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Box 51 Calculation of the birth rate for continuous reproduction by the eggratio method

The instantaneous birth rate for continuous reproduction can be estimated by the egg-ratio method. The principle can be most easily explained by the procedure introduced by Edmondson (1968). It assumes a uniform age distribution of eggs that is, there are equal proportions of eggs from each age class, freshly laid eggs as well as nearly developed embryos. In that case, a certain proportion of eggs will hatch in each time interval. This proportion equals the ratio of the time interval to the time needed by an egg for complete development (egg development time D). For example, if the egg development time is 3 days, then at the end of day 1 all eggs will have hatched that were 2 days old at the beginning of the day that is, one-third (1 D). The number of eggs in the population does not decrease during this period because hatched eggs will be replaced by freshly laid ones. If the average number of eggs carried per animal (egg ratio) is E, we can predict the proportional increase of the...

From Birth to the Opening of the Eyes

Body Part Upper Forearm Name

Newborn young have no teeth, but they do have powerful equipment and instincts for sucking. The jaws are relatively shorter than those of adults, and a massive shovel-shaped tongue takes up most of the space inside the mouth. Left alone, newborn young lie in a heap together, crawling under each other to avoid disturbance if one is separated it immediately struggles back into touch with the rest. Almost from birth they can produce a fine chirping sound, usually a sign of protest or distress. Most observers report that, at this stage, males and females are roughly the same size, and both are, on average, equally represented.

Age span of reproduction and birth rates

Although an overall decline in fecundity can be expected in the older age classes in an elephant population, these individuals may also be reproductively active. Postmortem examination of culled elephants at Kruger and Etosha showed that most cows in the 50- to 60-year age class were reproductively active as they were pregnant or lactating. Captive elephants aged 50-55 years in southern India also gave birth as frequently as did the younger cows, although a decline in fecundity could be seen beyond this age (fig. 7.2). The highest age of calving among these elephants was by a cow (named Tara) when she was 62 years old (she lived to 75 years). Age-specific birth rates in elephants. Fecundity mx is expressed as the number of female offspring born each year to a female elephant of a particular age. The values shown are for a wild African elephant population culled at Etosha, Namibia, in 1985 (based on Lindeque 1988) and for captive Asian elephants in southern Indian timber camps (based...

Fundamentals of population growth

Both fecundity and fertility are expressed as rates. That is, the mean number of offspring produced per individual (or per thousand individuals in human demography) in the population, per unit time. Often these values are also expressed for a given unit of area. For example, according to the Population Reference Bureau (Washington, DC), the fertility rate of the human population of the world declined from 28 per thousand in 1981, to 22 births per thousand in 2001. Meanwhile, the birth rate in North America moved slightly downward from 16 per thousand in 1981 to 14 per thousand in 2001 (Anonymous 1981-2004). In populations such as humans, however, which breed over a period of 30 years without respect to seasons, we need to know the fertility rate for each age category in order to accurately predict population growth. All references to human birth and death rates in this chapter are per year.

Food componentEnergy kcalg

Animals adjust their breeding patterns so that their highest physiological demands for energy and protein occur during the growing season. Thus northern ungulates give birth in spring so that lactation can occur during the growing period of plants, whereas tropical ungulates produce their young during or following the rains, allowing the mother to build up fat supplies to support lactation. Although most birds complete their entire breeding cycle during one season, the timing of breeding is closely associated with food supply (Perrins 1970). Very large birds such as ostrich behave like ungulates and start their reproductive cycle in the previous wet season so that the precocial chicks hatch at the start of the next wet season (Sinclair 1978). Carnivores also adapt their breeding to coincide with maximum food supply. Thus, wolves which follow the caribou on the tundra of northern Canada have their young at the time caribou calves are born. Schaller (1972) records that lions have their...

Correlation of field data

A causal relationship can be misleading if both variables are actually dependent on a third variable that has not been considered, rather than on one another. A common mistake is to conclude there is a causal relationship based on trends in a time series. An example of such an apparent correlation is the simultaneous decrease in the human birth rate and in the number of storks in the wealthy countries of Europe.

Size rate per rate per increase per population less millions thousand thousand individual r than 15 years of age

Per time unit (for example, per year) in a population, estimated as b - d, where b is the birth rate per individual per year, and d is the death rate per individual per year. The rate of growth per individual is From Table 1.1 we see that Asia had a positive growth rate, whereas Europe actually had a negative projected growth rate in 2001. If the intrinsic rate of increase of these two populations suddenly converged on the same value (a decrease in the Asian birth rate and an increase in Europe's fertility rate, combined with similar changes in the death rates), the population growth of Asia would still be greater than that of Europe for several decades, due to the higher abundance of reproductive individuals. Asia has a shorter generation time, which would affect population growth for a number of years. The estimated growth rate parameter, r (Eqn. 1.1), ignores the age distribution and generation time and actually assumes a stable age distribution (defined above). By age distribution...

What Is Population Dynamics

Population changes over time because of reproduction (birth rate), mortality (e.g., predation, starvation, parasitism, and senescence), immigration, and emigration. Increases and decreases in the numbers of a population are controlled by factors that eventually can limit population growth, and are therefore called 'limiting factors' (see later).

The maintenance of sex

The problem of the relative persistence of sexual species versus asexual clones has traditionally been thought of in terms of the so-called 'two-fold cost' of sex. Female parthenogens can increase in number at twice the rate of their sexual counterparts because they do not give birth to males, which cannot themselves give birth (Figure 2.6). Sexual organisms may even suffer a number of additional costs, such as finding a mate. All of this suggests that sexual organisms should be the ones with the higher extinction rates. It was this problem that eventually became the focus of Hamilton's research why was it that clones, once they arose, did not quickly send their sexual parents extinct Hamilton became convinced that the answer lay with one of the short-term advantages of recombination, in particular the Red Queen hypothesis. There is evidence to support his contention. First, some

Estimate rate per rate per individual in numbers per billions thousand thousandyear millions

Population growth in North America (Table 1.4) is rather variable, but reached a relative peak in 1991-92 when around two million people were added to the population per year. The data from 2003, however, reflect the fact that the 2000 census for the United States came in at almost seven million more than expected. Meanwhile, the US birth rate has fallen to 2.034 births per female (replacement rate is 2.10 births per female) (PRB, Anonymous 1981-2004).

Homogeneous populations exponential and geometric growth and decay

We are now ready to apply the mathematical ideas of Chapter 2 to some ecological problems. Let's start with the simplest case of a population in which birth and death occur continuously and there is a constant per capita birth rate and death rate amongst all individuals of a population. The model we are to develop could be an analog of a population of bacteria in a Petri dish, for example. The total number of births occurring at any time is simply the per capita birth rate, b, times the population density, N, and the total number of deaths is likewise the per capita death rate, d, times the population density. The change in the population at any one time is the number of births minus the number of deaths, or

Impact of the Antiinsecticide Movement

Ehrlich predicted in the prologue of his book that In the 1970s and 1980s hundred of millions of people will starve to death in spite of any crash programs embarked upon today. At this late date nothing can prevent a substantial increase in world death rate, He said there were only two solutions to our problems, either a death rate solution or a birth rate solution. Ehrlich blamed population growth on medical science, stating that .medical science was the straw that broke the camel's back. While lowering death rates in the ODCs overly developed countries was due in part to other factors, there is no question that 'instant death control,' exported by the ODCs, has been responsible for the drastic lowering of death rates in the UDCs under developed countries . In these comments, Ehrlich was mostly referring to use of DDT in national malaria control programs. He referred to use

Densityindependent population dynamics

The serious limitation of density-independent dynamics is that they predict an unrealistic world either eventually covered in one species (when X 1) or without a given species (when X 1). There is also the possibility of no change in population size if the death rates are exactly balanced by the birth rates X 1. This is also unrealistic because birth and death rates have to be exactly matched or balanced by immigration emigration for an indefinite period of time. This is the model of the ball balanced on the pin-head (Fig.

Plague Yersinia pestis

McNeill argues that the destruction of the Byzantine Roman empire in the sixth century AD was wrought by the plague of Justinian, arguably the first visitation of Yersinia pestis to Europe.27 The Plague acted as a stressor or a solvent on the machinery of empire, resulting in the attenuated erosion of societal and state cohesion, prosperity, and power during the sixth century AD. This emergent pathogen was one of the first negative consequences of the early phases of globalization, as trade and migration along the Silk Road saw the dissemination of Yersinia pestis from its natural reservoirs in Central Asia to Europe and East Asia.28 Consequently, the contagion resulted in massive mortality among immunologically naive populations throughout the Mediterranean region.29 The demographer Josiah Russell has argued that all the available data indicate that before the arrival of the contagion the populations of the Byzantine Roman Empire and the Persian Empire were robust and enjoying a...

Population dynamics of diatoms with a single limiting resource

-1dN birth rate-death rate (6.1) In the simplest case (Figure 6.1), both the birth rate and death rate are density-independent, and this leads to either exponential growth (when the birth rate exceeds the death rate) or exponential decline (when the death rate exceeds the death rate). Numbers change through time as the integral of the differential equation To keep things a simple as possible, we shall assume that the birth rate of the diatoms is a function of silicate but that the death rate is independent of resource supply. When silicate concentration is greater than 4.4 mM (say) then the birth rate exceeds the death rate and the population increases exponentially. If the silicate concentration falls below 4.4 mM then the death rate will exceed the birth rate and the population will decline exponentially. The silicate concentration, however, is not constant, but depends on the population of plankton. Silicate is removed from the water and tied up in the cell walls of the algae, so...

Nonlinear density dependence of birth and death rates and the Allee effect

As mentioned above, density-dependent birth and death rates are assumed to vary linearly with density (Fig. 2.9). Although it is known from both laboratory (Smith and Cooper 1982) and field studies (Arcese and Smith 1988) that birth and death rates are often nonlinear (Fig. 2.10), such differences seem to have a minimal impact on natural populations. One major exception, however, is known as the Allee effect (Allee 1931). Allee proposed that many species have a minimum viable population (MVP) size. As described in Chapter 1, although Allee may have had a specific number in mind, below which death rates rise and or birth rates collapse, a more modern view is that the probability of extinction has become unacceptably high when a population becomes small (Shaffer 1981, Miller and Lacy 2003), but there is no one specific number described as a MVP. Why should there be higher death rates in very small populations Proposals include (i) group cooperation reduces losses from predators (ii)...

Two or more plant species with a single limiting resource

Our assumption that there is only a single limiting resource, it is certain that one of the two species will go extinct. The only question concerns the identity of the species that survives. Tilman's R* theory allows us to predict the identity of the winner, because irrespective of its initial population growth rate, the eventual dominant will be the species with the lowest value of R* (see Chapter 7 in this volume). The species with the highest birth rate will increase fastest and will soon become substantially more abundant than the other species. But does this mean that the species that grows fastest to begin with will persist It might do, but it might not. The long-term outcome depends on the relative magnitude of the R* values for the two species and not necessarily on their initial growth rates. Inevitably, one of the species is driven to extinction, and the resource level is reduced to the lower of the two R* values. This is the process of competitive exclusion.

Use and Limitations of Dimensions

In addition to its utility in specific applications, the method of dimensional grouping is an important avenue for interdisciplinary understanding of ecological processes. One of the advantages in using dimensional groupings to reason about ecological problems is that this method is routinely used in reasoning about physiological processes that connect organisms to their environment. The method is used by physiologists working at space and time scales relevant to the cell or the individual. It is also used by physical scientists working at global time and space scales. So this method should be of considerable use to ecologists who work in between, where physiological performance (growth rate, birth rate) interacts with the dynamics of the physical environment.

Ontogeny Of Habitat

In wood-feeding cockroaches, juvenile food and habitat is set when the parent chooses a log to colonize. The horizontal distribution of cockroaches in caves is often related to the resting positions of bats, which determine the placement of guano and other organic matter. Gautier (1974a, 1974b) calculated the spatial distribution of burrowing Blaberus nymphs in caves by counting the number of individuals in 50 cm2 samples to a depth of 15 cm. He found that nymphs were concentrated in zones where bat guano, fruit, and twigs dropped by the bats accumulated, and were absent from zones of dry soil, stones, or pebbles. In many cave cockroaches, females descend from their normal perches on the cave walls to oviposit or give birth on the cave floor in or near guano (e.g., Blaberus, Eublaberus, Periplaneta Crawford and Cloudsley-Thompson, 1971 Gautier, 1974b Deleporte, 1976), where the nymphs remain until they are at least half grown. They then climb onto the cave walls, where they...

Chordates Including the Vertebrates

Most mammals have mating seasons, timed to produce young at a favorable season for rearing. Mating is limited by the female, who is receptive to mating only during a brief period in the mating season known as estrus. Old World monkeys and humans have a different cycle, the menstrual cycle. Mammals exhibit three ways of giving birth. Mono-tremes, such as the duck-billed platypus, is a mammal that lays eggs. Animals that lay The third way to give birth is that of the placental mammals, which comprise 94 of all mammals. Gestation in utero is prolonged. The embryo is nourished by a placenta, a membrane structure produced by and surrounding the embryo. The placenta grows thousands of tiny fingerlike projections called villi into the lining of the mother's uterus to absorb nutrients and oxygen from the maternal blood supply without there being an actual exchange of maternal and fetal blood. The fetus is connected to the placenta by the umbilical cord. Once born, the mammal may be more or...

Logn seed abundance mgm

For mammals, density-dependent juvenile mortality has been recorded for red deer on the island of Rhum, Scotland (Clutton-Brock et al. 1985) (Fig. 8.10a), for reindeer in Norway (Skogland 1985) (Fig. 8.10b), for feral donkeys (Equus asinus) in Australia (Choquenot 1991), and for greater kudu in South Africa (Owen-Smith 1990). Adult mortality was density dependent for African buffalo in Serengeti (Sinclair 1977). In each case, the cause was lack of food at critical times of year. Reproduction is known to be density dependent in both birds (Arcese et al. 1992) and mammals (Clutton-Brock et al. 1991). Figure 8.10c shows that the proportion of Soay sheep that give birth at 12 months of age declines with density. Fowler (1987) reports over

What is population regulation

Population regulation does not occur in the absence of density dependence. Thus a population showing pure exponential growth or decline would be unregulated. If population density had no effect on the per capita growth rate, there could be no range of population densities to which the population would return. In this context, Turchin (1995) uses the Murdoch and Walde (1989) definition of density dependence as a dependence of per capita population growth on present and or past population densities. While density dependence is a property of the overall population dynamics, which may involve time lags, no specific mechanism is necessarily responsible (Turchin 2003). That is, one aspect of the life history, such as birth rates, may not be density-dependent.

Modes of Species Coexistence

If species are very similar to each other, such that they do not differ substantially in their utilization of resources, the competitive exclusion can take a very long time. If the replacement of old individuals by young ones is basically a random process, that is, all individuals regardless of species identity have equal chances to give birth to their descendants within an environment, populations of all involved species will fluctuate randomly and the prevalence of a particular species is just a matter of chance. However, due to these stochastic fluctuations and due to the fact that the species which incidentally prevails in a time step will have higher probability to further increase its abundance, this process will finally lead to apparent competitive exclusion. This process, called 'community drift', can be relatively slow and may be further slowed down by dispersal limitations (leading to random prevalence of different species in different local communities isolated by migration...

Modelling complex life cycles

Imagine a species, the individuals of which breed once a year, starting at age 3 years and which live to a maximum of 5 years. The reproduction and survival of these organisms can be described by a set of first-order difference equations. These give either the survival of individuals of different age or the reproductive output of individuals aged 3-5 years. Assume that the age-specific fecundity and survival parameter values are density-independent and are constant from year to year. For example, survival from birth to age 1 is described as The fraction of individuals surviving from birth (age 0) to age 5 is therefore the multiple of the separate survival values from ages 0 to 1, 1 to 2 and so on that is, s0,1s1,2s2,3s3,4s4,5. We will assume that any individuals surviving to reproduce at age 5 then die. Therefore for any given value of N0, N5 could be predicted.

Population Model Case Study Interpretation of Chronic Toxicity Test Data

Where n(t) refers to the number of individuals in age class i at time t, Fj represents the fecundity, or birth rate, of individuals in age class i, and Sj refers to the survival rate of individuals in age class i. Note that this is a relatively simple model of a population without density-dependent feedback on vital rates of mortality and birth. The matrix model is applied to successive time steps of the population to project population size and age structure. After several time steps, the population approaches a stable age distribution (i.e., the proportion of individuals in each age class remains constant over time). In this stage, the population grows (or declines) exponentially at a rate determined by the largest eigen value of the population projection matrix

Species traits as predictors for conservation and harvest management priorities

Cortes (2002) has explored the relationship between body size, age at maturity, generation time and the finite rate of population increase X (referred to in Section 4.7 as R), by generating age-structured life tables (see Chapter 4) for 41 populations of 38 species of sharks that have been studied around the world. A three-dimensional plot of X against generation time and age at maturity shows what Cortes (2002) calls a 'fast-slow' continuum, with species characterized by early age at maturity, short generation times and generally high X at the fast end of the spectrum (bottom right hand corner of Figure 7.10a). Species at the slow end of the spectrum displayed the opposite pattern (left of Figure 7.10a) and also tended to be large bodied (Figure 7.10b). Cortes (2002) further assessed the various species' ability to respond to changes in survival (due, for example, to human disturbance such as pollution or harvesting). 'Fast' sharks, such as Sphyrna tiburo, could compensate for a 10...

Population growth rate

Zoologists generally use the term growth rate to mean the net change in abundance that result from additions and losses. For microbiologists and phy-toplanktologists working with cultures, on the other hand, growth rate means the rate of reproduction (corresponding to see Section 4.3.3), since there is negligible mortality in cultures lacking predators. This is equivalent to birth rate in zoological nomenclature. Phytoplanktologists who work in the field usually use gross growth rate for the reproduction rate and net growth rate to describe the observed changes in abundance. where b is the birth rate and d the death rate (unit t 1)

Predators and their prey

Onment forced a linear decline in per capita birth rates and a linear increase in per capita death rates, without specifying the mechanism of these phenomena. We then introduced the symbol K to simplify the appearance of the logistic model. K, therefore, has nothing explicitly to do with the surrounding environment, including other species. Its connection with the environment is thus an empirical one, not one that is forced on us by the mathematics.

Fecundity and Fertility in Population Dynamical Models Genetic Considerations Further Reading

Is no inherent reason why fecundity should be restricted to females. Regardless, ecologists have defaulted to using the gender-general term of 'reproductive success' to describe the reproductive output of both males and females. We adhere to these traditions and restrict our definition of fecundity to apply to females only. However, reproductive success is not equivalent to fecundity because the former is a measure of an individual's genetic contribution to subsequent generations. As such, reproductive success can vary among individuals due to the effects of maternal age, fitness of progeny from clutches of different size, and other life-history characteristics. Fecundity is therefore a genetical and developmental trait that evolves within a particular selective framework. The term 'fertility' differs from fecundity in that it describes the actual (or current) reproductive performance of (typically) a female, and it is a generalization of the terms 'maternity', 'birth rate' and...

Fecundity and Fertility in Population Dynamical Models

Stage-structured models provide an estimate of the stable stage distribution, which is the theoretical proportional allocation of individuals within the population to the defined stages (e.g., age groups, size classes, developmental stages) resulting from constant demographic rates. The stable stage distribution is a useful metric because it provides the theoretical composition of a population exhibiting a fixed birth rate, so factors such as environmental variation or intrinsic regulation that alter this theoretical distribution can be ranked for their effects on the future composition of a population. This introduces the concept of'reproductive value' - a measure of the combined effects of fecundity, fertility, and survival that takes an individual's proportional contribution to the future status of its population into account. It is formally expressed as the sum of the current and future reproductive values, and is considered the currency used by natural selection to produce a...

Detecting Stability and Causes of Change in Population Density

The concept of a balance of nature goes back to the very early days of ecology. It is obvious that unlimited capacity of all animals to increase in population size or density is inevitably checked by competition for resources or the action of natural enemies. If any of these factors cause systematic changes in survival or fecundity of a population as the density increases, they are said to be density dependent. If fecundity or survival decreases sufficiently as the population increases, then the per capita birth rate will decline to a value equal to or less than the per capita death rate and population growth will stop. In this manner, density-dependent processes constitute negative feedbacks on population growth that can maintain densities at or near an equilibrium value indefinitely.

Underlying Mathematical Structure

The i, j-th component of the matrix A equals the probability of a transition from h-state j to h-state i, multiplied with the corresponding survival probability, plus the average number of offspring with h-state i produced by an individual in h-state j. The matrix B is built up from per capita rates. The off-diagonal components equal the transition rates between the corresponding h-states plus the h-state-dependent average rates of offspring production differentiated according to their birth h-state. The diagonal components equal minus the overall rates of state transitions from the h-states, minus the h-state-dependent death rates, plus the average rates of giving birth to offspring with the parental h-state.

From Lifetime Offspring Number to Intrinsic Rate of Increase and Invasion Probability

In nonfluctuating environments, life histories with everybody born equal always allow an age representation, characterized by an average age-dependent effective birth rate (or ratio) A(a) (often seen decomposed into an age-dependent survival l(a) and conditional fecundity b(a) as A(a) l (a)b(a)), from which the intrinsic rate of increase r can be calculated by solving with Tb, the average age when giving birth,

More Than One Birth State

When individuals can be born in different birth states (think, for example, of different patches), the previous results generalize with little change. Let Xj (a) be the average rate (or ratio) at which an individual born in state j gives birth to offspring in state i, and A (a) (X j (a)). Then r has to be determined from

Growth Models in Population Dynamics

Where is the instantaneous birth rate per individual, M the instantaneous death rate, r 5S - Ms, N the population density and t the time. As seen, the equation represents first-order kinetics (see Section 2.8) and exponential growth (see Section 3.6). If r is constant, after integration, we get

Density Dependent Mechanisms

When ecologists speak of population regulation, they are often referring to density-dependent mechanisms. These mechanisms may be a product of the population itself, or a reaction to the population density. For example, a population of voles may increase exponentially until competitive intraspecific interactions cause either the birth rate to decrease or the death rate to increase, leading to a net decline in reproductive rate and subsequent decrease in population density. Alternatively, as the population of voles increases, the population may become more apparent to predators, causing an increase in herbivore consumption and subsequent changes in predator densities.

First and Second Order Dynamics

Some properties of herbivore populations themselves may cause negative feedback loops and thus may contribute to the maintenance of population cycles by causing or exacerbating the decline portions of the cycles. For example, increasing population densities may cause more competition for food or more aggression among conspeci-fics, leading to increased rates of mortality or decreased birth rates. Increased competition for shelter or mating sites may result in many individuals succumbing to prey or failing to recruit offspring into the next generation. These mechanisms, however, may not be sufficient to cause cycling, since there may be only short or even nonexistent time lags between consumption of food or space and subsequent reductions in herbivore densities. One prominent exception is the population cycles of Soay sheep populations on the St. Kilda archipelago off the coast of Scotland. This population goes through abrupt and somewhat regular fluctuations in number, and has been...

Growth and Development

According to Paul (1997), dinosaurs would have grown extremely rapidly. The larger the adults, the greater the number of eggs that they would have laid -probably many tens of thousands during the life spans of the largest sauro-pods. The extreme ratio between size on hatching and at adulthood would have necessitated very rapid growth for sexual maturity to have been reached within two or three decades. Breeding would have had to begin within that time scale if sufficient juveniles were to survive to sexual maturation. Dinosaurs could not have lived and grown for more than 100-150 years at most. Smaller dinosaurs may have been K-strategists, with low birth rates and advanced parental care, although with fast growth rates. Large species, on the other hand, were undoubtedly fast-breeding r-strategists, with high levels of egg deposition, fast growth and high juvenile mortality. Only small numbers of juveniles needed to reach sexual maturity to build up and maintain large populations....

Liebigs law of the minimum

Life table A summary of the survival rates of individuals in a population at different ages or at different stages in the life cycle. In a cohort life table or dynamic life table a group of individuals born within the same short time interval (i.e. a cohort) is followed from birth to death of the last survivor. This type of life table is suitable for annual species in which there is little or no overlap of generations. It is also suit

Other Types of Imprinting

Parental recognition of the young may also be acquired by an imprinting-like process. This process is atypical in the sense that it occurs during adulthood rather than during the early stages of development. It is of course beneficial for parents to recognize their young so that they can direct care to their own kin. In birds, as in a colony of seabirds, vocalization may be particularly important in this regard. In goats, an olfactory imprinting mechanism may help mothers to recognize their own kin at a very early stage. Development of very early offspring recognition is necessary in herds of goats because kids may lose contact with their mother and may then try to approach other females. A few minutes of contact with a kid may be sufficient for the mother to imprint on it. During this period, the mother may learn the smell of the kid, and label it further by licking. Afterwards, she may only allow such labeled kids to suckle. The high arousal of a female giving birth may facilitate...

Implications of Population Dynamic and Metapopulation Theory for Restoration

Understanding how populations change in the face of spatial and temporal variation or in response to environmental, genetic, and demographic uncertainty is central to planning any restoration effort or recovering any rare species. Interactive factors influencing population persistence are complex and much more research is needed in this area. Even basic data for estimating birth rates, death rates, rates of population increase, and habitat occupation is often lacking, yet it is essential for developing effective, reliable recovery and restoration plans (Schemske et al. 1994).

Modeling Pest Population Dynamics

A prevailing concept of IPM centers on the regulation of insect populations, which requires an understanding of population dynamics. Population dynamics is the study of change in insect numbers across space and time therefore, models simulating population behavior must be dynamic. To understand the dynamics of insect populations, the insect population should be considered as part of a system of interacting components. Thus, a systems approach to modeling insect population dynamics is useful in identifying the important components that influence the distribution and abundance of insect numbers. Fundamental population processes involved in modeling insect population dynamics typically include natality (birth rate), mortality (death rate), and dispersal (movement). These key processes are influenced by a host of biotic and abiotic factors, some of which are common to all insect species while others are unique to a given species. For example, populations and their effective environments...

Extinction and Conservation

We can better understand the reasons for this relation if we examine the key processes responsible for extinction. First, demographic stochasticity, the chance occurrence of a series of deaths before any member of a population can give birth, acts at low population sizes and can cause the population randomly to go to zero. Second, environmental stochasticity, represented as variation in species traits generated by extrinsic environmental factors that themselves are varying, is important at moderate-to-large population sizes. The environmental variation can be chronic, occurring more-or-less continuously over time, or catastrophic, occurring very infrequently but being much more severe. Finally, population ceilings are important no population has the capacity to increase indefinitely, but rather negative feedback (density-dependence) will set in as it expands, eventually forcing the population to hover at or near some ceiling in numbers. With lower and lower values of the ceiling, a...

Demographic variables in elephant populations

The most fundamental consideration in tracking the dynamics of a population is the estimation of birth rates and death rates. In some instances, the rates of immigration and emigration may also be important. While the overall birth and death rates of a population provide a simple picture of its trends, our understanding of its dynamics is considerably enhanced if we can estimate age-specific fecundity and age-specific mortality. We need to know the age at which a female first gives birth (and not merely becomes sexually mature, although the two are related), the number of young born with each pregnancy, the interval between successive births at different stages in life, the age of last birth, and the death rate at different ages for both males and females. Observations of both captive and wild elephant populations show that the birth of twin calves constitutes less than about 1 of all births (one exception being Etosha, with a 4 rate) and thus can be practically ignored for analyzing...

Reproductive adaptations

Courageously protecting them against marauders. Female pipefish lay their eggs in a pouch on the male's belly. Here they remain until they hatch as miniature adults. Amphipods and isopods, often very numerous on the shore, also retain their eggs within a brood-pouch from which fully formed young emerge. In Littorina saxatilis, L. rudis and L. neglecta the eggs remain in the mantle cavity until they hatch as minute winkles. The tiny bivalve Lasaea rubra, often abundant in rock crevices and empty barnacle shells, incubates its eggs and young within the gills until they are sufficiently developed to crawl out and maintain themselves near the parent. The viviparous blenny, Zoarces viviparus, gives birth to well-developed young about 4 cm in length.

Age and stage structure

All wildlife populations have individuals of different ages. The vital rates (i.e. birth rates and probabilities of survival and mortality) often vary with age. Hence, a population composed of old individuals might well exhibit a different potential for growth than does a younger population. Assessing these kinds of processes requires an age-specific model of population growth (Caswell 2001).

Approaches and Paradigms

Predict the trait or traits expected to maximize fitness for that set of circumstances. The most common approach has been to examine how traits such as age or size at maturity (through their effect on birth rates) influence population growth rate (often referred to as the Malthusian parameter r) and find the life-history pattern that maximizes r. This links life history explicitly to population dynamics.

Population changes in elephants of North Bunyoro Uganda

At the same time, there was an increase in the mean weight of an elephant over this time, from 1,894 kg in 1946 to 2,234 kg in 1966 (with reduced recruitment, there was a preponderance of older, heavier animals). A biomass calculation showed that the unit weights of elephants changed from 6,633 kg km2 in 1946 to only 6,561 kg km by 1966, or a 1 reduction. During this time, there was significant decline in habitat quality (conversion of woodland to grassland), strongly suggesting that density-dependent regulatory factors were responsible for the reduced birth rate and increased calf mortality rate.

Black Bears in the Oak Forest

While black bears can and do live in a variety of habitats, they are uniquely adapted to a forest existence. Their sharp, recurved claws make them excellent climbers, and they are often seen feeding high in the tops of oak trees (Pelton 1989). Throughout much of their range, adult females den in trees and give birth to their cubs in tree cavities high off

Characteristics and Structure of Ecotoxicological Models

Toxic substance models are most often biogeochemical models, because they attempt to describe the mass flows of the toxic substances considered, although there are effect models of the population dynamics which include the influence of toxic substances on the birth rate and or mortality and should therefore be considered toxic substance models.

Agestructured models of population dynamics

The growth rate r calculated from various combinations of the above birth and death rates gave insights into which factors might regulate populations. Under ideal conditions, an elephant population experiencing low mortality and high reproductive rates (short intercalving interval and long reproductive life span) could grow at an intrinsic rate r of 0.047. This actually translates into an annual population growth of 4.8 . Considering that it is unlikely for a population to experience such ideal conditions for long, Hanks and McIntosh concluded that, in practice, the rm of an elephant population is more likely to be about 0.040 and the annual growth rate to be just under 4 . This result also corrected earlier estimates of cropping rates of 6 as the sustained yield quotas for elephant populations in Africa based on crude estimates of birth rates alone. The overall results were even more interesting from another perspective. The model clearly showed that, while intercalving interval...

Demographic Variation

Other considerations affect persistence. The value of R (the birth rate minus the death rate) is critical. R can be negative (death rate exceeds birth rate) and the population can still persist for 100 years, which may seem counterintuitive. Furthermore, R can be positive (birth rate exceeds death rate) and the population can still go extinct. For example, suppose R is increased to 0.02 by making the birth rate 0.51 and the death rate 0.49. The persistence for A0 20 increases

Increased Offspring Viability

Ovoviviparity is viewed as a solution to this constant battle against predators and parasites, and is thought to have appeared in the Mesozoic as an evolutionary response to cockroach enemies that first appeared during that time (Vishniakova, 1968). Parasitoids have not been detected in the oothecae of ovoviviparous blaberids (LMR, pers. obs.). The eggs are exposed to the environment for only the brief period of time between formation of the ootheca and its subsequent retraction into the body, allowing only a narrow time frame for parasitoid oviposition. Once in this enemy free space, the eggs are subject only to the vicissitudes that beset the mother (Roth and Willis, 1954b). Nonetheless, nymphs of ovovi-viparous cockroaches are at risk from cannibalism at the time of hatch. Attempts by conspecifics to eat the hatch-lings as the female ejects the ootheca have been noted and may include pulling the still attached egg case away from the mother (Willis et al., 1958). We note, however,...

Modeling the dynamics of exploited populations

The exploitation of elephant populations has several demographic and genetic consequences. Many African elephant populations have remained depressed at a young age structure because of disproportionate removal of older individuals. Not only do age structures distort, but also sex ratios skew as males suffer higher rates of exploitation. Demographic changes also include changes in birth rates of the population. Thus, I found that a sex ratio extremely biased in favor of female elephants at Periyar in southern India had clearly depressed the birth rate. Similarly, Richard Barnes and E. B. Kapela recorded a decline in recruitment among the elephants at Ruaha in Tanzania that had been impacted by ivory poaching. The population genetic consequences include a reduction in the frequencies of genes for tusks, thus favoring the increase of tusklessness in the population. Among Asian elephants, the selective hunting of males is usually the most significant determinant of demography and...

Modeling hostmicroparasite interactions

N total host population density S susceptible host density I infected host density R recovered (immune) host density b host birth rate The growth rate of each segment of the population is written as a differential equation. The increase in the number of susceptible individuals (Eqn. 9.2) is based on the birth rate (bN) and the rate at which recovered individuals lose immunity (yR). Losses are due to the host mortality rate unrelated to the disease (mS), and to the conversion of individuals from the susceptible to infected classes (fiSI)

Modeling longterm trends in tusk inheritance

The Tiedemann-Kurt model for Asian elephants has been described in much greater detail in their 1995 publication. Their model combines stochastic population dynamics with population genetics at the individual level. The demographic data on birth and death probabilities are based on Kurt's field observations in Sri Lanka during the late 1960s and 1970s and my work in southern India during the 1980s. Males were assumed to begin reproducing at 20 years of age and females at 8 years, giving birth 2 years later. Such an early age in female reproduction is likely to be true only of Sri Lankan elephants, but not other Asian populations. A constraint of an upper limit of six females mated annually by one adult male was set. The minimum intercalving interval was taken as 4 years, with a certain probability that a female would actually conceive in a given year 4 years after a previous conception this translated into an average intercalving interval of 4.43 years, typical of observed populations.

Species Area Relationships Speciation and Phylogeny

The predictions of the UNT for phylogeny and coalescence theory are different from the results of the early explorations by Raup and colleagues of neutral phyloge-netic models, and the later analytical models of Nee and colleagues. Under the previous neutral models, lineages had preassigned equal probabilities of speciating or going extinct, and lineage abundance was ignored. Under the UNT, however, lineages per se have no preassigned spe-ciation and extinction rates. Instead, the probability of speciating or going extinct is determined by lineage abundance, the distribution of which is dictated by the fundamental biodiversity number, 0. The UNT leads to a number of different predictions for phylogeny. First, globally very abundant species are expected to be much older on average than rare species. Second, these globally abundant and widespread metacommunity species are expected to be the ancestors of many more modern species than are rare and local species. This is a consequence not...

Recent Developments in Neutral Theory

Proved that parameter x of the logseries is equal to the ratio of the metacommunity average per capita birth rate b to the average per capita death rate d. Values of x fitted to data are always very close to, but slightly less than, unity. The UNT says this must be so because at very large biogeographic scales, the total birth and death rates must be in near-perfect mass balance, that is, the metacommunity b d ratio will be only infinitesimally less than unity. At the metacommunity diversity equilibrium, the mass imbalance caused by the very slight deficit in birth rates relative to death rates is made up by the very slow addition of new species. Volkov and colleagues also obtained another remarkable result. They proved that Fisher's log series necessarily implies that per capita birth and death rates are density independent at the spatial scale of the entire metacommunity. This is intuitively reasonable when it is realized that changes in population density of a species in one...

Local dynamics Periodicity and endemic fadeout

Periodicities in the incidence of many infectious diseases have long been described (Hamer, 1906 Soper, 1929). These early studies, including Hamer's celebrated 1906 paper, identified that the depletion and replenishment of the pool of susceptible individuals is a key mechanism underlying the oscillations. An outbreak can only occur when a relatively large number of susceptibles is present. As the outbreak takes place, susceptibles become infected, so their number falls while the number of infectives rises. Eventually, the number of susceptibles falls to a level where there are insufficiently many remaining to sustain the outbreak and so the number of infectives falls. Over time, the susceptible pool is replenished by births and rises to a level at which another outbreak can occur. The process repeats, leading to recurrent epidemics. In this picture, the time between outbreaks is largely determined by the birth rate of the population. In many cases, periodicities are clear from visual...

Basic Population Model and Density Dependence

As suggested by Boyce (1992), Stacey and Taper (1992), and Burgman et al. (1993), density dependence is an important part of estimating a population's persistence. Lande (1993) demonstrates that the importance of environmental stochasticity and random catastrophes depends on the density-dependence mechanism operating in the population, based on the value of K carrying capacity. However, how density dependence is incorporated into the model greatly affects the estimates of persistence (Pascual et al. 1997). In persistence models, as a population declines, compensation for small population size takes the form of increased birth rates and decreased death rates (density dependence) and so is a significant factor in increasing population persistence.

World population and food supplies

In all communities, inadequate diet is closely connected with poverty. In such conditions infant mortality rates are usually high, partly the result of malnutrition. High infant mortality encourages high birth rates in compensation, and in some communities family planning is unlikely to reduce birth rates appreciably until there is a reasonable expectation that children will survive. Consequently, effective measures of population control require the raising of standards of nutrition, hygiene and health in the poorest populations. The problems of feeding the increasing world population, stabilizing its size and achieving a satisfactory balance between food supply and demand are therefore closely interrelated. It is not solely a matter of expanding food production but also of ensuring a more equitable distribution of wealth and a proper apportionment of food to bring all diets to adequate levels.

Early tests of the Lotka Volterra models

According to the Lotka-Volterra equations, the response of a predator population to an increase in a prey population is to increase its own numbers. This increase may be through an increase in the birth rate of the predator (perhaps combined with a decrease in death rate) or through immigration. Again, this is termed a numerical response. According to the Lotka-Volterra equations, the result of this increase in predation is a coupled numerical response in the prey population, which declines. Once the prey population has declined sufficiently, the negative consequences for the predator population results in its decline. Once predator numbers have decreased sufficiently, the prey population begins to recover, leading eventually to an increase in the predator population, and so on. A graph of the Lotka-Volterra results versus time look like a stable limit cycle (Fig. 10.1), though it is not. In a true limit cycle, if the populations are pushed out of the cycle by density-independent...

Otter numbers rejuvenated recruitment

In Chapter 12 it will be shown that otters face low survival rates and a fairly short life expectancy. Consequently, one might expect high birth rates to make up for this. However, none of the species Litter sizes of river otters are also similar to those of the Eurasian, varying between one and five, but usually there are one to three cubs. Mean fetal litter sizes were 2.3 (Hamilton and Eadie 1964), 2.7 (references in Melquist and Dronkert 1987) and 2.7 (Tabor and Wight 1977). The last authors noted that there were 2.3 cubs per female at the beginning of independence. Older females almost all become pregnant annually (Melquist and Dronkert 1987 Toweill and Tabor 1982) and they give birth in early spring, between December and April. The observations show that, although the American river otter and the Eurasian one belong to different genera, and show differences in the pattern of implantation, as a general picture the two are remarkably similar in their reproductive ecology. Sea...

Moving beyond simple synchrony Reinvasion waves and phase relationships

The statistical power of Cliff and Haggett's studies was limited by the relatively short length of their time series their four-year observation window covered just two major measles outbreaks. Grenfell and co-workers' longer time series (Grenfell et al., 2001) gave them more statistical power, but required an analysis that can cope with temporal changes in the dynamics of incidence, i.e., nonstationarity of the time series. Traditional linear techniques, such as autocorrelation or Fourier spectra, assume stationarity of time series. Measles dynamics, however, exhibit significant dynamical changes over time, such as changes in the oscillation period in response to variations in birth rate or level of vaccination (Earn et al., 2000). In such situations, wavelet analysis (Torrence and Compo, 1998 Grenfell et al., 2001) provides a useful tool. In common with Fourier analysis, wavelet analysis is a decomposition approach, but, instead of representing the data in terms of a collection of...

Inheritance Variability and Natural Selection

Darwinian natural selection examines the character of different specimens stability, amativeness, reproductive potential, etc. It is not always a struggle for existence often it is a struggle for leaving sufficient number of descendants. The main criterion is birth rate. If it is less than one, the species is doomed. intellectual man (the anthropic principle) and (3) survive in the course of competition with other species (Darwinian selection). Evolution eliminates evidently defective individuals other ones are not really exterminated, but rather 'squeezed' from the ecosystem because of low birth rate.

Botany and Plant Development

Although the structures of inflorescence show regular patterns (Figure 1), which have been described already long ago, the development of shrubs and trees looks more complicated and was not carefully studied before the apparition of plant architecture analysis that allows botanists to understand the link between bud functioning and the resulting three-dimensional (3-D) plant geometry and topology. Through relevant simplifications, the botanists Halle and Oldeman introduced in 1970 the fundamental criteria for classification, giving birth to 23 models of plant architecture (Figure 2). These condensed criteria concern inflorescence position, axis growth pattern and differentiation, and branching patterns. They allow classifying any kind of tree in one of the described models that is supposed to correspond to the stable endogenous developmental pattern of a given plant species. This gives a multiscale organization to the plant structure that gives birth to a stack of substructures analog...

Functional Structural Models and the Simulation of Plant Growth and Development

The terminal bud of a plant axis produces different kinds of metamers bearing axillary buds of various physiological ages. These buds themselves give birth to axillary branches and so on. A substructure is the complete plant structure that is generated after one or several cycles by a bud. In the deterministic case, all the substructures with the same physiological and chronological ages are identical if they have developed at the same moment in the tree architecture. At cycle t, a substructure is thus characterized by its physiological age p and its chronological age n. It is denoted by Sp (n). Since the physiological age of the main trunk is 1, at growth cycle t, the substructure of physiological age 1 and of chronological age t, S (t), represents the whole plant. Figure 12 illustrates the way substructures are organized. The total number of different substructures in a plant of chronological age t is very small, usually less than 30, even if the total number of organs is high....

Measuring Recruitment

The measure of recruitment is critically dependent on the life history stage at which death and or emigration of individuals is assessed. To illustrate this important point, we will consider for example a population of a large mammal in a temperate ecosystem. The births are highly synchronized over a short yearly pulse, producing one new cohort each spring. The 'life cycle graph' (Figure 1) describes the different stages that individuals may experience from birth to death. In our example, individuals may survive from birth to weaning (summer survival of juveniles), from weaning to i year of age (winter survival of juveniles), from i to 2 years of age (yearling survival), then each year from 2 to 7 years of age (prime-aged adult survival), and finally each year from 8 to the maximum longevity (senescent adult survival). Each cohort is the sum of newborns produced by 2-year-olds (primiparous females), and prime-aged and senescent females (mostly multiparous females). Recruitment can...

Immediate and Delayed Effects of Recruitment Variation on Population Dynamics

Give birth for the first time at age 4, produce two offspring per year between 4 and 8 years of age, then cease reproducing. Assume that the first-year survival is 0.75, the annual survival between 1 and 8 years of age is 0.90, and the annual survival beyond 8 years of age is 0.75. Running a simple pre-breeding Leslie matrix model (i.e., individuals observed just before a new cohort is produced so that all individuals are included from 1 year of age onward) leads to an asymptotic natural rate of increase of 1.15, with a stable age distribution of 56.15 individuals in the pre-reproductive stage, 36.14 in the prime-age stage, and 7.71 in the senior stage. Now let recruitment markedly decrease in a given year so that the first-year survival becomes 0.25 instead of 0.75. After the perturbation in recruitment, the natural rate of increase will decrease to 0.97 and the age structure 1 year later will be shifted toward old individuals with 48.01 , 42.86 , and 8.88 of animals in the...

Resilience and Temporal Variability

Comparative research has provided evidence that resilience, when viewed from a species point of view, is dependent on body size. Usually large-bodied species show low rates of increase and thus lower resilience. In contrast, small-bodied species usually have more frequent reproductive output, and thus a faster response to perturbation, that is, higher resilience. These species can recover more quickly from sharp declines in density as a result, it would make highly resilient species less variable. However, resilience can also lead to higher variability. This can be explained mainly by two processes one has to do with the ability of some populations with high resilience to over-respond to mortality caused by a disturbance. First the population will overshoot the equilibrium density, as mortality lags behind the population growth rate. Then, the overshoot is followed by an undershoot, as the population declines below its equilibrium, as the birth rate now lags behind the mortality rate....

Optimal Foraging and Population Size

Aging may permit predators to overexploit their prey. In almost any predator-prey model, overexploitation can arise an increase in per predator capture rates may reduce the number ofpredators a prey population can sustain. In the basic predator-prey model presented in section 11.3, the prey population equilibrates when the rate of prey recruitment matches the rate at which the predator consumes prey (in symbols, G(R) PB(R)). The predator population equilibrates when the predator birth rate equals the predator mortality (in symbols, when cB(R) m, or when B(R) m c). We combine these two expressions to find that that the predicted abundance for the predator at equilibrium (the asterisk indicates equilibrium) is P* G(R*) B(R*) G(R*)c m. In words, the equilibrium density ofthe predator equals prey recruitment, times a conversion factor translating consumed prey into predator births, divided by predator mortality. If a predator exploits prey more efficiently (higher c), it needs to consume...

Ideal Free Distribution

As a population grows, it experiences a lower birth rate or a higher death rate because of density dependence (e.g., due to exploitative competition). In a constant environment, the population increases until it reaches a level at which births just match deaths (so that average fitness is unity). Modelers call the abundance at which this demographic balance occurs the carrying capacity. Now assume that our population exploits several distinct patches, each with its own resource renewal rate, leading to density dependence in each patch. If the population can achieve an ideal free distribution, and is in demographic balance, then we know two things overall fitness is unity, and all patches have the same fitness. For this to be true, we can infer that local birth rates match local death rates in each patch. Thus, each patch equilibrates at its own carrying capacity. The overall carrying capacity of a landscape for an ideal free forager is just the summed carrying capacities over the...

Historical Development of the rK Concept

The parameter r, intrinsic growth rate, is the difference between per capita birth rate and death rate at very low population densities. It is part of the logistic equation and also of the Euler-Lotka equation 1 xe-rxlxmx, where lx is the probability of surviving from birth to age x and mx is the number of daughters per female at age x. The Euler-Lotka equation links the parameter r with the life history of individuals. Hence, r is an individual trait that can be selected. The idea that environments differing in stability and population select for different phenotypes was formalized by MacArthur in a paper published in 1962 and by MacArthur and Wilson in their landmark book The Theory of Island Biogeography from 1967. In contrast to Dobzhansky, however, MacArthur and Wilson did not look at the population of environments by different species (i.e., biodiversity) but at the population density of species. Given the title of their book, it is no surprise that they looked at species...

Problems of the rK Concept

The parameter K is not directly biologically interpretable. While r is the difference between per capita birth rate and death rate at very low population densities and can be directly related to the life history of individuals, K is quite a complex parameter it is meant to give the maximum number of individuals that a given environment can sustain under constant conditions. This phenomenological parameter cannot be determined in natural populations and is thus not directly biologically interpretable. In models, K is defined as the unstable or stable point of equilibrium where death rates equal birth rates (dN dt 0 in time-continuous models, Nt+1 Nt in time-discrete models). In real populations, such points of equilibrium are rarely constant over time. How K relates to life-history traits is indefinable, too. Stearns in 1977 wrote ''K is not a population parameter, but a composite of a population, its resources, and their interaction. Calling K a population trait is an artifact of...

The Mac ArthurWilson theory of extinction time

We begin by assuming that the dynamics of the population are characterized by a birth rate ( ) and a death rate (w) when the population is size n (and for which there are at least some values of n for which l(n) ,u( ) because otherwise the population always declines on average and that is not interesting) in the sense that the following holds

Sex Ratio Effects on Population Growth Rate

Population growth is determined by the net recruitment rate of individuals to the population. Population growth in a given generation is a linear combination of its initial size, birth, death, immigration, and emigration rates. All four parameters are influenced by the ratio between the sexes in the population. Birth rate depends mainly on the number of females of reproduction age in the population. Here, the ratio between adult males and females affects the probability of a female to mate successfully. The number of females that are actually fertilized is the effective population size that determines the per capita birth rate. Survivorship rates may differ between males and females of all age classes but especially among the young. Theoretical models predict that offspring sex ratio should generally be close to equality after the period of parental care, but can be biased if the cost of rearing

Statural Growth in Elephants

Statural growth in an animal is the product of its genetic makeup as expressed under the influence of resources available in its environment. The environmental influence is possibly more important in determining the dynamics of growth, especially from birth well into adulthood. We know that Asian elephants kept in Western zoos, in which they are provided a high-nutrient diet but little physical activity, grow much faster than do their wild or tame counterparts in the range states. Fred Kurt (1995) observed that the zoo elephants not only grow faster, but also are 33 -78 heavier than captive animals of similar height in Asian timber camps. It is conceivable that levels of nutrition available for wild elephants would also determine their growth rate on both a seasonal or interannual basis and over their life span. Thus, wet season growth can be expected to be greater than dry season growth in highly seasonal habitats. Elephants in tropical rain forest may also be relatively smaller in...

Previous Releases of Captive Primates

A site was carefully evaluated and chosen where the released population would have limited contact with wild populations, individuals were screened for disease that might threaten wild populations as well as the individuals, and released individuals with and without radio collars were followed by observers (Ancrenaz et al. 1995, Tutin et al. 2001). After three years post reintroduction, at least 70 of released individuals survived (this survival rate could be as high as 90 since some mortality was not confirmed and disappearance could be due to outmigration), and more recently, females have successfully given birth (Beck 2007). Presumably in the future, this population will begin to contribute to the genetic diversity of the surrounding chimpanzee communities (Goossens et al. 2002), but meanwhile the release itself has generated significant media and governmental attention that has allowed for an increase in protection of the areas surrounding the release site....

Brief History of Optimal Foraging Theory

Do not mean to suggest that Tullock originated this approach, merely that his paper clearly expressed what many ecologists were thinking.) The idea of using an established concept set to investigate the foraging process from first principles animated many ecologists. This motivation fused with developing notions about natural selection (Williams 1966) and the importance of energy in ecological systems to give birth to optimal foraging theory (OFT). The new idea of optimal foraging theory was that feeding strategies evolved by natural selection, and it was a natural next step to use the techniques of optimization models.

Simple annuals cohort life tables

A life table and fecundity schedule are set out in Table 4.1 for the annual plant Phlox drummondii in Nixon, Texas (Leverich & Levin, 1979). The life table is known as a cohort life table, because a single cohort of individuals (i.e. a group of individuals born within the same short interval of time) was followed from birth to the death of the last survivor. With an annual species like Phlox, there is no other way of constructing a life table. The life cycle of Phlox was divided into a number of age classes. In other cases, it is more appropriate to divide it into stages (e.g. insects with eggs, larvae, pupae, etc.) or into size classes. The number

The population projection matrix

Life Cycle Graph Matrix

With different rates of fecundity and survival life cycle stages, perhaps, or size classes, rather than simply different ages. The resultant patterns can be summarized in a 'life cycle graph', though this is not a graph in the everyday sense but a flow diagram depicting the transitions from class to class over each step in time. Two examples are shown in Figure 4.14 (see also Caswell, 2001). The first (Figure 4.14a) indicates a straightforward sequence of classes where, over each time step, individuals in class i may (i) survive and remain in that class (with probability pi) (ii) survive and grow and or develop into the next class (with probability gi) and (iii) give birth to mi newborn individuals into the youngest smallest class. Moreover, as Figure 4.14b shows, a life cycle graph can also depict a more complex life cycle, for example with both sexual reproduction (here, from reproductive class 4 into 'seed' class 1) and vegetative growth of new modules (here, from 'mature module'...

Commensals in Animals

The mouth is one of the best-studied areas for commensal bacteria residence because of the regular influx of nutrients, presence of water and favorable pH, which provide numerous microniches that support bacterial growth. The mouth is also an excellent example of microbial succession over time. Newborns are bacteria free, but quickly obtain a microflora from passage through the birth canal, mother's skin (touching and during breast-feeding) and mouth (kissing), and from the environment. Many of these initial inhabitants are transient, but within a few months, streptococci and obligate anaerobes take residence. The upwelling of teeth at 6 months of age leads to a new set of microecosystems, including teeth enamel, which become colonized by Streptococcus sanguis and other bacteria. We start our lives alone, as bacteria-free organisms. Passage through the birth canal, kisses and hugs from parents and relatives, and suckling mother's milk exposes us to the organisms that will inhabit our...

A classification of survivorship curves

Survivorship Curves Oak Trees

Life tables provide a great deal of data on specific organisms. But ecologists search for generalities patterns of life and death that we can see repeated in the lives of many species. A useful set of survivorship curves was developed long ago by Pearl (1928) whose three types generalize what we know about the way in which the risks of death are distributed through the lives of different organisms (Figure 4.8). Type I describes the situation in which mortality is concentrated toward the end of the maximum lifespan. It is perhaps most typical of humans in developed countries and their carefully tended zoo animals and pets. Type II is a straight line that describes a constant mortality rate from birth to maximum age. It describes, for instance, the survival of seeds buried in the soil. Type III indicates extensive early mortality, but a high rate of subsequent survival. This is typical of species that produce many offspring. Few survive initially, but once individuals reach a critical...

Fecundity schedules and basic reproductive rates

This is followed in the next column by mx the individual fecundity or birth rate, i.e. the mean number of seeds produced per surviving individual. Although the reproductive season for the Phlox population lasts for 56 days, each individual plant is semelparous. It has a single reproductive phase during which all of its seeds develop synchronously (or nearly so). The extended reproductive season occurs because different individuals enter this phase at different times.

Adaptive decisionmaking and population dynamics

Imagine then a migratory bird population that breeds at one location in summer and then spends the winter in another site where it only feeds. Suppose one summer some of the winter-feeding habitat for the species is removed by a new housing development. What will happen to the population The modelling logic is roughly this (Goss-Custard and Sutherland 1997) the population migrating to the feeding ground for the winter must be packed into a smaller area of habitat. An ESS model such as the ideal free distribution is used to predict the relationship between bird density and per capita food intake rate in the new smaller habitat. By making some appropriate assumptions relating food intake to winter mortality, we can describe the relationship between density and mortality for the new smaller habitat. An ESS model can also be used to describe the way that bird breeding-habitat fills up and responds to density, and using some appropriate assumptions, how birth rate relates to density. The...

Aggregation of risk and spatial density dependence

Negative Density Dependence

How does this stability arise out of aggregation The answer lies in what has been called 'pseudo-interference' (Free et al., 1977). With mutual interference, as predator density increases, predators spend an increasing amount of time interacting with one another, and their attack rate therefore declines. With pseudo-interference, attack rate also declines with parasitoid density, but as a result of an increasing fraction of encounters being wasted on hosts that have already been attacked. The crucial point is that 'aggregation of risk' amongst hosts tends to increase the amount of pseudo-interference. At low parasitoid densities, a parasitoid is unlikely to have its attack rate reduced as a result of aggregation. But at higher parasitoid densities, parasitoids in aggregations (where most of them are) will increasingly be faced with host patches in which most or all of the hosts have already been parasitized. As para-sitoid density increases, therefore, their effective attack rate (and...

Net recruitment curves

An alternative general view of intraspecific competition is shown in Figure 5.8a, which deals with numbers rather than rates. The difference there between the two curves ( births minus deaths' or 'net recruitment') is the net number of additions expected in the population during the appropriate stage or over one interval of time. Because of the shapes of the birth and death curves, the net number of additions is small at the lowest densities, increases as density rises, declines again as the carrying capacity is approached and is then negative (deaths exceed births) when the initial density exceeds K (Figure 5.8b). Thus, total recruitment into a population is small when there are few individuals available to give birth, and small when intraspecific competition is intense. It reaches a peak, i.e. the population increases in size most rapidly, at some intermediate density.

Population and urban structure

Australia is well recognized for its low population and population density (17529000 inhabitants and 2.3 inhabitants per square kilometer, respectively, in 1992 ABS 1994b). Australia also has an aging population, with population growth due not so much to domestic birth rates as to high immigration rates (ABS 1994b). Australia has one of the highest proportions of urban population in the world (85 per cent in 1990) and urban growth remains steady (UNEP 1991). As discussed above, Australia's urban structure is highly resource-intensive. Hahn (1991) offers some excellent ecological urban restructuring strategies which could be applied, with local variations, to help dematerialize Australia's urban structure.

Xenarthrans Edentates

For most of their lives they hang from limbs in the crowns of trees, a position they maintain while eating, sleeping, mating, and giving birth. They descend to the ground once or twice a week to urinate and defecate, and will occasionally descend and move awkwardly along the ground to another tree. Two-toed sloths (Choloepus) have long limbs, with the front limbs being only slightly longer than the hind limbs. Their feet are narrow and curved, with two digits on the front feet and three on the hind. All digits of each foot are bound together by skin. The claws are very long, laterally compressed, and recurved. Three-toed sloths (Bradypus) have three digits on both front and hind feet, and each digit bears a long, recurved claw. The front limbs are much longer than the hind. Both kinds of sloths hang from branches by their long limbs and grappling claws. The tail is absent or vestigial in Choloepus but short and blunt in Bradypus. Tree sloths have shaggy,...

Using Corridors to Connect Disjunct Portions of Habitat

Habitat corridors offer another way for managing ecosystems beyond the immediate boundaries of core protected areas. In the past, most species lived in landscapes of well-connected habitats, but human activities increasingly fragment these habitats into smaller and smaller patches. The concept of wildlife corridors was developed to minimize the impact of fragmentation and enhance connectivity. Corridors are linear strips of land linking habitat patches. Ideally, they allow species to move among different areas for breeding, birthing, feeding, roosting, annual migrations, and dispersal of young animals away from their parents and to escape from predators or disturbance. Corridors may be a natural feature of a landscape, such as a riverbank, or they may be created intentionally to connect existing protected areas that are too small to sustain wide-ranging or area-sensitive species (such as cougars, grizzly bears, and tigers). Corridors can be many sizes, from a narrow hedgerow only a...

Chondrichthyes Sharks Rays Chimaeras

Sharks Intromittent Organ

Through maternal-fetal connections, and stingrays produce uterine milk. Even intrauterine cannibalism has been documented (mackerel sharks). Gestation strategies vary within certain orders, but about 40 percent of all species (including catsharks, skates, chimaeras) lay egg cases, while the rest give birth to live young directly. More than one egg is fertilized at a time, and there is no rearing of the pups after birth. Chondrichthyans sexually mature at advanced ages in comparison to bony fishes (more than thirty years for some species), produce relatively few young per gestation, and may have prolonged gestation periods (more than two years for the spiny dogfish).

Modeling hunting patterns from tusks in the ivory trade

The enormous volume of the international trade in African elephant tusks during the 1970s and 1980s generated the basic information on mortality patterns to explore population dynamics through simulations. Tom Pilgram and David Western used data on sizes of tusks that originated in Kenya and Tanzania to generate age structures for male and female elephants killed (appendix 2). They then used a deterministic Leslie matrix model to simulate and interpret the mortality patterns seen from the ivory trade. Reproduction was taken to be density dependent following Richard Laws and the Fowler-Smith model. Changes in birth rate with density, however, were varied in a stepwise fashion rather than as a continually varying function. Age at sexual maturity was set at 10 years and intercalving interval at 3 years at the lowest population density. These were increased by 0.5 year each year the population exceeded a set target. Mortality rates were based on studies by Richard Laws, Timothy Cor-field,...

Evolution of life history traits in elephants

The term life history broadly refers to a host of anatomical, physiological, and behavioral characteristics of a species, although it is often restricted to demographic traits, such as age-specific birth and death rates, or developmental traits, such as growth rates and body size. While aspects of reproductive behavior, social organization, or feeding ecology in elephants have been recognized as the outcome of natural selection, there has been little attempt to discuss demographic traits in populations in relation to selective forces. A possible exception is the discussion of changes in birth rates with density, for which the evidence in any case is equivocal. There has been insufficient appreciation of the possible influence of habitat and its characteristics in the evolution of (demographic) life history phenomena in elephant populations. Elephants after all inhabit regions from near-desert conditions to tropical lowland rain forests and montane forests. Adaptations needed to deal...

Responding to the challenges ahead

By two World Wars during the first part of the twentieth century gave birth to today's formal international system, intended to preserve global peace and foster collaboration among nations. Globalization has brought the world back full circle to the same fundamental challenges that public health pioneers in faced in the late nineteenth century, only on a global scale (see Figure 16.2).


Age distribution The number of individuals of each age in a population. When the birth rate and survival rates for each age remain unchanged for a long period of time, the population acquires a stable age distribution and the population will grow or decline at a constant rate per head. When the population is not changing in size, the stable age distribution is called the stationary age distribution. Such a population will usually have more older and fewer younger individuals than a growing population.

Types of models

Here dN dt measures the instantaneous growth of the population, N. On the left side of the equation, the symbol d is used to indicate change in N per change in the time interval, t. The intrinsic rate of increase, r (Eqn. 1.1a), measures the per capita birth rate minus the per capita death rate during these same small time intervals. In a sense, r measures the probability of a birth minus the probability of a death occurring in the population during a particular time interval.

Famine and Fate

Many other factors such as temperature, pH, oxygen concentration, inorganic and organic nutrients are necessary for many living creatures. Yet other constituents of aquatic ecosystems, which affect the growth and decline of plankton populations are parasites, fungi, and diseases. These factors can limit the population's performance the outcome is often that death rates equal birth rates and thus the population size reaches a stable stage.

Names and Symbols

Quantities should be read as names ( per capita birth rate ), not as symbols (B N), because a name conveys more meaning. Symbols appear in mathematical expressions for the sake of clarity and in prose for the sake of preciseness, but when encountered symbols should still be read as names. Facility in reasoning with quantities comes in associating a name with a symbol, with a mental image of the biology, and with some typical values. For example, the quantity per capita birth rate is associated with a symbol B N and with an image of the quantity, such as chicks jumping out of the nest of a pair of adult birds each year. Name, symbol, and image are further associated with a typical value obtained from calculation

Primer Pheromones

Many lambs are born to the flock in a short period of time, so each mother (ewe) needs to recognize her offspring to avoid the risk of erroneously distributing limited resources to alien neonates. An enduring bond between a mother and her lamb is usually established within 2 h after giving birth (parturition). The sensitive period for learning lasts 4-12 h after giving birth, and if ewes are deprived of their lamb during this period, the bond fails to develop. Perceiving olfactory cues of the lamb during this period triggers a cascade of neurochemi-cal and hormonal mechanisms, causing the mother to lick the amniotic fluid and learn the individual odors of her lamb. Afterward, she will exclusively nurse her own lambs, which she selectively recognizes by their smell. The lamb's odor phenotype, which acts as priming pher-omone, is influenced by a combination of genetic processes and environmental factors such as cues from the mother's saliva or milk.


For some particular cases of populations with non-overlapping generations we found that winter conditions can play the role of stabilizing regulator. Also, we found that even in the simplest cases when there is no self-regulation in population and the impacts of winter conditions are described by an exponential or fractional-linear function, we have a non-linear dependence of the birth rate on the parameter describing the influence of winter conditions on the population dynamics. Consequently, all models ( 11 , 49 , 24 , 21 , 20 ) of population dynamics that were constructed under the assumption of linear dependence of the birth rate on weather parameters need serious modifications.