Unit – 7A
Population Dynamics covering
Population dynamics is a dominant branch of mathematical biology, which has its history of more than 200
years, while more recently the scope of mathematical biology has greatly expanded.
In population dynamics we study short term and long term changes in the size and age composition of the population and the biological and environmental processes influencing those changes. It is the study of how population changes over time. Population dynamics overlap with other branches of research in mathematical biology, viz. mathematical epidemiology, the study of infectious disease affecting population. In last few decades Population dynamics has been complemented by evolutionary game theory, which was first developed by John Maynard Smith.
POPULATION GROWTH OF INDIA
Population of the India is currently growing at a rate of 1.44% per year, far surpassing China’s rate of 0.7%. This difference will result in India’s population size overtaking China's in less than 20 years. Differences in growth rate of southern Indian states and empowered action group (EAG) states, especially major states, Bihar, Madhya Pradesh, Rajasthan, Uttar Pradesh and Orissa are responsible for high growth rate (1.44% per year) of the country.
n 1952, India was the first country in the world to launch a national programme, emphasizing family planning to the extent necessary for reducing birth rates “to stabilize the population at a level consistent with the requirement of national economy. After1952, sharp declines in death rates were however not accompanied by similar drop in birth rates. The National health policy 1983 stated that replacement level of total fertility rate (TFR, 2.1) should be achieved by the year 2000. On May 2000 India was projected to have 1 billion (100 crore) people i.e. 16% of world population on 2.4% of global land area. As per 2001 Census, population of India was enumerated 1027 million on 31st march 2001, and country was observed in the middle of demographic transition. A lag in decline in fertility in relation to mortality has resulted in the sizeable growth of India’s population so for which will continue in the coming several decades. Decline in population growth process has been witnessed since 1980. The National population policy (NPP) -2000 documents clearly stated that population growth in India continues to be high on account of demographic momentum (estimated contribution 58%), higher unwanted fertility due to unmet need of contraception (estimated contribution 20%). India is at some point of demographic transition. As a result, a “bulge” or baby boom, generation distinctly larger than those preceding or following it, is moving through the age structure of population. These large cohorts create both opportunities and challenges for society. As this cohort moves into working age group; it will be potentially higher share of workers as compared with dependent population. If current trend is continued, India may overtake China in2045 to the most populous country of the world. While global population has increased three times during this century from 2 billion to 6 billion. The population of India has increased nearly five times from 238 million (23 crores) to 1 billion in the same period. India’s current annual increase in population of 15.5 million is large enough to neutralize efforts to conserve the resource endowment and environment.
THE COMPOSITION OF POPULATION
The population dynamics includes birth rates, death rates, immigration, and emigration age and sex composition. Birth and death rates, immigration and emigration are the four primary ecological events that influence the size of a population. This relationship can be expressed in a simple equation.
Change in population = (Birth + Immigration) - (Death + Emigration).
Birth and death rates are the most important determinants of population growth; in some countries net migration is also important. Until the mid-19th century birth rates were slightly higher than death rates, so the human population grew very slowly. Demographic profiles of the Indian states vary from region to region and state to state. Thus, heterogeneity in demographic profiles of the Indian states affects its population composition. Heterogeneity in demographic profiles of the six southern states (Andhra Pradesh, Karnataka, Kerala, Tamil Nadu, Maharashtra and Goa) and eight empowered action group (EAG) states (viz. Rajasthan, Uttar Pradesh, Uttarakhand, Bihar, Jharkhand, Madhya Pradesh, Chhattisgarh and Orissa) are very significant.
Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment, such as birth and death rates, and by immigration and emigration).
The discipline is important in conservation biology, especially in the development of population viability analysis which makes it possible to predict the long-term probability of a species persisting in a given patch of habitat.Although population ecology is a subfield of biology, it provides interesting problems for mathematicians and statisticians who work in population dynamics.
The population has the following characteristics:
1. Population Size and Density:
Total size is generally expressed as the number of individuals in a population.
Population density is defined as the numbers of individuals per unit area or per unit volume of environment. Larger organisms as trees may be expressed as 100 trees per hectare, whereas smaller ones like phytoplanktons (as algae) as 1 million cells per cubic metre of water.
In terms of weight it may be 50 kilograms of fish per hectare of water surface. Density may be numerical density (number of individuals per unit area or volume) when the size of individuals in the population is relatively uniform, as mammals, birds or insects or biomass density (biomass per unit area or volume) when the size of individuals is variable such as trees.
Since, the patterns of dispersion of organisms in nature are different population density is also differentiated into crude density and ecological density.
a. Crude density:
It is the density (number or biomass) per unit total space.
b. Ecological density or specific or economic density:
It is the density (number or biomass) per unit of habitat space i.e., available area or volume that can actually be colonized by the population.
This distinction becomes important due to the fact that organisms in nature grow generally clumped into groups and rarely as uniformly distributed. For example, in plant species like Cassia tora, Oplismemis burmanni, etc, individuals are found more crowded in shady patches and few in other parts of some area. Thus, density calculated in total area (shady as well as exposed) would be crude density, whereas the density value for only shady area (where the plants actually grow) would be ecological density.
2. Population dispersion or spatial distribution:
Dispersion is the spatial pattern of individuals in a population relative to one another. In nature, due to various biotic interactions and influence of abiotic factors, the following three basic population distributions can be observed:
(a) Regular dispersion:
Here the individuals are more or less spaced at equal distance from one another. This is rare in nature but in common is cropland. Animals with territorial behaviour tend towards this dispersion.
(b) Random dispersion:
Here the position of one individual is unrelated to the positions of its neighbours. This is also relatively rare in nature.
(c) Clumped dispersion:
Most populations exhibit this dispersion to some extent, with individuals aggregated into patches interspersed with no or few individuals. Such aggregations may result from social aggregations, such as family groups or may be due to certain patches of the environment being more favourable for the population concerned.
3. Age structure:
In most types of populations, individuals are of different age. The proportion of individuals in each age group is called age structure of that population. The ratio of the various age groups in a population determines the current reproductive status of the population, thus anticipating its future. From an ecological view point there are three major ecological ages in any population. These are, pre-reproductive, reproductive and post reproductive. The relative duration of these age groups in proportion to the life span varies greatly with different organisms.
Age pyramid:
The model representing geometrically the proportions of different age groups in the population of any organism is called age pyramid. According to Bodenheimer (1938), there are following three basic types of age pyramids.
(a) A pyramids with a broad base (or triangular structure):
It indicates a high percentage of young individuals. In rapidly growing young populations birth rate is high and population growth may be exponential as in yeasty house fly, Paramecium, etc. Under such conditions, each successive generation will be more numerous than the preceding one, and thus a pyramid with a broad base would result (Fig. A).
(b) Bell-Shaped Polygon:
It indicates a stationary population having an equal number of young and middle aged individuals. As the growth rate becomes slow and stable, i.e., the pre-
reproductive and reproductive age groups become more or less equal in size, post-reproductive group remaining as the smallest (Fig. B).
(c) An urn-shaped structure:
It indicates a low percentage of young individuals and shows a declining population. Such an un-shaped figure is obtained when the birth rate is drastically reduced the pre-reproductive group dwindles in proportion to the other two age groups of the population. (Fig. C).
4. Natality (birth rate):
Population increases because of natality. It is simply a broader term covering the production of new individuals by birth, hatching, by fission, etc. The natality rate may be expressed as the number of organisms born per female per unit time. In human population, the natality rate is equivalent to the birth-rate. There are distinguished two types of natality.
(a) Maximum natality:
Also called as absolute or potential or physiological natality, it is the theoretical maximum production of new individuals under ideal conditions which means that there are no ecological limiting factors and that reproduction is limited only by physiological factors. It is a constant for a given population. This is also called fecundity rate.
(b) Ecological natality:
Also called realized natality or simply natality, it is the population increase under an actual, existing specific condition. Thus it takes into account all possible existing environmental conditions. This is also designated as fertility rate.
Natality is expressed as
∆Nn/∆ t = Absolute Natality rate (B)
∆Nn/N ∆ t = Specific natality rate (b) (i.e., natality rate per unit of population).
Where N = initial number of organisms.
n = new individuals in the population.
t = time.
Further, the rate at which females produce offsprings is determined by the following three population characteristics:
(a) Clutch size or the number of young produced on each occasion.
(b) The time between one reproductive event and the next and
(c) The age of first reproduction.
Thus, Natality usually increases with the period of maturity and then falls again as the organism gets older.
5. Mortality (death rate):
Mortality means the rate of death of individuals in the population. Like natality, mortality may be of following types:
(a) Minimum mortality:
Also called specific or potential mortality, it represents the theoretical minimum loss under ideal or non-limiting conditions. It is a constant for a population.
(b) Ecological or realised mortality:
It is the actual loss of individuals under a given environmental condition. Ecological mortality is not constant for a population and varies with population and environmental conditions, such as predation, disease and other ecological hazards.
In evolutionary ecology, an ecotype sometimes called ecospecies, describes a genetically distinct geographic variety, population or race within a species, which is geno typically adapted to specific environmental conditions.
An ecotype is a variant in which the phenotypic differences are too few or too subtle to warrant being classified as a subspecies. These different variants can occur in the same geographic region where distinct habitats such as meadow, forest, swamp, and sand dunes provide ecological niches. Where similar ecological conditions occur in widely separated places, it is possible for a similar ecotype to occur in the separated locations. An ecotype is different than a subspecies, which may exist across a number of different habitats. In animals, ecotypes owe their differing characteristics to the effects of a very local environment. Therefore, ecotypes have no taxonomic rank.
Ecotypes are closely related to morphs. In the context of evolutionary biology, genetic polymorphism is the occurrence in the equilibrium of two or more distinctly different phenotypes within a population of a species, in other words, the occurrence of more than one form or morph. The frequencyof these discontinuous forms (even that of the rarest) is too high to be explained by mutation In order to be classified as such, morphs must occupy the same habitat at the same time and belong to a panmictic population (whose all members can potentially interbreed). Polymorphism is actively and steadily maintained in populations of species by natural selection (most famously sexual dimorphism in humans) in contrast to transient polymorphisms where conditions in a habitat change in such a way that a "form" is being replaced completely by another.
Range and distribution
Experiments indicate that sometimes ecotypes manifest only when separated by great spatial distances (of the order of 1,000 km). This is due to hybridization whereby different but adjacent varieties of the same species (or generally of the same taxonomic rank) interbreed, thus overcoming local selection. However, other studies reveal that the opposite may happen, i.e., ecotypes revealing at very small scales (of the order of 10 m), within populations, and despite hybridization.
In ecotypes, it is common for continuous, gradual geographic variation to impose analogous phenotypic and genetic variation. This situation is called cline. A well-known example of a cline is the skin colour gradation in indigenous human populations worldwide, which is related to latitude and amounts of sunlight. But often the distribution of ecotypes is bimodal or multimodal. This means that ecotypes may display two or more distinct and discontinuous phenotypes even within the same population. Such phenomenon may lead to speciation and can occur if conditions in a local environment change dramatically through space or time.
Population genetics is the study of genetic variation within populations, and involves the examination and modelling of changes in the frequencies of genes and alleles in populations over space and time. Many of the genes found within a population will be polymorphic - that is, they will occur in a number of different forms (or alleles). Mathematical models are used to investigate and predict the occurrence of specific alleles or combinations of alleles in populations, based on developments in the molecular understanding of genetics, Mendel's laws of inheritance and modern evolutionary theory. The focus is the population or the species - not the individual.
Gene pool and genetic diversity
Genetic diversity is the total number of genetic characteristics in the genetic makeup of a species, it ranges widely from the number of species to differences within species and can be attributed to the span of survival for a species. It is distinguished from genetic variability, which describes the tendency of genetic characteristics to vary.
Genetic diversity serves as a way for populations to adapt to changing environments. With more variation, it is more likely that some individuals in a population will possess variations of alleles that are suited for the environment. Those individuals are more likely to survive to produce offspring bearing that allele. The population will continue for more generations because of the success of these individuals.
The academic field of population genetics includes several hypotheses and theories regarding genetic diversity. The neutral theory of evolution proposes that diversity is the result of the accumulation of neutral substitutions. Diversifying selection is the hypothesis that two subpopulations of a species live in different environments that select for different alleles at a particular locus. This may occur, for instance, if a species has a large range relative to the mobility of individuals within it.
The collection of all the alleles of all of the genes found within a freely interbreeding population is known asthe gene pool of the population. Each member of the population receives its alleles from other members of the gene pool (its parents) and passes them on to other members of the gene pool (its offspring). Population genetics is the study of the variation in alleles and genotypes within the gene pool, and how this variation changes from one generation to the next.
Factors influencing the genetic diversity within a gene pool include population size, mutation, genetic drift, natural selection, environmental diversity, migration and non-random mating patterns. The Hardy-Weinberg model describes and predicts a balanced equilibrium in the frequencies of alleles and genotypes within a freely interbreeding population, assuming a large population size, no mutation, no genetic drift, no natural selection, no gene flow between populations, and random mating patterns.
In biology, polymorphism is the occurrence of two or more clearly different morphs or forms, also referred to as alternative phenotypes, in the population of a species.
Put simply, polymorphism is when there are two or more possibilities of a trait on a gene. For example, there is more than one possible trait in terms of a jaguar's skin colouring; they can be light morph or dark morph. Due to having more than one possible variation for this gene, it is termed 'polymorphism'. However, if the jaguar has only one possible trait for that gene, it would be termed "monomorphic". For example, if there was only one possible skin colour that a jaguar could have, it would be termed monomorphic.
The term polymorphism can be used to clarify that the different forms arise from the same genotype. Genetic polymorphism is a term used somewhat differently by geneticists and molecular biologists to describe certain mutations in the genotype, such as single nucleotide polymorphisms that may not always correspond to a phenotype, but always corresponds to a branch in the genetic tree.
Polymorphism is common in nature; it is related to biodiversity, genetic variation, and adaptation. Polymorphism usually functions to retain variety of form in a population living in a varied environment. The most common example is sexual dimorphism, which occurs in many organisms. Other examples are mimetic forms of butterflies (see mimicry), and human haemoglobin and blood types.
According to the theory of evolution, polymorphism results from evolutionary processes, as does any aspect of a species. It is heritable and is modified by natural selection. In polyphenism, an individual's genetic makeup allows for different morphs, and the switch mechanism that determines which morph is shown is environmental. In genetic polymorphism, the genetic makeup determines the morph.
The term polymorphism also refers to the occurrence of structurally and functionally more than two different types of individuals, called zooids, within the same organism.
References:
1. Žiga Turk (2014), Global Challenges and the Role of Civil Engineering, Chapter 3 in: Fischinger M. (eds) Performance-Based Seismic Engineering: Vision for an Earthquake Resilient Society. Geotechnical, Geological and Earthquake Engineering, Vol. 32. Springer, Dordrecht
2. Brito, Ciampi, Vasconcelos, Amarol, Barros (2013) Engineering impacting Social, Economical and Working Environment, 120th ASEE Annual Conference and Exposition
3. NAE Grand Challenges for Engineering (2006), Engineering for the Developing World, The Bridge, Vol 34, No.2, Summer 2004.
4. Allen M. (2008) Cleansing the city. Ohio University Press. Athens Ohio.
5. Ashley R., Stovin V., Moore S., Hurley L., Lewis L., Saul A. (2010). London Tideway Tunnels Programme – Thames Tunnel Project Needs Report – Potential source control and SUDS applications: Land use and retrofit options
6. Ashley R M., Nowell R., Gersonius B., Walker L. (2011). Surface Water Management and Urban Green Infrastructure. Review of Current Knowledge. Foundation for Water Research FR/R0014
7. Barry M. (2003) Corporate social responsibility – unworkable paradox or sustainable paradigm? Proc ICE Engineering Sustainability 156. Sept Issue ES3 paper 13550. p 129-130
8. Blackmore J M., Plant R A J. (2008). Risk and resilience to enhance sustainability with application to urban water systems. J. Water Resources Planning and Management. ASCE. Vol. 134, No. 3, May.
9. Bogle D. (2010) UK’s engineering Council guidance on sustainability. Proc ICE Engineering Sustainability 163. June Issue ES2 p61-63
10. Brown R R., Ashley R M., Farrelly M. (2011). Political and Professional Agency Entrapment: An Agenda for Urban Water Research. Water Resources Management. Vol. 23, No.4. European Water Resources Association (EWRA) ISSN 0920-4741.
11. Brugnach M., Dewulf A., Pahl-Wostl C., Taillieu T. (2008) Toward a relational concept of uncertainty: about knowing too little, knowing too differently and accepting not to know. Ecology and Society 13 (2): 30
12. Butler D., Davies J. (2011). Urban Drainage. Spon. 3rd Ed.
13. Cavill S., Sohail M. (2003) Accountability in the provision of urban services. Proc. ICE. Municipal Engineer 156. Issue ME4 paper 13445, p235-244.
14. Charles J A. (2009) Robert Rawlinson and the UK public health revolution. Proc ICE Eng History and Heritage. 162 Nov. Issue EH4. p 199-206
