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Lecture 24 November 20, 2014 Population Ecology 53.2-53.5 I) Introduction a) Population = group of potentially interbreeding organisms of same species i) living in same area/ same time ii) share common gene pool iii) share same resources iv) influenced by same environmental factors b) Ecology = study of interactions between living organisms and physical environment c) Population Ecology: i) Considers number of individuals of a species in an area & pop dynamics d) Populations Dynamics i) Study of change in population ii) How and why pop size increases or decreases over time iii) determine processes common to all populations iv) Different features of population studied II) Changes in Population Size: Pop Growth a) Evaluation of Change in population i) All populations have potential to change in size over time (1) Change in population size = Births + Immigrants entering population - Death - Emigrants leaving populations III) Change in Population Size Over Time a) Let's consider just births (B) and deaths (D) and no immigration or emigration Ξπ b) Population Growth Rate can be expressed mathematically as: Ξ π‘ = π΅ β π· i) ΞN = change in population size ii) Ξ t = time interval iii) B = number of births iv) D = number of deaths IV) Per Capita (Per individual0 Growth Rate a) Now express B as average birth (bN) per capita (per individual) per year β i) b= per capita birth rate β number offspring produced per year by average member of population β calculate ii) divide total number birth by total number of individuals (1) Ex: 75 births per year in population of 1,000 individuals (a) b= 75/1000 = 0.075 births per individuals iii) B=bN = expected number of births per year in population of any size (1) Ex: In a population of 200 individuals (2) B (number of births) = 0.075 births per individual x 200 individuals = 15 births b) now express D as average death (mN) per capita (per individual) per year β i) m= per capita death rate β (= mortality) expected number deaths per year β calculate (1) divide total number of death by total number of individuals (a) Ex: 20 deaths per year in population in 1,000 individuals Lecture 24 November 20, 2014 (i) m = 20/1000 = 0.020 mortality ii) D = mN = expected number of deaths per year in population of any size (1) Ex: In a population of 200 individuals (2) D ( number of deaths) = 0.020 deaths per individuals x 200 individuals = 4 deaths per year Ξπ c) The population growth equation can be revised Ξ π‘ = π΅ β π· = ππ β ππ = π(π β π) d) Population ecologists β most interested in difference between per capita birth rate & per capita death rate e) Per capita rate of increase = r = b - m i) Ξπ Ξπ = ππ ii) if r < 0 β population declining iii) if r > 0 β population increasing iv) if r = 0 β zero population growth (ZPG) V) Instantaneous Growth Rate a) Ecologists prefer to use calculus to express population growth instantaneously rather than over long time periods b) Instantaneous growth rate can be expressed as dN dt = πinstN c) Where rinst is the instantaneous per capita rate of increase VI) Exponential Growth a) Exponential population growth = population increase under idealize conditions (lot of food + free max breeding) b) β rate of increase at maximum = rmax > 0 and is constant c) The equation of exponential population growth is dN dt = πinstN VII) Models of Population Growth a) Exponential Growth model i) members of population has abundant food + free to reproduce at physiological capacity: growing at its rmas ii) Exponential population growth β a J-shaped curve iii) Equation: dN dt = πinstN VIII) Exponential Growth Model Limitation a) Exponential growth model is not very good because doesn't really happen in nature β not realistic i) Can't continue indefinitely because of environmental resistance β limits set by environment ii) would run out of food resources, living space, & would build up toxic wastes b) Certain populations have exponential growth for short time but over longer periods, growth rate βslow down and decrease to nearly zero β next model IX) The Logistic Growth Model a) Takes into account environment resistance b) Carrying capacity (K) = maximum population size the environment can support Lecture 24 November 20, 2014 c) Show population grows more slowly near its carrying capacity β more realistic d) Sigmold or S-shaped curve: first part is exponential growth then leveling out near carrying capacity X) The Logistic Growth Model Equation a) first part of equation same as exponential growth b) KβN K dN dt = πinstN ( KβN ) K reflects decline in growth as population reaches K c) If N is small (not close to K) β term (K-N)/K will be close to 1 & rate of population growth high d) If N close to K β term (K-N)/K will approach 0 & rate of population growth will decline e) When N= K (K-N)/K = 0 population stops growing XI) The Logistic Model and Real Population a) The logistic model fits few real population β better than exponential model i) Ex: Growth of lab population of paramecia fits an S - shaped curve β grown in a constant environment no predators/ competitors XII) The Logistic Model Limitation a) But curves in nature usually not perfectly logistic i) Populations tend to fluctuate around K (carrying capacity) ii) Environment β never constant iii) K itself may change b) Most populations tend to fluctuate in size around some central mean XIII) Life History Traits: How Organisms Maximize Reproduction While Ensure Survival (Why) a) Organism's life history β trade-offs between survival and reproductive sucess b) Life history traits are evolutionary outcomes c) 3 main variables: i) Age at first reproduction ii) How often organisms reproduces iii) How many offspring produced per reproductive episode XIV) The Different Strategies in Life History a) Semelparity = big=bang reproduction β species reproduce once and die i) many insects, plants, fish ii) Strategy favored in species where (1) survival rate of offspring in low (2) living in highly variable/unpredictable environment (3) Adults less likely to survive so producing lots of offspring β ensures some will survive b) Iteroparity = repeated reproduction β species reproduce many times i) most vertebrates ii) Strategy favored in species where: (1) environment is less variable (2) adults more likely to survive to reproduce again (3) competition for resources may be intense c) Timing of reproduction in iteroparous involves tradeoffs i) Reproduce early in life Lecture 24 November 20, 2014 (1) May reduce likelihood of survival (2) Expending E toward reproduction instead toward own growth ii) Reproduce later in life (1) expending E toward own growth, but reduces time for later reproduction XV) Two extremes of Life History Strategies in Most Vertebrates a) Which traits are favored at different population density? b) Population density = number of individuals of a species per unit of area or volume at a given time i) Ex: number of dandelions in front yard β 200 plants/ 200 square feet c) Life history strategies: 2 extremes selections: i) r-Selected Species = density-independent selection (1) Favored at low density ii) K-Selected Species = density-dependent selection (1) Favored at high density d) r-selected species: Favored at low density i) Have life history traits that maximize reproduction: (1) small body size (2) early maturity (early production of offspring) (3) many babies, same time (4) little/no parental care (5) short life span ii) Found in variable, temporary, or unpredictable environment iii) Focus: rapidly producing many offspring (high growth rate) e) K-Selected Species: Favored at high density i) Selects for life history traits sensitive to population size (1) long life span with slow development (2) large body size (3) high competitive ability (4) more defenses against predators (5) low reproductive rate (6) parental care of young (7) older age reprodction ii) Population size close to K most of time iii) Usually in relatively stable environment XVI) Factors Influencing Population Size a) What are the factors that regulate population growth? 2 basic categories: i) Density -Independent Factors ii) Density- Dependent Factors XVII) Density-Independent Factors a) Environment factors β operate without relation to density of population b) Tend to be abiotic factors β elements of nonliving world i) Ex: volcano wipes out 1/2 population of palm trees Lecture 24 November 20, 2014 ii) Ex: weather drought β pond dries up β all fish die c) β birth or death rate does not change with population density d) β r-selection XVIII) Density-Dependent Factors a) Environment factors whose impact on population is affected by population density i) change in population density β factor affect population b) In general, act as negative feedback system i) as population density increases: (1) density-dependent factors slow population growth (2) Either β birth rate and/ or β death rate ii) as population density decreases (1) density-dependent factors increase population growth (2) Either β birth rate and/or β death ate XIX) Density-Dependent Factors a) Tend to cause population to maintain itself at relative constant size near K b) Tend to be biotic factors β elements of the living world that affect organism c) Ex: of density-dependent factors i) Intraspecific competition for limited resources (food or territory) ii) Infectious disease iii) Predation iv) Accumulation of toxic wastes v) Parasites Territoriality XX)