Linear age-dependent population growth with seasonal harvesting

A population growth is modelled by the Von Foerster PDE with accompanying Lotka-Volterra integral equation describing the birth rate; the age specific death and fertility rates are assumed to depend only on age and not time. A harvesting policy where a fraction of the population of age greater than a given age is harvested for a fraction of a given season. This introduces a time dependence, but this difficulty is circumvented by devising approximate timeindependent models whose birthrates bracket the true birthrate-the standard renewal equation theory applies to the approximate models so quantitative results can be obtained.The author wishes to thank Professors J. J. Levin and R. K. Miller for some useful remarks. This research was partially supported by NIH Grant GMO 7661-02.     

An adaptive management approach to an octocoral fishery based on the Beverton-Holt model

Coral reef species are frequently the focus of bio-prospecting, and when promising bioactive compounds are identified there is often a need for the development of responsible harvesting based on relatively limited data. The Caribbean gorgonian Pseudopterogorgia elisabethae has been harvested in the Bahamas for over a decade. Data on population age structure and growth rates in conjunction with harvest data provide an opportunity to compare fishery practices and outcomes to those suggested by a Beverton-Holt fishery model. The model suggests a minimum colony size limit of 7–9 years of age (21–28 cm height), which would allow each colony 2–4 years of reproduction prior to harvesting. The Beverton-Holt model assumes that colonies at or above the minimum size limit are completely removed. In the P. elisabethae fishery, colonies are partially clipped and can be repeatedly harvested. Linear growth of surviving colonies was up to 3 times that predicted for colonies that were not harvested and biomass increase was up to 9 times greater than that predicted for undisturbed colonies. The survival of harvested colonies and compensatory growth increases yield, and yields at sites that had previously been harvested were generally greater than predicted by the Beverton-Holt model. The model also assumes recruitment is independent of fishing intensity, but lower numbers of young colonies in the fished populations, compared to unfished populations, suggest possible negative effects of the harvest on reproduction. This suggests the need for longer intervals between harvests. Because it can be developed from data that can be collected at a single time, the Beverton-Holt model provides a rational starting point for regulating new fisheries where long-term characterizations of population dynamics are rarely available. However, an adaptive approach to the fishery requires the incorporation of reproductive data.     

An extension of the Leslie matrix model to include a variable immature period

An extension to the Leslie matrix is presented in which the age of transformation from immature to adult has a log—normal distribution. The major effect of this is shown to be on the second largest eigenvalue. The ratio of the largest to the second largest eigenvalue |λ₁/λ₂|, which is an index of the rate of approach to the stable age distribution, is greater in the new model, even though the value of λ₁ is effectively the same. The differences in the models are most pronounced where the population is subjected to a harvesting regime.     

An evaluation of the maximum radius of the rosette as a growth index for subterranean clover

Summary The maximum radius of the rosette, defined as the distance from the centre shoot to the base of the leaf furthest from it, is highly correlated with yield of dry matter (r=0.98 to 0.93) over the earlier vegetative period, but becomes progressively less sensitive on approaching inflorescence.The maximum radius was tested for fidelity as a rapid index of dry-matter yield using data from other factorial eperiments. It proved satisfactory in nutrient experiments for the comparison of treatment means prior to harvesting, provided that correlation at harvest was greater thanr=0.85.The limitations of the index are discussed.     

Culling Versus Density Effects in Management of a Deer Population

Abstract: Wildlife managers often manipulate hunting regulations to control deer populations. However, few empirical studies have examined the level of hunting effort (hunter-days) required to limit population growth and demographic effects through harvesting of females. Moreover, the relative importance of density effects on population growth has not been quantified. We reconstructed a sika deer [Cervus nippon] population over a period of 12 years (1990–2001) using age- and sex-specific harvest data. Using cohort analysis, we analyzed population dynamics, focusing on 1) the relationship between hunting effort and hunting-induced mortality rate, 2) relative contributions of hunting mortality and recruitment of yearlings to annual changes in population growth rate, and 3) annual variation in recruitment rate. Population size increased until 1998 and declined thereafter. The population growth rate changed more in response to annual changes in recruitment rate than hunting mortality rate. Temporal variation in recruitment rate was not controlled by birth rate alone; direct density dependence, intensities of hunting mortality for fawns, and for females (≥2 yr of age), which accounted for the fawn survival rate, were required as factors to explain temporal variation. Density effects on the recruitment rate were not strong enough to regulate the population within the study period; high hunting mortality, with intensive female harvesting, was necessary to prevent population growth. Hunting effort was a good predictor of the hunting mortality rate, and female harvest had a negative effect on the recruitment rate through fawn survival. We suggest that >3,500 hunter-days and prioritization of female harvesting are required to prevent increases in this deer population.     

The effect of optimal harvesting on the dynamics of size and genetic composition of a two-age population

The effect of optimal stationary harvesting at a constant harvest rate on the dynamics of a two-age population is considered. It has been shown analytically that harvesting a fixed rate of the population size of only one age cohort is optimal. As has been observed, the maximum of revenue function is unattainable in the case of concurrent harvesting of both age cohorts. It has been demonstrated that the direction of natural selection does not explicitly change when unselectively harvesting individuals; however, the adaptive genetic diversity of an unharvested population can be lost due to harvesting.     

The effects of harvesting of the South African kelp (Ecklonia maxima) on kelp population structure, growth rate and recruitment

Ecklonia maxima is an economically important kelp in South Africa. The harvested kelp is used mainly as feed for cultured Haliotis midae (abalone) on farms all along the South African South and West Coast. The effects that different harvesting methods have on the growth of sub-canopy kelps, kelp population structure and kelp recruitment were tested in a kelp bed at Bordjies Rif near Cape Town. Two 30 × 10 m sites were set up, about 100 m apart, in near monoculture stands of E. maxima. Each 30×10 m area was subdivided into three treatments. In treatment 1 (T1) the whole ‘head’ of each kelp sporophyte that reached the surface was cut off between the bulb and the primary blade (‘lethal’ method). In treatment 2 (T2) (‘non-lethal’ method), the secondary fronds of all sporophytes that reached the surface were cut 20–30 cm from their junction with the primary blade, and removed. In the control plot, the kelp plants were not treated. Harvesting treatments were done approximately every four months, at low spring tide, from 3 March 2003 to 3 November 2003 (three treatments). The effects of harvesting on the kelps depend largely on the size of plant and the time the fronds were removed; however, no seasonal pattern could be observed. The different treatments had no effect on the growth rate, population structure or recruitment of the kelp. This means that factors other than light play an important role in the growth, structure and recruitment of the kelp beds in False Bay. Results are discussed in relation to current commercial harvesting practices.     

Effects of illumination intensity on bacteriochlorophyllc homolog distribution inChloroflexus aurantiacus grown under controlled conditions

Green photosynthetic bacteria contain a mixture of stereoisomers and homologs of their major light harvesting pigment, bacteriochlorophyll (BChl)c. We have determined the distribution of photosynthetic pigments in the green filamentous bacteriumChloroflexus aurantiacus grown in turbidostat culture under light-limited conditions at 5 different illumination intensities. Pigments were extracted from isolated cells, analyzed by HPLC, and the homologs of BChlc identified by their mass spectra. The ratio between BChlc, BChla and carotenoid remained constant at low illumination intensities; at higher intensities BChla and carotenoid increased in parallel compared to BChlc. The BChlc homolog distribution changed even under conditions where the ratio of the total amount to the other pigments was unchanged, but there were no evidence for a constant stoichiometric ratio between any pair of homologs.     

The implications of harvesting on the population structure and sediment characteristics of the mangroves at Mngazana Estuary,Eastern Cape,South Africa

The Mngazana Estuary has the third largest area of mangroves in South Africa (118 ha) and one of the main environmental threats is the cumulative effects of long term small scale harvesting from local communities. This study investigated the change in aerial cover of the mangrove forest over time and assessed the effect of harvesting on the microenvironment and the population structure of Rhizophora mucronata (preferred harvested species) in both harvested and non-harvested sites. In 1982 there were 150 ha of mangroves of all species and since then 32 ha (21%) of the forest area has been lost. Areas of the estuary where mangroves have been completely removed showed significant differences in sediment characteristics. Changes in population size, ratios of adult trees to juveniles (harvested sites—1:5.5, non-harvested sites 1:3.4) and significant differences in height structure are some of the indications that harvesting is affecting the mangrove populations. Results show that while it is necessary to suggest proposals aimed at the sustainable use of the Mngazana mangroves, it is equally important in the short-term to make available alternative sources of materials to replace mangrove poles for building. The formation of the Mngazana Mangrove Management Forum provides an ideal opportunity to drive Participatory Forest Management (PFM) but this would require scientific and management support. The data shown here will provide ecological information required for PFM.     

Nutrient status in needles of Norway spruce and Scots pine following harvesting of logging residues

Nutrient concentrations in current and 1-year old needles from two Picea abies (L.) Karst and two Pinus sylvestris L. stands in Sweden were determined 8–10, 16–18 and 22–24 years after clear-felling and experimental manipulation of harvesting intensity. On all sites, three levels of harvest intensity had been applied in a randomized block design (n=4); (i) conventional stem-only harvesting, where all logging residues (i.e. tops, branches and needles) were evenly distributed on the ground, (ii) harvesting all above-ground tree parts except needles and (iii) above-ground whole-tree harvesting (no residues left on site). At stand age 8–10 years, nitrogen concentrations in the current year needles in plots where all residues or needles only were retained were higher than in whole-tree harvested plots, whereas concentrations of K, Ca and Mg were lower. The latter response was interpreted as a dilution effect. P:N, K:N, Ca:N, Mg:N, Mn:N and Zn:N were in general higher after whole-tree harvesting treatments than after the treatments where all residues or only needles had been left on site. At stand age 16–18 years, no significant differences in nitrogen concentrations were observed between treatments, but the levels of Ca, Mg and Mn in both current and 1-year-old needles were lower after whole-tree harvesting than after the treatments where logging residues remained on site. By contrast, potassium levels in the foliage were highest in treatments where only the needles were left on site, whereas the lowest levels were observed for treatments where all residues was left. At stand age 22–24 years, the treatment effects had diminished, except for the effects on Ca and K on the southern Norway spruce stand. It is concluded that the nutrient release from logging residues enhances nutrient uptake in trees of the succeeding forest generation, but this effect does not occur simultaneously for all elements. This revised version was published online in June 2006 with corrections to the Cover Date.     

Wild boar (Sus scrofa) harvesting using the espera hunting method: side effects and management implications

Harvesting of wildlife by man has been linked to demographic and evolutionary impacts in many populations. We investigated the sex ratio and age class structure in hunting bags of wild boar harvested by espera—nocturnal single hunt at bait—during four hunting seasons in Alentejo (Portugal). In addition, we assessed whether the hunting method is a significant predictor of the probability of harvesting an animal of a particular gender, of particular age class or of a particular combination of these two attributes. We found that the espera hunting method allows very selective harvesting regimes, and thus, it seems a highly effective population management tool. Removing a large proportion of adult males, however, may bias the population sex ratio towards females, reduce male life expectancy and raise the degree of polygyny. Our results suggest that recruitment rates are resilient to this skewed sex ratio, and possibly the higher proportion of females in the adult population may even increase productivity.

     

Modeling the Dynamics of Viral Evolution Considering Competition Within Individual Hosts and at Population Level: The Effects of Treatment

We consider two viral strains competing against each other within individual hosts (at cellular level) and at population level (for infecting hosts) by studying two cases. In the first case, the strains do not mutate into each other. In this case, we found that each individual in the population can be infected by only one strain and that co-existence in the population is possible only when the strain that has the greater basic intracellular reproduction number, R _0c , has the smaller population number R _0p . Treatment against the one strain shifts the population equilibrium toward the other strain in a complicated way (see Appendix B). In the second case, we assume that the strain that has the greater intracellular number R _0c can mutate into the other strain. In this case, individual hosts can be simultaneously infected by both strains (co-existence within the host). Treatment shifts the prevalence of the two strains within the hosts, depending on the mortality induced by the treatment, which is, in turn, dependent upon the doses given to each individual. The relative proportions of the strains at the population level, under treatment, depend both on the relative proportions within the hosts (which is determined by the dosage of treatment) and on the number of individuals treated per unit time, that is, the rate of treatment. Implications for cases of real diseases are briefly discussed.     

Stochastic demography and population dynamics in the red kangaroo Macropus rufus

1.  Many organisms inhabit strongly fluctuating environments but their demography and population dynamics are often analysed using deterministic models and elasticity analysis, where elasticity is defined as the proportional change in population growth rate caused by a proportional change in a vital rate. Deterministic analyses may not necessarily be informative because large variation in a vital rate with a small deterministic elasticity may affect the population growth rate more than a small change in a less variable vital rate having high deterministic elasticity.
2.  We analyse a stochastic environment model of the red kangaroo ( Macropus rufus ), a species inhabiting an environment characterized by unpredictable and highly variable rainfall, and calculate the elasticity of the stochastic growth rate with respect to the mean and variability in vital rates.
3.  Juvenile survival is the most variable vital rate but a proportional change in the mean adult survival rate has a much stronger effect on the stochastic growth rate.
4.  Even if changes in average rainfall have a larger impact on population growth rate, increased variability in rainfall may still be important also in long-lived species. The elasticity with respect to the standard deviation of rainfall is comparable to the mean elasticities of all vital rates but the survival in age class 3 because increased variation in rainfall affects both the mean and variability of vital rates.
5.  Red kangaroos are harvested and, under the current rainfall pattern, an annual harvest fraction of c . 20% would yield a stochastic growth rate about unity. However, if average rainfall drops by more than c . 10%, any level of harvesting may be unsustainable, emphasizing the need for integrating climate change predictions in population management and increase our understanding of how environmental stochasticity translates into population growth rate.     

Optimal harvesting of stochastically fluctuating populations

 We obtain the optimal harvesting plan to maximize the expected discounted number of individuals harvested over an infinite future horizon, under the most common (Verhulst-Pearl) logistic model for a stochastically fluctuating population. We also solve the problem for the standard variants of the model where there are constraints on the admissible harvesting rates. We use stochastic calculus to derive the optimal population threshold at which individuals are harvested as well as the overall value of the population in the sense of the model. We show that except under extreme conditions, the population is never depleted in finite time, but remains in a stationary distribution which we find explicitly. Needless to say, our results prove that any strategy which totally depletes the population is sub-optimal. These results are much more precise than those previously obtained for this problem. Received 24 June 1996; received in revised form 7 April 1997     

Tradeoffs between hydraulic efficiency and mechanical strength in the stems of four co-occurring species of chaparral shrubs

Possible tradeoffs between efficiency of water transport and mechanical strength were examined in stems of two congeneric pairs of co-occurring chaparral shrubs. First, since previously published results indicated that Adenostoma sparsifolium (Rosaceae) had greater specific conductivity (k _s or hydraulic conductivity per xylem transverse area) than A. fasciculatum, it was hypothesized that A. sparsifolium would have greater vessel lumen area per square millimeter of xylem area, and less mechanical strength, than A. fasciculatum. Secondly, since Ceanothus megacarpus (Rhamnaceae) is a non-sprouter (unable to sprout from the root crown following fire or other major disturbance) whereas C. spinosus is a sprouter and thus able to form new stems following disturbance, it was hypothesized that C. megacarpus would have greater mechanical strength, but lower k _s, than C. spinosus. Both hypotheses were supported. Based upon computer-aided image analyses, A. sparsifolum had significantly higher mean and maximum vessel diameters (16.4, 40.5 vs. 14.6, 35.7 μm), a 34% greater percent vessel lumen area, and a two-fold greater measured and theoretical k _s than A. fasciculatum. This corresponded to 14% lower stem density (wet weight/volume) and less mechanical strength, with a 37% lower modulus of elasticity (MOE) and a 30% lower modulus of rupture (MOR) than A. fasciculatum. Similarly, C.␣spinosus had a significantly higher maximum vessel diameter (52.7 vs. 41.8 μm) and a 92% higher theoretical k _s (and 43% higher measured k _s) than C. megacarpus. This corresponded to a 9% lower stem density and 20% lower MOR than for C. megacarpus. Thus, at least within these two congeneric pairs of chaparral shrubs growing together in the same habitat, there may be tradeoffs between mechanical strength and conductive efficiency of the stem xylem which correspond to differences in transport physiology and life history traits of sprouter versus non-sprouter species.     

Laboratory observations of prey behaviour for prey acquisition by a predator among three larval mosquitoes

The effect of prey behaviour on prey acquisition by a predator was examined in the laboratory, using three larval mosquitoes.Aedes albopictus was acquired by the predator,Toxorhynchites towadensis, at a higher rate thanOrthopodomiya anopheloides. Toxorphynchites towadensis was a sit-and-wait predator.Aedes albopictus was more active thanO. anopheloides. Orthopodomiya anopheloides ran away before the predator attacked, butA. albopictus did not. The escape ratio inO. anopheloides was higher than that inA. albopictus. These results suggest that the difference in the prey acquisition ratio by the predator between prey species is caused by different behavioural patterns of the prey to the predator.     

Demographic consequences of age-structure in extreme environments: population models for arctic and alpine ptarmigan

Organisms living in arctic and alpine environments are increasingly impacted by human activities. To evaluate the potential impacts of global change, a better understanding of the demography of organisms in extreme environments is needed. In this study, we compare the age-specific demography of willow ptarmigan (Lagopus lagopus) breeding at arctic and subalpine sites, and white-tailed ptarmigan (L. leucurus) breeding at an alpine site. Rates of egg production improved with age at the alpine and subalpine sites, but the stochastic effects of nest and brood predation led to similar rates of annual fecundity among 1-, 2-, and 3+-year-old females. All populations had short generation times (T<2.7 years) and low net reproductive rates (R ₀<1.2). Stable age distributions were weighted towards 1-year-old females in willow ptarmigan (>59%), and to 3+-year-old females in white-tailed ptarmigan (>47%). High damping ratios (ρ>3.2) indicated that asymptotic estimates were likely to match natural age distributions. Sensitivity and elasticity values indicated that changes in juvenile survival would have the greatest impact on the finite rate of population change (λ) in willow ptarmigan, whereas changes to the survival of 3+-year-old females would have a greater effect in white-tailed ptarmigan. High survivorship buffers white-tailed ptarmigan in alpine environments against the potential effects of climate change on annual fecundity, but may make the species more sensitive to the effects of pollutants or harvesting on adult survival. Conversely, processes that reduce annual fecundity would have a greater impact on the population viability of willow ptarmigan in arctic and subalpine environments. If these same demographic patterns prove to be widespread among organisms in extreme environments, it may be possible to develop general recommendations for conservation of the biological resources of arctic and alpine ecosystems.     

Population dynamics of Turbo militaris (Gastropoda: Turbinidae) on rocky shores in a subtropical marine park: implications for management

Understanding the relative impacts of harvesting across an area such as a marine park is vital if the goals of fisheries management are to be met. Given their accessibility, densities of targeted intertidal turbinids should be relatively simple to quantify; however, natural spatial and temporal variability in these populations has hampered this effort. This study aimed to quantify short-term population dynamics of Turbo militaris in relation to current zoning regulations and accessibility. While our results reflected the variability found by other studies, we also detected significantly lower densities at a headland where harvesting is known to occur, and found a trend towards denser aggregations at more remote locations. Importantly, we found that densities at some locations were so low that current fisheries bag limits may be ineffective for protecting populations at local scales. Comparisons between study sites suggest a combination of no-take zoning and inaccessibility may provide the most effective protection for this species. However, a greater understanding of the wider impacts of harvesting, and processes affecting recovery, are essential to ensure sustainable management of this fishery.     

Direct and indirect interactions between ants (Pheidole megacephala), scales (Coccus viridis) and plants (Pluchea indica)

Summary This study investigated direct and indirect interactions between the ant, Pheidole megacephala (Fabr.), the green scale, Coccus viridis (Green), and the scale's host plant, Pluchea indica (L.). To examine the influence of ants on scales and host plants, scale population densities, scale mortality rates, and plant performance were studied on control host plants with ants and host plants from which ants had been removed. Plants with ants present had significantly greater scale population densities and scale reproductive rates than did plants without ants. Scale mortality from both parasitism and other causes was increased on plants without ants relative to plants with ants. Predator introduction experiments showed that P. megacephala removes predatory coccinellid larvae, even when they are covered with a protective coating. Host plants from which ants had been removed had significantly higher degrees of honeydew accumulation, which resulted in greater colonization by sooty mold and greater rates of leaf death and abscission. Ants also removed herbivorous lepidopteran larvae from plants. Results are discussed in terms of the potential of P. megacephala to exert direct and indirect positive effects on scale populations and an indirect positive effect on Pluchea indica.     

Evolution of condition-dependent dispersal: A genetic-algorithm search for the ESS reaction norm

Many insects produce two types (winged and wingless) of offspring that greatly differ in dispersal ability. The ratio of the two types often depends on the quality of the local habitat and the crowding experienced by the mother. Here we studied the condition-dependent dispersal that is evolutionarily stable. The model is also applicable to annual plants that produce two types of seeds differing in dispersal rates. The model assumptions are: the population is composed of a number of sites each occupied by a single adult. The total number of offspring produced by a mother depends on the environmental quality of the site that varies over the years and between sites. The ESS fraction of dispersing type as a function of the quality of the habitat (or ESS reaction norm) states that dispersers should not be produced if habitat qualitym is smaller than a critical valuek. Ifm is larger thank, the number of dispersers should increase withm and that of nondispersers should be kept constant. Second, we developed an alternative way of searching for the ESS: the reaction norm is represented as a three-layered neural network, and the parameters (weights and biases) are chosen by genetic algorithm (GA). This method can be extended easily to the cases of multiple environmental factors. There was an optimal (relatively wide) range of mutation rates for weights and biases, outside of which the convergence of the network to the valid ESS was likely to fail. Recombination, or crossing-over, was not effective in improving the success rate. The learned network often shows several characteristic ways of deviation from the ESS. We also examined the case in which the quality of different sites was correlated. In this case the ESS fraction of dispersers increases both with the quality of the site and with the average quality of the whole population in that year.