Two-patch dispersal-linked compensatory-overcompensatory spatially discrete population models

We study the role of asynchronous and synchronous dispersals on discrete-time two-patch dispersal-linked population models, where the pre-dispersal local patch dynamics are of mixed compensatory and overcompensatory types. Single-species dispersal-linked models behave as single-species single-patch models whenever all pre-dispersal local patch dynamics are compensatory and dispersal is synchronous. However, the dynamics of the corresponding two-patch population model connected by asynchronous dispersal depends on the dispersal rates. The species goes extinct on at least one patch when the asynchronous dispersal rates are high, while it persists when the rates are low. We use numerical simulations to show that in both synchronous and asynchronous mixed compensatory and overcompensatory systems, symmetric and asymmetric dispersals can control and impede the onset of cyclic population oscillations via period-doubling reversal bifurcations. Also, we show that in mixed systems both asynchronous and synchronous dispersals are capable of altering the pre-dispersal local patch dynamics from overcompensatory to compensatory dynamics. Dispersal-linked population models with ‘unstructured’ overcompensatory pre-dispersal local dynamics connected by synchronous dispersal can generate multiple attractors with fractal basin boundaries. However, mixed compensatory and overcompensatory systems appear to exhibit single attractors and not coexisting (multiple) attractors.     

Two-patch dispersal-linked compensatory-overcompensatory spatially discrete population models

We study the role of asynchronous and synchronous dispersals on discrete-time two-patch dispersal-linked population models, where the pre-dispersal local patch dynamics are of mixed compensatory and overcompensatory types. Single-species dispersal-linked models behave as single-species single-patch models whenever all pre-dispersal local patch dynamics are compensatory and dispersal is synchronous. However, the dynamics of the corresponding two-patch population model connected by asynchronous dispersal depends on the dispersal rates. The species goes extinct on at least one patch when the asynchronous dispersal rates are high, while it persists when the rates are low. We use numerical simulations to show that in both synchronous and asynchronous mixed compensatory and overcompensatory systems, symmetric and asymmetric dispersals can control and impede the onset of cyclic population oscillations via period-doubling reversal bifurcations. Also, we show that in mixed systems both asynchronous and synchronous dispersals are capable of altering the pre-dispersal local patch dynamics from overcompensatory to compensatory dynamics. Dispersal-linked population models with 'unstructured' overcompensatory pre-dispersal local dynamics connected by synchronous dispersal can generate multiple attractors with fractal basin boundaries. However, mixed compensatory and overcompensatory systems appear to exhibit single attractors and not coexisting (multiple) attractors.     

Interplay between local dynamics and dispersal in discrete-time metapopulation models

The effects of synchronous dispersal on discrete-time metapopulation dynamics with local (patch) dynamics of the same (compensatory or overcompensatory) or mixed (compensatory and overcompensatory) types are explored. Single-species metapopulation models behave as single-species single-patch models, whenever all local patches are governed by compensatory dynamics. Dispersal gives rise to multiple attractors with complex basin structures, whenever some local patches are under overcompensatory dynamics. In mixed systems, dispersal is capable of altering the local dynamics from compensatory to overcompensatory dynamics and vice versa. Examples are provided of metapopulation models supporting multiple attractors with intermingled basins of attraction.     

Demographic diversity and sustainable fisheries

Fish species are diverse. For example, some exhibit early maturation while others delay maturation, some adopt semelparous reproductive strategies while others are iteroparous, and some are long-lived and others short-lived. The diversity is likely to have profound effects on fish population dynamics, which in turn has implications for fisheries management. In this study, a simple density-dependent stage-structured population model was used to investigate the effect of life history traits on sustainable yield, population resilience, and the coefficient of variation (CV) of the adult abundance. The study showed that semelparous fish can produce very high sustainable yields, near or above 50% of the carrying capacity, whereas long-lived iteroparous fish can produce very low sustainable yields, which are often much less than 10% of the carrying capacity. The difference is not because of different levels of sustainable fishing mortality rate, but because of difference in the sensitivity of the equilibrium abundance to fishing mortality. On the other hand, the resilience of fish stocks increases from delayed maturation to early maturation strategies but remains almost unchanged from semelparous to long-lived iteroparous. The CV of the adult abundance increases with increased fishing mortality, not because more individuals are recruited into the adult stage (as previous speculated), but because the mean abundance is more sensitive to fishing mortality than its standard deviation. The magnitudes of these effects vary depending on the life history strategies of the fish species involved. It is evident that any past high yield of long-lived iteroparous fish is a transient yield level, and future commercial fisheries should focus more on fish that are short-lived (including semelparous species) with high compensatory capacity.     

A model for the interaction between gadoid larvae and their nauplii prey

A continuous model for the growth and death of gadoid larvae, including ecological interactions with their nauplii prey, is examined. The present model has a simpler structure than the model due to Cushing and Horwood [D.H. Cushing, J.W. Horwood, The growth and death of fish larvae. J. Plankt. Res. 16 (3) (1994) 291-300] as it does not explicitly incorporate larval metabolism, although indirectly metabolism is included by means of equations for larval growth. Despite this, the model yields related, although not entirely equivalent, results to those obtained by Cushing and Horwood.In the present model, overcompensation (cf. [W.E. Ricker, Stock and Recruitment, J. Fish. Res. Board. Can. 11 (1954) 559-623]) occurs at limited initial food levels, while at infinite food levels, the recruitment curve becomes monotonically increasing towards an upper limit (cf. [R.J.H. Beverton, S.J. Holt, On the dynamics of exploited fish populations. Fish. Invest. Lond. I 19 (1957)]).Moreover, the present study suggests that the duration of the larval stage, the metamorphosis time τ is highly important to the recruitment process, in accordance with Cushing and Horwood. When food is limited the metamorphosis is delayed, causing the larval population to experience (density dependent) mortality for a sufficient long time to make the recruitment curve overcompensatory.It is not necessarily the desire to derive a particular formula for the recruitment curve, as this is probably impossible anyway, except for particular examples. However, reduced versions of the model that in some sense are close to the original model, are examined, and it is argued that many general features of the general model are retained in such examples.     

Constant proportion harvest policies: dynamic implications in the Pacific halibut and Atlantic cod fisheries

Overfishing, pollution and other environmental factors have greatly reduced commercially valuable stocks of fish. In a 2006 Science article, a group of ecologists and economists warned that the world may run out of seafood from natural stocks if overfishing continues at current rates. In this paper, we explore the interaction between a constant proportion harvest policy and recruitment dynamics. We examine the discrete-time constant proportion harvest policy discussed in Ang et al. (2009) and then expand the framework to include stock-recruitment functions that are compensatory and overcompensatory, both with and without the Allee effect.We focus on constant proportion policies (CPPs). CPPs have the potential to stabilize complex overcompensatory stock dynamics, with or without the Allee effect, provided the rates of harvest stay below a threshold. If that threshold is exceeded, CPPs are known to result in the sudden collapse of a fish stock when stock recruitment exhibits the Allee effect. In case studies, we analyze CPPs as they might be applied to Gulf of Alaska Pacific halibut fishery and the Georges Bank Atlantic cod fishery based on harvest rates from 1975 to 2007. The best fit models suggest that, under high fishing mortalities, the halibut fishery is vulnerable to sudden population collapse while the cod fishery is vulnerable to steady decline to zero. The models also suggest that CPP with mean harvesting levels from the last 30 years can be effective at preventing collapse in the halibut fishery, but these same policies would lead to steady decline to zero in the Atlantic cod fishery. We observe that the likelihood of collapse in both fisheries increases with increased stochasticity (for example, weather variability) as predicted by models of global climate change.     

Larval Connectivity and the International Management of Fisheries

Predicting the oceanic dispersal of planktonic larvae that connect scattered marine animal populations is difficult, yet crucial for management of species whose movements transcend international boundaries. Using multi-scale biophysical modeling techniques coupled with empirical estimates of larval behavior and gamete production, we predict and empirically verify spatio-temporal patterns of larval supply and describe the Caribbean-wide pattern of larval connectivity for the Caribbean spiny lobster (Panulirus argus), an iconic coral reef species whose commercial value approaches $1 billion USD annually. Our results provide long sought information needed for international cooperation in the management of marine resources by identifying lobster larval connectivity and dispersal pathways throughout the Caribbean. Moreover, we outline how large-scale fishery management could explicitly recognize metapopulation structure by considering larval transport dynamics and pelagic larval sanctuaries.     

Facilitation of fisheries by natural predators depends on life history of shared prey

Predators commonly share prey with human exploiters, intuitively suggesting that there is an inherent human–predator conflict through competition for prey. Here we studied the effects of fishing and predation mortality on biomass distributions and yields of shared prey using a size‐structured model of competing populations, describing the life histories of Baltic Sea sprat and herring. Whereas both species responded in a similar fashion to increased fishing mortality, with decreasing juvenile and adult biomasses, we found that responses to predation mortality differed between species. Sprat only display weak compensatory responses with increasing predation mortality, while over a substantial range of mortalities there was a strong increase in adult (and total) herring biomass, i.e. overcompensation. The observed biomass overcompensation results from relaxed intraspecific competition as predation mortality increased, allowing for faster individual growth rates that in turn lead to a change in population composition (juvenile:adult biomass ratio). Our results suggest that the potential for biomass overcompensation is higher for species exhibiting substantial growth after maturation. Differences in size‐selectivity of predators and fishing mortality resulted in a positive effect of predation mortality on fisheries yields, which can be explained by an overcompensatory response in adult herring biomass. Thus, somewhat counter intuitive, our results suggest that fishermen, depending on prey life history, may actually benefit from allowing for a higher abundance of predators, despite competing for shared prey.     

Interspecific Variation in Compensatory Regrowth to Herbivory Associated with Soil Nutrients in Three Ficus (Moraceae) Saplings

Plant compensatory regrowth is an induced process that enhances plant tolerance to herbivory. Plant behavior against herbivores differs between species and depends on resource availability, thus making general predictions related to plant compensatory regrowth difficult. To understand how soil nutrients determine the degree of compensatory regrowth for different plant species, we selected saplings of three Ficus species and treated with herbivore insects and artificial injury in both glasshouse conditions and in the field at two soil nutrient levels. Compensatory regrowth was calculated by biomass, relative growth rate and photosynthetic characteristics. A similar pattern was found in both the glasshouse and in the field for species F. hispida, where overcompensatory regrowth was triggered only under fertile conditions, and full compensatory regrowth occurred under infertile conditions. For F. auriculata, overcompensatory regrowth was stimulated only under infertile conditions and full compensatory regrowth occurred under fertile conditions. Ficus racemosa displayed full compensatory regrowth in both soil nutrient levels, but without overcompensatory regrowth following any of the treatments. The three Ficus species differed in biomass allocation following herbivore damage and artificial injury. The root/shoot ratio of F. hispida decreased largely following herbivore damage and artificial injury, while the root/shoot ratio for F. auriculata increased against damage treatments. The increase of shoot and root size for F. hispida and F. auriculata, respectively, appeared to be caused by a significant increase in photosynthesis. The results indicated that shifts in biomass allocation and increased photosynthesis are two of the mechanisms underlying compensatory regrowth. Contrasting patterns among the three Ficus species suggest that further theoretical and empirical work is necessary to better understand the complexity of the plant responses to herbivore damage.     

From patterns to processes and back: analysing density-dependent responses to an abiotic stressor by statistical and mechanistic modelling

Our knowledge about population-level effects of abiotic stressors is limited, largely due to lack of appropriate time-series data. To analyse interactions between an abiotic stressor and density-dependent processes, we used experimental time-series data for stage-structured populations (the blowfly Lucilia sericata) exposed to the toxicant cadmium through 20 generations. Resource limitation results in competition both in the larval and the adult stages. The toxicant has only negative effects at the organism level, but nevertheless, there were positive population-level effects. These are necessarily indirect, and indicate overcompensatory density-dependent responses. A non-parametric model (generalized additive model) was used to investigate the density-dependent structures of the demographic rates, without making assumptions about the functional forms. The estimated structures were used to develop a parametric model, with which we analysed effects of the toxicant on density-dependent and density-independent components of the stage-specific demographic rates. The parameter estimates identified both synergistic and antagonistic density-toxicant interactions. It is noteworthy that the synergistic interaction occurred together with a net positive effect of the toxicant. Hence, the effects of such interactions should be considered together with the capacity for compensatory responses. The combination of the two modelling approaches provided new insight into mechanisms for compensatory responses to abiotic stressors.     

Strengthened currents override the effect of warming on lobster larval dispersal and survival

Human‐induced climate change is projected to increase ocean temperature and modify circulation patterns, with potential widespread implications for the transport and survival of planktonic larvae of marine organisms. Circulation affects the dispersal of larvae, whereas temperature impacts larval development and survival. However, the combined effect of changes in circulation and temperature on larval dispersal and survival has rarely been studied in a future climate scenario. Such understanding is crucial to predict future species distributions, anticipate ecosystem shifts and design effective management strategies. We simulate contemporary (1990s) and future (2060s) dispersal of lobster larvae using an eddy‐resolving ocean model in south‐eastern Australia, a region of rapid ocean warming. Here we show that the effects of changes in circulation and temperature can counter each other: ocean warming favours the survival of lobster larvae, whereas a strengthened western boundary current diminishes the supply of larvae to the coast by restricting cross‐current larval dispersal. Furthermore, we find that changes in circulation have a stronger effect on connectivity patterns of lobster larvae along south‐eastern Australia than ocean warming in the future climate so that the supply of larvae to the coast reduces by ~4% and the settlement peak shifts poleward by ~270 km in the model simulation. Thus, ocean circulation may be one of the dominant factors contributing to climate‐induced changes of species ranges.     

Compensatory dynamics and the stability of phytoplankton biomass during four decades of eutrophication and oligotrophication

The link between compensatory dynamics and regime shifts is not well understood. We analyse a regime shift in phytoplankton in a large lake with respect to: (1) environmental forcing and (2) the type of dynamics (compensatory or synchronous) between phytoplankton groups. The regime shift in phytoplankton was related to gradual changes in nutrient levels, but unrelated to an almost concurrent shift in climatic conditions. The relationship between total phytoplankton biomass and phosphorus concentrations was sigmoid. Trajectories of phytoplankton biomass and community dynamics suggest that eutrophication effects can successfully be reversed when management efforts decrease nutrient loading to a level sufficiently low to overcome community resilience. The regime shift was associated with a loss of biomass compensation and compensatory dynamics among the phytoplankton groups. This suggests that the type of interactions is important for a better understanding of the existence and shape of nonlinear responses of phytoplankton biomass to environmental change.     

Trophic Cascades Induced by Lobster Fishing Are Not Ubiquitous in Southern California Kelp Forests

Fishing can trigger trophic cascades that alter community structure and dynamics and thus modify ecosystem attributes. We combined ecological data of sea urchin and macroalgal abundance with fishery data of spiny lobster (Panulirus interruptus) landings to evaluate whether: (1) patterns in the abundance and biomass among lobster (predator), sea urchins (grazer), and macroalgae (primary producer) in giant kelp forest communities indicated the presence of top-down control on urchins and macroalgae, and (2) lobster fishing triggers a trophic cascade leading to increased sea urchin densities and decreased macroalgal biomass. Eight years of data from eight rocky subtidal reefs known to support giant kelp forests near Santa Barbara, CA, USA, were analyzed in three-tiered least-squares regression models to evaluate the relationships between: (1) lobster abundance and sea urchin density, and (2) sea urchin density and macroalgal biomass. The models included reef physical structure and water depth. Results revealed a trend towards decreasing urchin density with increasing lobster abundance but little evidence that urchins control the biomass of macroalgae. Urchin density was highly correlated with habitat structure, although not water depth. To evaluate whether fishing triggered a trophic cascade we pooled data across all treatments to examine the extent to which sea urchin density and macroalgal biomass were related to the intensity of lobster fishing (as indicated by the density of traps pulled). We found that, with one exception, sea urchins remained more abundant at heavily fished sites, supporting the idea that fishing for lobsters releases top-down control on urchin grazers. Macroalgal biomass, however, was positively correlated with lobster fishing intensity, which contradicts the trophic cascade model. Collectively, our results suggest that factors other than urchin grazing play a major role in controlling macroalgal biomass in southern California kelp forests, and that lobster fishing does not always catalyze a top-down trophic cascade.     

The role of density-dependent individual growth in the persistence of freshwater salmonid populations

Theoretical and empirical models of populations dynamics have paid little attention to the implications of density-dependent individual growth on the persistence and regulation of small freshwater salmonid populations. We have therefore designed a study aimed at testing our hypothesis that density-dependent individual growth is a process that enhances population recovery and reduces extinction risk in salmonid populations in a variable environment subject to disturbance events. This hypothesis was tested in two newly introduced marble trout (Salmo marmoratus) populations living in Slovenian streams (Zakojska and Gorska) subject to severe autumn floods. We developed a discrete-time stochastic individual-based model of population dynamics for each population with demographic parameters and compensatory responses tightly calibrated on data from individually tagged marble trout. The occurrence of severe flood events causing population collapses was explicitly accounted for in the model. We used the model in a population viability analysis setting to estimate the quasi-extinction risk and demographic indexes of the two marble trout populations when individual growth was density-dependent. We ran a set of simulations in which the effect of floods on population abundance was explicitly accounted for and another set of simulations in which flood events were not included in the model. These simulation results were compared with those of scenarios in which individual growth was modelled with density-independent Von Bertalanffy growth curves. Our results show how density-dependent individual growth may confer remarkable resilience to marble trout populations in case of major flood events. The resilience to flood events shown by the simulation results can be explained by the increase in size-dependent fecundity as a consequence of the drop in population size after a severe flood, which allows the population to quickly recover to the pre-event conditions. Our results suggest that density-dependent individual growth plays a potentially powerful role in the persistence of freshwater salmonids living in streams subject to recurrent yet unpredictable flood events. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Representing Density Dependent Consequences of Life History Strategies in Aquatic Ecosystems: EcoSim II

EcoSim II uses results from the Ecopath procedure for trophic mass-balance analysis to define biomass dynamics models for predicting temporal change in exploited ecosystems. Key populations can be represented in further detail by using delay-difference models to account for both biomass and numbers dynamics. A major problem revealed by linking the population and biomass dynamics models is in representation of population responses to changes in food supply; simple proportional growth and reproductive responses lead to unrealistic predictions of changes in mean body size with changes in fishing mortality. EcoSim II allows users to specify life history mechanisms to avoid such unrealistic predictions: animals may translate changes in feeding rate into changes in reproductive rather than growth rates, or they may translate changes in food availability into changes in foraging time that in turn affects predation risk. These options, along with model relationships for limits on prey availability caused by predation avoidance tactics, tend to cause strong compensatory responses in modeled populations. It is likely that such compensatory responses are responsible for our inability to find obvious correlations between interacting trophic components in fisheries time-series data. But Ecosim II does not just predict strong compensatory responses: it also suggests that large piscivores may be vulnerable to delayed recruitment collapses caused by increases in prey species that are in turn competitors/predators of juvenile piscivores. Received 24 February 1999; accepted 3 August 1999.     

Synchronous dynamics of zooplankton competitors prevail in temperate lake ecosystems

Although competing species are expected to exhibit compensatory dynamics (negative temporal covariation), empirical work has demonstrated that competitive communities often exhibit synchronous dynamics (positive temporal covariation). This has led to the suggestion that environmental forcing dominates species dynamics; however, synchronous and compensatory dynamics may appear at different length scales and/or at different times, making it challenging to identify their relative importance. We compiled 58 long-term datasets of zooplankton abundance in north-temperate and sub-tropical lakes and used wavelet analysis to quantify general patterns in the times and scales at which synchronous/compensatory dynamics dominated zooplankton communities in different regions and across the entire dataset. Synchronous dynamics were far more prevalent at all scales and times and were ubiquitous at the annual scale. Although we found compensatory dynamics in approximately 14% of all combinations of time period/scale/lake, there were no consistent scales or time periods during which compensatory dynamics were apparent across different regions. Our results suggest that the processes driving compensatory dynamics may be local in their extent, while those generating synchronous dynamics operate at much larger scales. This highlights an important gap in our understanding of the interaction between environmental and biotic forces that structure communities.     

Overcompensating plants: their expression of resistance traits and effects on herbivore preference and performance

Overcompensation is a plant tolerance response in which plants have higher fitness after herbivory than without damage. Although it has been demonstrated that plants are able to simultaneously express resistance and tolerance traits, it remains unclear whether overcompensating plants are also inducing resistance‐mediating secondary metabolite production and how herbivores perform on plants that overcompensate. Our previous work has shown that a potato variety [Solanum tuberosum L. cv. Pastusa Suprema (Solanaceae)] from Colombia can express overcompensatory responses to damage by larvae of the Guatemalan potato moth, Tecia solanivora Povolny (Lepidoptera: Gelechiidae). Here we investigated (1) whether potatoes that express overcompensatory responses also induce resistance traits and (2) how the previous damage affects Guatemalan potato moth preference and performance. Our results show that larval feeding not only systemically induces higher tuber biomass but also an increased production of resistance‐related compounds, such as phenolics and proteinase inhibitors. Pupal mass increased with increasing tuber size, whereas changes in tuber secondary metabolism did not correlate with any metric of larval performance. Oviposition preference did not change between induced and undamaged plants. Our data show that potato plants expressing overcompensatory responses also induce secondary compounds known to increase resistance against herbivores. However, the induced response was relatively small, reducing the opportunities for a negative effect on the herbivore. Hypotheses for why larvae perform better in larger tubers and are not affected by the secondary metabolism are discussed. From an ecological and agricultural point of view, our results suggest that the expression of overcompensatory traits could have positive effects on herbivore performance.     

Reduced Global Genetic Differentiation of Exploited Marine Fish Species

Knowledge on genetic structure is key to understand species connectivity patterns and to define the spatiotemporal scales over which conservation management plans should be designed and implemented. The distribution of genetic diversity (within and among populations) greatly influences species ability to cope and adapt to environmental changes, ultimately determining their long-term resilience to ecological disturbances. Yet, the drivers shaping connectivity and structure in marine fish populations remain elusive, as are the effects of fishing activities on genetic subdivision. To investigate these questions, we conducted a meta-analysis and compiled genetic differentiation data (F_ST/Φ_ST estimates) for more than 170 fish species from over 200 published studies globally distributed. We modeled the effects of multiple life-history traits, distance metrics, and methodological factors on observed population differentiation indices and specifically tested whether any signal arising from different exposure to fishing exploitation could be detected. Although the myriad of variables shaping genetic structure makes it challenging to isolate the influence of single drivers, results showed a significant correlation between commercial importance and genetic structure, with widespread lower population differentiation in commercially exploited species. Moreover, models indicate that variables commonly used as proxy for connectivity, such as larval pelagic duration, might be insufficient, and suggest that deep-sea species may disperse further. Overall, these results contribute to the growing body of knowledge on marine genetic connectivity and suggest a potential effect of commercial fisheries on the homogenization of genetic diversity, highlighting the need for additional research focused on dispersal ecology to ensure long-term sustainability of exploited marine species.     

Effects of parasitoid community structure upon the population dynamics of the honeysuckle leafminer,Chromatomyia suikazurae (Diptera: Agromyzidae)

Population dynamics of a leafminer,Chromatomyia suikazurae (Agromyzidae, Diptera) and its parasitoid community were studied for ten years at seven natural populations along an altitudinal gradient in Japan. This species which mines leaves of a forest shrub,Lonicera gracilipes (Caprifoliaceae), was attacked by 25 hymenopterous parasitoid species. Annually, the parasitoid community structure varied less within a population than among populations. The seven parasitoid communities were clustered into three groups corresponding to the altitudinal gradient: (a) lowland communities dominated by late-attacking, generalist pupal idiobiont eulophids and with highest species diversity, (b) hillside communities dominated by an early-attacking, specialist larval-pupal koinobiont braconid and (c) highland communities dominated by an early-attacking, generalist larval idiobiont eulophid. Annual changes of the host larval densities among the local populations were largely synchronous rather than cyclic. Among these populations, host density levels and mortality patterns greatly varied. By analyzing these inter-populational differences of host mortality patterns, the following conclusions were drawn: (1) The host mortality patterns were determined by the host utilization patterns of the locally dominant species. (2) The host pupal mortality but not larval mortality was related to species diversity but not to species richness itself of each parasitoid community. (3) Density dependence was detected only in pupal mortality at a lowland population dominated by late-attacking pupal parasitoids. These results suggest that interspecific interactions of parasitoids add additive effects to host population dynamics dissimilarly among local populations with different parasitoid communities.     

Overcompensatory recruitment and generation delay in discrete age-structured population models

 The effect of overcompensatory recruitment and the combined effect of overcompensatory recruitment and generation delay in discrete nonlinear age-structured population models is studied. Considering overcompensatory recruitment alone, we present formal proofs of the supercritical nature of bifurcations (both flip and Hopf) as well as an extensive analysis of dynamics in unstable parameter regions. One important finding here is that in case of small and moderate year to year survival probabilities there are large regions in parameter space where the qualitative behaviour found in a general n+1 dimensional model is retained already in a one-dimensional model. Another result is that the dynamics at or near the boundary of parameter space may be very complicated. Generally, generation delay is found to act as a destabilizing effect but its effect on dynamics is by no means unique. The most profound effect occurs in the n-generation delay cases. In these cases there is no stable equilibrium X ^* at all, but whenever X ^* small, a stable cycle of period n+1 where the periodic points in the cycle are on a very special form. In other cases generation delay does not alter the dynamics in any substantial way. Received 25 April 1995; received in revised form 21 November 1995