Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L-infinity. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

Predicting dispersal and recruitment of Miconia calvescens (Melastomataceae) in Australian tropical rainforests

Miconia calvescens (Melastomataceae) is a serious invader in the tropical Pacific, including the Hawaiian and Tahitian Islands, and currently poses a major threat to native biodiversity in the Wet Tropics of Australia. The species is fleshy-fruited, small-seeded and shade tolerant, and thus has the potential to be dispersed widely and recruit in relatively intact rainforest habitats, displacing native species. Understanding and predicting the rate of spread is critical for the design and implementation of effective management actions. We used an individual-based model incorporating a dispersal function derived from dispersal curves for similar berry-fruited native species, and life-history parameters of fecundity and mortality to predict the spatial structure of a Miconia population after a 30 year time period. We compared the modelled population spatial structure to that of an actual infestation in the rainforests of north Queensland. Our goal was to assess how well the model predicts actual dispersion and to identify potential barriers and conduits to seed movement and seedling establishment. The model overpredicts overall population size and the spatial extent of the actual infestation, predicting individuals to occur at a maximum 1,750 m from the source compared with the maximum distance of any detected individual in the actual infestation of 1,191 m. We identify several characteristic features of managed invasive populations that make comparisons between modelled outcomes and actual infestations difficult. Our results suggest that the model’s ability to predict both spatial structure and spread of the population will be improved by incorporating a spatially explicit element, with dispersal and recruitment probabilities that reflect the relative suitability of different parts of the landscape for these processes.

Variation in exotic and native seed arrival and recruitment of bird dispersed species in subtropical forest restoration and regrowth

Invasive bird-dispersed plants often share the same suite of dispersers as co-occurring native species, resulting in a complex management issue. Integrated management strategies could incorporate manipulation of dispersal or establishment processes. To improve our understanding of these processes, we quantified seed rain, recruit and seed bank density, and species richness for bird-dispersed invasive and native species in three early successional subtropical habitats in eastern Australia: tree regrowth, shrub regrowth and native restoration plantings. We investigated the effects of environmental factors (leaf area index (LAI), distance to edge, herbaceous ground cover and distance to nearest neighbour) on seed rain, seed bank and recruit abundance. Propagule availability was not always a good predictor of recruitment. For instance, although native tree seed rain density was similar, and species richness was higher, in native plantings, compared with tree regrowth, recruit density and species richness were lower. Native plantings also received lower densities of invasive tree seed rain than did tree regrowth habitats, but supported a similar density of invasive tree recruits. Invasive shrub seed rain was recorded in highest densities in shrub regrowth sites, but recruit density was similar between habitats. We discuss the role of microsite characteristics in influencing post-dispersal processes and recruit composition, and suggest ways of manipulating these processes as part of an integrated management strategy for bird-dispersed weeds in natural areas.

Maximum likelihood estimation of natural mortality and quantification of temperature effects on catchability of brown tiger prawn (Penaeus esculentus) in Moreton Bay (Australia) using logbook data

It is common to model the dynamics of fisheries using natural and fishing mortality rates estimated independently using two separate analyses. Fishing mortality is routinely estimated from widely available logbook data, whereas natural mortality estimations have often required more specific, less frequently available, data. However, in the case of the fishery for brown tiger prawn (Penaeus esculentus) in Moreton Bay, both fishing and natural mortality rates have been estimated from logbook data. The present work extended the fishing mortality model to incorporate an eco-physiological response of tiger prawn to temperature, and allowed recruitment timing to vary from year to year. These ecological characteristics of the dynamics of this fishery were ignored in the separate model that estimated natural mortality. Therefore, we propose to estimate both natural and fishing mortality rates within a single model using a consistent set of hypotheses. This approach was applied to Moreton Bay brown tiger prawn data collected between 1990 and 2010. Natural mortality was estimated by maximum likelihood to be equal to 0.032 ± 0.002 week−1, approximately 30% lower than the fixed value used in previous models of this fishery (0.045 week−1).

Interactions of age-dependent mortality and selectivity functions in age-based stock assessment models

The natural mortality rate (M) of fish varies with size and age, although it is often assumed to be constant in stock assessments. Misspecification of M may bias important assessment quantities. We simulated fishery data, using an age-based population model, and then conducted stock assessments on the simulated data. Results were compared to known values. Misspecification of M had a negligible effect on the estimation of relative stock depletion; however, misspecification of M had a large effect on the estimation of parameters describing the stock recruitment relationship, age-specific selectivity, and catchability. If high M occurs in juvenile and old fish, but is misspecified in the assessment model, virgin biomass and catchability are often poorly estimated. In addition, stock recruitment relationships are often very difficult to estimate, and steepness values are commonly estimated at the upper bound (1.0) and overfishing limits tend to be biased low. Natural mortality can be estimated in assessment models if M is constant across ages or if selectivity is asymptotic. However if M is higher in old fish and selectivity is dome-shaped, M and the selectivity cannot both be adequately estimated because of strong interactions between M and selectivity.

VPA estimates of fishing mortality and exploited biomass from Sardinella aurita catch-at-length data in eastern Venezuela

In this study, length-frequency data on Spanish sardine (Sardinella aurita) from northeastern Venezuela were analyzed for the period 1967-1989. Average growth parameters for the von Bertalanffy equation were established as L sub( infinity )= 26.6 cm (TL) and K = 1.26 year super(-1). The number of recruits to the fishing area, estimated from length-structured Virtual Population Analysis, varied from <10 super(8) in the late 1960s to >10 super(9) at the end of the 1980s. Exploited biomass estimates for the same period varied from less than 20,000 t in the first year to more than 100,000 in 1989. Both recruitment and exploited biomass showed different seasonal patterns between 1976-1983 and 1984-1988. Despite some uncertainty regarding these estimates, it is considered that major population tendencies are adequately represented by this analysis

Growth, mortality and yield-per-recruit of the poor cod, Trisopterus minutus capelanus, from the Strait of Sicily

Length-based methods (LBMs) were used to study the growth of Trisopterus minutus capelanus in the Strait of Sicily (Messina Strait). A total of 16,304 'merluzzetto' or poor cod collected by experimental trawling off the southern coast of Sicily during spring, summer, autumn 1986 and winter 1987 were measured in order to estimate the length structure of the population. Length-frequency distribution were analyzed and normal components were discriminated. Von Bertalanffy growth parameters were derived from the mean length of the normal components. The growth parameters obtained by weighted non-linear regression were: K=0.462 (yr super(1)), L sub( infinity )=222.3 (TL,mm) and t sub(o)=-0.679 yr. The resulting growth performance index ( Phi ') was 4.36, a value slightly lower than those derived for Western Mediterranean (mean Phi '=4.45) and Adriatic ( Phi '=4.58) populations and slightly higher than that derived for Hellenic waters ( Phi '=4.27). On the basis of the von Bertalanffy parameters estimated, an array of age-specific instantaneous natural mortality rate (M sub(t)=0.5-1.1) and an average value of total natural mortality rate (Z=2.1 yr super(1)) were estimated and used in the Thompson and Bell yield per recruit (Y/R) analysis in order to evaluate the status of the fishery and forecast the effects of changes in the fishing pattern. Results indicate that this resource is overexploited and that Y/R could be increased by postponing the age at first capture from 0.5 to 1.0 yr. Even a slight reduction in fishing mortality could improve the performance of the fishery. At the present level of exploitation, and assuming a constant recruitment, the spawning stock biomass per recruit (SPR) is well below the conservative threshold of 30% of the pristine or unexploited SPR.

Age, growth, mortality, and radiometric age validation of gray snapper (Lutjanus griseus) from Louisiana

The gray snapper (Lutjanus griseus) is a temperate and tropical reef fish that is found along the Gulf of Mexico and Atlantic coasts of the southeastern United States. The recreational fishery for gray snapper has developed rapidly in south Louisiana with the advent of harvest and seasonal restrictions on the established red snapper (L. campechanus) fishery. We examined the age and growth of gray snapper in Louisiana with the use of cross-sectioned sagittae. A total of 833 specimens, (441 males, 387 females, and 5 of unknown sex) were opportunistically sampled from the recreational fishery from August 1998 to August 2002. Males ranged in size from 222 to 732 mm total length (TL) and from 280 g to 5700 g total weight (TW) and females ranged from 254 to 756 mm TL and from 340 g to 5800 g TW. Both edge analysis and bomb radiocarbon analyses were used to validate otolith-based age estimates. Ages were estimated for 718 individuals; both males and females ranged from 1 to 28 years. The von Bertalanffy growth models derived from TL at age were Lt = 655.4{1–e[–0.23(t)]} for males, Lt = 657.3{1–e[– 0.21(t)]} for females, and L t = 656.4{1–e[– 0.22 (t)]} for all specimens of known sex. Catch curves were used to produce a total mortality (Z) estimate of 0.17. Estimates of M calculated with various methods ranged from 0.15 to 0.50; however we felt that M= 0.15 was the most appropriate estimate based on our estimate of Z. Full recruitment to the gray snapper recreational fishery began at age 4, was completed by age 8, and there was no discernible peak in the catch curve dome.

Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L∞. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

An individual-based model of the early life history of mackerel (Scomber scombrus) in the eastern North Atlantic, simulating transport, growth and mortality

The main purpose of this paper is to provide the core description of the modelling exercise within the Shelf Edge Advection Mortality And Recruitment (SEAMAR) programme. An individual-based model (IBM) was developed for the prediction of year-to-year survival of the early life-history stages of mackerel (Scomber scombrus) in the eastern North Atlantic. The IBM is one of two components of the model system. The first component is a circulation model to provide physical input data for the IBM. The circulation model is a geographical variant of the HAMburg Shelf Ocean Model (HAMSOM). The second component is the IBM, which is an i-space configuration model in which large numbers of individuals are followed as discrete entities to simulate the transport, growth and mortality of mackerel eggs, larvae and post-larvae. Larval and post-larval growth is modelled as a function of length, temperature and food distribution; mortality is modelled as a function of length and absolute growth rate. Each particle is considered as a super-individual representing 10 super(6) eggs at the outset of the simulation, and then declining according to the mortality function. Simulations were carried out for the years 1998-2000. Results showed concentrations of particles at Porcupine Bank and the adjacent Irish shelf, along the Celtic Sea shelf-edge, and in the southern Bay of Biscay. High survival was observed only at Porcupine and the adjacent shelf areas, and, more patchily, around the coastal margin of Biscay. The low survival along the shelf-edge of the Celtic Sea was due to the consistently low estimates of food availability in that area.

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

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

Impacts of invasive browsers on demographic rates and forest structure in New Zealand

Background/Question/Methods

Assessing the large scale impact of deer populations on forest structure and composition is important because of their increasing abundance in many temperate forests. Deer are invasive animals and sometimes thought to be responsible for immense damage to New Zealand’s forests. We report demographic changes taking place among 40 widespread indigenous tree species over 20 years, following a period of record deer numbers in the 1950s and a period of extensive hunting and depletion of deer populations during the 1960s and 1970s.

Results/Conclusions

Across a network of 578 plots there was an overall 13% reduction in sapling density of our study species with most remaining constant and a few declining dramatically. The effect of suppressed recruitment when deer populations were high was evident in the small tree size class (30 – 80 mm dbh). Stem density decreased by 15% and species with the greatest annual decreases in small tree density were those which have the highest rates of sapling recovery in exclosures indicating that deer were responsible. Densities of large canopy trees have remained relatively stable. There were imbalances between mortality and recruitment rates for 23 of the 40 species, 7 increasing and 16 in decline. These changes were again linked with sapling recovery in exclosures; species which recovered most rapidly following deer exclusion had the greatest net recruitment deficit across the wider landscape, indicating recruitment suppression by deer as opposed to mortality induced by disturbance and other herbivores. Species are not declining uniformly across all populations and no species are in decline across their entire range. Therefore we predict that with continued deer presence some forests will undergo compositional changes but that none of the species tested will become nationally extinct.

Impacts of invasive browsers on demographic rates and forest structure in New Zealand. Available from: http://www.researchgate.net/publication/267285500_Impacts_of_invasive_browsers_on_demographic_rates_and_forest_structure_in_New_Zealand [accessed Oct 9, 2015].

Amazonian tree mortality during the 1997 El Nino drought

In 1997, the Amazon Basin experienced an exceptionally severe El Nino drought. We assessed effects of this rare event on mortality rates of trees in intact rainforest based on data from permanent plots. Long-term (5- to 13-year) mortality rates averaged only 1.12% per year prior to the drought. During the drought year, annual mortality jumped to 1.91% but abruptly fell back to 1.23% in the year following El Nino. Trees dying during the drought dirt not differ significantly in site or species composition from those that died previously, and there was no detectable effect of soil texture on mortality rates. These results suggest that intact Amazonian rainforests are relatively resistant to severe El Nino events.

Fire and the reproductive phenology of endangered Madagascar sclerophyllous tapia woodlands

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Towards greater accuracy in individual-tree mortality regression

Background mortality is an essential component of any forest growth and yield model. Forecasts of mortality contribute largely to the variability and accuracy of model predictions at the tree, stand and forest level. In the present study, I implement and evaluate state-of-the-art techniques to increase the accuracy of individual tree mortality models, similar to those used in many of the current variants of the Forest Vegetation Simulator, using data from North Idaho and Montana. The first technique addresses methods to correct for bias induced by measurement error typically present in competition variables. The second implements survival regression and evaluates its performance against the traditional logistic regression approach. I selected the regression calibration (RC) algorithm as a good candidate for addressing the measurement error problem. Two logistic regression models for each species were fitted, one ignoring the measurement error, which is the “naïve” approach, and the other applying RC. The models fitted with RC outperformed the naïve models in terms of discrimination when the competition variable was found to be statistically significant. The effect of RC was more obvious where measurement error variance was large and for more shade-intolerant species. The process of model fitting and variable selection revealed that past emphasis on DBH as a predictor variable for mortality, while producing models with strong metrics of fit, may make models less generalizable. The evaluation of the error variance estimator developed by Stage and Wykoff (1998), and core to the implementation of RC, in different spatial patterns and diameter distributions, revealed that the Stage and Wykoff estimate notably overestimated the true variance in all simulated stands, but those that are clustered. Results show a systematic bias even when all the assumptions made by the authors are guaranteed. I argue that this is the result of the Poisson-based estimate ignoring the overlapping area of potential plots around a tree. Effects, especially in the application phase, of the variance estimate justify suggested future efforts of improving the accuracy of the variance estimate. The second technique implemented and evaluated is a survival regression model that accounts for the time dependent nature of variables, such as diameter and competition variables, and the interval-censored nature of data collected from remeasured plots. The performance of the model is compared with the traditional logistic regression model as a tool to predict individual tree mortality. Validation of both approaches shows that the survival regression approach discriminates better between dead and alive trees for all species. In conclusion, I showed that the proposed techniques do increase the accuracy of individual tree mortality models, and are a promising first step towards the next generation of background mortality models. I have also identified the next steps to undertake in order to advance mortality models further.