{"id":173,"date":"2019-11-05T19:14:51","date_gmt":"2019-11-06T00:14:51","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/chapter\/topic-4-2-introduction-to-forecast-climate\/"},"modified":"2021-06-06T21:18:17","modified_gmt":"2021-06-07T01:18:17","slug":"topic-4-2-introduction-to-forecast-climate","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/chapter\/topic-4-2-introduction-to-forecast-climate\/","title":{"raw":"Topic 4.2. Introduction to Genecology functions","rendered":"Topic 4.2. Introduction to Genecology functions"},"content":{"raw":"<h1><img class=\"alignnone size-medium wp-image-65\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd-300x105.png\" alt=\"\" width=\"300\" height=\"105\"><\/h1>\nVideo #1 and #2: Concept of genecology\n\n[video width=\"1920\" height=\"1080\" mp4=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_1a.mp4\"][\/video]\n\n[video width=\"1920\" height=\"1080\" mp4=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_1b.mp4\"][\/video]\n\nVideo #3: Transfer functions:\n\n[video width=\"1920\" height=\"1080\" mp4=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_2-1.mp4\"][\/video]\n\nVideo #4: Genecology functions and predictors:\n\n[video width=\"1920\" height=\"1080\" mp4=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_3-gv-and-cv.mp4\"][\/video]\n<h1>Contents<\/h1>\n<a href=\"#_1\"> 1. Overview<\/a>\n<a href=\"#_2\"> 2. Definition of genecology<\/a>\n<a href=\"#_21\">2.1. Definition<\/a>\n<a href=\"#_22\">2.2. Some relevant terms<\/a>\n<a href=\"#_23\">2.3. Objectives of genecology<\/a>\n<a href=\"#_3\">3. Transfer functions<\/a>\n<a href=\"#_31\">3.1. Provenance test<\/a>\n<a href=\"#_32\">3.2. Transfer functions<\/a>\n<a href=\"#_33\">3.3.\u00a0 Features and limitations<\/a>\n<a href=\"#_4\">4. General transfer functions<\/a>\n<a href=\"#_41\">4.1.\u00a0 General transfer functions<\/a>\n<a href=\"#_42\">4.2. Relative performance-based general transfer functions<\/a>\n<a href=\"#_43\">4.3.\u00a0 Limitations of general transfer functions<\/a>\n<a href=\"#_44\">4.4.\u00a0 Universal transfer functions<\/a>\n<a href=\"#_5\">5. Genecology functions<\/a>\n<a href=\"#_51\">5.1. Genecology functions<\/a>\n<a href=\"#_52\">5.2. The difference in genecology functions among environments<\/a>\n<a href=\"#_6\">6. Geographic vs. climatic variables<\/a>\n<a href=\"#_61\">6.1. Representation of environmental variables<\/a>\n<a href=\"#_62\">6.2. Accessibility<\/a>\n<a href=\"#_63\">6.3 local vs. universal<\/a>\n<a href=\"#_64\">6.4. Applicability for climate change<\/a>\n<a href=\"#_65\">6.5. Non-climatic factors<\/a>\n\n&nbsp;\n\n&nbsp;\n<h1><a id=\"_1\" href=\"\"><\/a>1. Overview<\/h1>\nAs mentioned in the previous topic and shown in Figure 1, climatic mismatches occur in two dimensions. One is the mismatch in the climatic niche at the species level (horizontally), and another is the mismatch at the population level (vertically). The niche-based models at the species level can be used to predict the shift in the climatic niche at the species level. Genecology functions are to predict among-population variations within a species.\n\n[caption id=\"attachment_65\" align=\"alignnone\" width=\"1024\"]<img class=\"wp-image-156 size-large\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2019\/11\/f421-1-1024x461.png\" alt=\"\" width=\"1024\" height=\"461\"> Figure 1. Illustration of mismatches caused by climate change in terms of climatic niche and among-population variation, and the role of gynecology in coping with the mismatches. Image by Tongli Wang under CC BY 4.0.[\/caption]\n<h1><a id=\"_2\" href=\"\"><\/a>2. Definition of genecology<\/h1>\n<h2><a id=\"_21\" href=\"\"><\/a>2.1. Definition<\/h2>\nGenecology is the study of intraspecific genetic variation in relation to environmental conditions. In other words, it is to study the relationships between genetic variation and environmental gradients within a species.\n\nGenecology is often referred to as ecological genetics, which is actually more widely used. However, strictly speaking, ecological genetics is the study of how ecologically relevant traits evolve in natural populations, which covers inter-species interactions. Nevertheless, these two terms are used interchangeably.\n<h2><a id=\"_22\" href=\"\"><\/a>2.2. Some relevant terms<\/h2>\nProvenance \u2013 the place of seed origin (or seed source).\n\nPopulation \u2013 a group of individuals of the same species that live in a particular geographical area, and have the capability of interbreeding. Individuals from the same provenance is called a population.\n\nProvenance is often used to refer a population although it is not accurate. Thus, provenance and population are often interchangeably in genecology.\n\nProvenance test (or provenance trial) \u2013 a common garden experiment that compares trees or plants collected from different provenances. Typically provenance tests compare widely separated seed sources. The test may contain multiple test sites.\n\nGenetic variation \u2013 can be defined at the individual level as the difference in DNA among individuals, or at the population level as among-population variation due to difference in allele frequency.\n\nGenetic cline - a geographic or climatic pattern of change in a trait.\n\nGenetic and environment interaction (GxE) - different genotypes respond to environmental variation in different ways.\n<h2><a id=\"_3\" href=\"\"><\/a>2.3. Objectives of genecology<\/h2>\nOperational objectives:\n<ul>\n \t<li>To determine how far seed can be moved<\/li>\n \t<li>To delineate geographic breeding zones<\/li>\n \t<li>To select optimal provenances<\/li>\n<\/ul>\nTheoretical objectives:\n<ul>\n \t<li>Testing evolutionary and ecological theories about factors limiting the evolution of species range<\/li>\n \t<li>Predicting response to climate change<\/li>\n \t<li>Dependency on climatic drivers<\/li>\n \t<li>Determining the underlying genetic basis of adaptive traits: Ecological genomics<\/li>\n<\/ul>\n<h1><a id=\"_3\" href=\"\"><\/a>3. Transfer functions<\/h1>\nTransfer functions are most commonly used in genecology to reflect the effect of transfer distance of populations in terms of geographical or climatic variables. A provenance test is required for developing a transfer function.\n<h2><a id=\"_31\" href=\"\"><\/a>3.1. Provenance test<\/h2>\nFigure 2 shows a typical provenance test. Populations from 140 provenances range-wide were planted in 60 common garden trials (planting sites) in British Columbia (BC), Canada. At each site, an incomplete block design was used to include 60 populations due to a large number of populations. Thus, not every population was tested at all the 60 sites except seven reference populations. Tree height was measured at age 20.\n\n[caption id=\"attachment_65\" align=\"alignnone\" width=\"557\"]<img class=\" wp-image-157\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f422.png\" alt=\"\" width=\"557\" height=\"418\"> Figure 2. A provenance test comprising 140 provenances of lodgepole pine in western North America and tested in British Columbia. Image by Tongli Wang under CC BY 4.0.[\/caption]\n\nAs illustrated in Figure 3, populations are transferred from their origins to a test site in the mid of BC in the provenance test. Those populations grow under new environmental conditions, and their performances may be affected. As the populations are grown under the same climatic conditions (at the same test site), the difference in the performance of populations is supposed to be due to genetic variation among the populations.\n\n[caption id=\"attachment_65\" align=\"alignnone\" width=\"783\"]<img class=\"size-full wp-image-158\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423.png\" alt=\"\" width=\"783\" height=\"406\"> Figure 3. Illustration of population transfers in the provenance test of lodgepole pine. Image by Tongli Wang under CC BY 4.0.[\/caption]\n<h2><a id=\"_32\" href=\"\"><\/a>3.2. Transfer functions<\/h2>\nThe genetic variation observed in a provenance trial at each test site may be associated with the population transfer distance. It is hypothesized that the longer the transfer distance, the larger the transfer effect. Thus, the transfer distance is used as a predictor in a transfer function as:\n\n<img class=\"alignnone wp-image-159\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423f.png\" alt=\"\" width=\"396\" height=\"70\">\n\nWhere, <em>Y<\/em> is the performance of a population; <em>x<\/em> is the transfer distance; and <em>a<\/em>, <em>b<\/em>, and <em>c<\/em> are parameters to be estimated to fit the model.\n\nThe transfer distance can be in a physical distance for geographical variables (e.g., latitude, longitude, or elevation), or in units for climatic variables (e.g., temperature and precipitation). Climatic variables are increasingly used as they have many advantages over geographical variables, particularly for predicting the impact of climate change on forests.\n\nClimatic variables are needed for all the provenances to build a transfer function using the transfer distance in climatic variables, as shown in Figure 4. A map of mean annual temperature (MAT) covering the lodgepole pine distribution and a transfer function for a test in the mid of BC.\n\n[caption id=\"attachment_65\" align=\"alignnone\" width=\"953\"]<img class=\"size-full wp-image-160\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424.png\" alt=\"\" width=\"953\" height=\"597\"> Figure 4. A map of mean annual temperature (MAT) covering the lodgepole pine distribution (left) and a transfer function for a test in the mid of BC (right). Image by Tongli Wang under CC BY 4.0.[\/caption]\n\n&nbsp;\n\nThe transfer distance in MAT (MAT_CTD) is calculated as:\n\n<em>MAT_CTD <\/em>=<em> MAT_s \u2013 MAT_p\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em>[2]\n\nWhere, MAT_s is the MAT of the test site, MAT_p is the MAT of the provenance. Then, the transfer function is written as:\n\n<img class=\"alignnone size-full wp-image-161\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424f.png\" alt=\"\" width=\"473\" height=\"71\">\n\nPopulations with negative transfer distances on the left of the plot were transferred northward (from warmer climates to cooler climates). On the other hand, populations with positive transfer distances on the right of the plot were transferred southward (from cooler climates to warmer climates).\u00a0 Populations with zero and around zero transfer distance are considered local populations. The local populations have the best performance; however, the peak of the curve is not always exactly at the zero transfer distance point, as shown in Figure 4.\n<h2><a id=\"_33\" href=\"\"><\/a>3.3.\u00a0 Features and limitations<\/h2>\nA transfer function represents the transfer effect of populations. It reflects the <strong>genetic effect<\/strong> of climate on populations. It is intuitive and easy to build. However, there are several limitations for transfer functions. A transfer function built for one site may be different from the one built for another site, even with the same group of populations. Thus, a transfer function developed for one site, strictly speaking, only represents the transfer effect of populations under the particular environment of that test site. The number of test sites is limited for most tree species, and people tend to oversell the results drawn from these sites. Therefore, we need to be aware of such a risk of using a transfer function built for one environment to represent the situations for other environments.\n<h1><a id=\"_4\" href=\"\"><\/a>4. General transfer functions<\/h1>\n<h2><a id=\"_41\" href=\"\"><\/a>4.1.\u00a0 General transfer functions<\/h2>\nDue to the limitation of transfer functions discussed above, general transfer functions were proposed. The only difference between a transfer function and a general transfer function is that data from all test sites are pooled together in developing a general transfer function. The formulas [1] \u2013 [3] all apply to a general transfer function.\n\nThe curve of a general transfer function shown in Figure 5 was developed based on the observations from the same provenance test mentioned above. The relationship between the performance and transfer distance of populations in a transfer function is usually weak.\n\n[caption id=\"attachment_65\" align=\"alignnone\" width=\"580\"]<img class=\"size-full wp-image-162\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f425.png\" alt=\"\" width=\"580\" height=\"523\"> Figure 5. A general transfer function that combines observations across all tests. Image by Tongli Wang under CC BY 4.0.[\/caption]\n<h2><a id=\"_42\" href=\"\"><\/a>4.2. Relative performance-based general transfer functions<\/h2>\nThe most important reason for a general transfer function being weak is the difference in the performance of populations among sites. For example, the outliers at the bottom of Figure 5 are populations growing at several cold sites in the north. Their total height at age 20 is less than a meter. An approach was developed to overcome this problem by using relative performance. With this approach, the performances of populations are converted to proportions relative to the performance of the local population.\u00a0 It can substantially improve the relationship of the general transfer function, as shown in Figure 6. It worths of reminding that the relative performance needs to be converted back to actual performance in applications of this model.\n\n[caption id=\"attachment_65\" align=\"alignnone\" width=\"593\"]<img class=\"wp-image-163 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f426-1.png\" alt=\"\" width=\"593\" height=\"547\"> Figure 6. A general transfer function using relative performance. Image by Tongli Wang under CC BY 4.0.[\/caption]\n<h2><a id=\"_43\" href=\"\"><\/a>4.3.\u00a0 Limitations of general transfer functions<\/h2>\nIn addition to the weak relationships of general transfer functions as mentioned above, there are other limitations for general transfer functions. As discussed earlier, the transfer effects of populations are different among test sites. By pooling the data across all test sites to develop a general transfer function, the difference in the transfer effect of populations among test sites is averaged out, as illustrated in Figure 7. This compromises the prediction power of general transfer functions. In addition, the same amount of transfer distance may have different transfer effects. For example, for a -2\u00b0C transfer distance in temperature, the transfer from 2\u00b0C to 0\u00b0C may be different from the transfer from 10\u00b0C to 8\u00b0C. This point will be further discussed later in comparison with genecology functions. Nevertheless, general transfer functions are the simplest to implement; thus it is still commonly used.\n\n[caption id=\"attachment_65\" align=\"alignnone\" width=\"724\"]<img class=\"wp-image-164 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f427_poolData.gif\" alt=\"\" width=\"724\" height=\"780\"> Figure 7. Illustration of difference in transfer effect between two test sites. Image by Tongli Wang under CC BY 4.0.[\/caption]\n<h2><a id=\"_44\" href=\"\"><\/a>4.4. Universal transfer functions<\/h2>\n<div>\n<div>An improved version of general transfer function was proposed recently (Leites et al 2012). It can be called \u201cUniversal transfer functions\u201d. <span style=\"font-size: 14pt\">A universal transfer function also pools data across test sites. The difference is that it includes provenance climate and an interaction term in addition to transfer distance, as well as some random effects. The function can be written as:<\/span><\/div>\n<\/div>\n<div><img class=\"alignnone wp-image-165 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/utf.png\" alt=\"\" width=\"637\" height=\"63\"><\/div>\nWhere,\nX is transfer distance;\nP is provenance climate;\nXP is the interaction term;\nrs are some random effect terms.\n\nThe universal transfer function can overcome the problems listed above, but the random terms cause additional problems. The model is too complicated and often fail to converge. It used only one climate variable in applications so far, which can compromise the model capability.\n\n.\n<h1><a id=\"_5\" href=\"\"><\/a>5. Genecology functions<\/h1>\n<h2><a id=\"_51\" href=\"\"><\/a>5.1. Genecology functions<\/h2>\nA genecology function uses the environmental variables of provenances, rather than transfer distance used in both transfer functions and general transfer functions. Thus, a genecology function represents the relationship between the performance of populations and environmental variables of the population origins (or provenances), which exactly reflects the definition of genecology. A genecology function can be written as:\nY=<strong>a<\/strong> + <strong>b<\/strong>x + cx<sup>2<\/sup>\nWhere, <em>Y<\/em> is the performance of a population; <em>x<\/em> is an environmental variable of provenance; and <em>a,<\/em> <em>b<\/em>, and <em>c<\/em> are parameters to be estimated to fit the model.\n\nUsing the same data for building a transfer function in Figure 4, a genecology function is developed, as shown in Figure 8. Although the shapes of the curves are quite different, the R square values are identical between the two functions.\n\n[caption id=\"attachment_65\" align=\"alignnone\" width=\"1024\"]<img class=\"size-large wp-image-166\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f428-1024x666.png\" alt=\"\" width=\"1024\" height=\"666\"> Figure 8. A map of mean annual temperature (MAT) covering the lodgepole pine distribution (left) and a genecology function for a test in the mid of BC (right). Image by Tongli Wang under CC BY 4.0.[\/caption]\n<h2><a id=\"_52\" href=\"\"><\/a>5.2. The difference in genecology functions among environments<\/h2>\nGenecology functions developed for different environments show different relationships (Figure 9). Thus, a genecology function built based on information from one environment may not represent the relationship for other environments. This is the same as for the transfer function.\n\n[caption id=\"attachment_65\" align=\"alignnone\" width=\"1024\"]<img class=\"wp-image-167 size-large\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f429-1024x670.png\" alt=\"\" width=\"1024\" height=\"670\"> Figure 9. genecology functions developed at six test sites from cold to warm climates. Image by Tongli Wang under CC BY 4.0.[\/caption]\n\n<span style=\"font-family: Helvetica, Arial, 'GFS Neohellenic', sans-serif;font-size: 1.2em;font-weight: bold\"><a id=\"_6\" href=\"\"><\/a>6. Geographic vs. climatic variables<\/span>\n\nBoth transfer functions and genecology functions can be built with either geographic or climatic variables. There are advantages and disadvantages to use geographic or climatic variables as predictors. We will make a detailed comparison between the two.\n<h2><a id=\"_61\" href=\"\"><\/a>6.1. Representation of environmental variables<\/h2>\nGeographic variables are not direct environmental variables, whereas climatic variables are. However, geographic variables are related to environmental variables. For example, elevation is strongly related to temperature, which affects plant performance, as illustrated in Figure 10. Thus, they are often used to substitute environmental variables. However, if we build a greenhouse at the top of the mountain, we can grow any plant that can only grow at the bottom of the valley. It suggests elevation itself does not affect plant growth.\n\n[caption id=\"attachment_65\" align=\"alignnone\" width=\"600\"]<img class=\"wp-image-168\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f42_10.png\" alt=\"\" width=\"600\" height=\"450\"> Figure 10. \"Little Lakes Valley viewed from about 11,000 feet elevation, hiking along the Mono Pass Trail, Eastern Sierra Mountains, California (mono14xy)\" by mlhradio is licensed under CC BY-NC 2.0[\/caption]\n<h2><a id=\"_62\" href=\"\"><\/a>6.2. Accessibility<\/h2>\nGeographic variables are more accessible than climatic variables. That is why they were more often used for experimental design and data analysis in the past. With increasingly available climate data, accessing climatic variables are becoming as easy as accessing geographic variables. Especially with the scale-free climate models ClimateNA and ClimateAP, climatic variables can be easily obtained for any specific location within their coverage.\n<h2><a id=\"_63\" href=\"\"><\/a>6.3 local vs. universal<\/h2>\nA transfer function or a genecology function built with geographic variables only works for the region where the model is built. This is because of the effect of a geographic variable changes from region to region, or location to location. For example, 2000 m in elevation in California is suitable for many plants to growth; but the same elevation in BC is beyond the treeline. Also, an increase in elevation by 100 m in California will result in a decrease in temperature by 0.65\u00b0C; but the same change in northern BC will only result in a decrease in temperature by about 0.2\u00b0C.\u00a0 In contrast,\u00a0 a transfer function or a genecology function built with climatic variables can be applied anywhere.\n<h2><a id=\"_64\" href=\"\"><\/a>6.4. Applicability for climate change<\/h2>\nA transfer function or a genecology function built with geographic variables cannot be used for assessing the impact of climate change as geographic variables are static and have no future projections. In contrast, climatic variable based functions can predict the past and future. That is the reason why genecology has been a hot area.\n<h2><a id=\"_65\" href=\"\"><\/a>6.5. Non-climatic factors<\/h2>\nGeographic variables are still useful to reflect some important non-climatic factors. Genetic variations among populations are also affected by spatial autocorrelation involving migration and gene flow related to physical barriers and distance. Those factors sometimes need to be included in genecology functions. We will discuss this further in the next topic.\n\n<img class=\"alignnone size-medium wp-image-65\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd-300x105.png\" alt=\"\" width=\"300\" height=\"105\">\n\nBy Tongli Wang, Climate Modelling and Forest Applications is licensed under\u00a0<a class=\"inline_disabled external\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/\" target=\"_blank\" rel=\"noopener\">Creative Commons &lt;CC BY-NC-ND 4.0&gt; License<\/a>","rendered":"<h1><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-65\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd-300x105.png\" alt=\"\" width=\"300\" height=\"105\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd-300x105.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd-65x23.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd-225x79.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd-350x122.png 350w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd.png 403w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/h1>\n<p>Video #1 and #2: Concept of genecology<\/p>\n<div style=\"width: 1920px;\" class=\"wp-video\"><video class=\"wp-video-shortcode\" id=\"video-173-1\" width=\"1920\" height=\"1080\" preload=\"metadata\" controls=\"controls\"><source type=\"video\/mp4\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_1a.mp4?_=1\" \/><a href=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_1a.mp4\">https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_1a.mp4<\/a><\/video><\/div>\n<div style=\"width: 1920px;\" class=\"wp-video\"><video class=\"wp-video-shortcode\" id=\"video-173-2\" width=\"1920\" height=\"1080\" preload=\"metadata\" controls=\"controls\"><source type=\"video\/mp4\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_1b.mp4?_=2\" \/><a href=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_1b.mp4\">https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_1b.mp4<\/a><\/video><\/div>\n<p>Video #3: Transfer functions:<\/p>\n<div style=\"width: 1920px;\" class=\"wp-video\"><video class=\"wp-video-shortcode\" id=\"video-173-3\" width=\"1920\" height=\"1080\" preload=\"metadata\" controls=\"controls\"><source type=\"video\/mp4\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_2-1.mp4?_=3\" \/><a href=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_2-1.mp4\">https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_2-1.mp4<\/a><\/video><\/div>\n<p>Video #4: Genecology functions and predictors:<\/p>\n<div style=\"width: 1920px;\" class=\"wp-video\"><video class=\"wp-video-shortcode\" id=\"video-173-4\" width=\"1920\" height=\"1080\" preload=\"metadata\" controls=\"controls\"><source type=\"video\/mp4\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_3-gv-and-cv.mp4?_=4\" \/><a href=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_3-gv-and-cv.mp4\">https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/4.1_3-gv-and-cv.mp4<\/a><\/video><\/div>\n<h1>Contents<\/h1>\n<p><a href=\"#_1\"> 1. Overview<\/a><br \/>\n<a href=\"#_2\"> 2. Definition of genecology<\/a><br \/>\n<a href=\"#_21\">2.1. Definition<\/a><br \/>\n<a href=\"#_22\">2.2. Some relevant terms<\/a><br \/>\n<a href=\"#_23\">2.3. Objectives of genecology<\/a><br \/>\n<a href=\"#_3\">3. Transfer functions<\/a><br \/>\n<a href=\"#_31\">3.1. Provenance test<\/a><br \/>\n<a href=\"#_32\">3.2. Transfer functions<\/a><br \/>\n<a href=\"#_33\">3.3.\u00a0 Features and limitations<\/a><br \/>\n<a href=\"#_4\">4. General transfer functions<\/a><br \/>\n<a href=\"#_41\">4.1.\u00a0 General transfer functions<\/a><br \/>\n<a href=\"#_42\">4.2. Relative performance-based general transfer functions<\/a><br \/>\n<a href=\"#_43\">4.3.\u00a0 Limitations of general transfer functions<\/a><br \/>\n<a href=\"#_44\">4.4.\u00a0 Universal transfer functions<\/a><br \/>\n<a href=\"#_5\">5. Genecology functions<\/a><br \/>\n<a href=\"#_51\">5.1. Genecology functions<\/a><br \/>\n<a href=\"#_52\">5.2. The difference in genecology functions among environments<\/a><br \/>\n<a href=\"#_6\">6. Geographic vs. climatic variables<\/a><br \/>\n<a href=\"#_61\">6.1. Representation of environmental variables<\/a><br \/>\n<a href=\"#_62\">6.2. Accessibility<\/a><br \/>\n<a href=\"#_63\">6.3 local vs. universal<\/a><br \/>\n<a href=\"#_64\">6.4. Applicability for climate change<\/a><br \/>\n<a href=\"#_65\">6.5. Non-climatic factors<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<h1><a id=\"_1\" href=\"\"><\/a>1. Overview<\/h1>\n<p>As mentioned in the previous topic and shown in Figure 1, climatic mismatches occur in two dimensions. One is the mismatch in the climatic niche at the species level (horizontally), and another is the mismatch at the population level (vertically). The niche-based models at the species level can be used to predict the shift in the climatic niche at the species level. Genecology functions are to predict among-population variations within a species.<\/p>\n<figure id=\"attachment_65\" aria-describedby=\"caption-attachment-65\" style=\"width: 1024px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-156 size-large\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2019\/11\/f421-1-1024x461.png\" alt=\"\" width=\"1024\" height=\"461\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/f421-1-1024x461.png 1024w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/f421-1-300x135.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/f421-1-768x346.png 768w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/f421-1-65x29.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/f421-1-225x101.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/f421-1-350x158.png 350w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/f421-1.png 1044w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption id=\"caption-attachment-65\" class=\"wp-caption-text\">Figure 1. Illustration of mismatches caused by climate change in terms of climatic niche and among-population variation, and the role of gynecology in coping with the mismatches. Image by Tongli Wang under CC BY 4.0.<\/figcaption><\/figure>\n<h1><a id=\"_2\" href=\"\"><\/a>2. Definition of genecology<\/h1>\n<h2><a id=\"_21\" href=\"\"><\/a>2.1. Definition<\/h2>\n<p>Genecology is the study of intraspecific genetic variation in relation to environmental conditions. In other words, it is to study the relationships between genetic variation and environmental gradients within a species.<\/p>\n<p>Genecology is often referred to as ecological genetics, which is actually more widely used. However, strictly speaking, ecological genetics is the study of how ecologically relevant traits evolve in natural populations, which covers inter-species interactions. Nevertheless, these two terms are used interchangeably.<\/p>\n<h2><a id=\"_22\" href=\"\"><\/a>2.2. Some relevant terms<\/h2>\n<p>Provenance \u2013 the place of seed origin (or seed source).<\/p>\n<p>Population \u2013 a group of individuals of the same species that live in a particular geographical area, and have the capability of interbreeding. Individuals from the same provenance is called a population.<\/p>\n<p>Provenance is often used to refer a population although it is not accurate. Thus, provenance and population are often interchangeably in genecology.<\/p>\n<p>Provenance test (or provenance trial) \u2013 a common garden experiment that compares trees or plants collected from different provenances. Typically provenance tests compare widely separated seed sources. The test may contain multiple test sites.<\/p>\n<p>Genetic variation \u2013 can be defined at the individual level as the difference in DNA among individuals, or at the population level as among-population variation due to difference in allele frequency.<\/p>\n<p>Genetic cline &#8211; a geographic or climatic pattern of change in a trait.<\/p>\n<p>Genetic and environment interaction (GxE) &#8211; different genotypes respond to environmental variation in different ways.<\/p>\n<h2><a id=\"_3\" href=\"\"><\/a>2.3. Objectives of genecology<\/h2>\n<p>Operational objectives:<\/p>\n<ul>\n<li>To determine how far seed can be moved<\/li>\n<li>To delineate geographic breeding zones<\/li>\n<li>To select optimal provenances<\/li>\n<\/ul>\n<p>Theoretical objectives:<\/p>\n<ul>\n<li>Testing evolutionary and ecological theories about factors limiting the evolution of species range<\/li>\n<li>Predicting response to climate change<\/li>\n<li>Dependency on climatic drivers<\/li>\n<li>Determining the underlying genetic basis of adaptive traits: Ecological genomics<\/li>\n<\/ul>\n<h1><a id=\"_3\" href=\"\"><\/a>3. Transfer functions<\/h1>\n<p>Transfer functions are most commonly used in genecology to reflect the effect of transfer distance of populations in terms of geographical or climatic variables. A provenance test is required for developing a transfer function.<\/p>\n<h2><a id=\"_31\" href=\"\"><\/a>3.1. Provenance test<\/h2>\n<p>Figure 2 shows a typical provenance test. Populations from 140 provenances range-wide were planted in 60 common garden trials (planting sites) in British Columbia (BC), Canada. At each site, an incomplete block design was used to include 60 populations due to a large number of populations. Thus, not every population was tested at all the 60 sites except seven reference populations. Tree height was measured at age 20.<\/p>\n<figure id=\"attachment_65\" aria-describedby=\"caption-attachment-65\" style=\"width: 557px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-157\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f422.png\" alt=\"\" width=\"557\" height=\"418\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f422.png 480w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f422-300x225.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f422-65x49.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f422-225x169.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f422-350x263.png 350w\" sizes=\"auto, (max-width: 557px) 100vw, 557px\" \/><figcaption id=\"caption-attachment-65\" class=\"wp-caption-text\">Figure 2. A provenance test comprising 140 provenances of lodgepole pine in western North America and tested in British Columbia. Image by Tongli Wang under CC BY 4.0.<\/figcaption><\/figure>\n<p>As illustrated in Figure 3, populations are transferred from their origins to a test site in the mid of BC in the provenance test. Those populations grow under new environmental conditions, and their performances may be affected. As the populations are grown under the same climatic conditions (at the same test site), the difference in the performance of populations is supposed to be due to genetic variation among the populations.<\/p>\n<figure id=\"attachment_65\" aria-describedby=\"caption-attachment-65\" style=\"width: 783px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-158\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423.png\" alt=\"\" width=\"783\" height=\"406\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423.png 783w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423-300x156.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423-768x398.png 768w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423-65x34.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423-225x117.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423-350x181.png 350w\" sizes=\"auto, (max-width: 783px) 100vw, 783px\" \/><figcaption id=\"caption-attachment-65\" class=\"wp-caption-text\">Figure 3. Illustration of population transfers in the provenance test of lodgepole pine. Image by Tongli Wang under CC BY 4.0.<\/figcaption><\/figure>\n<h2><a id=\"_32\" href=\"\"><\/a>3.2. Transfer functions<\/h2>\n<p>The genetic variation observed in a provenance trial at each test site may be associated with the population transfer distance. It is hypothesized that the longer the transfer distance, the larger the transfer effect. Thus, the transfer distance is used as a predictor in a transfer function as:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-159\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423f.png\" alt=\"\" width=\"396\" height=\"70\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423f.png 396w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423f-300x53.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423f-65x11.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423f-225x40.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f423f-350x62.png 350w\" sizes=\"auto, (max-width: 396px) 100vw, 396px\" \/><\/p>\n<p>Where, <em>Y<\/em> is the performance of a population; <em>x<\/em> is the transfer distance; and <em>a<\/em>, <em>b<\/em>, and <em>c<\/em> are parameters to be estimated to fit the model.<\/p>\n<p>The transfer distance can be in a physical distance for geographical variables (e.g., latitude, longitude, or elevation), or in units for climatic variables (e.g., temperature and precipitation). Climatic variables are increasingly used as they have many advantages over geographical variables, particularly for predicting the impact of climate change on forests.<\/p>\n<p>Climatic variables are needed for all the provenances to build a transfer function using the transfer distance in climatic variables, as shown in Figure 4. A map of mean annual temperature (MAT) covering the lodgepole pine distribution and a transfer function for a test in the mid of BC.<\/p>\n<figure id=\"attachment_65\" aria-describedby=\"caption-attachment-65\" style=\"width: 953px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-160\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424.png\" alt=\"\" width=\"953\" height=\"597\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424.png 953w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424-300x188.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424-768x481.png 768w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424-65x41.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424-225x141.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424-350x219.png 350w\" sizes=\"auto, (max-width: 953px) 100vw, 953px\" \/><figcaption id=\"caption-attachment-65\" class=\"wp-caption-text\">Figure 4. A map of mean annual temperature (MAT) covering the lodgepole pine distribution (left) and a transfer function for a test in the mid of BC (right). Image by Tongli Wang under CC BY 4.0.<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p>The transfer distance in MAT (MAT_CTD) is calculated as:<\/p>\n<p><em>MAT_CTD <\/em>=<em> MAT_s \u2013 MAT_p\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em>[2]<\/p>\n<p>Where, MAT_s is the MAT of the test site, MAT_p is the MAT of the provenance. Then, the transfer function is written as:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-161\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424f.png\" alt=\"\" width=\"473\" height=\"71\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424f.png 473w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424f-300x45.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424f-65x10.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424f-225x34.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f424f-350x53.png 350w\" sizes=\"auto, (max-width: 473px) 100vw, 473px\" \/><\/p>\n<p>Populations with negative transfer distances on the left of the plot were transferred northward (from warmer climates to cooler climates). On the other hand, populations with positive transfer distances on the right of the plot were transferred southward (from cooler climates to warmer climates).\u00a0 Populations with zero and around zero transfer distance are considered local populations. The local populations have the best performance; however, the peak of the curve is not always exactly at the zero transfer distance point, as shown in Figure 4.<\/p>\n<h2><a id=\"_33\" href=\"\"><\/a>3.3.\u00a0 Features and limitations<\/h2>\n<p>A transfer function represents the transfer effect of populations. It reflects the <strong>genetic effect<\/strong> of climate on populations. It is intuitive and easy to build. However, there are several limitations for transfer functions. A transfer function built for one site may be different from the one built for another site, even with the same group of populations. Thus, a transfer function developed for one site, strictly speaking, only represents the transfer effect of populations under the particular environment of that test site. The number of test sites is limited for most tree species, and people tend to oversell the results drawn from these sites. Therefore, we need to be aware of such a risk of using a transfer function built for one environment to represent the situations for other environments.<\/p>\n<h1><a id=\"_4\" href=\"\"><\/a>4. General transfer functions<\/h1>\n<h2><a id=\"_41\" href=\"\"><\/a>4.1.\u00a0 General transfer functions<\/h2>\n<p>Due to the limitation of transfer functions discussed above, general transfer functions were proposed. The only difference between a transfer function and a general transfer function is that data from all test sites are pooled together in developing a general transfer function. The formulas [1] \u2013 [3] all apply to a general transfer function.<\/p>\n<p>The curve of a general transfer function shown in Figure 5 was developed based on the observations from the same provenance test mentioned above. The relationship between the performance and transfer distance of populations in a transfer function is usually weak.<\/p>\n<figure id=\"attachment_65\" aria-describedby=\"caption-attachment-65\" style=\"width: 580px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-162\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f425.png\" alt=\"\" width=\"580\" height=\"523\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f425.png 580w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f425-300x271.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f425-65x59.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f425-225x203.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f425-350x316.png 350w\" sizes=\"auto, (max-width: 580px) 100vw, 580px\" \/><figcaption id=\"caption-attachment-65\" class=\"wp-caption-text\">Figure 5. A general transfer function that combines observations across all tests. Image by Tongli Wang under CC BY 4.0.<\/figcaption><\/figure>\n<h2><a id=\"_42\" href=\"\"><\/a>4.2. Relative performance-based general transfer functions<\/h2>\n<p>The most important reason for a general transfer function being weak is the difference in the performance of populations among sites. For example, the outliers at the bottom of Figure 5 are populations growing at several cold sites in the north. Their total height at age 20 is less than a meter. An approach was developed to overcome this problem by using relative performance. With this approach, the performances of populations are converted to proportions relative to the performance of the local population.\u00a0 It can substantially improve the relationship of the general transfer function, as shown in Figure 6. It worths of reminding that the relative performance needs to be converted back to actual performance in applications of this model.<\/p>\n<figure id=\"attachment_65\" aria-describedby=\"caption-attachment-65\" style=\"width: 593px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-163 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f426-1.png\" alt=\"\" width=\"593\" height=\"547\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f426-1.png 593w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f426-1-300x277.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f426-1-65x60.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f426-1-225x208.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f426-1-350x323.png 350w\" sizes=\"auto, (max-width: 593px) 100vw, 593px\" \/><figcaption id=\"caption-attachment-65\" class=\"wp-caption-text\">Figure 6. A general transfer function using relative performance. Image by Tongli Wang under CC BY 4.0.<\/figcaption><\/figure>\n<h2><a id=\"_43\" href=\"\"><\/a>4.3.\u00a0 Limitations of general transfer functions<\/h2>\n<p>In addition to the weak relationships of general transfer functions as mentioned above, there are other limitations for general transfer functions. As discussed earlier, the transfer effects of populations are different among test sites. By pooling the data across all test sites to develop a general transfer function, the difference in the transfer effect of populations among test sites is averaged out, as illustrated in Figure 7. This compromises the prediction power of general transfer functions. In addition, the same amount of transfer distance may have different transfer effects. For example, for a -2\u00b0C transfer distance in temperature, the transfer from 2\u00b0C to 0\u00b0C may be different from the transfer from 10\u00b0C to 8\u00b0C. This point will be further discussed later in comparison with genecology functions. Nevertheless, general transfer functions are the simplest to implement; thus it is still commonly used.<\/p>\n<figure id=\"attachment_65\" aria-describedby=\"caption-attachment-65\" style=\"width: 724px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-164 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f427_poolData.gif\" alt=\"\" width=\"724\" height=\"780\" \/><figcaption id=\"caption-attachment-65\" class=\"wp-caption-text\">Figure 7. Illustration of difference in transfer effect between two test sites. Image by Tongli Wang under CC BY 4.0.<\/figcaption><\/figure>\n<h2><a id=\"_44\" href=\"\"><\/a>4.4. Universal transfer functions<\/h2>\n<div>\n<div>An improved version of general transfer function was proposed recently (Leites et al 2012). It can be called \u201cUniversal transfer functions\u201d. <span style=\"font-size: 14pt\">A universal transfer function also pools data across test sites. The difference is that it includes provenance climate and an interaction term in addition to transfer distance, as well as some random effects. The function can be written as:<\/span><\/div>\n<\/div>\n<div><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-165 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/utf.png\" alt=\"\" width=\"637\" height=\"63\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/utf.png 637w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/utf-300x30.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/utf-65x6.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/utf-225x22.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/utf-350x35.png 350w\" sizes=\"auto, (max-width: 637px) 100vw, 637px\" \/><\/div>\n<p>Where,<br \/>\nX is transfer distance;<br \/>\nP is provenance climate;<br \/>\nXP is the interaction term;<br \/>\nrs are some random effect terms.<\/p>\n<p>The universal transfer function can overcome the problems listed above, but the random terms cause additional problems. The model is too complicated and often fail to converge. It used only one climate variable in applications so far, which can compromise the model capability.<\/p>\n<p>.<\/p>\n<h1><a id=\"_5\" href=\"\"><\/a>5. Genecology functions<\/h1>\n<h2><a id=\"_51\" href=\"\"><\/a>5.1. Genecology functions<\/h2>\n<p>A genecology function uses the environmental variables of provenances, rather than transfer distance used in both transfer functions and general transfer functions. Thus, a genecology function represents the relationship between the performance of populations and environmental variables of the population origins (or provenances), which exactly reflects the definition of genecology. A genecology function can be written as:<br \/>\nY=<strong>a<\/strong> + <strong>b<\/strong>x + cx<sup>2<\/sup><br \/>\nWhere, <em>Y<\/em> is the performance of a population; <em>x<\/em> is an environmental variable of provenance; and <em>a,<\/em> <em>b<\/em>, and <em>c<\/em> are parameters to be estimated to fit the model.<\/p>\n<p>Using the same data for building a transfer function in Figure 4, a genecology function is developed, as shown in Figure 8. Although the shapes of the curves are quite different, the R square values are identical between the two functions.<\/p>\n<figure id=\"attachment_65\" aria-describedby=\"caption-attachment-65\" style=\"width: 1024px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"size-large wp-image-166\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f428-1024x666.png\" alt=\"\" width=\"1024\" height=\"666\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f428-1024x666.png 1024w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f428-300x195.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f428-768x499.png 768w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f428-1536x998.png 1536w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f428-2048x1331.png 2048w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f428-65x42.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f428-225x146.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f428-350x227.png 350w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption id=\"caption-attachment-65\" class=\"wp-caption-text\">Figure 8. A map of mean annual temperature (MAT) covering the lodgepole pine distribution (left) and a genecology function for a test in the mid of BC (right). Image by Tongli Wang under CC BY 4.0.<\/figcaption><\/figure>\n<h2><a id=\"_52\" href=\"\"><\/a>5.2. The difference in genecology functions among environments<\/h2>\n<p>Genecology functions developed for different environments show different relationships (Figure 9). Thus, a genecology function built based on information from one environment may not represent the relationship for other environments. This is the same as for the transfer function.<\/p>\n<figure id=\"attachment_65\" aria-describedby=\"caption-attachment-65\" style=\"width: 1024px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-167 size-large\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f429-1024x670.png\" alt=\"\" width=\"1024\" height=\"670\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f429-1024x670.png 1024w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f429-300x196.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f429-768x502.png 768w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f429-1536x1005.png 1536w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f429-65x43.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f429-225x147.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f429-350x229.png 350w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f429.png 1628w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption id=\"caption-attachment-65\" class=\"wp-caption-text\">Figure 9. genecology functions developed at six test sites from cold to warm climates. Image by Tongli Wang under CC BY 4.0.<\/figcaption><\/figure>\n<p><span style=\"font-family: Helvetica, Arial, 'GFS Neohellenic', sans-serif;font-size: 1.2em;font-weight: bold\"><a id=\"_6\" href=\"\"><\/a>6. Geographic vs. climatic variables<\/span><\/p>\n<p>Both transfer functions and genecology functions can be built with either geographic or climatic variables. There are advantages and disadvantages to use geographic or climatic variables as predictors. We will make a detailed comparison between the two.<\/p>\n<h2><a id=\"_61\" href=\"\"><\/a>6.1. Representation of environmental variables<\/h2>\n<p>Geographic variables are not direct environmental variables, whereas climatic variables are. However, geographic variables are related to environmental variables. For example, elevation is strongly related to temperature, which affects plant performance, as illustrated in Figure 10. Thus, they are often used to substitute environmental variables. However, if we build a greenhouse at the top of the mountain, we can grow any plant that can only grow at the bottom of the valley. It suggests elevation itself does not affect plant growth.<\/p>\n<figure id=\"attachment_65\" aria-describedby=\"caption-attachment-65\" style=\"width: 600px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-168\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2021\/06\/f42_10.png\" alt=\"\" width=\"600\" height=\"450\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f42_10.png 1023w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f42_10-300x225.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f42_10-768x576.png 768w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f42_10-65x49.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f42_10-225x169.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2021\/06\/f42_10-350x262.png 350w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><figcaption id=\"caption-attachment-65\" class=\"wp-caption-text\">Figure 10. &#8220;Little Lakes Valley viewed from about 11,000 feet elevation, hiking along the Mono Pass Trail, Eastern Sierra Mountains, California (mono14xy)&#8221; by mlhradio is licensed under CC BY-NC 2.0<\/figcaption><\/figure>\n<h2><a id=\"_62\" href=\"\"><\/a>6.2. Accessibility<\/h2>\n<p>Geographic variables are more accessible than climatic variables. That is why they were more often used for experimental design and data analysis in the past. With increasingly available climate data, accessing climatic variables are becoming as easy as accessing geographic variables. Especially with the scale-free climate models ClimateNA and ClimateAP, climatic variables can be easily obtained for any specific location within their coverage.<\/p>\n<h2><a id=\"_63\" href=\"\"><\/a>6.3 local vs. universal<\/h2>\n<p>A transfer function or a genecology function built with geographic variables only works for the region where the model is built. This is because of the effect of a geographic variable changes from region to region, or location to location. For example, 2000 m in elevation in California is suitable for many plants to growth; but the same elevation in BC is beyond the treeline. Also, an increase in elevation by 100 m in California will result in a decrease in temperature by 0.65\u00b0C; but the same change in northern BC will only result in a decrease in temperature by about 0.2\u00b0C.\u00a0 In contrast,\u00a0 a transfer function or a genecology function built with climatic variables can be applied anywhere.<\/p>\n<h2><a id=\"_64\" href=\"\"><\/a>6.4. Applicability for climate change<\/h2>\n<p>A transfer function or a genecology function built with geographic variables cannot be used for assessing the impact of climate change as geographic variables are static and have no future projections. In contrast, climatic variable based functions can predict the past and future. That is the reason why genecology has been a hot area.<\/p>\n<h2><a id=\"_65\" href=\"\"><\/a>6.5. Non-climatic factors<\/h2>\n<p>Geographic variables are still useful to reflect some important non-climatic factors. Genetic variations among populations are also affected by spatial autocorrelation involving migration and gene flow related to physical barriers and distance. Those factors sometimes need to be included in genecology functions. We will discuss this further in the next topic.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-65\" src=\"https:\/\/pressbooks.bccampus.ca\/fode010notebook\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd-300x105.png\" alt=\"\" width=\"300\" height=\"105\" srcset=\"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd-300x105.png 300w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd-65x23.png 65w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd-225x79.png 225w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd-350x122.png 350w, https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-content\/uploads\/sites\/1423\/2019\/11\/by-nc-nd.png 403w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>By Tongli Wang, Climate Modelling and Forest Applications is licensed under\u00a0<a class=\"inline_disabled external\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/\" target=\"_blank\" rel=\"noopener\">Creative Commons &lt;CC BY-NC-ND 4.0&gt; License<\/a><\/p>\n","protected":false},"author":120,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-nd"},"chapter-type":[],"contributor":[],"license":[57],"class_list":["post-173","chapter","type-chapter","status-publish","hentry","license-cc-by-nc-nd"],"part":138,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-json\/pressbooks\/v2\/chapters\/173","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-json\/wp\/v2\/users\/120"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-json\/pressbooks\/v2\/chapters\/173\/revisions"}],"predecessor-version":[{"id":174,"href":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-json\/pressbooks\/v2\/chapters\/173\/revisions\/174"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-json\/pressbooks\/v2\/parts\/138"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-json\/pressbooks\/v2\/chapters\/173\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-json\/wp\/v2\/media?parent=173"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-json\/pressbooks\/v2\/chapter-type?post=173"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-json\/wp\/v2\/contributor?post=173"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/climatemodellingforestadaptation\/wp-json\/wp\/v2\/license?post=173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}