class: center, middle, inverse, title-slide .title[ # 4. Population Growth and Intraspecific Competition ] .author[ ### Jasper Slingsby, BIO2014F ] .date[ ### 2024-04-23 ] --- ### The Hutchinsonian Niche .pull-left[ <br> G Evelyn Hutchinson proposed that _the niche is an n-dimensional hypervolume within which a species is **able to maintain a viable population**_ - [**Hutchinson 1957**](https://doi.org/10.1101%2Fsqb.1957.022.01.039) <br> Does the occurrence of a species at a locality mean it is able to maintain a viable population there...? ] .pull-right[ <img src="images/treurnicht2020_hutchinson.jpg" width="100%" style="display: block; margin: auto;" /> .footnote[Figure from [**Treurnicht et al. 2020**](http://dx.doi.org/10.1111/geb.13048)] ] --- class: center, middle ### What does maintaining a viable population even mean? --- class: center, middle ### It means maintaining population growth... --- class: center, middle ### But that's not easy... ### Especially where there is competition for resources... --- ### Population growth curve .pull-left[ Consider growth of a population, starting with 2 individuals at t = 0. - Assume a per-capita reproductive rate, `\(r\)` = 2 ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-2-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ Consider growth of a population, starting with 2 individuals at t = 0. - Assume a per-capita reproductive rate, `\(r\)` = 2 **Note:** _The per-capita reproductive rate ( `\(r\)` ) is the number of reproductively mature individuals contributed per individual from one generation to the next. Population growth is positive where `\(r > 0\)`_. _It is a fundamental biological parameter, determined by things like the number of eggs/seeds produced, the hatching/germination success of eggs/seeds, and the success with which hatchlings/germinants survive to reproductive maturity._ _It is the birth rate minus the death rate._ ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-3-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ Consider growth of a population, starting with 2 individuals at t = 0. - Assume a per-capita reproductive rate, `\(r\)` = 2 ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-4-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ Consider growth of a population, starting with 2 individuals at t = 0. - Assume a per-capita reproductive rate, `\(r\)` = 2 ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-5-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ Consider growth of a population, starting with 2 individuals at t = 0. - Assume a per-capita reproductive rate, `\(r\)` = 2 <br> _Growth is exponential!_ ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-6-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ Consider growth of a population, starting with 2 individuals at t = 0. - Assume a per-capita reproductive rate, `\(r\)` = 2 <br> _Growth is exponential!_ Using calculus, we can express growth as an instantaneous rate as `\(dN/dt\)`, the rate of change in number of organisms at a particular instant in time. Since our example is an exponential function, the slope of this curve is given by `\(dN/dt = rN\)` ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-7-1.png" width="100%" height="100%" /> ] --- .pull-left[ ### Is growth always exponential? <img src="images/Branch1975_F3.png" width="75%" style="display: block; margin: auto;" /> Resources available to individuals typically shrink as population size and density increase. Competition between individuals limits growth and reproductive output. .footnote[A study of the Pear Limpet, _Scutellastra cochlear_, by [**Branch 1975**](http://dx.doi.org/10.1111/geb.13048)] ] .pull-right[ <img src="images/Scutellastra cochlear.jpeg" width="65%" style="display: block; margin: auto;" /> <img src="images/Branch1975_F6.png" width="65%" style="display: block; margin: auto;" /> .footnote[image: Allan Ellis, [**iNaturalist**](https://www.inaturalist.org/observations/99128657)] ] --- ### Population growth curve .pull-left[ What does our curve look like once we include **density-dependent** effects like int*ra*specific competition (competition among individuals of the same species)? ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-11-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ What does our curve look like once we include **density-dependent** effects like int*ra*specific competition (competition among individuals of the same species)? It starts out much the same while resources are abundant... ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-12-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ What does our curve look like once we include **density-dependent** effects like int*ra*specific competition (competition among individuals of the same species)? It starts out much the same while resources are abundant... ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-13-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ What does our curve look like once we include **density-dependent** effects like int*ra*specific competition (competition among individuals of the same species)? It starts out much the same while resources are abundant... ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-14-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ What does our curve look like once we include **density-dependent** effects like int*ra*specific competition (competition among individuals of the same species)? It starts out much the same while resources are abundant... ...but slows as resources become limiting... ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-15-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ What does our curve look like once we include **density-dependent** effects like int*ra*specific competition (competition among individuals of the same species)? It starts out much the same while resources are abundant... ...but slows as resources become limiting... ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-16-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ What does our curve look like once we include **density-dependent** effects like int*ra*specific competition (competition among individuals of the same species)? It starts out much the same while resources are abundant... ...but slows as resources become limiting... ...and eventually flattens out... ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-17-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ What does our curve look like once we include **density-dependent** effects like int*ra*specific competition (competition among individuals of the same species)? It starts out much the same while resources are abundant... ...but slows as resources become limiting... ...and eventually flattens out... Any thoughts on the equation to fit this curve? `\(dN/dt = ?\)` ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-18-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ What does our curve look like once we include **density-dependent** effects like int*ra*specific competition (competition among individuals of the same species)? It starts out much the same while resources are abundant... ...but slows as resources become limiting... ...and eventually flattens out... Any thoughts on the equation to fit this curve? `\(dN/dt = rN (K – N)/K\)` A logistic function, or what we call the logistic growth curve. ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-19-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ The population growth curve including **density-dependent** effects like int*ra*specific competition (competition among individuals of the same species) is a logistic function, flattening out as resources become limiting. `\(dN/dt = rN (K – N)/K\)` <br> We know `\(N\)`, `\(t\)` and `\(r\)`, but what is `\(K\)`? ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-20-1.png" width="100%" height="100%" /> ] --- ### Population growth curve .pull-left[ The population growth curve including **density-dependent** effects like int*ra*specific competition (competition among individuals of the same species) is a logistic function, flattening out as resources become limiting. `\(dN/dt = rN (K – N)/K\)` <br> We know `\(N\)`, `\(t\)` and `\(r\)`, but what is `\(K\)`? `\(K\)` = carrying capacity Familiar? ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-21-1.png" width="100%" height="100%" /> ] --- <img src="images/terry_rvsK.png" width="65%" style="display: block; margin: auto;" /> .footnote[Terry Hedderson's lecture on life history models] --- ### Population growth curve .pull-left[ The population growth curve including **density-dependent** effects like int*ra*specific competition (competition among individuals of the same species) is a logistic function, flattening out as resources become limiting. `\(dN/dt = rN (K – N)/K\)` <br> `\(K\)` = carrying capacity **Note:** _Where `\(N\)` is small, the logistic growth curve approximates the exponential growth curve `\((rN)\)`, because `\((K – N)/K\)` is close to 1._ _It begins to deviate as `\(N\)` increases._ ] .pull-right[ <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-23-1.png" width="100%" height="100%" /> ] --- .pull-left[ ### Exponential growth `\(dN/dt = rN\)` Population growth rate, `\(r\)`, doesn't change with population size <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-24-1.png" width="80%" /> .footnote[Density independent population growth] ] .pull-right[ ### Logistic growth `\(dN/dt = rN (K – N)/K\)` Population growth rate, `\(r\)`, gets small as the population approaches carrying capacity, `\(K\)` <img src="4_PopulationGrowth_files/figure-html/unnamed-chunk-25-1.png" width="80%" /> .footnote[Density dependent population growth] ] --- ### What are the implications of density-dependent growth? --- ### What are the implications of density-dependent growth? Serotinous Proteaceae are well known for extreme population density fluctuations after fire. .pull-left[ <img src="images/proteas_Roets2006.jpg" width="70%" style="display: block; margin: auto;" /> .footnote[image: Roets et al 2006] ] -- .pull-right[ <img src="images/Bond1995.png" width="100%" style="display: block; margin: auto;" /> While some of this may be exogenous, driven by external forces like climate fluctuations or variability in the fire regime, [**Bond et al 1995**](http://dx.doi.org/10.1080/11956860.1995.11682291) demonstrated that it could be endogenous, driven by internal population dynamics due to density-dependent effects. .footnote[[**Bond et al 1995**](http://dx.doi.org/10.1080/11956860.1995.11682291)] ] --- ### Density-dependence in serotinous Cape Proteaceae .pull-left[ Empirical datasets showed evidence for a negative impact of density-dependence on: - recruitment (Figure 1) - fecundity (Figure 4) <br> Notice the exogenous effect of aridity on _Protea repens_ seedling establishment at the arid inland site (Figure 1, bottom). .footnote[[**Bond et al 1995**](http://dx.doi.org/10.1080/11956860.1995.11682291)] ] .pull-right[ <img src="images/Bond1995_F1_4.png" width="100%" style="display: block; margin: auto;" /> ] --- .pull-left[ ### Protea density-dependence They fed their empirical data into demographic models and projected population growth over multiple generations. Note that generations and fires are synonymous, because serotinous Proteaceae mostly only recruit after fire. .footnote[[**Bond et al 1995**](http://dx.doi.org/10.1080/11956860.1995.11682291)] ] .pull-right[ <br> <br> <img src="images/treurnicht2021.jpg" width="100%" style="display: block; margin: auto;" /> .footnote[Figure from [**Treurnicht et al 2021**](http://dx.doi.org/10.1111/1365-2664.13882). Ignore the harvesting...] ] --- .pull-left[ ### Protea density-dependence They fed their empirical data into demographic models and projected population growth over multiple generations. Note that generations and fires are synonymous, because serotinous Proteaceae mostly only recruit after fire. .footnote[[**Bond et al 1995**](http://dx.doi.org/10.1080/11956860.1995.11682291)] ] .pull-right[ <img src="images/Bond1995_F5.png" width="70%" style="display: block; margin: auto;" /> ] --- .pull-left[ ### Protea density-dependence They fed their empirical data into demographic models and projected population growth over multiple generations. Note that generations and fires are synonymous, because serotinous Proteaceae mostly only recruit after fire. Decreasing the starting population size ( `\(N_0\)` ), which would reduce the initial effect of density on population growth, increased the amplitude of population fluctuations, creating risk of total population crashes. This effect was stronger in _P. neriifolia_, because it had higher cone production (fecundity) and was more sensitive to population density. .footnote[[**Bond et al 1995**](http://dx.doi.org/10.1080/11956860.1995.11682291)] ] .pull-right[ <img src="images/Bond1995_F5.png" width="70%" style="display: block; margin: auto;" /> ] --- ### How does this relate to the original question at the start of the lecture? #### The Hutchinsonian Niche .pull-left[ G Evelyn Hutchinson proposed that _the niche is an n-dimensional hypervolume within which a species is **able to maintain a viable population**_ - [**Hutchinson 1957**](https://doi.org/10.1101%2Fsqb.1957.022.01.039) Does the occurrence of a species at a locality mean it is able to maintain a viable population there...? ] .pull-right[ <img src="images/treurnicht2020_hutchinson.jpg" width="100%" style="display: block; margin: auto;" /> .footnote[Figure from [**Treurnicht et al. 2020**](http://dx.doi.org/10.1111/geb.13048)] ] --- ### How does this relate to the original question at the start of the lecture? #### The Hutchinsonian Niche .pull-left[ G Evelyn Hutchinson proposed that _the niche is an n-dimensional hypervolume within which a species is **able to maintain a viable population**_ - [**Hutchinson 1957**](https://doi.org/10.1101%2Fsqb.1957.022.01.039) Does the occurrence of a species at a locality mean it is able to maintain a viable population there...? > No! We need estimates of their population growth rate ( `\(r\)` ). <br> We can estimate population growth rate ( `\(r\)` ) from demographic parameters that we can measure in the field (e.g. birth, death and dispersal rates) using demographic models. ] .pull-right[ <img src="images/treurnicht2020_hutchinson.jpg" width="100%" style="display: block; margin: auto;" /> .footnote[Figure from [**Treurnicht et al. 2020**](http://dx.doi.org/10.1111/geb.13048)] ] --- ### How does this relate to SDMs? .pull-left[ We can build SDMs based on demographic models that estimate population growth across different environmental conditions. <img src="images/Schurr2012.png" width="100%" style="display: block; margin: auto;" /> These types of SDMs are often called Demographic Distribution Models (DDMs), and can tell us where species should be able to maintain a viable population! ] .pull-right[ <img src="images/Schurr2012_F1.webp" width="100%" style="display: block; margin: auto;" /> .footnote[[**Schurr et al. 2012**](http://dx.doi.org/10.1111/j.1365-2699.2012.02737.x)] ] --- ### How does this relate to SDMs? Interestingly, positive population growth can be maintained using very different strategies. <img src="images/protearates.jpg" width="70%" style="display: block; margin: auto;" /> Here seeding vs sprouting serotinous Proteaceae show classic differentiation on the `\(r\)` (invest in recruitment) vs `\(K\)` (invest in survival) life history strategy spectrum [**(Treurnicht et al. 2020)**](http://dx.doi.org/10.1111/geb.13048). --- class: middle ## Take-home >*If population growth were density-independent, it would be exponential...* >*Most species exhibit density-dependent population growth due to intraspecific competition and other density-dependent factors (e.g. disease transmission), thus self-regulating their population size.* >*Density-dependence creates an endogenous control on populations and has big implications for their size and stability.* >*One needs estimates of population growth rates to know whether populations can be maintained and define the environmental conditions of the Hutchinsonian niche. This can be done if you can estimate birth, death and dispersal rates.* >*Newer SDMs can include a demographic modelling component to map species distributions based on the Hutchinsonion niche.* --- class: center, middle # Thanks! Slides created via the R packages: [**xaringan**](https://github.com/yihui/xaringan)<br> [gadenbuie/xaringanthemer](https://github.com/gadenbuie/xaringanthemer) The chakra comes from [remark.js](https://remarkjs.com), [**knitr**](http://yihui.name/knitr), and [R Markdown](https://rmarkdown.rstudio.com).