that PPMR would differ among predator groups. Ursin's PPMR (Ursin 1973) simulates equal availability by ...
How predator–prey mass ratios (PPMR) vary across taxa and body sizes has long-standing, unresolved relevance to ecosystem structure, function, and modeling. Mid-level fishes, or forage fishes, convey large amounts of trophic energy in coastal marine ecosystems, but uncertainty in the dependence of their PPMR on predator species and size hampers ecological understanding and model development. Late-summer (September) data (2000, 2001, and 2003) on three major zooplanktivorous forage fishes (capelin Mallotus catervarius, eulachon Thaleichthys pacificus, and juvenile walleye pollock Gadus chalcogrammus) in the western Gulf of Alaska, northeast Pacific Ocean, were used to determine how PPMR varied by species and body size. Differences in species’ ability to transition across prey taxa were associated with different allometric relationships in prey size. Transitioning across taxa allowed prey size to increase hyperallometrically resulting in negative size dependence of PPMR for capelin and juvenile walleye pollock, both marine species. In contrast, eulachon, an anadromous species, consumed euphausiids almost exclusively and exhibited positive size dependence of PPMR. Our findings suggest that some predator species differ in transitioning across size-structured taxonomic groups of prey and consequently differ in their size-PPMR relationship. They also suggest that incorporation of taxon-specific PPMR size dependency into multispecies size-based ecosystem models will improve model realism partly because the PPMR is linked theoretically to trophic transfer efficiency.
... Predator-prey interactions. In each predation event, we assume that predators have a preferred predator-prey mass ratio (PPMR) based on the rule "bigger ones eat smaller ones" [22]. A size selectivity matrix S by a predator in size class i on a prey in size class j composed of size preferences φ i,j (i>j) and zeros is described as follows: ...
... where φ i,j is given by a function that follows a lognormal distribution on the ratio of body masses of predator and prey, m i and m j , respectively [22]. Although resources are only placed at the first size class [m 1 ] in our model, we assume that they also extend to an imaginary size range [m −s ,m 0 ] (which is divided into logarithmically equally spaced s+1 size classes, and m 0 <m 1 ) in calculating φ i,j to ensure that small consumers can feed on preferred prey smaller than m 1 . ...
... ; gm p k Þ, describing the search rate of each predator individual in size class i. Note that the elements on the [23] p Exponent of searching rate 0.75 [13] υ Factor of preferred PPMR 100 [22] Τ Exponent of preferred PPMR 0 [22] σ Width of size preference 1.3 [22] v Factor of standard metabolic rate 2.4 yr -1 g 1-q [13] q Exponent of standard metabolic rate a 0.75 [24] μ 0 Factor of non-predation mortality 0.6 yr -1 g -d [11] d Exponent of non-predation mortality 0.25 [19] Adjusted from the factor of natural mortality rate in [4] to output a linear size spectrum. b Adjusted from the exponent of natural mortality rate in [4] to output a linear size spectrum. ...
Several types of size-based models have been developed to model the size spectra of marine communities, in which abundance scales strongly with body size, using continuous differential equations. In this study, we develop a size-structured matrix model, which can be seen as a discretization of the Mckendrick-von Foerster equation, to simulate the dynamics of marine communities. The developed model uses a series of simple body size power functions to describe the basic processes of predator–prey interactions, reproduction, metabolism, and non-predation mortality based on the principle of mass balance. Linear size spectra with slopes of approximately –1 are successfully reproduced by this model. Several examples of numerical simulations are provided to demonstrate the model’s behavior. Size spectra with cut-offs and/or waves are also found for certain parameter values. The matrix model is flexible and can be freely manipulated by users to answer different questions and is executed over a shorter numerical calculation running time than continuous models.
... Assumptions are made only at the level of the individuals in terms of their physiology, their encounter with prey, and their reproductive capability. The central assumption is that big individuals eat smaller individuals with a log-normal size-preference (Ursin 1973;M1). The size-preference is used to determine the amount of food that an individual encounters, which depends on a search rate that scales with individual weight (M2) and the available prey (M3). ...
... f The data of Winberg ((1956)) indicate a standard (resting) metabolism factor for fish of about 4 g 0.25 yr -1 at 10 o C. g Calculated from the other parameters as specified in Andersen and Pedersen (2010). h Ursin (1973) and Jennings et al. (2001). i Ursin (1973) finds σ ≈ 1 for a single species. ...
... h Ursin (1973) and Jennings et al. (2001). i Ursin (1973) finds σ ≈ 1 for a single species. To account for species diversity within trait class classes, this has been increased to σ = 1.3. ...
Under the ecosystem approach to fisheries, an optimal fishing pattern is one that gives the highest possible yield while having the least structural impact on the community. Unregulated, open-access African inland fisheries have been observed to sustain high catches by harvesting a broad spectrum of species and sizes, often in conflict with current management regulations in terms of mesh and gear regulations. Using a size- and trait-based model, we explore whether such exploitation patterns are commensurable with the ecosystem approach to fisheries by comparing the impacts on size spectrum slope and yield with the different size limit regimes employed in the Zambian and Zimbabwean sides of man-made Lake Kariba. Long-term multispecies data under fished and unfished conditions are used to compare and validate the model results. Both model and observations show that the highest yields and low structural impact on the ecosystem are obtained by targeting small individuals in the community. These results call for a re-evaluation of the size-based management regulations that are ubiquitous in most fisheries.
... In the multispecies size-spectrum model, each species shows different change patterns driven by specific life history characteristics, including growth, predation, mortality, and reproduction (Andersen and Beyer, 2006;Hartvig et al., 2011;Scott et al., 2014). A governing principle in the size-spectrum model is that the available energy gets from predation by larger species on smaller ones and used for growth and reproduction can be linked to the asymptotic size of the predator (Ursin, 1973;Andersen et al., 2015). ...
... The size spectrum N i (w) of a particular size class in the model can be measured in the unit of numbers per weight per volume (Andersen and Pedersen, 2010). The second assumption is that the food preference (ϕ) depends on the species and the individual weight, described by the lognormal selection model (Ursin, 1973): ...
Catch, bycatch and discard information is important for the assessment and management of fisheries. Using Chinese pelagic tuna longline observer data from 2010 to 2018, we studied the catch composition in the Chinese pelagic tuna longline fisheries in Atlantic targeting bigeye tuna (Thunnus obesus) and bluefin tuna (Thunnus thynnus), and analyzed the survival status and discard rates of common bycatch species. A total of 55 species, including tunas, billfishes, sharks, sea turtles, cetaceans, seabirds, and other pelagic species, were observed. The results indicated that the catch composition of the Chinese pelagic tuna longline fishery targeting bigeye tuna was significantly different from that targeting bluefin tuna. The annual discard rates of common species decreased over this period. Discard rate by length and discard mortality for common species were varied among species. This is the first study to estimate catch, bycatch, and discard using Chinese pelagic tuna longline observer data in the Atlantic Ocean, which is important for the management of Chinese tuna longline fisheries in Atlantic Ocean.
... In the multispecies size-spectrum model, each species shows different change patterns driven by specific life history characteristics, including growth, predation, mortality, and reproduction (Andersen and Beyer, 2006;Hartvig et al., 2011;Scott et al., 2014). A governing principle in the size-spectrum model is that the available energy gets from predation by larger species on smaller ones and used for growth and reproduction can be linked to the asymptotic size of the predator (Ursin, 1973;Andersen et al., 2015). ...
... The size spectrum N i (w) of a particular size class in the model can be measured in the unit of numbers per weight per volume (Andersen and Pedersen, 2010). The second assumption is that the food preference (ϕ) depends on the species and the individual weight, described by the lognormal selection model (Ursin, 1973): ...
The size-spectrum model has been considered a useful tool for understanding the structures of marine ecosystems and examining management implications for fisheries. Based on Chinese tuna longline observer data from the central and eastern tropical Pacific Ocean and published data, we developed and calibrated a multispecies size-spectrum model of twenty common and commercially important species in this area. We then use the model to project the status of the species from 2016 to 2050 under five constant-fishing-mortality management scenarios: (1) F=0; (2) F=Frecent, the average fishing mortality from 2013 to 2015; (3) F=0.5Frecent; (4) F=2Frecent and (5) F=3Frecent. Several ecological indicators were used to track the dynamics of the community structure under different levels of fishing, including the mean body weight, slope of community size spectra (Slope), and total biomass. The validation demonstrated that size-at-age data of nine main catch species between our model predictions and those empirical data from assessments by the Western and Central Pacific Fisheries Commission matched well, with the R2>0.9. The direct effect of fishing was the decreasing abundance of large-sized individuals. The mean body weight in the community decreased by ∼1 500 g (21%) by 2050 when F doubled from Frecent to 2Frecent. The higher the fishing mortality, the steeper the Slope was. The projection also indicated that fishing impacts reflected by the total biomass did not increase proportionally with the increasing fishing mortality. The biomass of the main target tuna species was still abundant over the projection period under the recent fishing mortality, except Albacore tuna (Thunnus alalunga). For sharks and billfishes, their biomass remained at relatively higher levels only under the F=0 scenario. The results can serve as a scientific reference for alternative management strategies in the tropical Pacific Ocean.
... The multispecies working group carefully examined both suitability and predation mortality in a more disaggregated fashion. Both the estimated suitability terms suit(A,S,a,s) and the estimated partial M2s for each predator (S) age (A), prey(s) age (a) combination by year (y) M2 (A,S,a,s,y) could be fitted using the Ursin log normal feeding relationship (Ursin, 1973;Andersen and Ursin, 1977): ...
... Dealing with zeros is difficult because some will be true zeros and some due to missing observations. The parameters of the Ursin (1973) feeding relationship are particularly relevant to our understanding of M2 and to our later work. The exp(μ(S)) values (i.e., the preferred W(S)/w(s) ratios) were low for cod (26), whiting (39) and mackerel (32) while being higher for saithe (160) and haddock (134). ...
The authors have collaborated for the past 40 years on a sequence of initiatives for a range of fisheries and marine ecosystems projects. These had natural mortality (M) as a common thread and have helped increase understanding of this elusive parameter. Here, we provide a reprise as well as an extension of our earlier results. Taken together, these help to develop an understanding of M of exploited fish stocks, particularly those of the North Sea. Firstly, a reprisal is given of the key findings about M due to predation by important fish stocks of the North Sea. Estimates were first produced by the ICES Multispecies Working Group using multispecies virtual population analysis (MSVPA) in combination with extensive stomach content data - collected for all four quarters and around the whole North Sea during 1981. Results from this initiative demonstrate that predation mortality (M2) represents a large portion of M for many North Sea fish species, but varies markedly both by age and by year, thus refuting the then widely adopted hypothesis that M was constant. Moreover, these variations were sufficiently large to overturn single species predictions of sustainable yield. M2 results from the 1980′s also indicated that mortality levels were related to prey size and species. The paper then reprises results from studies made by the private working group (PWG) that the authors formed to continue their collaboration. These focused first on size spectra of fish communities both by data analysis and by developing a simple trait-based model (cartoon) of the North Sea - the charmingly simple model (CSM). This modelling led to further questions about the basis of the coexistence of fish species in an ecosystem given that egg production scales approximately with asymptotic weight. This led to a plausible hypothesis that differential natural mortality rates are required that increase with the von Bertalanffy parameters of curvature K and asymptotic length L∞, but decrease with fish length. Data from the literature supported this hypothesis, which was further refined into canonical form: M=K(L∞/L)1.5. However, this hypothesis is also questioned because this form might not be compatible with the predicted and observable fact that size-spectra slopes become more negative with increased general levels of fishing. Clearly, changes in size spectra should cause changes in M2. Results of new modelling work are presented where the CSM is modified to include differential natural mortality rates by K and L∞. The results suggest that M responds both to general levels of fishing and the slope of the ensuing size spectrum. This suggests that a more general expression for predation mortality would be M2=α(F)K(L∞χ)(Lβ⁽F⁾), where χ is likely to be close to the 1.5 value used in the canonical form. The work thus provides a likely form for M2 but by no means a universally applicable formula. It remains a hypothesis needing to be tested and perhaps calibrated against data from the sea. Such calibrations might indeed point toward a universal formula for M2.
... We encourage further theoretical and empirical studies to use fully resolved food web data, metrics of dominance and habitat use, and multiple ecosystem functions to better understand the complexity of links and mechanisms between biodiversity, food web structure, and ecosystem functions. Width of selection function -1 (Ursin, 1973) 0 Home range of sized species 0 -2 2 (Hartvig, 2011) Preferred predator:prey mass ratio -100 (Ursin, 1973) Conversion ...
... We encourage further theoretical and empirical studies to use fully resolved food web data, metrics of dominance and habitat use, and multiple ecosystem functions to better understand the complexity of links and mechanisms between biodiversity, food web structure, and ecosystem functions. Width of selection function -1 (Ursin, 1973) 0 Home range of sized species 0 -2 2 (Hartvig, 2011) Preferred predator:prey mass ratio -100 (Ursin, 1973) Conversion ...
The concept of biodiversity–ecosystem functioning (BEF) has been studied over the last three decades using experiments, theoretical models and more recently observational data. While theoretical models revealed that species richness is the best metric summarizing ecosystem functioning, it is clear that ecosystem function is explained by other variables besides species richness. Additionally, theoretical models rarely focus on more than one ecosystem function, limiting ecosystem functioning to biomass or production. There is a lack of theoretical background to verify how other components of biodiversity and species interactions support ecosystem functioning.
Here, using simulations from a food web model based on a community assembly process and a trait‐based approach, we test how species biodiversity, food web structure and predator–prey interactions determine several ecosystem functions (biomass, metabolism, production and productivity).
Our results demonstrate that the relationship between species richness and ecosystem functioning depends on the type of ecosystem function considered and the importance of diversity and food web structure differs across functions. Particularly, we show that dominance plays a major role in determining the level of biomass, and it is at least as important as the number of species. We find that dominance occurs in the food web when species do not experience strong predation.
By manipulating the structure of the food web, we show that species using a wider trait space (generalist communities) result in more connected food webs and generally reach the same level of functioning with less species. The model shows the importance of generalist versus specialist communities on BEF relationships, and as such, empirical studies should focus on quantifying the importance of diet/habitat use on ecosystem functioning.
Our study provides a better understanding of BEF underlying mechanisms and generates research hypotheses that can be considered and tested in observational studies. We recommend that studies investigating links between biodiversity and ecosystem functions should include metrics of dominance, species composition, trophic structure and possibly environmental trait space. We also advise that more effort should be made into calculating several ecosystem functions and properties with data from natural multitrophic systems.
... The "realized PPMR" (i.e., PPMR based on ingested prey) of predators is emergent in the models and may change with predator size and prey relative abundance (Hartvig et al., 2011). Direct estimation of preferred PPMR is challenging because this requires knowledge of realized PPMR and the size composition and abundance of encountered prey (Floeter & Temming, 2003;Tsai, Hsieh, & Nakazawa, 2016;Ursin, 1973Ursin, , 1974. Alternatively, it may be possible to approximate preferred PPMR with a simple offset from realized PPMR. ...
... For dynamic size spectrum models, direct estimation of the preferred PPMR of predators requires information on diet composition as well as the size composition and abundance of encountered prey (Hartvig et al., 2011;Tsai et al., 2016). Given the complexities of estimating the latter quantities in the field, preferred PPMR is measured more precisely in experiments (e.g., Ursin, 1973), but these closed environments are likely to introduce artifacts (e.g., poor representation of predator and prey refuges, effects of changing light quality and turbidity, etc.). Moreover, such experiments would need to be conducted with many species and body size classes to provide preference functions which could realistically be applied to communities. ...
Food web structure and dynamics depend on relationships between body sizes of predators and their prey. Species‐based and community‐wide estimates of preferred and realized predator–prey mass ratios (PPMR) are required inputs to size‐based size spectrum models of marine communities, food webs, and ecosystems. Here, we clarify differences between PPMR definitions in different size spectrum models, in particular differences between PPMR measurements weighting prey abundance in individual predators by biomass (rbio) and numbers (rnum). We argue that the former weighting generates PPMR as usually conceptualized in equilibrium (static) size spectrum models while the latter usually applies to dynamic models. We use diet information from 170,689 individuals of 34 species of fish in Alaskan marine ecosystems to calculate both PPMR metrics. Using hierarchical models, we examine how explained variance in these metrics changed with predator body size, predator taxonomic resolution, and spatial resolution. In the hierarchical analysis, variance in both metrics emerged primarily at the species level and substantially less variance was associated with other (higher) taxonomic levels or with spatial resolution. This suggests that changes in species composition are the main drivers of community‐wide mean PPMR. At all levels of analysis, relationships between weighted mean rbio or weighted mean rnum and predator mass tended to be dome‐shaped. Weighted mean rnum values, for species and community‐wide, were approximately an order of magnitude higher than weighted mean rbio, reflecting the consistent numeric dominance of small prey in predator diets. As well as increasing understanding of the drivers of variation in PPMR and providing estimates of PPMR in the north Pacific Ocean, our results demonstrate that that rbio or rnum, as well as their corresponding weighted means for any defined group of predators, are not directly substitutable. When developing equilibrium size‐based models based on bulk energy flux or comparing PPMR estimates derived from the relationship between body mass and trophic level with those based on diet analysis, weighted mean rbio is a more appropriate measure of PPMR. When calibrating preference PPMR in dynamic size spectrum models then weighted mean rnum will be a more appropriate measure of PPMR. Predator‐to‐prey body mass ratios (PPMRs) are key parameters in size spectrum models, but are conceptualized differently depending on the type of model. We clarify the definitions which differ according to whether individual prey are weighted numerically or by biomass. Using diet data from 170,689 individual fish predators, we show that that the two metrics are not substitutable and evaluate how variance in PPMR metrics emerge across taxonomic levels and spatial scales.
... The Andersen-Ursin suitability function (Andersen and Ursin, 1977;Ursin, 1973), where suitability depends on the ratio between predator (L) and prey (l) lengths was used to represent the selection of Saduria (prey length was constant), herring and sprat: ...
... Herring and sprat length in predicted cod diet resulted from applying an Andersen-Ursin suitability function (Eq. (8), Andersen and Ursin, 1977;Ursin, 1973) on reconstructed length distributions of cod, herring and sprat. The function was simplified by assuming that p 3 =p 4 , i.e. the suitability function is symmetrical and not skewed. ...
Size of predator and prey determines, to a large extent, predator-prey interactions in aquatic systems. Understanding the relationship between predator and prey size in the individual predator's food selection process is a cornerstone of ecological modelling. Stomach content data are used to inform such models, as they provide prey species specific information about the predator diet in the wild. These data are strongly relevant as direct observations of species trophic interactions, but they have limitations, and are costly. Our objective was to develop and test a model which is able to predict changes in the Baltic cod diet by reconstructing the dynamics of cod and its prey, herring and sprat, populations, their length distributions, and parametrizing trophic interactions between them. We analysed time-series of cod stomach data and built an age-length structured multispecies model using Gadget. Both observed and predicted diets of smaller (juvenile) cod consisted mainly of benthos, while larger cod fed mostly on fishes (herring and sprat). Our model could predict the main patterns in species and length composition of cod diet. We also identified important knowledge gaps, especially on benthos dynamics and processes affecting prey availability and predator preference.
... The magnitude of cannibalistic mortality depends on the prey-size preference of the cannibals as well as on external factors such as availability of alternative prey. Many fish have a preferred prey-size range (Ursin 1973), however, since most fish lay small eggs relative to adult body size, juveniles will at some point fall within the prey size range of the adults. The preferred prey-size range is influenced by the probability of capture as well as the energetic pay-off (Christensen 1996), resulting in a predicted dome-shaped mortality curve centred on the preferred prey size (Persson 1987). ...
... where w m is the adult size and s defines the width of the selection function. For fish, typical parameter values are s 1 and b 100 (Ursin 1973). We assume that cannibalistic mortality rate is proportional to the size selection µ θ ...
Cannibalism may cause considerable mortality on juvenile fish and it has been hypothesised that it may exercise selection on offspring size in that larger offspring may enjoy a size refuge. For this to be evolutionarily advantageous the survival of individual offspring must compensate for the reduced fecundity implied by larger offspring size. We develop a model which combines standard assumptions of size-dependent mortality with adult cannibalism to investigate the potential for cannibalism to act as selective force on offspring size. We find that for this potential to be realised, the mortality due to cannibalism must exceed a threshold value that is a decreasing function of non-cannibalistic predation intensity, cannibalized size range width and the average cannibalized size. If cannibalism exceeds this threshold, the model predicts evolution of offspring size towards refuges above or below cannibalized size range depending on initial offspring size. Cannibalistic mortality cannot be so great that the population is non-viable, however, the range of parameter values describing cannibalistic intensity allowed within these boundaries is wide. On this basis, we suggest that cannibalism is a potential mechanism for offspring size selection.
... Or, as aptly put by Darwin [9]: "We have reason to be-30 lieve that species in a state of nature are limited in their ranges by the competition of other organic beings quite as much as, or more than, by adaptation to particular climates". 32 That climate change impacts cannot be understood solely from physiology is well illustrated by the recent exploration of shifting ranges of fish [10]. While, on average, populations move in the 34 direction of local climate change, there is a large variation in the response of different populations, and some populations even move in the opposite direction of climate change. ...
... Formally this interaction is described by a size-selection kernel '(w i /w j ) (N5) and a spatial interaction kernel (x i x j ) (N6). The size-selection kernel is a lognormal function [10], describing the preference of w i sized predators to w j sized prey, and attains its maximum when w i /w j equals the preferred predator-prey mass ratio . Thus, individuals with mass ratio far from have negligible interactions. ...
Climate change affects ecological communities through its impact on the physiological performance of individuals. However, the population dynamic of species well inside their thermal niche is also determined by competitors, prey and predators, in addition to being influenced by temperature changes. We use a trait-based food-web model to examine how the interplay between the direct physiological effects from temperature and the indirect effects due to changing interactions between populations shapes the ecological consequences of climate change for populations and for entire communities. Our simulations illustrate how isolated communities deteriorate as populations go extinct when the environment moves outside the species’ thermal niches. High-trophic-level species are most vulnerable, while the ecosystem function of lower trophic levels is less impacted. Open communities can compensate for the loss of ecosystem function by invasions of new species. Individual populations show complex responses largely uncorrelated with the direct impact of temperature change on physiology. Such complex responses are particularly evident during extinction and invasion events of other species, where climaticallywell-adapted species may be brought to extinction by the changed food-web topology. Our results highlight that the impact of climate change on specific populations is largely unpredictable, and apparently well-adapted species may be severely impacted. © 2017 The Author(s) Published by the Royal Society. All rights reserved.
... A key characteristic of fish is 51 that individuals grow through several orders of magnitude in body size through their 52 life. This, combined with the strong relationship between body-size and trophic niche 53 (Barnes et al. 2008; Gilljam et al. 2011), means that individuals change their trophic 54 niche throughout ontogeny (Werner and Gilliam 1984Elton 1927; Haldane 1928; Andersen et al. 63 2016a) because it correlates strongly with: metabolism (Kleiber 1932; Winberg 1956, 64 Brown et al. 2004), predator-prey relations (Ursin 1973; Barnes et al. 2008), encounter 65 rates (Acuña et al. 2011), functional responses (Rall et al. 2012), reproductive effort, and 66 other vital rates (Peters 1983). For application to fisheries, body size furthermore is an 67 excellent descriptor of mesh-size regulations and characterizes the value of a catch 68 (). ...
... The key process in the models is predator-prey encounters between individuals 172 governed by a formalization of the general rule, bigger fish eat smaller fish (Andersen 173 and Ursin 1977). Individuals prefer prey a certain fraction smaller than themselves (M1, 174Table 1) (Ursin 1973). The clearance rate (dimensions time -1 ) is an increasing function 175 of body size (larger fish clear a larger volume of water for prey per time than small fish) 176 ...
Size spectrum models have emerged from 40 years of basic research on how body size determines individual physiology and structures marine communities. They are based on commonly accepted assumptions and have a low parameter set, making them easy to deploy for strategic ecosystem-oriented impact assessment of fisheries. We describe the fundamental concepts in size-based models about food encounter and the bioenergetics budget of individuals. Within the general framework, three model types have emerged that differ in their degree of complexity: the food-web, the trait-based, and the community models. We demonstrate the differences between the models through examples of their response to fishing and their dynamic behavior. We review implementations of size spectrum models and describe important variations concerning the functional response, whether growth is food-dependent or fixed, and the density dependence imposed on the system. Finally, we discuss challenges and promising directions.
... donde: mín es el peso menor entre X ij y X kj , X ij es la ocurrencia (porcentaje en peso) del j-ésimo taxon de presa en el i-ésimo grupo de tamaño del predador; X kj es la ocurrencia (porcentaje en peso) del mismo taxon de presa en el k-ésimo grupo de tamaño del predador. La selectividad de presas por tamaño fue determinada usando la metodología de Ursin (1973), donde el tamaño relativo de cada presa en el estómago de cada predador es calculado como la razón entre el peso del predador y el peso de la presa, y cada razón es designada como un valor ISU. Las preferencias se reflejan como una distribución de frecuencias derivada del logaritmo natural de sus pesos cuya forma es: ...
... Los eufáusidos y Vinciguerria sp. no mostraron una distribución normal en el índice de selectividad, lo cual se explicaría con el postulado de Ursin (1973), que señala que la distribución de frecuencias del índice se aparta de una distribución normal cuando los recursos presa son abundantes en la naturaleza. Aunque en este estudio no se han identificado los eufaúsidos, Antezana (1970) afirma que Euphausia mucronata es la especie más frecuente y abundante en sectores costeros. ...
The trophic dynamic of jack mackerel Trachurus symmetricus murphyi, caught off the coast of northern Chile, between the spring 1993 and winter 1994, is described. Relative importance of prey taxa, identification of ontogenetic trophic units and prey selectivity by size was evaluated. The main prey in terms of relative importance were euphausids, for all seasons analyzed. Another important prey was mesopelagic fish Vinciguerria sp. Three ontogenetic trophic units were identified, within the size range of 21 to 35 cm fork length. The selectivity analysis of preys by size indicated that the large size prey in the stomach content was Engraulis ringens. Besides, this prey was the more selected together with Chaetognatha. The size frequency distribution of E. ringens in the stomach of jack mackerel overlapped partially with the sizes frequency distribution of E. ringens obtained from the commercial captures, being in the first case of smaller size that in the second.
... No association was found between prey and predator maximum length, although expected, given the widely acknowledged (positive) predator-prey size relationship (Ursin 1973, Scharf et al. 2000, Floeter & Temming 2003, Pinnegar et al. 2003. Similarly, another presumably significant relationship was not found, namely the association of prey maximum length and predator relative maxillary jaw length, which serves as a proxy for gape size (compare Toussaint et al. 2016, Su et al. 2019) and morphometrically limits ingestible prey size (e.g. ...
In marine ecosystems under ongoing long-term changes, reducing complex food webs to their functionally important properties enables systematic analysis of bottom-up/top-down regulations and species turnover. The assessment of feeding interactions in the form of predator and prey trait associations provides a better understanding of predators’ criteria for prey selection and thus is a promising approach to reduce complexity. Here, we tested RLQ ordination and fourth-corner analysis, complementary multivariate approaches, as tools to identify ecologically relevant associations between the traits of 8 demersal fish species in the southern North Sea and their fish or benthic prey. To scrutinize the trait-based results in their appropriateness to reflect selective feeding behaviour of the predator species, we compared them with a taxon-based electivity index, Chesson’s α. Among 7 predator traits investigated, body tissue composition represented by omega-3 polyunsaturated fatty acid content was significantly associated with prey traits, being positively correlated with energy density of the prey and negatively with prey of low mobility. Comparisons with the electivity indices showed that the prey preferred by predators corresponded relatively well with the identified prey trait preferences. The results of the tested analysis approach support its use when assessing the mutual dependences of predator and prey populations on a functional level. Provided the data availability and quality of feeding-related traits is sufficiently high, trait-based predator-prey analysis with RLQ and fourth-corner analyses offers new possibilities for understanding food web dynamics in the context of climate-change-induced species distribution shifts.
... For simplicity, we ignored the potential effects of temperature on encounter or clearance rates that could arise from an increase in activity associated with warmer environmental conditions. In Equation 3 (defined below), we used an empirically estimated constant of 0.07 to characterize the scaling of prey vulnerability with its mass (Andersen, 2019), which is based on estimates of preference windows of predators and the volume of water each clears per month that comes from empirical distributions of prey sizes in predator guts (Ursin, 1973). We also define a coefficient h, which modifies the probability of consumption -how likely a predator is to capture the focal individual (based on its capture efficiency) -and used the reported allometric exponent of −0.25 to represent how predation mortality scales with body size (Figure 2b; eq. ...
Understanding how growth and reproduction will adapt to changing environmental conditions is a fundamental question in evolutionary ecology, but predicting the responses of specific taxa is challenging. Analyses of the physiological effects of climate change upon life history evolution rarely consider alternative hypothesized mechanisms, such as size‐dependent foraging and the risk of predation, simultaneously shaping optimal growth patterns. To test for interactions between these mechanisms, we embedded a state‐dependent energetic model in an ecosystem size‐spectrum to ask whether prey availability (foraging) and risk of predation experienced by individual fish can explain observed diversity in life histories of fishes. We found that asymptotic growth emerged from size‐based foraging and reproductive and mortality patterns in the context of ecosystem food web interactions. While more productive ecosystems led to larger body sizes, the effects of temperature on metabolic costs had only small effects on size. To validate our model, we ran it for abiotic scenarios corresponding to the ecological lifestyles of three tuna species, considering environments that included seasonal variation in temperature. We successfully predicted realistic patterns of growth, reproduction, and mortality of all three tuna species. We found that individuals grew larger when environmental conditions varied seasonally, and spawning was restricted to part of the year (corresponding to their migration from temperate to tropical waters). Growing larger was advantageous because foraging and spawning opportunities were seasonally constrained. This mechanism could explain the evolution of gigantism in temperate tunas. Our approach addresses variation in food availability and individual risk as well as metabolic processes and offers a promising approach to understand fish life‐history responses to changing ocean conditions.
... Each of these mechanisms is governed by individual-level processes that relate to body size w and asymptotic size W ∞ . These processes determine how biomass moves through and accumulates within the fish community ( Fig. 1a) by describing how individual fish encounter and consume planktonic resources or prey of smaller size (Ursin 1973) to provide energy to fuel metabolism, reproduction, and growth. Metabolism expends energy according to size-dependent allometric rates (Kleiber 1932). ...
Fish contribute to the export of carbon out of the euphotic zone. They ingest organic carbon fixed by phytoplankton, store it in their tissues for their lifetime, and contribute to long-term sequestration by producing sinking fecal pellets, respiring at depth, or via their own sinking carcasses. While the flux of carbon through fish is small relative to the export flux by plankton, humans have a direct influence on fish communities and thus on the magnitude of carbon storage and flux. We use a size spectrum model to examine the combined effect of fishing and trophic dynamics on the total carbon stored as biomass of a simulated community of fish. By sampling 10,500 possible fishing strategies that randomize fishing mortality and size-selectivity, we consider optimal strategies that balance several UN Sustainable Development Goals addressing (1) food security, (2) climate action, and (3) marine conservation. The model shows that fishery management strategies that preferentially conserve large species increase overall carbon stored in the fish community. This study presents a perspective for considering carbon storage and sequestration in fisheries management alongside alternative objectives such as food production and biodiversity conservation. Our study focused on the state (total carbon in the living community). Incorporating rate processes like fecal pellet flux, vertical migration, and natural mortality would build toward a more holistic carbon approach to fisheries management.
... This encounter rate (the clearance rate) is 163 typically measured in units of volume per time, as aquatic species forage in a three-dimensional 164 habitat (Kiørboe and Hirst 2014). Again, we follow Andersen (2019), and use an empirically 165 estimated constant of 0.07 to characterize the scaling of prey vulnerability with mass, given 166 estimates of preference windows of predators and the volume of water each clears that come 167 from empirical distributions of prey sizes in predator guts (Ursin 1973). We also define a 168 coefficient h, which modifies the probability of consumption -how likely a predator is to capture 169 the focal individual (based on its hunger level or capture efficiency) -and use the reported 170 allometric exponent of -0.25 to represent how consumption scales with body size ( Figure 1B; 171 Andersen 2019). ...
Understanding how changing environmental conditions affect fish growth and reproduction is critical to predict the consequences of climate change, yet studies focused on the physiological effects of temperature upon life histories often ignore size-dependent foraging and risk of predation. We embedded a state-dependent energetic model in an ecosystem size spectrum model to characterize prey availability (foraging) and risk of predation (fear) experienced by individual fish as they grow. We examined how spectrum richness and temperature interact to shape growth, reproduction, and survival; we found that richer spectra led to larger body sizes, but effects of temperature on body size were small. We applied our model to scenarios corresponding to three ecological lifestyles (ecotypes) of tunas, in some cases including seasonal variation in conditions. We predicted realistic estimates of growth and body sizes of tunas and found that seasonality in resources and temperature could lead to giant body sizes (> 300 cm), due to the compression of reproduction into shorter timeframes. Our framework for predicting emergent life histories combines direct and indirect effects of productivity (foodscapes), individual risk (fearscapes), and metabolic processes. This approach can be used to reconcile disparate results on fish life history responses to changing ocean conditions.
... where , is the non-size based preference of species on species , and describes the weight-based preference from the log-normal selection model (see below) (Ursin 1973). ...
Resolving the combined effect of climate warming and exploitation in a food web context is key for predicting future biomass production, size‐structure, and potential yields of marine fishes. Previous studies based on mechanistic size‐based food web models have found that bottom‐up processes are important drivers of size‐structure and fisheries yield in changing climates. However, we know less about the joint effects of ‘bottom‐up’ and physiological effects of temperature; how do temperature effects propagate from individual‐level physiology through food webs and alter the size‐structure of exploited species in a community? Here we assess how a species‐resolved size‐based food web is affected by warming through both these pathways, and by exploitation. We parameterize a dynamic size spectrum food web model inspired by the offshore Baltic Sea food web, and investigate how individual growth rates, size‐structure, relative abundances of species and yields are affected by warming. The magnitude of warming is based on projections by the regional coupled model system RCA4‐NEMO and the RCP 8.5 emission scenario, and we evaluate different scenarios of temperature dependence on fish physiology and resource productivity. When accounting for temperature‐effects on physiology in addition to on basal productivity, projected size‐at‐age in 2050 increases on average for all fish species, mainly for young fish, compared to scenarios without warming. In contrast, size‐at‐age decreases when temperature affects resource dynamics only, and the decline is largest for young fish. Faster growth rates due to warming, however, do not always translate to larger yields, as lower resource carrying capacities with increasing temperature tend to result in declines in the abundance of larger fish and hence spawning stock biomass. These results suggest that to understand how global warming affects the size structure of fish communities, both direct metabolic effects and indirect effects of temperature via basal resources must be accounted for.
... Interactions between species are governed by a sizebased feeding-preference curve and by a matrix with size-independent pairwise species-interaction terms. The feeding preference of an individual is determined by the body-size ratio between predator and prey, described by Ursin's (1973) log-normal selection model. ...
Inland fisheries have a significant cultural and economic value around the globe, providing dietary protein, income, and recreation. Consequently, methods for monitoring and managing these important fisheries are continually being refined. In marine systems, multispecies size spectrum models have been increasingly used to explore management scenarios of important fish stocks within an ecosystem‐based fisheries management framework; however, these models have not been applied as extensively in freshwater systems. In this study, we developed a multispecies size spectrum model for the fish community of Lake Nipissing, a large, productive lake in Ontario, Canada. To the best of our knowledge, this is the first fully calibrated multispecies size spectrum model for an inland fishery. Using this model, we explored the impacts of potential fishing regimes and management scenarios on fish community dynamics while taking species interactions into account. Specifically, we examined how changes in fishing mortality affect (1) species biomass, (2) community size structure, and (3) stock recovery times. We found that community dynamics following changes in fishing mortality were driven by complex interactions among species, including competition and predation. The greatest changes in biomass and community size structure were observed following changes in fishing mortality of top predators, with community size structure most strongly influenced by changes in the mortality of the largest species. Counter to predictions based on generation time, the smallest species in our model exhibited the longest time to recovery due to strong competition and predation. Our results demonstrate the importance of considering species interactions in the management of inland fisheries and highlight the potential of size spectrum model use in freshwater systems.
... Within the model, interactions between species are governed by a size-based feeding-preference curve and by a matrix with pairwise species-interaction terms. The feeding preference of an individual is determined by the body-size ratio between predator (w) and prey (w p ), described by Ursin's (1973) log-normal selection model: ...
Ecosystem-based approaches that take species interactions into account have shifted to the forefront of fisheries modelling and management in recent years. As a result, multispecies size spectrum models have been increasingly used to explore impacts of fishing on marine community dynamics. The use of these models, which has been facilitated by the development of the R package mizer, requires the estimation of species-specific parameters related to growth, reproduction, and feeding. These parameters, which may be estimated from imperfect information, may contribute to model uncertainty and thus reduce the value of information available for management purposes. In this study of a freshwater fishery, we conduct a comprehensive global sensitivity analysis pairing the Morris and Sobol methods to identify life-history parameters having the largest influence on model outputs. Here, we focus on (i) the size spectrum slope, (ii) the scatter around the linear relationship of the size spectrum, (iii) total biomass, and (iv) species diversity. We found that parameters relating to growth, namely the von Bertalanffy growth coefficient and asymptotic mass, had the greatest influence on our size spectrum model results. This was particularly true for top predators and the most abundant species. Our results suggest that estimation of growth parameters of top predators be given priority to reduce uncertainty in model output, and ultimately, fisheries management.
... The definite relationship between predator and prey is specified by a log-normal size kernel / m=w ð Þ¼exp À log m=w ð ÞÀb ð Þ 2 2r 2 1 ; ! where r 1 determines the width of the size kernel and e b is the preferred predator-prey mass ratio (Ursin, 1973). The model (1) without the term R(N, m) is the classic McKendric-von Forerster equation (Kot, 2001;Benoȋt and Rochet, 2004). ...
Size-spectrum models are a recent class of models describing the dynamics of a whole community based on a description of individual organisms. The models are motivated by marine ecosystems where they cover the size range from multicellular plankton to the largest fish. We propose to extend the size-spectrum model with spatial components. The spatial dynamics is governed by a random motion and a directed movement in the direction of increased fitness, which we call ‘fitness-taxis’. We use the model to explore whether spatial irregularities of marine communities can occur due to the internal dynamics of predator-prey interactions and spatial movements. This corresponds to a pattern-formation analysis generalized to an entire ecosystem but is not limited to one prey and one predator population. The analyses take the form of Fourier analysis and numerical experiments. Results show that diffusion always stabilizes the equilibrium but fitness-taxis destabilizes it, leading to non-stationary spatially inhomogeneous population densities, which are travelling in size. However, there is a strong asymmetry between fitness-induced destabilizing effects and diffusion-induced stabilizing effects with the latter dominating over the former. These findings reveal that fitness taxis acts as a possible mechanism behind pattern formations in ecosystems with high diversity of organism sizes, which can drive the emergence of spatial heterogeneity even in a spatially homogeneous environment.
... The new fossil taxon possesses fang-like caniniform teeth, which is a typical feature of predatory fish (e.g., [245]). The fact that only a single specimen of †Warilochromis was found among the material recovered from the Waril site further supports this interpretation, as predators are expected to occur at much lower levels than their prey (e.g., [246][247][248]). Among African cichlids, predatory species are known from almost all tribes and lineages. ...
Background:
The diversification process known as the Lake Tanganyika Radiation has given rise to the most speciose clade of African cichlids. Almost all cichlid species found in the lakes Tanganyika, Malawi and Victoria, comprising a total of 12-16 tribes, belong to this clade. Strikingly, all the species in the latter two lakes are members of the tribe Haplochromini, whose origin remains unclear. The 'out of Tanganyika' hypothesis argues that the Haplochromini emerged simultaneously with other cichlid tribes and lineages in Lake Tanganyika, presumably about 5-6 million years ago (MYA), and that their presence in the lakes Malawi and Victoria and elsewhere in Africa today is due to later migrations. In contrast, the 'melting pot Tanganyika hypothesis' postulates that Haplochromini emerged in Africa prior to the formation of Lake Tanganyika, and that their divergence could have begun about 17 MYA. Haplochromine fossils could potentially resolve this debate, but such fossils are extremely rare.
Results:
Here we present a new fossil haplochromine from the upper Miocene site Waril (9-10 million years) in Central Kenya. Comparative morphology, supported by Micro-CT imaging, reveals that it bears a unique combination of characters relating to dentition, cranial bones, caudal skeleton and meristic traits. Its most prominent feature is the presence of exclusively unicuspid teeth, with canines in the outer tooth row. †Warilochromis unicuspidatus gen. et sp. nov. shares this combination of characters solely with members of the Haplochromini and its lacrimal morphology indicates a possible relation to the riverine genus Pseudocrenilabrus. Due to its fang-like dentition and non-fusiform body, †W. unicuspidatus gen. et sp. nov. might have employed either a sit-and-pursue or sit-and-wait hunting strategy, which has not been reported for any other fossil haplochromine cichlid.
Conclusions:
The age of the fossil (9-10 MYA) is incompatible with the 'out of Tanganyika' hypothesis, which postulates that the divergence of the Haplochromini began only 5-6 MYA. The presence of this fossil in an upper Miocene palaeolake in the Central Kenya Rift, as well as its predatory lifestyle, indicate that Haplochromini were already an important component of freshwater drainages in East Africa at that time.
... Even though the literature abounds with measurements 650 of stomach contents, as shown in Fig. 2.6, there are very few attempts to measure the preference for prey size. A pioneering effort was by Ursin (1973) who examined the stomach of cod and dab and corrected for the The predator-prey size preference function (Eq. 2.4) drawn with the prey:predator ratio w/w p on the x-axis. ...
Fish are one of the most important global food sources, supplying a significant share of the world's protein consumption. From stocks of wild Alaskan salmon and North Sea cod to entire fish communities with myriad species, fisheries require careful management to ensure that stocks remain productive, and mathematical models are essential tools for doing so. This book is an introduction to the modern size- and trait-based approach to fish populations and communities. It covers the theoretical foundations, mathematical formulations, and real-world applications of this powerful new modeling method, which is grounded in the latest ecological theory and population biology. It begins with fundamental assumptions on the level of individuals and goes on to cover population demography and fisheries impact assessments. The book shows how size- and trait-based models shed new light on familiar fisheries concepts such as maximum sustainable yield and fisheries selectivity—insights that classic age-based theory can't provide—and develops novel evolutionary impacts of fishing. It extends the theory to entire fish communities and uses it to support the ecosystem approach to fisheries management, and forges critical links between trait-based methods and evolutionary ecology. The book unifies the thinking in ecology and fisheries science and is an indispensable reference for anyone seeking to apply size- and trait-based models to fish demography, fisheries impact assessments, and fish evolutionary ecology.
... Even though the literature abounds with measurements 650 of stomach contents, as shown in Fig. 2.6, there are very few attempts to measure the preference for prey size. A pioneering effort was by Ursin (1973) who examined the stomach of cod and dab and corrected for the The predator-prey size preference function (Eq. 2.4) drawn with the prey:predator ratio w/w p on the x-axis. ...
This chapter looks into the differences and similarities between the two groups of fish: the teleosts and the elasmobranchs. In the data analyses done so far in this volume, the fish most considered were the teleosts ( Teleostei ), which represent by far the dominant group, in terms of both biomass and living number of species. Second in line comes the cartilaginous fishes—the elasmobranchs (sharks, rays, skates, and sawfish). This chapter describes the differences between teleosts and elasmobranchs from a population dynamics perspective. It shows that the main difference between the two groups is in their offspring size strategy: teleosts make small offspring; elasmobranchs make large offspring. The chapter uses this difference to quantify the sensitivity of elasmobranchs to fishing relative to teleosts. It also develops an evolutionary explanation for why the offspring size strategy differs between teleosts and elasmobranchs.
... With the introduction of MSSMs, intraspecific variation in predator diets can now be fully resolved within a dynamic food web modeling framework. Although there is experimental and observational evidence supporting aspects of the prey size-selection mechanism in MSSMs (Ursin 1973, Floeter and Temming 2003, Tsai et al. 2016, surprisingly, no attempts have been made to test model adequacy in relation to actual predator diets, thus leaving their level of realism with regard to ontogenetic diet shifts and the resulting trophodynamics an open question. ...
Ontogenetic diet shifts are pervasive in food webs, but rules governing their emergence and the implications for trophic cascades are only partly understood. Recent theoretical advances in multispecies size spectrum models (MSSMs) predict that the emergence of ontogenetic diet shifts are driven primarily by size‐selective predation and changes in the relative abundances of suitably sized prey. However, these assumptions have not yet been tested with data. Here, we developed alternative MSSMs based on different assumptions about the nature of species and size‐based preferences and tested them using an extensive dietary database for the Eastern Bering Sea (EBS). MSSMs with both size and species‐specific prey preferences correctly predicted approximately three‐fold more of the diet links than those that assumed fixed species preferences. Importantly, these model assumptions also had a profound effect on the strength of fishing‐induced trophic cascades and the emergent trophic structure of the community with and without fishing. The diet‐informed models exhibited lower predation mortality rates, particularly for small individuals (less than 1 g) which, in turn, reduced the intensity and reach of fishing‐induced trophic cascades up the size spectrum. If the level and size dependency of piscivory observed in EBS predators is typical of other systems, the potential for fishing‐induced trophic cascades may be over‐stated in MSSMs as they are currently formulated and parameterized. Representation of species‐specific ontogenetic shifts in diet can strongly influence system responses to perturbations, and the extensions we propose should accelerate adoption of MSSMs as frameworks for exploring size‐based food web theory and developing modeling tools to support strategic management decisions.
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... The second central assumption is that the preference of food is only determined by individual weight, not by the trait-value or species identity of prey. The preference for prey weight is described by the log-normal selection model (Ursin, 1973) which prescribes prey preference in terms of the ratio between the weight of predators and prey of weight w and w p respectively (M4) where is the preferred predator-prey mass ratio and the width of the weight selection function. ...
The strategic objectives for fisheries, which are enshrined in international conventions, are to maintain or restore stocks to produce maximum sustainable yield (MSY) and to implement the ecosystem approach, requiring that interactions between species be taken into account and conservation constraints be respected. While the yield and conservation aims are, to some extent, compatible when a fishery for a single species is considered, species interactions entail that MSY for a species depends on the species with which it interacts, and the yield and conservation objectives therefore conflict when an ecosystem approach to fisheries management is required. We applied a conceptual size- and trait-based model to clarify and resolve these issues by determining the fishing pattern that maximizes the total yield of an entire fish community in terms of catch biomass or economic rent under acceptable conservation constraints. Our results indicate that the eradication of large, predatory fish species results in a potential maximum catch at least twice as high as if conservation constraints are imposed. However, such a large catch could only be achieved at a cost of forgone rent; maximum rent extracts less than half of the potential maximum catch mass. When a conservation constraint is applied, catch can be maximized at negligible cost in forgone rent, compared with maximizing rent. Maximization of rent is the objective that comes closest to respecting conservation concerns.
... The second .involves the visual acuity, swimming speed and degree of hunger of the predator. Size as a controlling factor .in prey preference by fish is well documented [Ursin 1973;Werner and Hall 1974;Gibson 1975,1976; Moore and Moore 1976;Pearre 1982;Ma:in 1985]. The importance of predation as a biological factor influencing the structure of natural community has been a central issue of community ecology. ...
... Many of these rates, such as the metabolic rate, can be described by allometric scaling relationships both intra-and interspecifically (Glazier, 2005). Other rates, such as the intake and attack rate, follow allometric interspecific scaling relationships (Rall et al., 2012) and hump-shaped intraspecific scaling relationships (Ursin, 1973; typically assume that reproduction starts at birth. To include this aspect of life history in dynamical food-web models it is necessary to describe the way individuals grow and transition between life stages. ...
Introduction To grow and reproduce is fundamental for living organisms. In essence all organisms go through a life cycle with ontogenetically driven changes in their physiological rates and trophic interactions (Figure 9.1; Box 9.1). This ontogenetic development occurs even in unicellular organisms but is more striking in other groups. For example: dragonflies undergo metamorphoses that span several habitats, Atlantic marlin increase up to 500 times their length, and the cod-worm has different host requirements for each life-history stage. All of these ontogenetic changes correspond to large shifts in the ecological role of an individual. In spite of the drastic changes many individuals undergo over their life history, classical ecological theory typically assumes that all individuals within a population are identical. As a consequence, a large part of our ecological understanding relies on this assumption. This is surprising considering that ecological theory strongly links to evolution, which is critically dependent on variation among individuals. Acknowledging ecological variation of individuals within the species is relatively recent to food-web ecology. While individual variation can arise from genetic or stochastic processes, this chapter focuses on individual variation that relates to ontogenetic development. Biological interactions that are susceptible to ontogenetic variation include: resource use, vulnerability to predators and parasites, mutualistic interactions, cannibalism, and commensalism. Therefore the consideration of ontogeny has major implications for the way we consider food-web topology (Box 9.2). In a broader sense, the function of an organism, such as the nutrient fluxes it contributes to and the ecosystem services it takes part in, may also change over ontogeny. By ignoring the individual life history, ecologists focus on interactions between populations rather than between individuals, an abstraction that may be biologically inaccurate. In fact, differences between individuals within species can exceed, and have larger effects on food-web dynamics, than differences between individuals of different species. This suggests that the consideration of differences between life stages within populations is essential for our understanding of food-web structure and ecosystem functioning.
... The MA of marine fishes increases faster with length for carnivorous than omnivorous fishes [16] as illustrated in MA-TL relationship in Table 4: the carnivorous species display positive slope and stronger association (40%) than omnivorous fishes (10%); some omnivores like C. senegalensis and M. sebae indicate negative slopes. The predator:prey length ratio for various fishes is established at about 4 : 1 [58,59]. ...
Fish exploit the diversities of food organisms and habitats in their aquatic environments according to their structural morphology and feeding habits, hence its ecological roles and functions. Six morphological measurements and dietaries of 582 stomachs of eleven (11) species in the Cross River estuary, Nigeria, were examined from August-December, 2014 to establish interrelationship of diet and morphology. TrophLab ® estimated the trophic level (TL) for each species. Dietaries reveal 3 to 11 food items on which basis species were grouped into three functional trophic guilds: omnivore (6 species), detritivore-algivore (2 species) and carnivore (3 species). Positive linear relationship was established between total length (TL) and mouth area (MA) (r = 0.31-0.96; p < 0.5; r 2 > 0.5 in Cynoglossus senegalensis and Liza falcipinnis, r 2 < 0.5 for other species) except in the cichlid Ethmalosa fimbriata (r = 0.000267; p = 0.9997). Higher relationships were established in mouth area (MA) and mouth dimensions (MV and MH) with trophic levels (TLs) among species within same trophic guild than when non-related species were combined: detritivore (r 2 = 1.00), carnivore (r 2 = 0.91), omnivore (r 2 = 0.4348), and all species combined (r 2 = 0.1414). Cluster analysis reveal a positive trophic correlation whereby species of similar feed habits tend to exhibit similar diet-morphology traits than unrelated species. The canonical correspondence analysis reveal some level of morphological convergence in diet-morphological relationships, particularly, in traits like body depth-body height (BD/BH), mouth area and mouth area-trophic level (MA/TLs) and eye diameter (ED) among species. This study suggests trophic levels and mouth dimensions for similarly-sized samples of some species for which no information is available on their feeding habits could be estimated based on fish morphology of the species in study area.
... The model formulates the size spectrum as a function of mortality (μ) and growth rate (g) using the McKendric-von Foerster equation (M1 in Table 1) (McKendrick, 1925;von Foerster, 1959). Feeding kernel is governed by the size ratio between predators and prey (M2), described by a log-normal function (Ursin, 1973). The amount of encountered food is the product of available prey density and a size-specific search rate (M3 and M4). ...
Effects of fishing on the stability of fish populations have been examined in numerous studies; however, species interactions and their changes with life history stages may complicate such effects at the community level, which has not been well understood. We simulated trophic interactions within fish communities using a size-spectrum model and examined the effects of fishing on community stability for a variety of scenarios. We focused on two characteristics of community stability, the level of fluctuations in community status and recovery rates after perturbation, measured by spawning stock biomass (SSB) and two size-based indicators, mean body size (MW) and slope of the size spectrum (Slope). Increasing variability of fishing pressure was found to lead to linear increases in the variation of community status, whereas the impact was limited on integrated indicators such as MW, Slope and total SSB. The interaction of fishing pressure with given levels of recruitment variability amplified the fluctuations in SSB, but reduced those in MW and Slope. For a variety of random perturbations, all scenarios showed similar recovery trajectories, in which MW and Slope showed a steep decrease and slow recovery. Fishing pressure had substantial influences on the recovery of SSB and MW, but less effects on Slope, except for the non-fishing scenarios. The recovery time of SSB was highly variable among species and decreased with the increasing fishing pressure in general. The indirect effect of fishing on stability could be largely attributed to the changes in feeding conditions. Our stability evaluations have several implications for fisheries management, suggesting the potential and challenge for the recovery of depleted fisheries stocks in the absence of environmental changes.
... Size-spectrum models are based on individual-level processes and therefore have the advantage that most of the parameters can be derived from metabolic theory (Brown et al. 2004) or cross-species analysis (Hartvig et al. 2011). The models are based on a combination of the process of big individuals eating smaller ones (Ursin 1973) leading to predation mortality on prey and available energy for predators, and a bioenergetic submodel that links the available energy for growth and reproduction to the asymptotic size of predator species. Specifically, we apply the size-spectrum framework from Hartvig et al. (2011) and reviewed in Andersen et al. (2016), while we use the RAM stock assessment database to calibrate the models to observed biomass distributions of commercially exploited fish stocks (Ricard et al. 2012). ...
Managing fisheries presents trade-offs between objectives, for example yields, profits, minimizing ecosystem impact, that have to be weighed against one another. These trade-offs are compounded by interacting species and fisheries at the ecosystem level. Weighing objectives becomes increasingly challenging when managers have to consider opposing objectives from different stakeholders. An alternative to weighing incomparable and conflicting objectives is to focus on win–wins until Pareto efficiency is achieved: a state from which it is impossible to improve with respect to any objective without regressing at least one other. We investigate the ecosystem-level efficiency of fisheries in five large marine ecosystems (LMEs) with respect to yield and an aggregate measure of ecosystem impact using a novel calibration of size-based ecosystem models. We estimate that fishing patterns in three LMEs (North Sea, Barents Sea and Benguela Current) are nearly efficient with respect to long-term yield and ecosystem impact and that efficiency has improved over the last 30 years. In two LMEs (Baltic Sea and North East US Continental Shelf), fishing is inefficient and win–wins remain available. We additionally examine the efficiency of North Sea and Baltic Sea fisheries with respect to economic rent and ecosystem impact, finding both to be inefficient but steadily improving. Our results suggest the following: (i) a broad and encouraging trend towards ecosystem-level efficiency of fisheries; (ii) that ecosystem-scale win–wins, especially with respect to conservation and profits, may still be common; and (iii) single-species assessment approaches may overestimate the availability of win–wins by failing to account for trade-offs across interacting species.
... (i) Trophic interactions (predation) are described by big individuals eating small individuals. A predator will prefer to eat prey that is roughly 100 times smaller than themselves (Ursin [1973], Jennings et al. [2001]). (ii) The main trait describing differences between species is the asymptotic size W (Andersen and Beyer [2006], Pope et al. [2006]). ...
Ecosystem externalities arise when one use of an ecosystem affects its other uses through the production functions of the ecosystem. We use simulations with a size-spectrum ecosystem model to investigate the ecosystem externality created by fishing of multiple species. The model is based upon general ecological principles and is calibrated to the North Sea. Two fleets are considered: a “forage fish” fleet targeting species that mature at small sizes and a “large fish” fleet targeting large piscivorous species. Based on the marginal analysis of the present value of the rent, we develop a benefit indicator that explicitly divides the consequences of fishing into internal and external benefits. This analysis demonstrates that the forage fish fleet has a notable economic impact on the large fish fleet, but the reverse is not true. The impact can be either negative or positive, which entails that for optimal economic exploitation, the forage fishery has to be adjusted according to the large fish fishery. With the present large fish fishery in the North Sea, the two fisheries are well adjusted; however, the present combined exploitation level is too high to achieve optimal economic rents
... (1) Individual food preference is determined by the body size ratio between predator and prey, which follows a log-normal function (Ursin, 1973): ...
Multispecies ecological models have been used for predicting the effects of fishing activity and evaluating the performance of management strategies. Size-spectrum models are one type of physiologically-structured ecological model that provide a feasible approach to describing fish communities in terms of individual dietary variation and ontogenetic niche shift. Despite the potential of ecological models in improving our understanding of ecosystems, their application is usually limited for data-poor fisheries. As a first step in implementing ecosystem-based fisheries management (EBFM), this study built a size-spectrum model for the fish community in the Haizhou Bay, China. We describe data collection procedures and model parameterization to facilitate the implementation of such size-spectrum models for future studies of data-poor ecosystems. The effects of fishing on the ecosystem were exemplified with a range of fishing effort and were monitored with a set of ecological indicators. Total community biomass, biodiversity index, W-statistic, LFI (Large fish index), MeanW (mean body weight) and Slope (slope of community size spectra) showed a strong non-linear pattern in response to fishing pressure, and largest fishing effort did not generate the most drastic responses in certain scenarios. We emphasize the value and feasibility of developing size-spectrum models to capture ecological dynamics and suggest limitations as well as potential for model improvement. This study aims to promote a wide use of this type of model in support of EBFM. © 2016, The Chinese Society of Oceanography and Springer-Verlag Berlin Heidelberg.
... This was not observed here and there was generally a good agreement between length at age 1 in the end of the growth season and length at age 2 in the beginning of the season the subsequent year, as demonstrated by the estimated season length which depended on the close correspondence between length at the end of the seasons and in the beginning of the subsequent season (Supplementary data). Mortality of fish prey is often reported to be size dependent (Ursin, 1973; Cook, 2004). However, though such size dependence would affect the parameters estimated, it is unlikely to explain the differences in length at age between north and south and low and high temperature areas reported in this study. ...
Lesser sandeel, Ammodytes marinus, is a key prey to a variety of North Sea predators, including species such as single load seabirds which are highly sensitive to prey size and condition. Whilst differences in weight at age across the North Sea have been investigated previously, the scale and cause of this variation as well as the potential link to spatial differences in predator performance remains unknown. This study presents an analysis of spatial patterns in length and condition of the lesser sandeel in the North Sea and the relationship of these with physical and biological factors. Both mean length at age and condition was higher on warmer, deeper and central/north eastern fishing grounds. Sandeel in the water column exhibited large changes in condition over the season, having an initially low condition following spring emergence rising to a pronounced peak by June. Weight at age varied considerably both spatially and temporally, resulting in 4 fold and 1.9 fold variations in the number of sandeels required to obtain a specific weight, respectively. Hence, the value of sandeel as prey to single load predators varies considerably with values in central and northeastern North Sea being substantially higher than in northwestern and southern areas.
... These are strong sweeping statements that dismiss a large body of work, built on .40 years of empirical and theoretical work (much more than can be cited here): observations of biomass size spectra (Sheldon and Prakash, 1972;Boudreau and Dickie, 1992) and size-based predator-prey relationship (e.g. Ursin 1973; Barnes et al., 2010, Jennings et al., 2001 over steady-state models (e.g. Sheldon et al., 1977;Kerr and Dickie, 2001;Andersen and Beyer, 2006) with application to fisheries (e.g. ...
A recent publication about balanced harvesting (Froese et al., ICES Journal of Marine Science; doi:10.1093/icesjms/fsv122) contains several erroneous statements about size-spectrum models. We refute the statements by
showing that the assumptions pertaining to size-spectrum models discussed by Froese et al. are realistic and consistent. We further show that the assumption about density-dependence being described by a stock recruitment
relationship is responsible for determining whether a peak in the cohort biomass of a population occurs late or early in life.
Finally, we argue that there is indeed a constructive role for a wide suite of ecosystem models to evaluate fishing strategies
in an ecosystem context.
... pronounced size-selective effects of predation have been clearly demonstrated in the fossil record is probabl still correct. However. this illustrates only the difficulty in demonstrating such effects. not that they do not occur. Data from Recent environments indicate that size-selective predation is more the rule than the exception (see Daan 1973. Ursin 1973, and Kuipers 1977 for fish: van der Veer and Bergman 1987 for shrimps). Vermeij (1978) and Reise (1985) give examples of size-selective predation on molluscs. Size-selective transport by predators is demonstrated in this paper for the Wadden Sea where it might involve at least 5 to l0 of the total shelis produced. ...
Size-selective transport of shells is demonstrated in the Dutch Wadden Sea for herring gull Larus argentatus and oystercatcher Haematopus ostralegus: only larger shells were transported. Size-selective transport of shells by predators is one of the taphonomic processes altering the size-frequency distribution of shells in the death assemblages, hampering use of size-frequency distribution for studies of population dynamics in fossil assemblages. -from Author
... The second .involves the visual acuity, swimming speed and degree of hunger of the predator. Size as a controlling factor .in prey preference by fish is well documented [Ursin 1973;Werner and Hall 1974;Gibson 1975,1976; Moore and Moore 1976;Pearre 1982;Ma:in 1985]. The importance of predation as a biological factor influencing the structure of natural community has been a central issue of community ecology. ...
As part of a comprehensive study concerning the trophic interrelationship of fish assemblage in the Northwest Arabian Gulf the characteristic ratios of predator-prey weights for 12 common species were calculated. This technique was used to assess the prey size selection by predator fish. Three preference modes of prey size were obtained. The first represents specialised predation on large prey, the second includes species showing less specialisation to select large prey. The third has exhibited specialisation for selection of small prey.
... Previous models of size-spectrum dynamics have not allowed for diet broadening as body size increases. Typically, the distribution (feeding kernel) i ͑x,x ͒ of preferred food item sizes x= for an individual of species i at size x has been assumed to be log-normal (Ursin 1973), with a fixed mean (log of a preferred predator-prey mass ratio (PPMR)  i ) and a fixed diet breadth i . This shifts the feeding kernel towards larger prey as predators increase in size without changing its shape on the log mass scale. ...
... Previous models of size-spectrum dynamics have not allowed for diet broadening as body size increases. Typically, the distribution (feeding kernel) i ͑x,x ͒ of preferred food item sizes x= for an individual of species i at size x has been assumed to be log-normal (Ursin 1973), with a fixed mean (log of a preferred predator-prey mass ratio (PPMR)  i ) and a fixed diet breadth i . This shifts the feeding kernel towards larger prey as predators increase in size without changing its shape on the log mass scale. ...
Fluctuations in the abundance of anchovy (Engraulis spp.) and sardine (Sardinops sagax) are widespread in marine ecosystems, but the causes still remain uncertain. Differences between the planktonic prey availability, selectivity, and predation between anchovy and sardine have been suggested as factors influencing their dynamics. Using a dynamical multispecies size-spectrum model, we explore the consequences of changes in plankton size composition, together with intraguild predation and cannibalism, on the coexistence of these species. The shift towards smaller plankton has led to a reduction in the growth rate of both species. The effect was more deleterious on anchovy growth because it is unable to filter small particles. In model scenarios that included the effects of cannibalism and predation, anchovy typically collapsed under conditions favouring smaller sized plankton. The two species coexisted under conditions of larger sized plankton, although strong predation in conjunction with weak cannibalism led to the loss of sardine. The model provides new testable predictions for the consequences of plankton size structure on anchovy and sardine fluctuations. Further empirical work is needed to test these predictions in the context of climate change.
... Skipjack Tuna has a TL of 4.3, while phytoplankton has a TL of 1). Important to note is that in the sea, high TL organisms tend to be larger (typically three to four times in terms of body length) than their prey (Ursin, 1973), and need more time to reach maturity and reproduce (Denney et al., 2002). This makes high TL organisms very susceptible to overfishing (Sadovy & Cheung, 2003). ...
A great deal of literature exists regarding the global fisheries crisis. However, the human element has been largely overlooked. This study seeks to understand the relationship that traditional Fante-speaking peoples have with oceanic resources. Interviews with artisanal fishers, trades-women, and influential elders from the coastal village of Anomabo in the Central Region of Ghana were conducted over a six-week period. Interviews revealed the degree to which artisanal fishers compete with industrial fleets (both domestic and foreign), the nutritional and economic importance of the artisanal industry as well as the cultural practices embedded within maritime subsistence activities. Industrial fisheries threaten global marine stocks, and with them, the survival of cultures tied to the sea. This study suggests a necessity for swift policy change in order to ensure the health of West African marine stocks, and to protect the nutritional, economic, and cultural basis of Fante-speaking communities.
Resolving the combined effect of climate warming and exploitation in a food web context is key for predicting future biomass production, size-structure, and potential yields of marine fishes. Previous studies based on mechanistic size-based food web models have found that bottom-up processes are important drivers of size-structure and fisheries yield in changing climates. However, we know less about the joint effects of "bottom-up" and "top-down" effects of temperature: how do temperature effects propagate from individual-level physiology through food webs and alter the size-structure of exploited species in a community? Here we assess how a species-resolved size-based food web is affected by warming through both these pathways, and by exploitation. We parameterize a dynamic size spectrum food web model inspired by the offshore Baltic Sea food web, and investigate how individual growth rates, size-structure, relative abundances of species and yields are affected by warming. The magnitude of warming is based on projections by the regional coupled model system RCA4-NEMO and the RCP 8.5 emission scenario, and we evaluate different scenarios of temperature dependence on fish physiology and resource productivity. When accounting for temperature-effects on physiology in addition to on basal productivity, projected size-at-age in 2050 increases on average for all fish species, mainly for young fish, compared to scenarios without warming. In contrast, size-at-age decreases when temperature affects resource dynamics only, and the decline is largest for young fish. Faster growth rates due to warming, however, do not always translate to larger yields, as lower resource carrying capacities with increasing temperature tend to result in declines in the abundance of larger fish and hence spawning stock biomass (the part of the population exposed to fishing). These results show that to understand how global warming impacts the size structure of fish communities, both direct metabolic effects and indirect effects of temperature via basal resources must be accounted for.
Multi-species size spectrum models (MSSMs) have been widely used to investigate and understand the dynamics of marine communities impacted by fishing and environmental changes to support ecosystem-based fisheries management. The continuous nature of the modelled processes makes it challenging to incorporate periodic biological processes and discontinuous life-history traits into MSSMs; therefore, a discrete multi-species model is needed. We developed a new size-structured matrix model with discrete processes to describe multi-species interactions and energy flows through predation, reproduction, metabolism, and mortality in matrix forms. A framework for assessing the population-level consequences of capital and income breeding strategies was developed, with seasonal properties. Preliminary investigations were conducted on a theoretical community comprising eight interacting species with different reproductive strategies. The utility of our model was demonstrated by showing emergent properties in the seasonal dynamics of marine communities and life-history traits such as survival, growth, and reproduction of capital and income breeders. The model enabled exploration of population dynamics caused by migration at the ecosystem level. An example application of the model in marine protected areas (MPAs), where species undertook seasonal spawning migrations, indicated that the size of MPAs may affect their potential conservation and economic benefits to fisheries. This model has the potential to unravel the relationships between drivers and seasonal dynamics and to assess the effectiveness of fisheries management strategies such as seasonal closure of fishing.
Climate variability and predation influence the fluctuations in the recruitment of exploited marine populations. This study analyses the dynamics of the recruitment of the nylon shrimp (Heterocarpus reedi Bahamonde 1955) over the period 1968 and 2015, considering the influence of climate variability and the biomass of hake (Merluccius gayi), as a proxy for predation in its distribution area. We collected the Humboldt Current Index (HCI) and Southern Oscillation Index (SOI) time series as climate variables and estimates of recruitment and spawning biomass of nylon shrimp, as well as biomass of hake. Annual deviations in nylon shrimp recruitment showed increased sensitivity to climate variability and hake biomass, expressed through a significant cumulative correlation over time. The recruitment drives the spawning biomass, implying an environmentally driven shrimp recruitment dynamic. Generalized Linear Models showed that hake biomass and climate indices affect negative and positively the shrimp recruitment during the recruitment year, respectively. A path diagram with Structural Equation Models showed that SOI impacted HCI, negatively impacting the hake stock. Hake negatively affected the shrimp stock biomass and recruitment, and SOI either directly or indirectly, through its effect on the hake. The hake impact on the shrimp's spawning stock and recruitment is due to predation under concurrent climate variability on longer-term periods.
The food web structure of a coastal fish community (western Dutch Wadden Sea) was studied based on stomach content data from samples collected between 2010 and 2018. In total, 54 fish species were caught and 72 different prey items were identified. Fish species consumed from only a few up to >30 different prey species, suggesting the presence of both opportunistic and more specialized feeders. We found no significant differences between years or switches in food source with fish size. The trophic positions of the Wadden Sea fish community ranged from 2.0 to 4.7, with most trophic positions above 3.0. In the past, (near)-resident species were the most abundant guild in spring, and juvenile marine migrants in autumn. At present, all guilds are present in similar but low abundances. The (near)-resident community consisted of about 20 species that fed primarily on amphipod crustaceans, brown shrimps and juvenile herring. There was only a slight overlap in diet with the group of juvenile marine migrants (5 species of juvenile flatfishes and clupeids), whose preferred prey were copepods, polychaetes and brown shrimps. About 15 species of marine seasonal visitors showed an overlap in diet with both the (near)-resident and the juvenile marine migrants, especially for brown shrimps and to a lesser extent herring and gobies. Our results illustrate (1) the pivotal position of a few key prey species (amphipod crustaceans, brown shrimps, juvenile herring and gobies) for the coastal Wadden Sea fishes and (2) that the substantial prey overlap in the diet of some predators cannot exclude intra- and inter-specific competition among these predators.
Fisheries advice is based on demographic calculations, which assume that density-dependent processes regulating recruitment occur only in early life. This assumption is challenged by laboratory and lake studies and some recent indications from marine systems that demonstrate density-dependent regulation late in life. By accounting for spatial dynamics of a population, something that has previously been ignored in models of fish, we show that density-dependent regulation is determined by the size of the habitat: in small habitats, for example small lakes, regulation occurs late in life, while it can occur early in large habitats. When regulation happens late in life, fisheries yield is maximized by exploitation of mainly juvenile fish, while exploiting mature fish maximizes yield if regulation happens early. We review and interpret observations of density dependence in the light of the theory. Our results challenge the current assumption that density dependence always occurs early in life and highlights the need for an increased understanding of density-dependent processes. This can only come about by a change of focus from determining stock-recruitment relationships towards understanding when and how density-dependent regulation occurs in nature.
A multispecies virtual population analysis (MSVPA) model for the southern Chilean demersal fishery was developed. Species included the Southern Hake Merluccius australis, Pink Cusk-eel Genypterus blacodes (hereafter, “Kingklip”), Southern Blue Whiting (SBW) Micromesistius australis, and Patagonian Grenadier (also known as Argentine Straptail) Macruronus magellanicus (hereafter, “Hoki”). Due to a lack of stomach content data, we constructed suitability coefficients based on predator–prey size ratios. Terminal fishing mortality (Fterm) was estimated by fitting a cohort analysis model to estimates of abundance from single-species models developed by the Chilean Instituto de Fomento Pesquero (IFOP; Institute for Fishing Development). Values of Fterm were used as input data in the MSVPA, driving the dynamics of the species and producing adult abundance estimates that were similar to IFOP estimates. Comparison of MSVPA and IFOP estimates suggested consistency in adult abundance and total abundance estimates for SBW. Differences were identified for adult Hoki abundance estimates. Differences in recruitment estimates were small for SBW, whereas greater differences were found for Hoki. The MSVPA revealed high estimates of predation mortality for Hoki, while predation played a minor role in SBW population dynamics. Cannibalism and predation by Southern Hake were the main components of predation mortality for age-0 Hoki; Southern Hake were the most important source of predation for age-1 Hoki. Sensitivity analysis suggested that Hoki response variables were sensitive to 10% perturbations in suitability coefficients, while SBW response variables were not. This study is a first step toward building a multispecies framework that could provide complementary information for the sustainable management of fishing resources in southern Chile.
Received October 11, 2015; accepted March 5, 2016
Marine fisheries have a direct impact on the resources they exploit but also indirectly affect other species, habitats and the way ecosystems work. Ecosystem approach to fisheries (EAF) is a major aspect for the exploitation of marine resources and conservation of species. An ecosystem is set formed by a community of living beings and their biological, geological, edaphic, hydrological, climatic environment. Organisms are distributed as patches across a wide continuum of spatiotemporal scales. The marine strategy framework directive (MSFD) proposes an ecosystem approach for the assessment of the marine environment. Bottom-up control of predator fish through small pelagic fish has been noticed in the Benguela and Humboldt Current and in Guinea, since several predator fish suffer when their prey stock collapses. The scientific community needs to set up a long-term scientific strategy in order to enhance its ability to provide suitable competences for the ecosystem approach to marine resources.
The main reason to study laboratory populations is that they may serve as simplified models of field populations. The i-machinery is by definition a property of individuals , and as such independent of whether we deal with these individuals
in the lab or in the field. What is different, however, is the structure of the environment. In the field this in general
is much less homogeneous, both in space and in time. As Dur i-models are necessarily simplified and the quality
of a simplification is dependent both on the range and the temporal dynamies of the inputs encauntered by the individuals, the transplantation of lab based models 10 the field is not straightforward. Moreover, often the species we are interested in are difficult 10 keep in the laboratory other than for short parts of their life cycle. As a result structured
models for field populations offen have population data as their main empirical basis, even if they are theoretically
based on our preconceptions about the adequate state representation of individuals. The resulting necessity of deducing details of the supposedly underlying i-model from population data leads inexorably to the so-called inverse problem: the deduction of (some of) the assumptions of a model from its predictions.
In an earlier paper (Gushing, 1971), an analogy was drawn between the production cycle in upwelling areas and that in temperate waters. Production stops in winter in middle and high latitudes and, when the spring increase gets under way, the algae grow more rapidly than do the herbivores because the herbivores do not start to reproduce until there is enough algal food available. The delay between the start of algal production and the appearance of sufficient grazing capacity to reduce it affects the amplitude and spread of the production cycle although both are modified by other factors, for example, the rate of change of the algal reproductive rate. In contrast to the spring outburst in temperate waters, that of low latitude seas is continuous and of low amplitude because the delay period may be so short as not to exist at all.
The use of size distributions as descriptors of ecosystems goes back at least to Elton (1927), although quantitative applications have appeared only during the past decade. Elton noted that there was a characteristic difference between terrestrial and aquatic ecosystems; on land the organisms in the lower trophic levels tend to be larger than the organisms which feed on them (e.g. trees, giraffes, tigers), while in the sea the reverse is true (phytoplankton, zooplankton, fish). The value of this observation was dramatically emphasized by the advent of automated particle size measurement devices and their use in marine biology, which occurred in the 1960’s (Sheldon and Parsons 1967). A Coulter counter was used on the 1970 circumnavigation of the western hemisphere by the Canadian research vessel Hudson and this provided the first opportunity to compare particle size distributions from widely distributed pelagic marine environments, including both polar regions and the tropical waters of the Atlantic and Pacific oceans (Sheldon et al. 1972). This work greatly extended Elton’s observation by showing that there are also patterns in the size distributions from temperate and polar regions which are characteristically different from those found in tropical waters.
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