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6 Populations Factors that Regulate Population Abundance and Distribution • • • • • Population size- symbol N- total number of individuals within a defined area at a given time. Population density- number of individuals/unit area Population distribution- how individuals are distributed with respect to one another. Population sex ratio- the ratio of males to females Population age structure- how many individuals fit into particular age categories. Populations Are Patchy in Space and Dynamic over Time Population distribution Abundance varies on several spatial scales. Geographic range—region in which a species is found Within the range, species may be restricted to specific environments or habitats. Habitat patches are “islands” of suitable habitat separated by areas of unsuitable habitat. Factors that Influence Population Size • • • • Density-dependent factors- size of the population will influence an individual’s probability of survival. Resources, space, food, water, etc Density-independent factors- size has no effect on the individual’s probability of survival. Disease, hunting, development Populations Are Patchy in Space & Dynamic over Time Density of one species population may be related to density of other species populations. Concept 43.5 Extinction and Recolonization Affect Population Dynamics Small subpopulations in habitat patches are vulnerable to environmental disturbances and chance events and may go extinct. Individuals from other subpopulations can recolonize the patch if dispersal is possible. Think oak trees, deer and tick populations. Exponential Growth Model • J-shaped curve- when graphed the exponential growth model looks like this. Concept 43.4 Populations Grow Exponentially, but Not for Long. Why? Population growth is multiplicative—(exponential) an ever-larger number of individuals is added in each successive time period. Logistic Growth Model • • Logistic growth- population growth is initially exponential, but slows as the population approaches the carrying capacity. when graphed the logistic growth model produces an “S”. Concept 43.4 Populations Grow Exponentially, but Not for Long Exponential growth has a constant doubling time. The time it takes a population to double in size can be calculated if r (rate) is known. To calculate :doubling time=70/r, AKA , Rule of 70. Example how many years will it take to double a population if rate increase is 20%? 3.5 years this graph shows Rate –r slows when population Reaches K=carrying capacity Steady state Variations of the Logistic Model • If food becomes scarce, the population will experience an overshoot by becoming larger than the spring carrying capacity and will result in a die-off, or population crash. Reproductive Strategies • • K-selected species- the population of a species that grows slowly until it reaches the carrying capacity. • Ex. elephants, whales, and humans. R-selected species- the population of a species that grows quickly and is often followed by overshoots and die-offs. • Ex. mosquitoes and dandelions Which animal is a K? Which is an r? Math Practice go to: Population worksheet & print this out to follow along Concept 43.2 Births Increase and Deaths Decrease Population Size Change in population size depends on the number of births and deaths over a given time. “Birth–death” or BD model of population change: Example” Population 200 = 1,000 births-800 deaths t-time, =N=population, B=birth, d=death Nt 1 Nt B D Births Increase and Deaths Decrease Population Size Population growth rate (how fast it is changing): Δ= change, all other letters same as last slide Example (easier than below) BR-DR/10 Why 10? express as % Example 1000-800/10=20% Nt 1 Nt N B D For the bottom equation example use the Worksheet to guide you. This is rate change over time. Problem a. 300 Falcons N BD BD BD T (t 1) t 1 Births Increase and Deaths Decrease Population Size Per capita birth rate (b)—number of offspring individual produces Per capita death rate (d)—average individual’s chance of dying Per capita growth rate (r) = (b – d) = average individual’s contribution to total population growth rate If b > d, then r > 0, and the population grows. If b < d, then r < 0, and the population shrinks. If b = d, then r = 0, and population size does not change. Problem b. Growth rate of falcons (B-D)/N Problem b. What is the per capita growth rate? rmaxN rmax (maximum that the per capita growth rate can be) Use this formula much easier: rmax=(B-D)/N (50-30)/300 =.066, .067 X 100=6.7%/year Extinction and Recolonization Affect Population Dynamics The BIDE model of population growth adds the number of immigrants (I) and emigrants (E) to the BD growth model. Nt 1 Nt B I D E Example : N=1,000 N=1,040 B=50 I=15 D=20 E=5 Problem d. Find the avg. rate of change 2013-2018 Average rate of change =slope 2013, 300 2018, 414 414-300/2018-2013= 22.8 Logistical Growth Rate Carrying capacity Kentwood N=49,000 K=60,000 rmax=.9 Are they above or below K? a. Below b. What will be the population growth rate for 2013? rmax N((K-N)/K) (.9)(49,000)(60,000-49,000)/60,000) 8085 peeps/year Concept 43.2 Births Increase and Deaths Decrease Population Size Which of the following factors can explain a decline in the size of a population through time? a. Per capita birth rates b have decreased b. Per capita death rates d have decreased c. Per capita death rates d have increased d. Both a and c Examining the following graph, how would you describe the population growth of Daphnia grown in the laboratory? a. Up until day 60, growth appears to be exponential and density-independent. b. The population initially overshoots its carrying capacity. c. The carrying capacity appears to be about 180 individuals. d. Both a and b Concept 43.3 Life Histories Determine Population Growth Rates Species’ distributions reflect the effects of environment on per capita growth rates. A study of temperature change in a lizard’s environment, combined with knowledge of its physiology and behavior, led to conclusions about how climate change may affect survivorship, fecundity, and distribution of these lizards. Concept 43.3 Life Histories Determine Population Growth Rates What’s the take away about resource acquisition? The more we take, the more resources are available to us as humans, the less available they are to other organisms. This leads to stress on an community and can lead to death, extinction, loss of diversity. Concept 43.4 Populations Grow Multiplicatively, but Not for Long The human population is unique. It has grown at an everfaster per capita rate, as indicated by steadily decreasing doubling times. Technological advances have raised carrying capacity by increasing food production and improving health. Figure 43.9 Human Population Growth (Part 1) Figure 43.9 Human Population Growth (Part 2) Concept 43.4 Populations Grow Multiplicatively, but Not for Long Many believe that the human population has now overshot its carrying capacity for two reasons: Reduction in resources • Technological advances and agriculture have depended on fossil fuels, a finite resource. • Reduction in the quality of resources • Climate change and ecosystem degradation have been a consequence of 20th century population expansion. Competition • Competition- the struggle of individuals to obtain a limiting resource . Mutualism • Mutualism- A type of interspecific interaction where both species benefit. Commensalism • • Commensalism- a type of relationship in which one species benefits but the other is neither harmed nor helped. Remora feeds on leftover food of shark Keystone Species • Keystone species- a species that plays a role in its community that is far more important than its relative abundance might suggest.