"THE STRUGGLE FOR SURVIVAL" "There is a fierce struggle in a bid for life's essentials." "Mutual tolerance, momentary unions, and social and moral instincts are all part of this struggle, which governs evolution through the process of elimination examined here." "UNLIMITED GROWTH OF A POPULATION" "Consider a population of rodents in good living conditions." "DESCENDANTS OF A PAIR OF MICE UNDER IDEAL CONDITIONS this population doubles every two months." "Without dangerous enemies, and with plentiful food, the population grows indefinitely, without limit." "This graph shows this growth, with time on the horizontal axis and the number of individuals on the vertical axis." "Among invertebrates such as locusts the even more rapid pace of procreation means that a single pair would generate, over a few years, a total mass of descendants greater than Earth's mass." "A steady birth rate is represented by a straight line, as is a steady mortality rate." "Under these theoretical conditions a consistently greater number of births compared with deaths would result in unlimited growth of the population." "In practice, a number of obstacles check population growth." "SHORTAGE OF FOOD" "SHORTAGE OF SPACE" "PREDATORS" "EPIDEMICS the introduction of these limiting factors competition WITHIN A SPECIES halts population growth, OR BETWEEN DIFFERENT SPECIES which then reaches a saturation po�nt representing a state of equilibrium with the environment." "When the growth of a population is regularly limited, it's known as a logistic population." "population GROWTH WHICH IS REGULARLY LIMITED is KNOWN AS A LOGISTIC population" "A population of Drosophila reaches an equilibrium, or saturation po�nt, over 45 days with 346 individuals." "The state of equilibrium reached an era theoretically unlimited time is therefore reached in practice in a very short period of time." "OVERALL EFFECT OF LIMITING FACTORS" "A population can reach its limit not only in a steady fashion, as in the case of a logistic population, but in any manner." "Every time two individuals encounter one another competition comes into play." "This competition is one of the principal limiting factors." "MATHEMATICAL ANALYSIS OF THE LIMITING FACTOR OF competition in LOGISTIC DEVELOPMENT - HOMOGENEOUS population." "A calculation of the probabilities demonstrates that the total number of encounters is proportional to the square of the population when the population is sufficiently large." "We can thus conclude that the overall effect of the limiting factor of competition is proportional to N2/2," "A LOGISTIC EXAMPLE-." "THE DEVELOPMENT OF THE USA" "Between 1790 and 1930 the enormous size of the United States and its resources counterbalanced all disturbances - war and civil war, conquest, immigration, economic crisis - and population growth followed a logistic law." "But this law, setting a maximum of 20 inhabitants per square kilometer, must be replaced by a new law when this maximum is exceeded, as is the case in Belgium, with 266 inhabitants per square kilometer." "population WITH IRREGULAR GROWTH" "NON-LOGISTIC population-." "E. COLI" "In other cases due to a shortage of food or space, or a build up of organic waste, equilibrium is never reached, and the increase in mortality leads to the complete disappearance of the population." "PRINCIPLE OF ENCOUNTERS IN A mixed population" "Now consider competition not between individuals of the same species but between individuals of different species." "According to the principle of encounters, competition is proportional to the product of the number of individuals of each species" " M x N." "the struggle for survival between different species ends either in the total or partial disappearance of the species or in a fixed or fluctuating equilibrium." "1." "TOTAL DISAPPEARANCE take one species of acarids, the Aleuroglyphus, which eats flour, and a larger species, Cheyletus, which eats only the first species." "Then mix the two species." "elimination OF A PREY GROUP BY PREDATORS" "The prey acarids eventually die out, and their disappearance leads to the disappearance of the predator acarids, because the predator does not eat flour and there's nothing else to eat." "2." "PARTIAL DISAPPEARANCE" "TWO COMPETITORS FOR A COMMON FOOD SOURCE lf we consider population growth in each group separately," "both reach a state of equilibrium," "This graph shows the population growth of the Glaucoma scintillans." "This one shows the population growth of the Paramecium aurelia." "If we now mix the two species, the Paramecium dies out... as there is no longer enough food for it." "3." "PERFECT EQUILIBRIUM" "RESULTING EQUILIBRIUM IN A MIXED population" "Now let us consider cultures of Paramecium aurelia and Paramecium bursaria." "If we mix the two populations, we can see a resulting equilibrium for both species, with a high threshold for the bursaria and a low threshold for the aurelia." "In the graph on the left, there are two lines showing the number of bursaria and the number of aurelia at each point." "In the graph on the right, the number of individuals of each species is represented by one coordinate of each point on the line, with the time marked alongside that." "4." "FLUCTUATING EQUILIBRIUM" "Barnacles which are sessile crustaceans are invaded by mussels... and eaten by the Murex mollusk." "The mollusk population decreases after they've cleared the rocks." "A new batch of barnacle larva can then settle and the cycle starts over," "The phenomenon was set out by the well-known mathematician Volterra as the Law of the Periodic Cycle." "Prey which cannot be totally wiped out by predators decrease in number and thus bring about a decrease in number in the predator species." "This leads to the possibility of an increase in prey, quickly followed by an increase in predators." "The oscillations always center around the same average values for the numbers of prey and predators." "This is Volterra's Second Law," "Changes in the conditions supporting life bring about changes in these average values, for example, when fishing in the Adriatic Sea was interrupted between 1915 and 1918 the number of predators increased due to the more plentiful prey." "Hence Volterra's Third Law,- the Disturbance of Averages." "If the number of predators decreases, the number of prey increases, and if the number of prey decreases, the number of predators decreases," "Extremely complex biological equations show that the probability of a stable or cyclical equilibrium is low compared to the probability of the total disappearance of the constituent populations and becomes lower still as the size of the population of the species increases." "An inheritable change can arise within an individual in a species - a mutation." "Thus, among normal Drosophila, there are mutations with bean-shaped eyes, fringed wings, no wings, and so on..." "hybridization - PEAS WITH RED/WHITE FLOWERS" "The same is true for peas." "The population contains examples of the parent species, examples of the mutated species, and hybrids resulting from the crossing of the two species." "Mendel's laws give the following proportions for the descendants." "White and red- four hybrids." "Two hybrids - one red, two hybrids, and one white." "One red and one hybrid- two red and two hybrids." "One white and one hybrid- two white and two hybrids." "We find the same results with corn... where there are yellow grains, blue grains, and the hybrid violet grains." "One yellow and one blue give four hybrids." "Two hybrids give one yellow, two hybrids, and one blue." "One yellow and one hybrid give two yellow and two hybrids." "And one blue and one hybrid give two blue and two hybrid." "Hybrids are fragile and can be considered virtually nonviable." "They will therefore die out except where very unusual circumstances favor them,- geographical or physiological isolation, human intervention, etc." "Because mutated examples are generally uncommon, and since they cannot rely on hybrids to maintain a new species, such a new species will ultimately be eliminated by the parent species, even if it shows an adaptive advantage over this parent species." "This results in great stability within species, with, however an undeniable evolution if we allow a period of time long enough for infinitely small probabilities in the development of a mutation to come into play." "Thus, in the evolution of the horse it took millions of years for the ancestral form the size of a fox to evolve to its modern-day form."