# S-shaped growth Flowers. dA / dt = r * A * (K-A) / K If A< Published byJacob Black Modified over 3 years ago

## Presentation on theme: "S-shaped growth Flowers. dA / dt = r * A * (K-A) / K If A< 1 S-shaped growth Flowers { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_1.jpg", "name": "S-shaped growth Flowers", "description": "S-shaped growth Flowers", "width": "800" } 2 dA / dt = r * A * (K-A) / K If A< { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_2.jpg", "name": "dA / dt = r * A * (K-A) / K If A< 3 dA / dt = r * A * (K-A) / K = r*A - r*A*(A/K) If A< { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_3.jpg", "name": "dA / dt = r * A * (K-A) / K = r*A - r*A*(A/K) If A< 4 r net growth rate for non-stressed growth K carrying capacity Ao – initial population (or Area) { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_4.jpg", "name": "r net growth rate for non-stressed growth K carrying capacity Ao – initial population (or Area)", "description": "r net growth rate for non-stressed growth K carrying capacity Ao – initial population (or Area)", "width": "800" } 5 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_5.jpg", "name": "", "description": "", "width": "800" } 6 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_6.jpg", "name": "", "description": "", "width": "800" } 7 S-shaped growth FlowersVerifys { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_7.jpg", "name": "S-shaped growth FlowersVerifys", "description": "S-shaped growth FlowersVerifys", "width": "800" } 8 Problems with Logistic Equation Simple One example of s-shaped growth The linear decrease in growth rate is often not true in real life. The logistic equation fails to highlight the mechanisms responsible for limited growth. i.e. is it a decrease in birth rate or an increase in death rate. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_8.jpg", "name": "Problems with Logistic Equation Simple One example of s-shaped growth The linear decrease in growth rate is often not true in real life.", "description": "The logistic equation fails to highlight the mechanisms responsible for limited growth. i.e. is it a decrease in birth rate or an increase in death rate..", "width": "800" } 9 Sales of Widgets Stella { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_9.jpg", "name": "Sales of Widgets Stella", "description": "Sales of Widgets Stella", "width": "800" } 10 A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_10.jpg", "name": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth", "description": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth", "width": "800" } 11 A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_11.jpg", "name": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth", "description": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth", "width": "800" } 12 A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_12.jpg", "name": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth", "description": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth", "width": "800" } 13 A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_13.jpg", "name": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth", "description": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth", "width": "800" } 14 A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth Growth rate=rate*(1-stock/100) { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_14.jpg", "name": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth Growth rate=rate*(1-stock/100)", "description": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth Growth rate=rate*(1-stock/100)", "width": "800" } 15 A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth Growth rate=rate*(1-stock/100) { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_15.jpg", "name": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth Growth rate=rate*(1-stock/100)", "description": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth Growth rate=rate*(1-stock/100)", "width": "800" } 16 A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_16.jpg", "name": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth", "description": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth", "width": "800" } 17 A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_17.jpg", "name": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth", "description": "A.Exponential growth B.Exponential decay (goal seeking) to zero C.Exponential decay (goal seeking) to a non- zero level D.S-shaped growth", "width": "800" } 18 The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 80? A.Series 1 B.Series 2 C.Series 3 D.Series 4 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_18.jpg", "name": "The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80.", "description": "Which of the series have a carrying capacity of 80. A.Series 1 B.Series 2 C.Series 3 D.Series 4.", "width": "800" } 19 The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 80? A.Series 1 B.Series 2 C.Series 3 D.Series 4 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_19.jpg", "name": "The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80.", "description": "Which of the series have a carrying capacity of 80. A.Series 1 B.Series 2 C.Series 3 D.Series 4.", "width": "800" } 20 A.Series 1 B.Series 2 C.Series 3 D.Series 4 The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 80 and an intrinsic growth rate of 5 %? { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_20.jpg", "name": "A.Series 1 B.Series 2 C.Series 3 D.Series 4 The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80.", "description": "Which of the series have a carrying capacity of 80 and an intrinsic growth rate of 5 % .", "width": "800" } 21 A.Series 1 B.Series 2 C.Series 3 D.Series 4 The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 80 and an intrinsic growth rate of 5 %? { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_21.jpg", "name": "A.Series 1 B.Series 2 C.Series 3 D.Series 4 The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80.", "description": "Which of the series have a carrying capacity of 80 and an intrinsic growth rate of 5 % .", "width": "800" } 22 The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 100 and an initial value of 4? A.Series 1 B.Series 2 C.Series 3 D.Series 4 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_22.jpg", "name": "The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80.", "description": "Which of the series have a carrying capacity of 100 and an initial value of 4. A.Series 1 B.Series 2 C.Series 3 D.Series 4.", "width": "800" } 23 The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80. Which of the series have a carrying capacity of 100 and an initial value of 4? A.Series 1 B.Series 2 C.Series 3 D.Series 4 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/677212/slides/slide_23.jpg", "name": "The graphs above used growth rates of 5 or 10% and carrying capacities of 100 or 80.", "description": "Which of the series have a carrying capacity of 100 and an initial value of 4. A.Series 1 B.Series 2 C.Series 3 D.Series 4.", "width": "800" }

Similar presentations