 The topic for today is dynamics in a population, but before we move further, we need to define a few terms. Say for example, a group of individuals belonging to the same species occupying the same place at the same time is what we call as a population. When we study population, this is an area in population ecology concerned with factors influencing its expansion, decline and maintenance. So this includes the effects of four demographic processes such as births, deaths, immigration and emigration. So why is the study of population dynamics important? We need this for the conservation of diverse plants and animals. This determines whether or not a species is going extinct. Population dynamics is also useful in controlling noxious pests, including human parasites and pathogens. We also use our knowledge of population dynamics in maintaining economically important plant and animal populations. For example, we have the social insects such as bees from the species apismilifera. Bees, for example, have a caste system that means they have an egg laying queen which reproduces around 1500 eggs a day. And workers who take care of the younger bees, they get food, they get pollen, they also protect the colony. They also even maintain the temperature of the colony. And drones, which are the male portion of the population that mates with a queen. Knowing the dynamics of these bees ensures more honey production for the beekeeper. So demography actually describes population throughout the life cycle of an organism. This is commonly used in human populations, but for today we use it for generalistic purposes. So populations are affected by birth or we call also as natality. When members of the population die, this is what we term as mortality, immigration are new members of the population entering the system or entering the population, but not through birth. And some members of the population also leave it thereby reducing population size through emigration. And emigration happens because of some dispersal mechanisms of certain populations. Spiderlings, for example, these are baby spiders. They produce silk, they hang on to the tips of leaves and they produce silk and wait for the wind to take them wherever they want to. This allows for the species to be dispersed and also prevents competition from happening. Dispersal can either increase or decrease population densities. This could lead to population expansion resulting to increase in geographic range. Say, for example, the ballooning effect of spiders. And these normally happens when environmental conditions in the original habitat become unfavorable. Say, for example, the food is no longer available. These species expand through dispersal mechanisms. There are inherent intrinsic population growth mechanisms and these arise because of the reproductive ability of individuals in the population. We compute this using the formula Nt plus 1 equals birth plus emigration minus death plus emigration. So B here is represented by the per capita birth rate and D is represented by the per capita death rate. Such that if B or the per capita birth rate is greater than D, we assume that the population is increasing. On the other hand, if B is less than the death rate of the population, we have to expect a population decline. Biotic potential is the property of capacity of population to multiply. They have a maximum reproductive rate for each organism and this is normally high for most species. And biotic potential is also influenced by the sex ratio and the age distribution. So a favorable environment enables the species to realize their full biotic potential and population shall increase. So ecologists, whether they are plant ecologists or animal ecologists, determine methods by which population occurs at any given time. And this is represented as R or the percent increase. So in this formula, you will be seeing changes in population at time T, which is N sub T and N sub T minus 1, which is the previous population size. So T would be the time interval between T and T minus 1. So for example, you have the Philippine population size of 86.97 million in 2006. By 2012, it became 97.1. The percent increase shall now be 1.94 or the R being 0.0194. So population growth as predicted in this equation is adapted from this formula. So you see the change in population, the T sub N over the T over time, you have R max times N. The R max is the intrinsic rate of increase. This is what we term as the Lotcavolterra equation. So if you represent this equation into a graph, you'll have a J-shaped curve. That means population size is increasing indefinitely. However, we have to realize that there are environmental limits to population growth, changing birth and death rates within carrying capacity of the environment. We represent carrying capacity as K. So from the original formula, the R max multiplied by N, which is the number of individuals, is now changed to the effect of carrying capacity which is K minus N over K. That is what we term as logistic growth. Here we have a feedback mechanism operating. So in this case, it is no longer a J-shaped curve. It is now S-shaped in nature. This is what we term as a sigmoidal or logistic population growth curve. So what are the parts of this curve? It starts out as a lag phase, wherein there is a small population size. The resources are abundant and because the resources are abundant, population will then steadily increase, producing an exponential phase. But realizing that the environment has limits, there's carrying capacity. The environment can only support a specific number of individuals. So we can go into a stationary phase, wherein there is zero population growth and carrying capacity is reached. And at that point, competition and other biotic inaction also increase, thereby leading to what we call as the death phase. At this point, the population has exceeded carrying capacity. So this is another illustration wherein a lag phase, the carrying capacity is reached, showing you biotic interaction pushing onto population size. Now let's deal with environmental resistance. These are limiting factors. When we say limiting factors, it could be in the form of raw materials, energy supply, accumulation of waste products, and this is also influenced by the carrying capacity of the environment. Humans, for example, have increased the carrying capacity of the environment by pursuing different technologies like culture, fisheries. So we have extended our limits. So at this point, we suspend the first discussion on nature's way of converting exponential to logistic population growth. We now move on to the discussion on the properties of the population, specifically age structure and survivorship curve. Carrying capacity changes with changes in the environment. Humans have increased capacity. For example, we have pursued agriculture to increase our food needs. We also construct buildings to increase our need to occupy habitations that are previously limited to us. So these are examples by which humans have increased carrying capacity.